Latest revision as of 13:51, 7 December 2018

Modeling

Mathematical model

Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab

Description

Edinburgh model

WaitDrop Groeningen model COMSOL model Thermo Switches model

The β-barrel Assembly Machinery Complex

Outer membrane proteins (OMPs) of Gram-negative bacteria are synthesized in the cytoplasm and transported across the inner membrane by SecYEG translocon into the periplasm. The survival factor A (SurA) chaperones carry the unfolded membrane proteins across the periplasm to the BAM complex, which is responsible for the insertion and assembly of OMPs into the outer membrane [1].

In E. coli BAM complex consists of a membrane protein BamA and four lipoprotein subunits BamBCDE. These subunits associate with BamA through periplasmic POTRA domains. In vitro reconstitution of the E. coli BAM complex and functional assays showed that all five subunits are required to achieve the maximum activity of BAM [1].

In theory, recruiting the BAM complex in a cell-free system could be extremely beneficial as it could integrate OmpA and lgA protease beta-domain into the membranes of liposomes from the inside without requiring any additional protein complexes. Also, this would make a cell-free system more ubiquitous, because BAM complex does not require any signal sequence for proper protein insertion. In order to ensure quick integration, BamA needs to be consistently present at high yields throughout the expression of OmpA and lgA. For this reason, it is essential to stimulate its expression by an initial addition of mRNA, ensuring rapid expression of BamA. For this reason, with the help of Edinburgh iGEM team (special thanks to Freddie Starkey), a mathematical model for BamA kinetics was created.

Mass Action Equations

First of all, to represent chemical reactions and to render a start for mechanistic modelling, Mass Action Equations were used. It is known that the laws of mass action state that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. The mass action equations in Figure 1 can be used to represent basic protein expression:

Fig. 1 Mass Action Equations for Protein Expression

Each of these equations is used in triplicate to represent the expression of BamA, OmpA and lgA respectively and from these mass action equations a system of ordinary diﬀerential equations can be derived.

Ordinary Differential Equations

The model uses a set of differential equations:

Fig. 2 System of differential equations for BamA kinetics

Determination of the System Values

In order to solve this system it is ﬁrst necessary to derive values for all the parameters used:

1. copies_BamA, copies_OmpA, copies_IgA - Relative number of plasmid copies.

It is important to consider the eﬀect of diﬀerent starting masses of DNA of BamA, OmpA, and lgA, therefore to calculate the number of plasmids from which each protein can be expressed. Assuming that we add 25-1000 ng of DNA to our system [1], a single base pair has mass of 650 Da, and the length of each plasmid is known, mass of each plasmid was calculated:

peT2Ab with BamA - 5089.5 kDa
pRSETb with OmpA - 2550.95 kDa
pRSETb with lgA - 2490.8 kDa

Knowledge that 1 ng equals to 6.022∗10¹⁷ kDa, allows to calculate the number of plasmids present for a particular number of ng of DNA added (Tab. 1).

Tab. 1 Number of plasmids present for a particular number of ng of DNA added

peT2AB with BamA
DNA added (ng)	Number of copies
25	2.985*10¹⁵
250	2.958*10¹⁶
1000	1.183*10¹⁷
pRSETb with OmpA
DNA added (ng)	Number of copies
25	5.902*10¹⁵
250	5.902*10¹⁶
1000	2.361*10¹⁷
pRSETb with IgA
DNA added (ng)	Number of copies
25	6.044¹⁵
250	6.044¹⁶
1000	2.418¹⁷

2. tr_BamA, tr_OmpA, tr_IgA - Transcription rate.

Transcription rate of T7 RNA polymerase is approximately 60 nucleotides per second [2]. Length of each gene was 2430 nucleotides for BamA, 1038 nucleotides for OmpA, and 945 nucleotides for lgA. Transcription rate per minute for each gene was calculated:

tr_BamA = (60/2430)∗60 = 1.48 mRNAs per minute
tr_OmpA = (60/1038)∗60 = 3.47 mRNAs per minute
tr_lgA = (60/945)∗60 = 3.81 mRNAs per minute

3. deg_{mRNA BamA}, deg_{mRNA OmpA}, deg_{mRNA IgA} - mRNA degradation rate.

Degradation rate is calculable from half-life using the formula: degX = ln(2)/halflife [3], where X shows the transcript of the target gene. Average mRNA half-life approximately is 5 minutes, however we screened half-lives of 1, 5, 10, and 15 minutes for each protein in order to more precisely evaluate the variability of the results. Degradation rates per minute were calculated:

1 minute half-life - 0.69 mRNAs per minute
5 minute half-life - 0.14 mRNAs per minute
10 minute half-life - 0.07 mRNAs per minute
15 minute half-life - 0.05 mRNAs per minute

4. trl_BamA, trl_OmpA, trl_IgA - Protein translation rate.

Translation rate is about 20 amino acids per second [2]. Lengths of target proteins are 2430 nucleotides for BamA, 1038 nucleotides for OmpA, and 945 nucleotides for lgA. Translation rates per minute were calculated:

trl_BamA = (20/810)∗60 = 1.48 proteins per minute
trl_OmpA = (20/346)∗60 = 3.47 proteins per minute
trl_lgA = (20/315)∗60 = 3.81 proteins per minute

5. deg_BamA, deg_OmpA, deg_IgA - Protein degradation rate.

Protein half-life was determined using ProtParam Tool, which uses the N-end rule [4] to determine protein half-life. The estimates given for each of BamA, OmpA, and lgA are >10 hrs in E. coli. In order to reﬂect the inexact nature of these computationally derived half-lives, we screened over possible half-lives of 10, 20, and 30 hours for each of BamA, OmpA, and lgA. Applying prior used degradation rate formula degX = ln(2)/halflife [3], this yielded degradation rates per minute of:

10 hour half-life - 1.16∗10⁻³ proteins per minute
20 hour half-life - 5.78∗10⁻⁴ proteins per minute
30 hour half-life - 3.85∗10⁻⁴ proteins per minute

Starting Conditions

In order to examine the eﬀects of higher initial mass of BamA RNA, 6 diﬀerent values were screened over (Tab. 2). Assuming that addition of RNA in IVTT system is between 1 and 5 µg, the masses of sense and antisense strands of BamA in kDa [6] are 830.382 and 820.8, respectively, and conversion is 1 µg = 6.022∗10²⁰ kDa, the number of RNA molecules added can be calculated using the formula µgadded∗(6.022∗10²⁰/((830.382+820.8)/2)).

Tab. 2 Initial BamA mRNA

RNA added (µg)	RNA added (molecules)
0	0
1	7.29*10¹⁷
2	1.46*10¹⁸
3	2.19*10¹⁸
4	2.92*10
5	3.65*10¹⁸

The primary aim of this model was to identify parameters leading to rapidly-achieved and consistently high levels of BamA under conditions of co-expression of BamA, OmpA, and lgA. Prior to this it was important to identify particular parameters leading to these conditions and to examine some general trends. The number of molecules of mRNA and protein for each average, minimum and maximum plot and each of BamA, OmpA, and lgA after 2 hours were calculated (Fig. 3) and summarized (Tab. 3).

Fig. 3 Minimum, maximum and average levels of mRNAs and protein for BamA, OmpA and lgA

Tab. 3Average, minimum and maximum number of protein molecules after 2 hours

Protein	Number of molecules
Average
BamA	2.8*10²⁰
OmpA	2.78*10²¹
IgA	3.44*10²¹
Minimum
BamA	1.95*10¹⁸
OmpA	2.13*10¹⁹
IgA	2.63*10¹⁹
Maximum
BamA	1.28*10²¹
OmpA	1.28*10²²
IgA	1.58*10²²

In average, minimum, and maximum cases the protein expression of OmpA, lgA, and BamA follows the same trend which is unaﬀected by ﬂuctuations of mRNA level. Each protein is expressed at a rate primarily proportional to its length and to a magnitude primarily dependent on the mass of available DNA.

Sensitivity Analysis

Fourier Amplitude Sensitivity Testing (FAST) indices represent the proportion of the output variance of the model attributable to a particular variable and its interactions. Focusing on BamA expression as the protein of interest, total order FAST sensitivity indices were calculated using the BamA protein level each 20 minutes as the model output (Fig. 4).

Fig. 4 FAST sensitivity analysis of BamA

As it can be seen from the graph, number of BamA plasmid copies contributes most to output variance over the whole time span. Also, BamA mRNA degradation rate is considerably faster than BamA degradation rate - with mRNA halﬂife of the order of minutes and protein halﬂife of the order of hours - hence the greater FAST index.

Conclusions

Prior to starting the wet lab experiments, we had hypothesized that the addition of mRNA into our system would ensure that BamA folded and inserted into liposome membrane more efficiently, thus enhancing the expression of OmpA and IgA. Therefore it was decided to purify BamA mRNA and add it to the reaction mixture as a template instead of DNA as we assumed that skipping the transcription step would increase protein synthesis rate. After creating a mathematical model that calculated the necessity of mRNA addition to IVTT system, we were able to generate a more efficient transcription-translation system in which we used both the purified BamA mRNA and DNA. This model clearly revealed that using both mRNA and plasmid DNA in our system was essential as BamA mRNA did increase the rate of protein expression while this eﬀect was proportional to the mass of initial DNA. However, after experimenting in the wet lab, we chose to use purified BamA as it was desired to reach higher expression yields of membrane proteins and it proved to be more effective as BamA mRNA degradation rate was considerably faster than BamA protein degradation rate.

References

Gu, Y. et al. Structural basis of outer membrane protein insertion by the BAM complex. Nature 531, 64-69 (2016).
Biolabs, N. PURExpress® In Vitro Protein Synthesis Kit | NEB. International.neb.com (2018). at < https://international.neb.com/
Philips, R. What is faster, transcription or translation?. Book.bionumbers.org (2018). at
Exponential decay. En.wikipedia.org (2018). Accession: at
Bachmair, A., Finley, D. & Varshavsky, A. In vivo half-life of a protein is a function of its amino-terminal residue. Science 234, 179-186 (1986).
RNA Molecular Weight Calculator | AAT Bioquest. Aatbio.com (2018). Accession: at

eXplaY

Edinburgh model Groeningen model COMSOL model Thermo Switches model

Background

During the past several decades, display systems have been successfully implemented in linking the genotype to phenotype of particular proteins. While some of these systems naturally occur in nature, some are artificially created in laboratory. Overall, the display systems have been widely used for protein research. For a brief overview of these systems, click here.

One of the nearest future applications of SynDrop is liposome surface display. It stands out from the other display methods as it has fully controllable settings of an experiment such as the optimized interior composition for synthesis and adjusted exterior configuration for protein folding. Unlike cells, liposomes are free of unnecessary cross-talk and biological noise. Additionally, high-throughput production of liposomes might reduce the experimental time substantially.

To achieve this goal, we chose a prokaryotic membrane protein - OmpA (Outer membrane protein A) - it was successfully used as a membrane protein which enables the display of a fused globular protein in prokaryotes¹. In our case, we wanted to demonstrate two different proteins: scFv with affinity to vaginolysin² and camelid nanobody, capable to interact with a GFP molecule³ . These membrane proteins were chosen to mimic targets of current display systems.

In nature, OmpA surface display system flips the selective protein from the inside of the living organism to the outside of its’ surface⁴. By achieving this in liposomes, the bottom-up approach would allow us to understand the mechanism and relevant components of the flipping process. For this reason, we decided to model a simple system with few variables to evaluate the activity of the fusion protein containing OmpA and Anti_GFP - it seemed like a good starting point to investigate well characterized parts. This is where molecular dynamics GROMACS package came in handy. GROMACS is a powerful open-sourced tool to build simulations of protein folding and lipids interactions. With a huge help from iGEM team Groningen molecular thermodynamics model with GROMACS was built.

Setup

Sequence of particular fusion protein was built BBa_K2622029.

Fig. 1 Sequence scheme of Lpp_OmpA and Anti_GFP nanobody fusion protein.

Next, the fusion protein was constructed. The sequences of OmpA and anti-GFP (PDB: 3OGO) were joined exactly where they will be fused according to the DNA sequence using PyMOL (Fig. 2). To start, the structure of OmpA (PDB: 1QJP) had to be reconstructed as parts of it are missing in the crystal structure. This was achieved using the “modeler” software, a python module for homology modeling. The same structure was used as the reference structure and so the filled in structure only serves to complete the molecule.

Then the fusion protein was coarse grained by the martinize script, producing a well calibrated coarse grained bead mapping for the fusion protein in the MARTINI 2 forcefield. The fusion protein was then inserted in a DOPC bilayer constructed by the insane.py script.

GFP was also coarse grained using martinize and inserted in the system containing the fusion protein and the DOPC bilayer, after which the system was solvated with regular water beads. 150 mM equivalence of NaCl was added to neutralize the system. For both coarse grained structures, an elastic network was applied with a cutoff of 0.5 nm such that the beta-barrels of the proteins are maintained.

Fig 2 The molecular system. Left image represents the fused Lpp_OmpA+anti_GFP inserted to a DOPC lipid bilayer while the coarse grained structure of GFP is presented on the right.

To set up a calculation, the system having the simplest and least variables containing configuration was chosen:

Lipid membrane, containing DOPC lipids only
GFP molecules surrounding the membrane
Lpp_OmpA+Anti_GFP (transmembrane protein + globular protein with affinity to GFP)

Common parameters for martini were used for minimization and equilibration, and the model was setup to run for about 10 microseconds with berendsen temperature coupling and Parrinello-Rahman pressure coupling. The system runs at 300 K and a pressure of 1 bar.

The building process is documented on the project’s github page

Results

Binding between anti-GFP and GFP was visualized over time in Fig. 3 to validate that the model functions as expected. Fig. 3 shows that binding occurs after roughly 1 ms and is quite strong as expected.

Fig 3 Distance between GFP and anti-GFP measured over time. Strong binding occurs over roughly 1 ms of simulation.

The Root Mean Square Deviation (RMSD) was computed over time using GROMACS and plotted in Fig. 4 to show OmpA unfolding over time. The entire event takes place over a time scale of roughly 1 ms.

Fig 4 OmpA unfolding visualized over time by computing the Root Mean Square Deviation from the starting conformation. Unfolding occurs roughly over a time scale of 1 ms.

Due to a strong tendency to shield charged residues within the remaining barrel structure from interacting with apolar lipids tails, a part of the transmembrane OmpA stays anchored in the lipid bilayer Fig. 5. The figure shows clearly that red and blue (charged) side chains are kept within the remnants of the beta barrel and only apolar and slightly polar side chains are exposed to the lipid environment.

Another observation is that the end of the unfolded beta-barrel is sticking out of the membrane, and contains many charged side chains as well, while the boundary between this part and the transmembrane domain is quite apolar. Overall this structure gives the impression to be still highly stable, but perhaps less stable than the native beta-barrel, anchored in the lipid bilayer.

Fig 5 Van der Waals representation of the side chains of OmpA in the membrane. The membrane is represented by dashed lines. The protein backbone is colored in magenta. White beads represent non-polar side chains, green beads represent polar side chains (of varying polarity, there are 5 different levels of polarity in Martini and they are all colored green), blue beads represent positively charged side chains and red beads represent negatively charged side chains.

As this large scale conformational change should have a large effect on the behaviour of the protein, the angle between OmpA and the membrane normal was measured over time. To visualize trends in the data, a running average was calculated with a window of 100 frames. Fig 6. shows that this angle oscillates stably around 84.9 degrees. However after 10 ms of simulation, the angle suddenly shifts to 84 degrees. This could be an indication that the usual right-angle of OmpA is perhaps not so stable in the new conformation this fusion protein adopts.

Fig 6 Angle between OmpA and membrane normal, running average over time. The angle oscillates stably around 84.9 then suddenly drops to 84.

Under the assumption that the fusion protein indeed retains this conformation, the unfolding beta-barrel and subsequent stable anchoring in the membrane is a novel insight. As the system is meant to function as a display mechanism for soluble proteins binding to it, it is likely that this change in conformation contributes to this mechanism. It is hypothesized that the protein-ligand complex flips across the lipid bilayer entirely to function as a display system, generally assisted by chaperone proteins. Since the angle between OmpA and the membrane normal becomes more acute over the time scale of the simulation, unfolding of the beta-barrel structure may contribute to OmpA flipping over the lipid bilayer to display its ligand.

Fig 7 A. OmpA-anti-GFP fusion structure at the start of the simulation represented on the left. OmpA is colored in green, anti-GFP is colored in red. Martini elastic bonds are colored in orange. Membrane position is indicated with dashed lines. B. Fusion protein after 10ms of simulation. GFP is colored in blue.

Conclusions

In conclusion, it seems that the system is working as intended, as the OmpA-anti-GFP fusion protein stays anchored in the lipid bilayer and remains able to strongly bind GFP as expected. Whether this is the real situation is however impossible to know as the fusion abolishes some beta-sheets in OmpA that are important for beta-barrel formation.

Discussion

It is always difficult when modeling these kinds of processes to predict the time scale of the whole event. The current model helps us to predict that the flipping process is very slow or unfeasible at all. The latter hypothesis might be reasonable enough and it would allow us to predict that the surface display system requires additional machinery which is found in living organisms. Therefore, it is unlikely to achieve a more accurate model without extra experimental information.

In eXplaY we model a system in a pure DOPC bilayer, which is also a simplified version of natural systems. Original E. coli lipids composition can make a huge impact to the model and its’ results as well.

Potential of mean force(PMF) simulations on pulling the anti-GFP across the membrane needs to be made in order to prove that the energy barrier is really high and the process can not occur naturally. Additionally, to observe flipping in a modeled system, higher temperature (37°C) might be a promising solution.

References

Freudl, R. Insertion of peptides into cell-surface-exposed areas of the Escherichia coli OmpA protein does not interfere with export and membrane assembly. Gene 82, 229-236, doi:https://doi.org/10.1016/0378-1119(89)90048-6 (1989).
Pleckaityte, M., Mistiniene, E., Lasickiene, R., Zvirblis, G. & Zvirbliene, A. Generation of recombinant single-chain antibodies neutralizing the cytolytic activity of vaginolysin, the main virulence factor of Gardnerella vaginalis. BMC biotechnology 11, 100, doi:10.1186/1472-6750-11-100 (2011).
Twair, A., Al-Okla, S., Zarkawi, M. & Abbady, A. Q. Characterization of camel nanobodies specific for superfolder GFP fusion proteins. Molecular biology reports 41, 6887-6898, doi:10.1007/s11033-014-3575-x (2014).
Benhar, I. Biotechnological applications of phage and cell display. Biotechnology Advances 19, 1-33, doi:https://doi.org/10.1016/S0734-9750(00)00054-9 (2001).

COMSOL model

Edinburgh model Groeningen model COMSOL model Thermo Switches model

Background

Phase-field modeling overview

Phase-field models are mathematical models used for solving interfacial problems. They are based on the generalized free-energy functional approach (lattice Boltzmann), meaning that the system evolution is driven by the minimisation of free energy. Important thing to note is that sharp fluid interfaces in the models are replaced by a thin transition region where the interfacial forces are distributed in a smooth manner. This provides model an easy treatment of topological variations at the interface1. In order to describe phases in numerical form, equations use phase variables ϕ. In three-phase systems, phase variables are described as ϕ_i , where i = A, B, C, and the variable is equal to 1 in the phase i and 0 outside.

Typically used phase-field models for two and three phase fluid systems couple fourth order nonlinear advection-diffusion equations, called Cahn-Hilliard equations, which represent the evolution of the phase variables with the Navier-Stokes equations for the fluid motion² . Equations (1), (2) and (3) form the traditional Cahn-Hilliard equation, and Eq. (4) is Navier-Stokes equation - both of them are used in our calculations on COMSOL

M₀ is the mobility tuning parameter that determines the relaxation time of interface and the time scale of diffusion in C-H equation. It should be noted, that interfacial diffusion (the Gibbs-Thomson effect) is inevitable in phase phase field method because the diffusion term is used in the right side of Eq. (1). Due to this, prolonged simulations of our system result in spheres diffusing and constantly changing their size (Fig. 1). Because of that, we have chosen to analyze only the first few spheres formed in every simulation as their size proved to be most accurate.

ϵ (interface thickness parameter) is also an important parameter as it defines the width of transition between phases and affects both the surface tension force and the relaxation time of interface. Usually it is compared to the characteristic length of the system and must be chosen small enough to depict interface changes accurately, yet too small of a thickness shall cause instabilities in calculations.

Most of the time the model can be described with several dimensionless parameters, such as capillary number calculated for the continuous phase, Ca =μ_cv_c/γ, the Reynolds number Re =ρv_cL/μ_c, the viscosity ratio λ=μ_d/μ_c, and the flow rate ratio Q=v_d/v_c³. In our model Reynolds number is small (Re < 1) and does not influence droplet size, so we mainly focus on Ca, λ and Q and consider the influence of the latter two on the liposome formation.

Fig. 1 Visual comparison of modeled and real life liposome formation process. A slight diffusion is observed in a model due to the diffusion term in C-H equations, which makes long simulations unreliable. In the plot, phase variables A, B and C have values of 1 (blue), 2 (green) and 3 (red) respectively.

Geometry

Since the microfluidic devices were designed by ourselves, we were able to extract the exact geometry from the CAD file. The part that interested us was the junction at which all of three phases contacted and started forming droplets (Fig. 2). However, we then proceeded to minimize the geometry (Fig. 3) in order to reduce the computation times and improve solution qualities:

Device height was greater than our largest expected droplets, so 2D model was sufficient;
Since our devices were technically perfectly symmetrical, it was more efficient to do calculations for only half of it and mirror the results;
Usually only the first few droplets need to be analyzed, so the length of post-junction part could be decreased;
Microchannels usually contain only one phase, so their length was not crucial.

Fig. 2 Original 3D junction geometry extracted from the CAD file. Because of its size, it is too inefficient to simulate this whole piece of device.

Fig. 3 Minimized geometry with main measurements and boundaries described, used in all simulations. The inflow rates of LO and OA phases are divided by 2, because their channels split into two in order to press the stream of IA phase in junction.

Mesh

For solving the model we used finite element method, which divides geometry into small mesh elements, where partial differential equations are solved. Interface capturing method incorporated in it keeps the mesh fixed and the boundary discontinuities are smeared out over the finite width ϵ ^3,4. To successfully capture interface movement between different phases, mesh size should be small enough, but not too small, as every single element adds more time to computing and quality of the results stops improving substantially at a certain point.

Most of the time we only control the size of mesh elements. For our channel domains a predefined normal sized mesh was used, as they only contained one phase and interface problems did not occur there. For junction and post-junction parts, a predefined extra fine mesh was used with maximum element size value set to 1µm, which is 1/10 size of a smallest expected droplet and also 1/10 of our characteristic length, which has been chosen to be the width of horizontal IA channel (Fig. 4)

Fig. 4 Generated mesh used in all simulations. Refined grid in junction and post-junction helps with realistic interface capturing.

Materials

Our system consists of three different fluids: OA (Outer Aqueous), IA (Inner Aqueous) and LO (Lipid carrying organic) phases. It should be noted that experiments have been carried with fluids of many different compositions, but here we use only one for each. IA and OA phases are quite similar so for simplicity, we set the same densities for both of them. It has a negligible influence on the results since in most microfluidic configurations buoyancy-driven speeds are much smaller than the actual flow speeds ³. Parameters and compositions of materials are shown in Tab. 1.

Tab. 1 Main parameters of our fluid system. To simplify the system and approximate the viscosity closest to reality, only the content of glycerol, octanol and water was taken into account.

Phase	Density ρ(kg/m³)	*Dynamic viscosity µ (Pas)**	Real composition
OA	1000	0.00119	Pure`frex` custom buffer and surfactant (treated as 7% glycerol and 93% water)
IA	1000	0.00115	Pure`frex` IVTT reaction mixture (treated as 6% glycerol and 94% water)
LO	830	0.00736	98% octanol 2% lipids

Description of the System

Fig. 3 shows our flow focusing model configuration with boundaries specified. There is one main inlet for IA phase, and two for each LO and OA phases on the left side. On the right side, there is an outlet with outflow pressure set to p = 0. For laminar flow, wall condition is set to no slip, which states that the flow velocity at the walls is always v = 0 and it gives a good approximation of the whole system.

In experimental set-up, we coat the OA channels, junction and post-junction with PVA to make it hydrophilic, contrary to hydrophobic PDMS, which is the material of which the microfluidic devices are made. This provides a good setting for liposome formation⁵, and we take that into account by adjusting contact angles at the wetted walls for ternary phase field node. With respect to model limitations, all the contact angles in IA and LO channels are set to 90 degrees. In the coated side, we assume phase OA has a perfect wetting condition on the channel walls against both IA and LO phases, while the contact angle between the latter two is set at 30 degrees.

The aforementioned interface thickness parameter ϵ is set to 1.4 µm as it is the lowest stable value regarding our mesh and mobility tuning parameter, though it is more than enough to accurately depict the results of simulations. Surface tension is another important aspect to be considered and it is set to σ = 0.0085 N/m, which is an interfacial tension between octanol and water ⁶, for all three interfaces between phases (See Limitations).

In order to make our model as realistic as possible, several other parameters are taken from a single baseline wet lab experiment with similar materials and geometry as mentioned before.

Flow rates are transformed into flow velocities for COMSOL and calculated as described in Tab. 2.

Tab. 2 Specifications of baseline set-up fluid flows.

Channel	Inlet area(µm²) ρ(kg/m³)	Flow rate(µL/h)	Flow velocity (m/s)
OA	273	240	0.244
LO	157	14.57	0.0258
IA	193	11.36	0.0164

Mobility parameter in this model is crucial. As its value becomes higher, droplet size in micro-channel increases. This can be explained by the parameters’ mathematical function - raising values causes the increase in interface relaxation time, meaning the diffusion gets stronger as well ¹. So we have compared the numerical and experimental results of liposome synthesis (Fig. 5) and approximated our characteristic mobility tuning parameter to be M₀ = 2E-12 m³>/s. The diameter of the droplet with this value was 12.1µm, which is a close match to the real size.

Fig. 5 A comparison between a modeled baseline experiment and actual view of the junction. Both of them produce vesicles of around 12 µm, though slight variations occur in real setting due to unsteady flow caused by micro-pumps. Results of both systems concur well enough to assume that our model setup is reliable and close to reality.

Results

Parametric sweeps and example of liposome radius calculation

In order to investigate how our system depends on certain parameters, we have performed parametric sweeps on every one of these parameters separately. By doing so, COMSOL Multiphysics resolved our model with every parametric value specified automatically and stored the results under a single node. To find out the size of the liposomes, the first fully formed droplet was taken and 2D cut line data set was created going through the middle of the sphere in y-axis direction (Fig. 6). Next, the variation of phase variable C (which stands for our IA phase) was extracted from the data set and results were depicted in graphs. The exact point of phase edge for all studies performed has been assumed as ϕc = 0.5.

Fig. 6 An example of data sets analysed (yellow line in Fig.). One fully formed sphere for every parametric sweep step was measured by extracting ϕc values from similar linear data sets.

Liposome size dependence on viscosity ratio λ

First of all, the impact of IA and OA phase viscosity ratio ( λ = µ_IA/µ_OA) was investigated. Studies suggest, that increasing λ also increases the generated droplet size ⁷. Though the changes are more significant in high capillary numbers, where droplet formation is driven by viscosity. In our case, the capillary number was relatively small (Ca ≈ 0.034), so the flow was more surface tension-dominated. The simulation was run with a set of different OA phase dynamic viscosity values (Tab. 3) and results are presented in Fig. 7 and Fig. 8.

Tab. 3 Values of OA phase dynamic viscosity used for parametric sweep; µ_IA = 0.00115 Pa*s.

No.	*OA dynamic viscosity µ_OA (Pas)**	Viscosity ratio λ
1	0.00050	2.300
2	0.00119	0.966
3	0.00130	0.885
4	0.00150	0.767
5	0.00200	0.575
6	0.00300	0.383
7	0.00800	0.144

Fig. 7 Sphere radius dependency on viscosity ratio λ. Graph shows the simulated results of liposome radius for every given viscosity parameter, which here are depicted as ratio between viscosities of IA and OA phases. In our simulated range of parameters the radius varies from 5.08 µm to 6.75 µm.

Fig. 8 Sphere diameter dependence on viscosity ratio λ. Simplified graph shows that sphere size increases linearly up until λ = 1 and viscosity regulation above this value results in less changes.

As we see, droplet size increases almost linearly up to λ = 0.996, meaning that increasing viscosity of OA phase leads to formation of smaller liposomes. However, it should be noted that by increasing viscosity in real life, we may encounter other problems, such as impeded droplet formation or liposomes bursting due to differences in osmotic pressure between inside and outside environments. Given these limitations, we can still effectively control our liposome size in about 1µm range. Thus, we can conclude that viscosity ratio, while having a moderate effect, is still not a decisive parameter in vesicle size determination.

Liposome size dependency on velocity ratio V

Flow rates of our fluids were easiest and fastest to control as a parameter, so they certainly needed to be studied more deeply. The flow of the continuous phase here was fixed, so the Capillary number could be considered as a constant. Thus, only the flow rate of disperse IA phase was varied and the effect of flow rate ratio (Q = Q_IA/Q_OA) could be assessed. The simulation was run with a set of different IA phase flow velocity values (Tab. 4) and results are presented in Fig. 9 and Fig. 10.

Tab. 4 Values of IA phase flow velocities used for parametric sweep and reference flow rates and ratios; v_OA= 0.244 m/s, Q_OA= 240µl/h.

No.	IA flow velocity v_IA (m/s)	IA flow rate Q_IA(µl/h)	Flow rate ratio Q
1	0.0050	3.46	0.014
2	0.0100	6.93	0.029
3	0.0164	11.36	0.047
4	0.0500	34.63	0.144
5	0.0750	51.95	0.216
6	0.1000	69.27	0.289
7	0.2000	138.54	0.577

Fig. 9 Sphere radius dependency on flow rate ratio Q. It should be noted that x-axis doesn’t start from zero in order to distinguish between first three values. In comparison with λ, Q seems to affect liposome radius at a greater magnitude. In our simulated range of parameters the radius varies from 6.05 µm to 8.56 µm.

Fig. 10 Sphere diameter dependency on flow rate ratio Q. Simplified graph shows that liposome diameter variation range is 5.5 µm in our configurations, which can be considered good enough for fine-tuning.

Relying on the results we can safely assume, that liposome size depends directly on IA phase flow rate. However studies suggest that this dependency is not linearly proportional because the droplet formation process is also affected by the surface tension force and the dynamic energy equilibrium¹. This seems to be true considering given data.

In contrary to dynamic viscosity ratio variation, flow rate ratio can be experimentally modified in a broad range of values, meaning we can effectively synthesize liposomes from 12 µm to around 17 µm with our current set-up. Nevertheless, we have found that when Q = 0.7, spheres cannot form anymore, as the OA phase cannot cut the stream of IA phase and it transforms into a continuous flow (Fig. 11). Therefore, Q = 0.7 is the critical value for liposome synthesis in our system. In conclusion, the regulation of IA phase flow rate gives us an effective and fast method to vary the size of our liposomes in a range of few micrometers.

Fig. 11 Liposomes stop forming in our system when Q > 0.7, or V > 1 ( v_IA/v_OA). It means that in given dimensions, these values are critical for vesicle formation.

Liposome size dependency on IA channel width `w`

While our goal has always been to attain cell-sized liposomes, which stretch from 5 µm to 30 µm, theoretically we had yet only managed to produce 10 µm to around 17 µm sized vesicles by modifying dynamic viscosity and flow rates of our fluids. It became clear that in order to expand this range, we had to start from the microfluidics device design. Possibilities of the design are virtually infinite, but here we focused on the width of IA phase channel, which we assumed to have the biggest impact on sphere size.

In our model configuration, we have added an additional parameter w_y, which is the width expansion of the device parallel to the symmetry axis (See Geometry). The simulation was run with a set of different wy values (Tab. 5.) and results are present in Fig. 12 and Fig. 13

Tab. 5 Values of w_y used for parametric sweep, the width of channels with parameter applied and IA phase inflow velocities, which were varied in order to keep the flow rate constant.

No.	w_y(µm)	IA channel width (µm)	IA flow velocity v_IA(m/s)
1	0	10	0.0164
2	0.5	11	0.0148
3	1	12	0.0135
4	1.5	13	0.0125
5	2	14	0.0116
6	2.5	15	0.0108

Fig. 12 Sphere radius dependency on IA channel width. Changes in IA channel width seem to cause greatest impact to the output. By increasing it by 5µm, liposome radius grows by 2.86µm.

Fig. 13 Sphere diameter dependency on IA channel width. Simplified graph shows an explicit tendency of liposome growth with increased width parameter. This implies that increasing or reducing the parameter should affect our system in a highly predictable manner.

As we can see, channel width has a huge impact on the size of liposomes. Even by keeping flow rates of all phases the same, droplet radius variations depend solely on channel dimensions. We have tested channels from 10 µm to 15 µm, but other widths should also comply with given results and the only limit on minimal channel dimensions could be the quality of photolithography used in production of microfluidic devices.Using given results we can now calculate the required width of the channel in order to produce liposomes of needed size as well as synthesize them in whole range of 5-30 µm.

Conclusion

From the simulations we’ve gained much invaluable information about liposome size determination in silico, which led us to saving some of our most expensive reagents, such as Purefrex IVTT system. Also, we could conclude that the system worked just as expected and it matched real life experiments surprisingly well. All of the studied parameters affected liposome size to some extent, IA channel-junction width being the most sensitive and effective, flow rate ratio being easiest to control for fine adjustments, while dynamic viscosity ratio tuning may be used in tandem with flow rate regulation.

Discussion

Although we can choose from a vast selection of different parameter values to achieve needed results, there are consequences to every change since microfluidics’ experiments are so delicate. For this reason, parameters for every experiment should be properly evaluated in order to evade failed attempts and wasted materials. For example, proper junction between all three phases sometimes might be so sensitive, that even slight variations can disrupt the flow. In this case, it might be wiser to avoid extreme flow rate changes and design devices with a bit different channel dimensions at first. Moreover, liposome velocity increases with IA phase flow rate, so by colliding with each other in post-junction, risk of them bursting also increases. This is also the case with viscosity changes because it may sometimes be hard to regulate dynamic viscosity ratio without disrupting osmotic pressure. To conclude, every experiment should begin with selection of the right channel design, while flow rate and viscosity regulation should only be used for fine-tuning

Model Limitations

Our model has some limitations. Due to the nature of phase-field model and minimal free energy principle, it proved to be an invidious task to model liposomes exactly like in the real life. Since we cannot characterize lipids and surfactants inside our materials to act as in reality, LO phase just forms a distinct sphere outside of junction instead of surrounding the IA phase.

However, LO phase doesn’t impact the size of liposomes in any meaningful way and just needs to barely reach the junction to subsequently form a pocket for inner fluid. So, in order to mimic the reality as best as possible, we have made a few adjustments:

The surface tension between IA and OA phases was set the same as LO and OA, to depict the interface movement correctly.
While IA phase is hydrophilic, it was set as a fully de-wetting phase to form veracious droplets

References

Bai, F., He, X., Yang, X., Zhou, R. & Wang, C. Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation. Int. J. Multiph. Flow 93, 130–141 (2017).
Kim, J. Phase-Field Models for Multi-Component Fluid Flows. Commun. Comput. Phys. 12, 613–661 (2012).
De Menech, M., Garstecki, P., Jousse, F. & Stone, H. A. Transition from squeezing to dripping in a microfluidic T-shaped junction. J. Fluid Mech. 595, (2008).
Boyer, F., Lapuerta, C., Minjeaud, S., Piar, B. & Quintard, M. Cahn–Hilliard/Navier–Stokes Model for the Simulation of Three-Phase Flows. Transp. Porous Media 82, 463–483 (2010).
Deshpande, S., Caspi, Y., Meijering, A. E. C. & Dekker, C. Octanol-assisted liposome assembly on chip. Nat. Commun. 7, 10447 (2016).
Demond, A. H. & Lindner, A. S. Estimation of interfacial tension between organic liquids and water. Environ. Sci. Technol. 27, 2318–2331 (1993).
Nekouei, M. & Vanapalli, S. A. Volume-of-fluid simulations in microfluidic T-junction devices: Influence of viscosity ratio on droplet size. Phys. Fluids 29, 032007 (2017).

Thermo Switches model

Edinburgh model Groeningen model COMSOL model Thermo Switches model

Background

RNA thermometers are RNA-based genetic control tools that react to temperature changes ¹. Low temperatures keep the mRNA at a conformation that masks the ribosome binding site within the 5’ end untranslated region (UTR). Masking of the Shine-Dalgarno (SD) sequence restricts ribosome binding and subsequent protein-translation. Higher temperatures melt the hairpins of RNA secondary structure allowing the ribosomes to access SD sequence to initiate translation ¹. In terms of applicability of RNA thermometers in in vitro systems, they display certain advantages over ribo- or toehold switches: they do not require binding of a ligand, metabolite or trigger RNA to induce the conformational change ^2,3, therefore are especially compatible with liposome IVTT system.

Although some acquirable and already tested thermoswitches can be found in literature ^1,4, the field is still particularly underexplored. Possibility to design countless synthetic thermoswitches corresponding to different temperatures and of varying structure, is facilitated by computational models and RNA bioinformatics approaches. Together with two pioneers in this field from Vienna University (see Attributions), we have de novo designed six heat-inducible RNA thermometers previously never mentioned in any paper or literature review. Not only did they complement SynDrop, but also helped expanding the library of well characterized and widely-applicable biobricks.

Concept of the Model

We have optimized the opening energy of the ribosome docking site, which is a stretch of 30 nucleotides starting at the beginning of the Shine-Dalgarno (SD) sequence downstream into the coding sequence. This region corresponds to the binding footprint of the assembled initiation ribosome and must be unfolded prior to the assembly of the ribosome machinery. The model optimized for that region to have a high opening energy (meaning low translation efficiency) at low temperatures and a low opening energy (high translation efficiency) at high temperatures. Opening energies were calibrated around the mean value of opening energies observed for all protein coding genes in E. coli. When designing custom synthetic RNA thermometers, it was important to take into account the upstream and downstream sequences of our constructs and to model different structures and sequences in order to select only the best ones for practical implementation. Therefore 10 designs for each construct was designed (see figures below) out of which only 1 was selected based on the computed plots of translation efficiency vs. temperature.

Results

the model computed total 40 different thermoswitches for our composite parts, 10 for each:

Mstx-OmpA-GFP Nanobody;
GFP Nanobody-Iga-Mstx;
Mstx-OmpA-His;
His-Iga-Mstx.

Only 1 design was selected based on the computed plots of translation efficiency vs. temperature.

Fig. 1 Plots of translation efficiency vs. temperature. On the left hand side: plots of 10 modelled thermoswitches for Mstx-OmpA-GFP Nanobody. On the right hand side: plot of the selected thermoswitch to use with Mstx-OmpA-GFP Nanobody. RNA thermometer termed sw_6 displayed no artifacts, with near control-identical translation efficiency at high temperature and low efficiency at < 25 C.

Fig. 2 Plots of translation efficiency vs temperature. On the left hand side: plots of 10 modelled thermoswitches for GFP Nanobody-Iga-Mstx. On the right hand side: plot of the selected thermoswitch to use with GFP Nanobody-Iga-Mstx. RNA thermometer termed sw_5 displayed no artifacts, with relatively high translation efficiency at high temperature and largely lower efficiency at < 25 C.

Fig. 3 Plots of translation efficiency vs. temperature. On the left hand side: plots of 10 modelled thermoswitches for Mstx-OmpA-His. On the right hand side: plot of the selected thermoswitch to use with Mstx-OmpA-His. RNA thermometer termed sw_8 displayed no artifacts, with near control-identical translation efficiency at high temperature and low efficiency at < 25 C.

Fig. 4 Plots of translation efficiency vs temperature. On the left hand side: plots of 10 modelled thermoswitches for His-Iga-Mstx. On the right hand side: plot of the selected thermoswitch to use with His-Iga-Mstx. RNA thermometer termed sw_4 displayed no artifacts, with relatively high translation efficiency at high temperature and largely lower efficiency at < 25 C.

Thermoswitches were initially designed to appropriately melt and function at 37 C. Comparing the first curve in each plot which resembles the original sequence of our constructs without incorporated thermoswitch (control), it can be seen that novel designs show much stronger temperature dependence. However, they did not manage to achieve quite exact 37 C and displayed marginally lower translation efficiency than controls. Some sequences displayed artifacts that showed up as jumps in the efficiency plots. The believed reason was the usage of different SD sequences at low and high temperatures. For in vivo testing we selected designs that did not exhibit such jumps. Another interesting finding was that all thermoswitches designed for Iga protease bearing constructs showed a considerably lower efficiency of translation even at higher temperatures compared to OmpA bearing constructs, meaning that this characteristic was probably attributed to membrane protein structure and would be needed to be addressed in the future.

The model was also applied to check the activity of thermoswitches that we have acquired from literature (see Design and Results/RNA Thermoswitches). Our model predicted fair, but viable switching effects for thermoswitch-GFP designs, which were later supported by in vivo measurements.

Fig. 5 Plots of translation efficiency vs. temperature of the “GJ” thermoswithes-GFP constructs. Thermoswitches GJ2, GJ3, GJ9, GJ10 display similarly fair translation efficiency at 37 C, except for GJ6, which displays notably higher translation efficiency. GJ thermoswitches significantly differ in their activity at lower temperatures, with GJ9 locking the transcription most tightly and GJ3 being the leakiest of all tested designs.

Model

A simple in-silico translation-initiation potential model⁵ to quantify the likelihood of in vitro translation of a given mRNA sequence from a series of interaction energy parameters at constant temperatures was developed. The model defines the translation-initiation potential σ as:

Fig. 6

where R is the Boltzmann constant, T the temperature, ΔE_SD the hybridization energy between the SD and anti-SD sequences, ΔE_tRNA the hybridization energy of the start codon and its respective anti-codon (i.e, the tRNA^Met), and ΔE_open the energy required to unfold the 30-nucleotide-long RDS. Here, ΔE_SD and ΔE_tRNA are constant since neither the SD nor the start codon are altered. Consequently, variations in σ are exclusively determined by ΔE_open. Applying the model to the plasmids with our constructs bearing thermoswitches, enabled us to rationalize translation events, as translatable constructs consistently scored higher σ, or lower ΔE_open, than non-translatable ones.

References

Neupert J, Karcher D, Bock R. Design of simple synthetic RNA thermometers for temperature-controlled gene expression in Escherichia coli. Nucleic Acids Res. [Internet]. Oxford University Press; 2008; 36:e124–e124.
Narberhaus F, Waldminghaus T, Chowdhury S. RNA thermometers. FEMS Microbiol. Rev. [Internet]. Wiley/Blackwell (10.1111); 2006; 30:3–16.
Storz G. An RNA thermometer. Genes Dev. [Internet]. Cold Spring Harbor Laboratory Press; 1999; 13:633–6.
Sen S, Apurva D, Satija R, Siegal D, Murray RM. Design of a Toolbox of RNA Thermometers. ACS Synth. Biol. [Internet]. 2017; 6:1461–70.
Zayni S, Damiati S, Moreno-Flores S, Amman F, Hofacker I, Ehmoser EK. Enhancing the cell-free expression of native membrane proteins by in-silico optimization of the coding sequence – an experimental study of the human voltage-dependent anion channel.ioRxiv [Internet]. Cold Spring Harbor Laboratory; 2018; 411694.

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      <div class="scroll-area">
          <p class="text-content">Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab</p>
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-   <h1 class="text-wall-heading">Design and Results</h1>
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-      <h2 class="text-wall-area-box-heading">Results</h2>
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-         <p class="text-content">Cell-free, synthetic biology systems open new horizons in engineering biomolecular systems which feature complex, cell-like behaviors in the absence of living entities. Having no superior genetic control, user-controllable mechanisms to regulate gene expression are necessary to successfully operate these systems. We have created a small collection of synthetic RNA thermometers that enable temperature-dependent translation of membrane proteins, work well in cells and display great potential to be transferred to any in vitro protein synthesis system.
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-            <span class="pagination-text">Description</span>
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-         <section class="design_subsections">
-            <h1 id="Liposomes">Liposomes</h1>
-            <div class="third_level_links">
-               <a href="#Liposomes">Liposomes</a>
-               <a href="#Ribosome_modifications">Ribosome modifications</a>
-               <a href="#BAM complex">BAM complex</a>
-               <a href="#RNA_Thermoswitches">RNA Thermoswitches</a>
-               <a href="#Mistic_fusion_protein">Mistic fusion protein</a>
-               <a href="#Surface_display_system">Surface display system</a>
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-        <h1 id="Ribosome_modifications">Ribosome modifications</h1>
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-           <a href="#Liposomes">Liposomes</a>
-           <a href="#Ribosome_modifications">Ribosome modifications</a>
-           <a href="#BAM complex">BAM complex</a>
-           <a href="#RNA_Thermoswitches">RNA Thermoswitches</a>
-           <a href="#Mistic_fusion_protein">Mistic fusion protein</a>
-           <a href="#Surface_display_system">Surface display system</a>
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-            <h1>
-                Background
-            </h1>
-            <p></p>
-            <p>
-                    Insertion of many membrane proteins in prokaryotes as well as the endoplasmic reticulum of eukaryotes is facilitated by various translocons. These complexes interact with the ribosome during protein synthesis and direct the newly forming peptide into the translocon pore, or directly into the membrane. However, for the translocon to function properly, it requires many auxiliary components (signalling sequence, chaperones, insertion mechanism), which would be far too many for our system to remain stable. Since we could not simply transfer the entire translocation system into SynDrop, we hypothesized that some of its functionality could be emulated in different ways.
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-            <p>
-                <h2>
-                        Nickel-chelating lipids and polyhistidine tags as potential solution
-                </h2>
-            </p>
-            <p>
-                    Specifically to localize the ribosomes near the membrane and reduce the exposure of MP transmembrane domains to the aqueous environment, we eventually chose a method that has already been successfully used to attach other proteins to membranes - via a his-tag to nickel ions, chelated by specific lipids composing membrane<sup>1,2</sup>. Our reasoning for this was threefold. Firstly, this would have allowed ribosomes to be correctly positioned. If the ribosomes were localized near the membrane, but the peptide exit tunnel hadn’t been consistently pointed towards the membrane, the entire benefit of reducing MP aggregation would be lost. By being able to create his-tagged fusion proteins specifically of the ribosomal subunits localized near the exit tunnel, we guaranteed that the exit tunnel could never point away from the membrane. Secondly, general protein synthesis should be the least impeded, compared to alternatives, such as introducing a lipid anchor via an enzyme, or creating a fusion protein with a self inserting MP. These latter methods would completely immobilize the ribosome onto the membrane, removing degrees of freedom. With the polyhistidine-nickel interaction the ribosome would simply exhibit a much greater affinity towards the membrane, while still being able to detach and reattach as needed. Lastly, the simplicity for this method seemed to be the greatest, as only modified ribosomes as well as the incorporation of nickel-chelating lipids during liposome synthesis was needed - this was far more important than it can appear, because it was vital for our overall system to be as robust as possible.
-            </p>
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-                    <div class="image-container">
-                    <img src="https://static.igem.org/mediawiki/2018/4/42/T--Vilnius-Lithuania--Fig1_Ribosomes.png"/>
-                    <strong>Fig. 1 </strong> Principle of ribosome attachment to the liposome membrane. The ribosome exit tunnel is localized near the membrane, resulting in transmembrane domains of newly synthesized peptides interacting with the membrane, reducing aggregation
-            </p>
-        </div>
-            <p></p>
-            <h1>Results</h1>
-            <p></p>
-            <p>
-                <h2>Designing the modifications</h2>
-            </p>
-            <p>
-                    The basic procedure we designed to obtain our modified ribosomes is as follows: first, using CRISPR-Cas9, we modify the genome of E. coli (native strain MG1655) to incorporate his-tags onto the ribosomal subunits, as well as a Strep-tag onto the L12 subunit for ease of purification<sup>3</sup>. In literature a his-tag was described to aid purification when fused to subunit L12, however we exchanged it for a Strep tag, as it is also short in sequence and while being biologically does not interfere with the functionality of other his-tags. The subunits localized near the exit tunnel we chose as potential targets, in order of priority, were L24, L23, and L29. These subunits were chosen as they had free, unfolded C ends exposed to the surface at nearest proximity to the exit tunnel. These subunits are also not integral to the overall function of the ribosome, meaning that our modifications would have little to no impact on peptide synthesis<sup>4,5,6,7</sup>. After the E. coli genome is successfully modified, the ribosomes are purified with the help of the previously incorporated Strep tag, and the final product is used for IVTT reactions.
-            </p>
-            <p>
-                <h2>
-                    Modification procedure
-                </h2>
-            </p>
-            <p>
-                    CRISPR-Cas9 was utilized via pCas9 and pTargetF plasmids <sup>8</sup>. pCas9 constitutively expresses Cas9, which induces a double-strand DNA break at a specific target sequence, that is complementary to the guide RNA. The guide RNA sequences for our targets were introduced via reverse PCR into the pTargetF plasmid series, which then supplies it to Cas9. After the double stranded break occurs, the HDR (homology directed repair) mechanism is activated, which repairs the genome according to a supplied donor sequence. This process is highly efficient with the assistance λ-red proteins, expressed from pCas9. The donor sequence has ~300 bp length homology arms and the insertion sequence that can include either the His or Strep tag to be fused with the chosen ribosomal subunit C’-end, as well as an in frame selection marker (select antibiotic resistance genes). pCas9 expresses a gRNA targeting the ori of pTargetF, therefore the cells are automatically cured from pTargetF after each modification. Additionally, pCas9 has a temperature-sensitive ori, it is cured by growing the cells at 37<sup>o</sup>C.
-            </p>
-            <p>
-                    <div class="image-container">
-                    <img src="https://static.igem.org/mediawiki/2018/f/fc/T--Vilnius-Lithuania--Fig2_Ribosomes.png"/>
-                   <strong>Fig. 2 </strong> Scheme of the genome modification process:
-                   <ol>
-                       <li>
-.  pCas9 is introduced into the target cells
-                       </li>
-                       <li>
-. pTargetF and the according donor DNA are electroporated into the cells
-                       </li>
-                       <li>
-. Cas9 and our custom gRNA form a complex that cuts the genome DNA at the target. The genome is repaired via HDR according to our donor DNA sequence - X1 (homology arm of target ribosomal subunit) with fused tag, X3 (antibiotic resistance gene) and X2 (second homology arm).
-                       </li>
-                       <li>
-. pTargetF is cured and the process can be repeated with a new target.
-                       </li>
-                   </ol>
-            </p>
-            <p>
-                </div>
-                    For multi-gene editing, we chose to supply the donor sequence as a linear DNA strand (PCR product). Due to financial reasons, to construct the donor DNA sequence we performed separate PCRs of the homology arms (from the E. coli genome), selection marker (antibiotic resistance genes from available plasmids) (Fig. 4). The oligomers had the his and strep tag sequences incorporated into them alongside 2 different restriction sites. In case the distance between the ribosomes and the membrane wall was too small for our system to be efficient, we also designed alternative variants the would feature the his-tags connected via a highly flexible two-glycine-four-serine linker (GGSSSS), which is a highly popular linker for artificial fusion proteins.
-            </p>
-            <p>
-                    When the homology arm and marker gene pcr products are restricted and ligated, the end result is a single sequence with an antibiotic resistance gene flanked on either side by ~300 bp homology arms, in addition to the according tag fused to the selected subunit’s gene. The entire linear DNA product was amplified via PCR using primers that annealed to the ends of the strand. Large amounts of nonspecific product was present even after performing PCR of the whole ligated sequence, therefore gel purification was necessary after each amplification (Fig. 5).
-            </p>
-            <p>
-                    <div class="image-container">
-                    <img src="https://static.igem.org/mediawiki/2018/a/a9/T--Vilnius-Lithuania--Fig3_Ribosomes.png"/>
-                    <strong> Fig.3 </strong> Example of a constructed donor sequence. The sequence of the selected tag is present in primer used for the PCR of the homology arm that encompasses the target subunit. As a result, the tag sequence is fused to the ribosomal subunit gene.
-            </p>
-        </div>
-            <p>
-                    <div class="image-container">
-                    <img src="https://static.igem.org/mediawiki/2018/d/d5/T--Vilnius-Lithuania--Fig4_Ribosomes.png"/>
-                    <strong> Fig. 4 </strong> PCR of homology arms, and antibiotic resistance genes
-            </p>
-        </div>
-            <p>
-                    <div class="image-container">
-                    <img src="https://static.igem.org/mediawiki/2018/8/86/T--Vilnius-Lithuania--Fig5_Ribosomes.png"/>
-                    <strong> Fig. 5 </strong> Constructed donor DNA sequences. The L29 donor DNA was not further revisited due to time constraints
-            </p>
-        </div>
-            <p>
-                    The genome modifications were then carried according to </p>
-                    <a href="https://static.igem.org/mediawiki/2018/3/34/T--Vilnius-Lithuania--e._PROTOCOLS_e.coli_genome_modif.pdf">
-                        our protocol
-                      </a>. Although cPCR gave us mixed results, we could not verify any colonies that afterwards grew on our selected marker antibiotics, and thus could not continue our experiments with them. It appears most likely that the genome modifications were not entirely successful, due to the somewhat unstable nature of the ligated linear DNA used for the donor sequence.
-            </p>
-            <p></p>
-            <h1>Conclusion and Discussion</h1>
-            <p></p>
-            <p>
-                    Although well described and planned in theory, our ribosome attachment system did not yield desired results. We hypothesize, that the underlying cause may include a flawed implementation of the CRISPR-Cas9 system: in our case we were forced to incorporate selection markers due to the functionality of the specific expression plasmids we used, which lead to the construction of unstable donor sequences. While this is unfortunate, we are still confident that our idea is worth further investigation: as we could not reproduce genome modifications on the subunit that has already been reportedly modified in a similar manner, it does not suggest that our primary concept is unworkable. Moving forward, we will most likely move to an alternative CRISPR-Cas9 expression system that would allow for optimized modifications, such as removing the requirement for a selection marker, which in turn would allow us to construct more robust donor sequences. Nonetheless, herein we provide a concept and initial tools for ribosome engineering. This demonstrates great potential in synthetic biology, especially in cell-free biomolecular systems like SynDrop.
-            </p>
-            <p></p>
-            <h2>References</h2>
-            <p>
-                <ol>
-                    <li>1.Chikh, G., Li, W., Schutze-Redelmeier, M., Meunier, J. & Bally, M. Attaching histidine-tagged peptides and proteins to lipid-based carriers through use of metal-ion-chelating lipids. Biochimica et Biophysica Acta (BBA) - Biomembranes 1567, 204-212 (2002).
-                    </li>
-                    <li>2.Blanchette, C., Fischer, N., Corzett, M., Bench, G. & Hoeprich, P. Kinetic Analysis of His-Tagged Protein Binding to Nickel-Chelating Nanolipoprotein Particles. Bioconjugate Chemistry 21, 1321-1330 (2010).
-                    </li>
-                    <li>3.Ederth, J., Mandava, C., Dasgupta, S. & Sanyal, S. A single-step method for purification of active His-tagged ribosomes from a genetically engineered Escherichia coli. Nucleic Acids Research 37, e15-e15 (2008).
-                    </li>
-                    <li>4.Spillmann, S. & Nierhaus, K. The ribosomal protein L24 of Escherichia coli is an assembly protein. Journal of Biological Chemistry (1978). at http://www.jbc.org/content/253/19/7047.long
-                    </li>
-                    <li>5.GU, S. The signal recognition particle binds to protein L23 at the peptide exit of the Escherichia coli ribosome. RNA 9, 566-573 (2003).
-                    </li>
-                    <li>6.STOFFLER-MEILICKE, M., DABBS, E., ALBRECHT-EHRLICH, R. & STOFFLER, G. A mutant from Escherichia coli which lacks ribosomal proteins S17 and L29 used to localize these two proteins on the ribosomal surface. European Journal of Biochemistry 150, 485-490 (1985).
-                    </li>
-                    <li>7.Noeske, J. et al. Synergy of Streptogramin Antibiotics Occurs Independently of Their Effects on Translation. Antimicrobial Agents and Chemotherapy 58, 5269-5279 (2014).
-                    </li>
-                    <li>8.Jiang, Y. et al. Multigene Editing in the Escherichia coli Genome via the CRISPR-Cas9 System. Applied and Environmental Microbiology 81, 2506-2514 (2015)
-                    </li>
-                </ol>
-            </p>
-        </div>
-         </section>
-         <section class="design_subsections">
-            <h1 id="BAM complex">BAM complex</h1>
-            <div class="third_level_links">
-               <a href="#Liposomes">Liposomes</a>
-               <a href="#Ribosome_modifications">Ribosome modifications</a>
-               <a href="#BAM complex">BAM complex</a>
-               <a href="#RNA_Thermoswitches">RNA Thermoswitches</a>
-               <a href="#Mistic_fusion_protein">Mistic fusion protein</a>
-               <a href="#Surface_display_system">Surface display system</a>
-            </div>
-            <div>
-               Lorem ipsum dolor, sit amet consectetur adipisicing elit. Esse beatae assumenda eaque ex recusandae pariatur sunt soluta modi facere laborum exercitationem odio iure magnam obcaecati quos voluptatibus placeat, ratione harum!
-               Provident, maxime ipsum veniam, rerum facere ad vero fugit ipsa natus recusandae sit voluptatum architecto laudantium vitae necessitatibus! Nesciunt illum porro sint odio sequi reprehenderit. Sint eligendi ex impedit recusandae!
-               Alias obcaecati impedit iure recusandae quas asperiores tempore sint, consectetur veniam provident iste nulla fugit velit aliquam expedita, assumenda repellat dolorem dolore! Sit quis dolorem ad pariatur repellat reiciendis officiis.
-               Asperiores molestiae eos quo inventore recusandae quae placeat delectus, natus sint. Ullam quas culpa nobis exercitationem omnis animi velit, deleniti fugit! Sapiente aperiam sit minima nostrum, rerum quae laudantium vero?
-               Qui blanditiis, excepturi veritatis eaque temporibus voluptate maxime facere laborum voluptatem rerum ex a ipsum voluptatibus tempore, saepe sunt omnis nostrum sint? Voluptatum facilis omnis ea accusantium explicabo magnam architecto!
-               Repellendus incidunt doloremque, a cum voluptates esse officia quia veniam architecto. Quibusdam deserunt nulla, dolore perspiciatis accusantium ad aliquam voluptatem iste iure, quae minus ipsa voluptates, sit voluptatum consequatur tempora?
-               Architecto impedit in repellendus, quo dolorum sequi voluptatum omnis maxime perspiciatis aspernatur obcaecati sint iusto tenetur praesentium labore. Natus eveniet quaerat recusandae dignissimos nam sed distinctio quos fugiat aliquid eligendi.
-               Molestias inventore nobis minus aspernatur recusandae asperiores excepturi ipsam voluptas quos, quae voluptatem voluptatibus vero veniam dolores fuga aliquid neque ut dolorem beatae cum temporibus tempora? Iure expedita debitis corrupti.
-               Quae quam earum impedit laborum, nobis aspernatur fugit enim consequuntur provident laboriosam obcaecati doloremque ipsam quis modi quos ratione ipsum beatae? Voluptas, debitis eum! Dolorem accusantium et rem. Veniam, dicta!
-               Sequi aut, eos id nemo maiores iste! Dicta cum eos, incidunt aperiam voluptate facilis vero vel deleniti inventore accusantium cupiditate saepe dolore atque quisquam voluptates aliquam amet a! Hic, consectetur.
-            </div>
-         </section>
-         <section class="design_subsections">
-            <h1 id="RNA_Thermoswitches">RNA Thermoswitches</h1>
-            <div class="third_level_links">
-               <a href="#Liposomes">Liposomes</a>
-               <a href="#Ribosome_modifications">Ribosome modifications</a>
-               <a href="#BAM complex">BAM complex</a>
-               <a href="#RNA_Thermoswitches">RNA Thermoswitches</a>
-               <a href="#Mistic_fusion_protein">Mistic fusion protein</a>
-               <a href="#Surface_display_system">Surface display system</a>
-            </div>
-            <div>
-               <p></p>
-<div class="image-container">
-               <img src="https://static.igem.org/mediawiki/2018/d/d8/T--Vilnius-Lithuania--Fig1_NEW_thermoswitches.png"/>
-               <p><strong>Fig. 1</strong> A simplified mechanism of action of RNA thermometers. At lower temperatures the secondary messenger RNA (mRNA) stem-loop masks the ribosome binding site (RBS). Higher temperature induces melting of the hairpin which reveals the RBS to allow ribosome binding and initiation of translation.</p>
-</div>
-               <h1>Background</h1>
-               <p></p>
-               <p>
-                  RNA thermometers are RNA-based genetic control tools that react to temperature changes<sup>1</sup>. Low temperatures keep the mRNA at a conformation that masks the ribosome binding site within the 5’ end untranslated region (UTR). Masking of the Shine-Dalgarno (SD) sequence restricts ribosome binding and subsequent protein-translation. Higher temperatures melt the hairpins of RNA secondary structure allowing the ribosomes to access SD sequence to initiate translation <sup>1</sup>. In terms of applicability of RNA thermometers in <var>in vitro</var> systems, they display certain advantages over ribo- or toehold switches: they do not require binding of a ligand, metabolite or trigger RNA to induce the conformational change<sup>2,3</sup>, therefore are especially compatible with our liposome IVTT system. Keeping that in mind we have explored literature <sup>1,4</sup> and found five different RNA thermoswitches that we decided to test and build into our system in order to delay the translation of fusion construct bearing beta-barrel membrane protein. Furthermore, understanding the importance of expanding the library of well characterized and widely-applicable biobricks, we have <var>de novo</var> designed (<a href="kristina"> check RNA Thermoswitches model</a>) six completely unique heat-inducible RNA thermometers.
-               </p>
-               <p></p>
-               <h1>Results</h1>
-               <p></p>
-               <p>
-                  With custom IDT primers with overhangs bearing thermoswitch sequences we performed a PCR  from a GFP gene containing plasmid and inserted RNA thermometers GJ<sub>x</sub> (link: <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622010">BBa_K2622010</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622011">BBa_K2622011</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622012">BBa_K2622012</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622013">BBa_K2622013</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622014">BBa_K2622014</a>) upstream the GFP gene. Another set of primers was used to produce RNA thermometers Sw<sub>x</sub> (link: <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622016">BBa_K2622016</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622017">BBa_K2622017</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622018">BBa_K2622018</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622019">BBa_K2622019</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622020">BBa_K2622020</a>, <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622021">BBa_K2622021</a>). PCR was successful and all products were the same size as expected for Sw<sub>x</sub> constructs ~76 bp (Fig. 2). DNA gel electrophoresis was not performed for GJx constructs, because whole plasmid was multiplied and only 40-60 bp were inserted.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/c/ca/T--Vilnius-Lithuania--THERMO_fig_2.png"
-                  <strong>Fig. 2</strong> Electrophoresis gel of PCR products: 6 - Sw2, 7 - Sw3, 8 - Sw6, 9 - Sw7, 10 - Sw9, 11 - Sw11.
-               </p>
-               <p>
-                  pRSET plasmid and Sw<sub>x</sub> PCR products were digested with restriction enzymes and ligated, while GJ<sub>x</sub> PCR products were phosphorylated and ligated to produce plasmids from linear products. DH5α competent cells were transformed and plated on lysogeny broth (LB) media with ampicillin (Amp) and grown for 16 hours. Positive colonies were selected by colony PCR or restriction analysis (Fig. 3 and Fig. 4) and grown in 5 mL LB media. Plasmids were purified and BL21 competent cells were transformed. Three tubes of every construct plus plasmid with GFP without RNA thermometer were grown till OD<sub>600</sub> reached 0.4. Control samples were taken and protein expression was induced with Isopropyl β-D-1-thiogalactopyranoside (IPTG). One tube of every construct was grown in 24 ˚C, 30 ˚C, and 37 ˚C. Samples were taken after 1 and 2 hours. SDS-PAGE was run (for elaborate protocol see Notebook/<a href="https://2018.igem.org/Team:Vilnius-Lithuania/Protocols">Protocols</a>). Fig. 5, Fig 6 and Fig. 7 depicts GFP expression at different temperatures. Although our RNA thermometers were designed to melt at 37 ˚C, some displayed leakiness to different extent. GJ3 (link:<a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622011">BBa_K2622011</a>) RNA thermometer was the leakeast and allowed for GFP translation at lower temperatures. On the other hand, when grown at 37 ˚C, it unlocked the translation of GFP to highest yields. GJ2 (link:<a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622010">BBa_K2622010</a>) was less leaky, but inhibited protein translation more strictly when grown at 37 ˚C. GJ6 (link: <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622012">BBa_K2622012</a>), GJ9 (link:<a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622013">BBa_K2622013</a>), and GJ10 (link: <a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_K2622014">BBa_K2622014</a>) suppressed GFP production at 24 ˚C and 30 ˚C at similar level. They also inhibited translation to some extent at higher temperatures, meaning their melting temperature was not reached. Altogether these results prove, that our synthetic thermoswitches are temperature-responsive and act in physiological temperature range needed for IVTT reaction and also for BamA folding and membrane insertion.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/d/d8/T--Vilnius-Lithuania--THERMO_fig_3.png"
-                  <strong>Fig. 3</strong> Restriction analysis of GJ<sub>x</sub> constructs
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/a/a4/T--Vilnius-Lithuania--THERMO_fig_4.png"
-                  <strong>Fig. 4</strong> Colony PCR of RNA thermometers in pSB1C3 plasmid.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/4/46/T--Vilnius-Lithuania--THERMO_fig_5.png"
-                  <strong>Fig. 5</strong> expression at 24 ˚C. On the right you can see GFP expression without RNA thermometer.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/d/dd/T--Vilnius-Lithuania--THERMO_fig_6.png"
-                  <strong>Fig. 6</strong> GFP expression at 30 ˚C. On the right you can see GFP expression without RNA thermometer.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/7/78/T--Vilnius-Lithuania--THERMO_fig_7.png"
-                  <strong>Fig. 7</strong> GFP expression in 37 ˚C. On the right you can see GFP expression without RNA thermometer.
-               </p>
-               <p></p>
-               <h1>Discussion</h1>
-               <p></p>
-               <p>
-                  As described in other sections of the Design and results page (<a href="Kristina">check BAM Complex</a>), beta-barrel bearing proteins are assembled into the membrane by the BAM protein complex machinery. The key protein BamA is itself a membrane protein, whose folding and insertion into membrane where it helps assemble target proteins, last up to two hours. In order to prevent the aggregation of our fusion proteins after encapsulating their gene-bearing plasmids and purified BamA mRNA into liposomes, we needed to develop a modulatory regulatory tool to lock the translation of our membrane proteins to allow enough time for the encapsulated BamA to fold and insert into the liposome membrane.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/a/af/T--Vilnius-Lithuania--Fig8_NEW_thermoswitches.png"
-                  <strong>Fig. 8</strong> Associational scheme of thermoswitches’ action in the SynDrop system. Not locking the concomitant translation of our target protein and BamA results in target protein aggregation due to insufficient membrane insertion and  assembling potential of BamA.
-               </p>
-               <p>
-                  <img src="https://static.igem.org/mediawiki/2018/8/8b/T--Vilnius-Lithuania--Fig9_NEW_thermoswitches.png"
-                  <strong>Fig. 9</strong> Associational scheme of thermoswitches’ action in the SynDrop system. Locking up translation gives time for proper folding and insertion of BamA and prevents undesirable aggregation of target membrane proteins.
-               </p>
-               <p>
-                  Additionally, while creating SynDrop, we have considered various options on how to make our complex cell-free system more user-controllable and predictable. Cell-free systems are becoming an attractive platform for <var>in vitro</var> compartmentalization and protein research, and although usually compositionally sensitive, they also offer a platform for building synthetic genetic regulatory tools or logic gates. Both the need to control the translation time of target genes and desire to provide more modularity for our synthetic system, led us to exploring RNA thermometers as a viable option to perform these tasks. They have minimal molecular burden and are easy to modulate. These properties encouraged us to developed a library of synthetic RNA thermometers suitable to translationally regulate the expression of our fusion constructs in bacteria with a further possibility to transfer them to IVTT systems. All of the RNA thermometers including those we found in literature and our <var>de novo</var> modelled ones were optimized for best performance at 37<sup>o</sup>C, bearing in mind their future transition to IVTT system, whose optimum performance temperature is also 37<sup>o</sup>C. Consequently, our experiments showed that our synthetic RNA thermometers, despite their simplistic structures compared to naturally occurring ones, efficiently triggered the expression of target constructs at 37<sup>o</sup>C, and successfully locked it at lower temperatures having made them an ideal complement to our liposome IVTT system. All of our thermoswitches unlocked the expression to similarly high levels at 37<sup>o</sup>C, but differed in terms of leakiness and success at inhibiting translation at lower temperatures.
-               </p>
-               <p></p>
-               <h1>Conclusions</h1>
-               <p></p>
-               <p>
-                  We proved that herein described synthetic RNA thermometers enable high-yield expression of our constructs in an inducible temperature range. What is more important, this spectrum of temperature is compatible with currently used in vitro transcription and translation systems. Synthetic Thermoswitches allow the user-controllable and responsive protein translation for custom experiments. Finally, we introduced six de novo designed RNA thermoswitches which will have been used by future iGEM teams having to work both with cell-free and in vivo synthetic biology systems.
-               </p>
-               <p></p>
-               <h2>References</h2>
-               <p></p>
-               <p>
-               <ol>
-                  <li> 1. Neupert J, Karcher D, Bock R. Design of simple synthetic RNA thermometers for temperature-controlled gene expression in Escherichia coli. Nucleic Acids Res. Oxford University Press; (2008); 36:e124–e124.</li>
-                  <li>  2. Narberhaus F, Waldminghaus T, Chowdhury S. RNA thermometers. FEMS Microbiol. Rev. Wiley/Blackwell (10.1111); (2006); 30:3–16.</li>
-                  <li> 3. Storz G. An RNA thermometer. Genes Dev. Cold Spring Harbor Laboratory Press; (1999); 13:633–6.</li>
-                  <li>    4. Sen S, Apurva D, Satija R, Siegal D, Murray RM. Design of a Toolbox of RNA Thermometers. ACS Synth. Biol. (2017); 6:1461–70.</li>
-               </ol>
-               </p>
-            </div>
-         </section>
-         <section class="design_subsections">
-            <h1 id="Mistic_fusion_protein">Mistic fusion protein</h1>
-            <div class="third_level_links">
-               <a href="#Liposomes">Liposomes</a>
-               <a href="#Ribosome_modifications">Ribosome modifications</a>
-               <a href="#BAM complex">BAM complex</a>
-               <a href="#RNA_Thermoswitches">RNA Thermoswitches</a>
-               <a href="#Mistic_fusion_protein">Mistic fusion protein</a>
-               <a href="#Surface_display_system">Surface display system</a>
-            </div>
-            <div>
-               <h1>Mistic Fusion Protein</h1>
-               <p></p>
-               <p>
-                  Self-inserting <var>Bacillus subtilis</var> protein called Mistic (MstX) is originally involved in biofilm formation<sup>1</sup>. It is thought that MstX might directly chaperon the membrane insertion of potassium ion channel YugO. Together these proteins create a positive autoregulatory feedback loop that assists biofilm assembly in a population of cells and is mediated by a pathway involving potassium ion efflux<sup>2</sup>.
-               </p>
-               <p>
-                  MstX comprises 110 residues that are arranged into a four-helix bundle exposing numerous polar and charged amino acids (Fig. 1). This α-helical protein is characterized by an uncommonly hydrophilic surface. Until this day there is a great debate on how MstX is able to autonomously associate with a lipid bilayer despite its hydrophilic surface <sup>2</sup>. It is known that three of the four MstX helices are much shorter than transmembrane helices of canonical integral MPs. In general, the four helices of this protein show no apparent differences in hydrophobicity or charge distribution among each other.
-               </p>
-               <p>
-                    <div class="image-container">
-                            <img src="https://static.igem.org/mediawiki/2018/d/d1/T--Vilnius-Lithuania--Fig1_Mistic.png"/>
-                            <p><strong>Fig. 1 </strong> NMR structure of Mistic (MstX). Protein is comprised of four ɑ-helices with a polar lipid-facing surface. Topology measurements have shown that both C-terminus and N-terminus of MstX are exposed at the same side. Adapted by Yarnell, 2005</p>
-               </div>
-               <p>
-                  MstX was identified back in 2005 by Rooslid and colleagues. Interestingly, until this day little is known about how MstX promotes integral protein targeting to the membrane<sup>3</sup>. Recently it has found a novel application as a fusion tag supporting the recombinant production and bilayer insertion of other membrane proteins (MPs)<sup>1</sup>. MstX, when fused to the N-terminus of integral MPs, enables the cargo proteins to fold into their native conformations in the membrane, thus yielding high-level expression. It is known that MstX autonomously targets proteins to the membrane bypassing the canonical secretory apparatus, like Sec translocon. In addition to this, it was indirectly presumed that MstX lacks any recognizable signal sequence <sup>2</sup>.
-               </p>
-               <p>
-                  According to this, we have decided to implement the advantages of MstX into our project. In order to boost protein expression yield MstX was fused with target integral membrane protein Outer membrane protein A (OmpA). Prior using these recombinant proteins in cell-free system, it has to be ensured that proteins are expressed in bacteria. To do so, <var>E. coli</var> BL21 stain cells were transformed and induced for 2 and 4 hours with isopropyl β-D-1-thiogalactopyranoside (IPTG). Results were analyzed by sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS-PAGE). This experiment was conducted in order to detect if there are any differences in protein production yield comparing native and MstX-fused proteins.
-               </p>
-               <p>
-                  First of all, it was concluded that MstX-OmpA-X and OmpA-X (X - additional part of the construct) are expressed in cells (Fig. 2).
-               </p>
-               <p>
-                    <div class="image-container">
-                            <img src="https://static.igem.org/mediawiki/2018/f/fa/T--Vilnius-Lithuania--Fig2_Mistic.png"/>
-                            <p><strong>Fig. 2 </strong> OmpA-X and MstX-OmpA-X (X - additional part of the construct; shown with arrows) expression in <var>E. coli</var>; SDS-PAGE after induction with IPTG for 2 hours and 4 hours; K - control, M - protein ladder </p>
-             </div>
-                  Also, we checked if we could fuse MstX with other integral membrane proteins. In this case, IgA protein (Fig. 3).
-               </p>
-                    <p>
-                            <div class="image-container">
-                                    <img src="https://static.igem.org/mediawiki/2018/3/31/T--Vilnius-Lithuania--Fig3_Mistic.png"/>
-                                    <p><strong>Fig. 3 </strong> IgA, IgA-MstX, and X-IgA-MstX (X - additional part of the construct; shown with arrows) expression in <var>E. coli</var>; SDS-PAGE; U4-2 - samples affected with 8M urea, S2-4 - samples affected with protein denaturation dye, K - control, M - protein ladder </p>
-                     </div>
-               </p>
-               <p>
-                  Analyzing electrophoresis gel, differences of native IgA protein and  recombinant IgA fused with MstX can be observed. It is extremely important that MstX in this case ensures higher-level yield of integral membrane proteins in <var>E. coli</var> as well.
-               </p>
-               <p>
-                  According to these results, we validated that chosen integral membrane proteins are expressed in cells. In addition to this, their expression in cell-free system could be also expected. Moreover, MstX increases these MPs yield by functioning as a chaperone and enabling our target proteins to fold into their native conformations in the membrane even more efficiently.
-               </p>
-               <p>
-                  Using MstX in cell-free systems is extremely advantageous as it allows effortless protein research without any need for additional protein purification step. Also, this fusion tag is universal as MstX it is compatible with different kinds of membrane proteins. In addition to this, the final task was to refine our cell-free system with MstX in order to make system more efficient and even more suitable for protein research.
-               </p>
-               <p>
-                  To demonstrate that MstX is beneficial to cell-free system not only for membrane protein expression, it was fused with single-chain variable fragment (scFv; Fig. 3). It was decided to do so as scFvs are usually prone to form aggregates and lose their function <var>in vitro</var>. We thought that MstX could stabilize scFvs and prevent aggregation. As a result, we observed that MstX fusion could enhance scFv solubility allowing it to use in cell-free systems.
-               </p>
-               <p>
-                    <div class="image-container">
-                            <img src="https://static.igem.org/mediawiki/2018/7/79/T--Vilnius-Lithuania--Fig4_Mistic.png"/>
-                            <p><strong>Fig. 4 </strong> Single-chain variable fragment (scFv) expression in IVTT system; SDS-PAGE. M - protein ladder, + - positive control DHFR, 1 - scFv, 2 - MstX-scFv, - negative control (without template DNA)</p>
-               </div>
-               <p>
-                  Analyzing the reaction samples, sediments in scFv were observed, which meant that scFv aggregated. However, in MstX-scFv sample there were no sediments. By analysing electrophoresis results (Fig. 4) it can be seen that MstX prevented formation of the aggregates which resulted in higher scFv expression yield.
-               </p>
-               <p></p>
-               <h2>References</h2>
-               <p></p>
-               <p>
-               <ol>
-                  <li>1. Broecker, J., Fiedler, S., Gimpl, K. & Keller, S. Polar Interactions Trump Hydrophobicity in Stabilizing the Self-Inserting Membrane Protein Mistic. <var>Journal of the American Chemical Society</var> 136, 13761-13768 (2014).  </li>
-                  <li>2. Textor., M. Reconstitution and Membrane Topology  of Mistic from <var>Bacillus subtilis</var> (Doctoral dissertation). <var>University of Kaiserslautern</var>. Retrieved from https://kluedo.ub.uni-kl.de </li>
-                  <li>3. Lundberg, M. E. Biochemical and functional characterization of MISTIC. (Doctoral dissertation). <var>UC San Diego</var>. Retrieved from https://escholarship.org/uc/item/5b594287 (2013).                        </li>
-               </ol>
-               </p>
-            </div>
-         </section>
-         <section class="design_subsections">
-            <h1 id="Surface_display_system">Surface display system</h1>
-            <div class="third_level_links">
-               <a href="#Liposomes">Liposomes</a>
-               <a href="#Ribosome_modifications">Ribosome modifications</a>
-               <a href="#BAM complex">BAM complex</a>
-               <a href="#RNA_Thermoswitches">RNA Thermoswitches</a>
-               <a href="#Mistic_fusion_protein">Mistic fusion protein</a>
-               <a href="#Surface_display_system">Surface display system</a>
-            </div>
-            <div>
-               <h1>ScFv Antibody</h1>
-               <h1>Background</h1>
-               <p>
-               </p>
-               <p>scFv consists of a minimal functional antigen-binding domain of an antibody (~30 kDa) (Fig. 1) , in which the heavy variable chain (VH) and light variable chain (VL) are connected by Ser and Gly rich flexible linker. [1] In most cases scFv is expressed in bacteria, where it is produced in cytoplasm, a reducing environment, in which disulfide bonds are not able to form and protein is quickly degraded or aggregated. Although poor solubility and affinity limit scFvs’ applications, their stability can be improved by merging with other proteins. [2] When expressed in cell free system, scFv should form disulfide bonds with the help of additional molecules. Merging to a membrane protein would provide additional stability and would display scFv on liposome membrane, where its activity could be detected. These improved qualities make ScFv recombinant proteins a perfect tool to evaluate, if SynDrop system acts in an anticipated manner. Of all possible scFvs we decided to use scFv-anti vaginolysin, which binds and neutralizes toxin vaginolysin (VLY). Its main advantage is rapid (< 1 h) and cheap detection of activity by inhibition of erythrocyte lysis (Fig. 2). Looking into future applications, scFvs are also attractive targets of molecular evolution, because one round of  evolution would last less than one day thus generating a and wide range of different scFv mutants. Those displaying the highest affinity for antigens could be selected and used as drugs or drug carriers. </p>
-               <img src="https://static.igem.org/mediawiki/2018/9/99/T--Vilnius-Lithuania--_Fig1_Surface-scFv.png"
-               <p><strong>Fig. 1 </strong>Simplified structure of scFv Antibody</p>
-               <img src="https://static.igem.org/mediawiki/2018/9/97/T--Vilnius-Lithuania--Fig2_NEW_real_Surface_scFV.png"
-               <p><strong>Fig. 2 </strong>Scheme of scFv_antiVLY and VLY interaction. Left- scFv_antiVLY binds to VLY, erythrocytes stay intact, Right- scFv_antiVLY does not bind and VLY lyse erythrocytes.</p>
-               <p></p>
-               <h1>Results</h1>
-               <p></p>
-               <p>scFv constructs were created BBa_K2622006"Kristina" and checked by colony PCR and DNA sequencing (link to Simas construct protocol"Kristina"). scFv synthesis was performed in a cell free system. Validation of protein expression was done by running a sodium dodecyl sulfate–polyacrylamide gel electrophoresis (SDS-PAGE), see (Fig. 3)</p>
-               <img src="https://static.igem.org/mediawiki/2018/8/83/T--Vilnius-Lithuania--_Fig2_Surface-scFv.png"
-               <p><strong>Fig. 3 </strong> SDS-PAGE of scFv. GFP is used as positive control, C- chaperone DnaK.</p>
-               <p>Red arrows in the photo indicate scFv anti-vaginolysin (~27 kDa). As successful synthesis was confirmed, the next step was to check if protein folded correctly and was able to bind its antigen -  vaginolysin. We examined this by erythrocyte-lysis test, which was performed by comparing erythrocytes incubated with VLY (erythrocytes burst open) and erythrocytes incubated with VLY that was previously incubated with scFv anti-vaginolysin (less or no erythrocyte lysis). Results revealed that scFv binded to vaginolysin and inhibited cell lysis. Graph in (Fig. 4) demonstrates that scFv indeed attenuated the lysis of erythrocytes. These result prove scFv activity in IVTT system.</p>
-               <img src="https://static.igem.org/mediawiki/2018/7/7b/T--Vilnius-Lithuania--_Fig3_Surface-scFv.png"
-               <p><strong>Fig. 4 </strong> Percentage of erythrocyte lysis at different +/-scFv dilutions.</p>
-               <p>We then went one step further and constructed MstX-scFv_antiVLY (BBa_K2622038"Kristina") fusion protein, aiming to increase the stability of scFv having in mind future applications and experiments of exposing it on liposome surface. Fusion protein was expressed in E.coli cells; yellow to red arrows in (Fig. 5A) indicate MstX-scFv expression after induction with IPTG.</p>
-               <p>Finally, we expressed the protein in a cell free system (Fig. 5B) along with scFv in order to compare how well scFv accomplishes its function alone or binded to other protein. In this case MstX-scFv_antiVLY fusion did not show superior activity than scFv_antiVLY alone (Fig. 6). These results also reveal that scFv_antiVLY is very sensitive and loses its activity with time. Ist and IInd attempts were separated by 1-2 hours. This amount of time is enough to measure decreasing activity. This must be taken into account when performing future experiments.</p>
-               <img src="https://static.igem.org/mediawiki/2018/9/9c/T--Vilnius-Lithuania--Fig_4._5._Surface_scFv.png"
-               <p><strong>Fig. 5 </strong>A- MstX-scFv_antiVLY expression in Escherichia coli. B- scFv_antiVLY and MstX-scFv_antiVLY expression in cell-free system.</p>
-               <img src="https://static.igem.org/mediawiki/2018/0/0c/T--Vilnius-Lithuania--_Fig6_Surface-scFv.png"
-               <p><strong>Fig. 6 </strong>Fig 6. Percentage of erythrocyte lysis at different scFv/MstX-scFv dilutions.</p>
-               <h1>Conclusions</h1>
-               <p>
-               </p>
-               <p>We successfully expressed scFv_antiVLY antibody and MstX-scFv_antiVLY construct in E.coli cells as well as in a cell free system. We demonstrated that our scFv anti-vaginolysin can bind to its target antigen vaginolysin and inhibit erythrocyte-lysis reaction. Based in scFv general properties in IVTT activity, we conclude that scFvs are an elegant addition to SynDrop liposome display system.</p>
-               <h1>Discussion</h1>
-               <p>
-               <p>Small size of scFv makes it a widely researched antibody. It’s ability to penetrate deeply into tissues and trait to elicit low to none organism’s immune response, makes scFv the one of the best candidates for medical, diagnostic, and research applications [3]. Efficient and fast method for scFv generation is in demand. SynDrop liposome display system offers an ability to produce scFv in IVTT system and display them on membranes to facilitate rapid antigen binding. scFv on the other hand can also help us prove that our system work either cost efficiently or with extreme precision. scFv surface display is compatible with using fluorescence assisted cell sorting (FACS) to detect well functioning liposomes. [4] This would reduce amount of time needed for mutant sorting compared with enzyme-linked immunosorbent assay. Second, scFv display is compatible with the experiments described in this section. We have performed erythrocyte-lysis tests to prove the functional activity of scFv anti-vaginolysin that was synthesized in the IVTT system. Not all experiments with VLY indicated positive antibody activity. We hypothesized that proteins could have aggregated very quickly after IVTT expression and the amount of active antibody left in the solution was not enough to inhibit VLY in quantities, what would have been detectable. This hypothesis was further supported by several experiments, which revealed decreasing scFv antibody’s functional activity with time. Moreover, not every experiment was done just after IVTT reaction completed and spend few hours in +4 ˚C. Another option to test scFv, single or displayed on liposomes to gain most reliable results, is an ELISA test. It requires specific antibodies and tags (His-6x or Strep-tag) on scFv or MstX-scFv. </p>
-               </p>
-               <h2>Refferences</h2>
-               <p>
-               <ol>
-                  <li>Monnier, P., Vigouroux, R. & Tassew, N. In Vivo Applications of Single Chain Fv (Variable Domain) (scFv) Fragments. Antibodies 2, 193-208 (2013).</li>
-                  <li>Wang, R. et al. Engineering production of functional scFv antibody in E. coli by co-expressing the molecule chaperone Skp. Frontiers in Cellular and Infection Microbiology 3, (2013).</li>
-                  <li>Ahmad, Z. et al. scFv Antibody: Principles and Clinical Application. Clinical and Developmental Immunology 2012, 1-15 (2012).</li>
-                  <li>Vorauer-Uhl, K., Wagner, A., Borth, N. & Katinger, H. Determination of liposome size distribution by flow cytometry. Cytometry 39, 166 (2000).</li>
-               </ol>
-               </p>
-            </div>
-         </section>
-      </div>
-   </div>
-   </div>
-   <div class="carrot-back">
-      <a class="carrot-anchor-back" href="">
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@@ Line 473: / Line 26: @@
     <h1 id="Edinburgh_model">Edinburgh model</h1>
     <div class="third_level_links">
-       <a href="#Edinburgh_model">Edinburgh model</a>
+       <a href="#Edinburgh_model">WaitDrop</a>
        <a href="#Groeningen_model">Groeningen model</a>
        <a href="#COMSOL_model">COMSOL model</a>
@@ Line 479: / Line 32: @@
     </div>
     <div>
-       Lorem ipsum dolor, sit amet consectetur adipisicing elit. Esse beatae assumenda eaque ex recusandae pariatur sunt soluta modi facere laborum exercitationem odio iure magnam obcaecati quos voluptatibus placeat, ratione harum!
+       <h1>The β-barrel Assembly Machinery Complex</h1>
-      Provident, maxime ipsum veniam, rerum facere ad vero fugit ipsa natus recusandae sit voluptatum architecto laudantium vitae necessitatibus! Nesciunt illum porro sint odio sequi reprehenderit. Sint eligendi ex impedit recusandae!
+<p></p>
-      Alias obcaecati impedit iure recusandae quas asperiores tempore sint, consectetur veniam provident iste nulla fugit velit aliquam expedita, assumenda repellat dolorem dolore! Sit quis dolorem ad pariatur repellat reiciendis officiis.
+<p>Outer membrane proteins (OMPs) of Gram-negative bacteria are synthesized in the cytoplasm and transported across the inner membrane by SecYEG translocon into the periplasm. The survival factor A (SurA) chaperones carry the unfolded membrane proteins across the periplasm to the BAM complex, which is responsible for the insertion and assembly of OMPs into the outer membrane [1].</p>
-      Asperiores molestiae eos quo inventore recusandae quae placeat delectus, natus sint. Ullam quas culpa nobis exercitationem omnis animi velit, deleniti fugit! Sapiente aperiam sit minima nostrum, rerum quae laudantium vero?
+<p>In E. coli BAM complex consists of a membrane protein BamA and four lipoprotein subunits BamBCDE. These subunits associate with BamA through periplasmic POTRA domains. In vitro reconstitution of the E. coli BAM complex and functional assays showed that all five subunits are required to achieve the maximum activity of BAM [1]. </p>
-      Qui blanditiis, excepturi veritatis eaque temporibus voluptate maxime facere laborum voluptatem rerum ex a ipsum voluptatibus tempore, saepe sunt omnis nostrum sint? Voluptatum facilis omnis ea accusantium explicabo magnam architecto!
+<p>In theory, recruiting the BAM complex in a cell-free system could be extremely beneficial as it could integrate OmpA and lgA protease beta-domain into the membranes of liposomes from the inside without requiring any additional protein complexes. Also, this would make a cell-free system more ubiquitous, because BAM complex does not require any signal sequence for proper protein insertion. In order to ensure quick integration, BamA needs to be consistently present at high yields throughout the expression of OmpA and lgA. For this reason, it is essential to stimulate its expression by an initial addition of mRNA, ensuring rapid expression of BamA. For this reason, with the help of Edinburgh iGEM team (special thanks to Freddie Starkey), a mathematical model for BamA kinetics was created.</p>
-      Repellendus incidunt doloremque, a cum voluptates esse officia quia veniam architecto. Quibusdam deserunt nulla, dolore perspiciatis accusantium ad aliquam voluptatem iste iure, quae minus ipsa voluptates, sit voluptatum consequatur tempora?
+<p></p>
-      Architecto impedit in repellendus, quo dolorum sequi voluptatum omnis maxime perspiciatis aspernatur obcaecati sint iusto tenetur praesentium labore. Natus eveniet quaerat recusandae dignissimos nam sed distinctio quos fugiat aliquid eligendi.
+<h1>Mass Action Equations</h1>
-      Molestias inventore nobis minus aspernatur recusandae asperiores excepturi ipsam voluptas quos, quae voluptatem voluptatibus vero veniam dolores fuga aliquid neque ut dolorem beatae cum temporibus tempora? Iure expedita debitis corrupti.
+<p></p>
-       Quae quam earum impedit laborum, nobis aspernatur fugit enim consequuntur provident laboriosam obcaecati doloremque ipsam quis modi quos ratione ipsum beatae? Voluptas, debitis eum! Dolorem accusantium et rem. Veniam, dicta!
+<p>First of all, to represent chemical reactions and to render a start for mechanistic modelling, Mass Action Equations were used. It is known that the laws of mass action state that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. The mass action equations in Figure 1 can be used to represent basic protein expression:</p>
-      Sequi aut, eos id nemo maiores iste! Dicta cum eos, incidunt aperiam voluptate facilis vero vel deleniti inventore accusantium cupiditate saepe dolore atque quisquam voluptates aliquam amet a! Hic, consectetur.
+<p>
+  <div class="image-container">
+                           <img src="https://static.igem.org/mediawiki/2018/6/6d/T--Vilnius-Lithuania--_Fig1_Edinburgh_Model.png"/>
+<p><strong>Fig. 1</strong> Mass Action Equations for Protein Expression </p>
+<p>Each of these equations is used in triplicate to represent the expression of BamA, OmpA and lgA respectively and from these mass action equations a system of ordinary diﬀerential equations can be derived.</p>
+</div>
+<p>
+</p>
+<h1>Ordinary Differential Equations</h1>
+<p>
+</p>
+<p>The model uses a set of differential equations:</p>
+<P>
+    <div class="image-container">
+                           <img src="https://static.igem.org/mediawiki/2018/2/2e/T--Vilnius-Lithuania--_Fig2_Edinburgh_Model.png"/>
+<p><strong>Fig. 2</strong> System of differential equations for BamA kinetics</p>
+</div>
+<p></p>
+<h1>Determination of the System Values</h1>
+<p>
+</p>
+<p>In order to solve this system it is ﬁrst necessary to derive values for all the parameters used:</p>
+ <p> 1. copies<sub>BamA</sub>, copies<sub>OmpA</sub>, copies<sub>IgA</sub> - <strong>Relative number of plasmid copies.</strong></p>
+ <p>It is important to consider the eﬀect of diﬀerent starting masses of DNA of BamA, OmpA, and lgA, therefore to calculate the number of plasmids from which each protein can be expressed. Assuming that we add 25-1000 ng of DNA to our system  [1], a single base pair has mass of 650 Da, and the length of each plasmid is known, mass of each plasmid was calculated:</p>
+ <ol>
+    <li>peT2Ab with BamA - 5089.5 kDa </li>
+    <li>pRSETb with OmpA - 2550.95 kDa</li>
+    <li>pRSETb with lgA - 2490.8 kDa</li>
+    </ol>
+<p>Knowledge that 1 ng equals to 6.022∗10<sup>17</sup> kDa, allows to calculate the number of plasmids present for a particular number of ng of DNA added (Tab. 1).</p>
+<p>Tab. 1 Number of plasmids present for a particular number of ng of DNA added</p>
+<table>
+        <thead>
+         <tr>
+          <th><strong>peT2AB with BamA</strong></th>
+          <th><Strong></Strong></th>
+         </tr>
+        </thead>
+        <tbody>
+             </tr>
+         <tr>
+            <td>DNA added (ng)</td>
+            <td>Number of copies</td>
+         </tr> <tr>
+                <td>25</td>
+            <td>2.985*10<sup>15</sup></td>
+       </tr> <tr>
+                <td>250</td>
+            <td>2.958*10<sup>16</sup></td>
+        </tr> <tr>
+                <td>1000</td>
+            <td>1.183*10<sup>17</sup></td>
+        </tr>  <tr>
+                <td><strong>pRSETb with OmpA</strong></td>
+            <td></td>
+        </tr>  <tr>
+                <td>DNA added (ng)</td>
+            <td>Number of copies</td>
+        </tr>  <tr>
+                <td>25</td>
+            <td>5.902*10<sup>15</sup></td>
+        </tr>  <tr>
+                <td>250</td>
+            <td>5.902*10<sup>16</sup></td>
+        </tr>  <tr>
+                <td>1000</td>
+            <td>2.361*10<sup>17</sup></td>
+        </tr>  <tr>
+                <td><strong>pRSETb with IgA</strong></td>
+            <td></td>
+        </tr>  <tr>
+                <td>DNA added (ng)</td>
+            <td>Number of copies</td>
+        </tr>  <tr>
+                <td>25</td>
+            <td>6.044<sup>15</sup></td>
+        </tr>  <tr>
+                <td>250</td>
+            <td>6.044<sup>16</sup></td>
+        </tr>  <tr>
+                <td>1000</td>
+            <td>2.418<sup>17</sup></td>
+        </tr>
+        </tbody>
+       </table>
+       <p> 2. tr<sub>BamA</sub>, tr<sub>OmpA</sub>, tr<sub>IgA</sub> - <strong>Transcription rate.</strong></p>
+<p>Transcription rate of T7 RNA polymerase is approximately 60 nucleotides per second [2]. Length of each gene was 2430 nucleotides for BamA, 1038 nucleotides for OmpA, and 945 nucleotides for lgA. Transcription rate per minute for each gene was calculated:</p>
+<ol>
+        <li>tr<sub>BamA</sub> = (60/2430)∗60 = 1.48 mRNAs per minute </li>
+        <li>tr<sub>OmpA</sub> = (60/1038)∗60 = 3.47 mRNAs per minute </li>
+        <li>tr<sub>lgA</sub> = (60/945)∗60 = 3.81 mRNAs per minute</li>
+        </ol>
+        <p>3. deg<sub>mRNA BamA</sub>, deg<sub>mRNA OmpA</sub>, deg<sub>mRNA IgA</sub> - <strong>mRNA degradation rate.</strong></p>
+<p>Degradation rate is calculable from half-life using the formula: degX = ln(2)/halflife [3], where X shows the transcript of the target gene. Average mRNA half-life approximately is 5 minutes, however we screened half-lives of 1, 5, 10, and 15 minutes for each protein in order to more precisely evaluate the variability of the results. Degradation rates per minute were calculated:</p>
+<ol>
+        <li>1 minute half-life - 0.69 mRNAs per minute  </li>
+        <li>5 minute half-life - 0.14 mRNAs per minute </li>
+        <li>10 minute half-life - 0.07 mRNAs per minute </li>
+        <li>15 minute half-life - 0.05 mRNAs per minute</li>
+        </ol>
+        <p>4. trl<sub>BamA</sub>, trl<sub>OmpA</sub>, trl<sub>IgA</sub> - <strong>Protein translation rate.</strong></p>
+<p>Translation rate is about 20 amino acids per second [2]. Lengths of target proteins are 2430 nucleotides for BamA, 1038 nucleotides for OmpA, and 945 nucleotides for lgA. Translation rates per minute were calculated: </p>
+<ol>
+        <li>trl<sub>BamA</sub> = (20/810)∗60 = 1.48 proteins per minute </li>
+        <li>trl<sub>OmpA</sub> = (20/346)∗60 = 3.47 proteins per minute</li>
+        <li>trl<sub>lgA</sub> = (20/315)∗60 = 3.81 proteins per minute
+            </li>
+        </ol>
+        <p>5. deg<sub>BamA</sub>, deg<sub>OmpA</sub>, deg<sub>IgA</sub> - <strong>Protein degradation rate.</strong></p>
+<p>Protein half-life was determined using ProtParam Tool, which uses the N-end rule [4] to determine protein half-life. The estimates given for each of BamA, OmpA, and lgA are >10 hrs in E. coli. In order to reﬂect the inexact nature of these computationally derived half-lives, we screened over possible half-lives of 10, 20, and 30 hours for each of BamA, OmpA, and lgA. Applying prior used degradation rate formula degX = ln(2)/halflife [3], this yielded degradation rates per minute of: </p>
+<ol>
+        <li>10 hour half-life - 1.16∗10<sup>−3</sup> proteins per minute</li>
+        <li>20 hour half-life - 5.78∗10<sup>−4</sup> proteins per minute </li>
+        <li>30 hour half-life - 3.85∗10<sup>−4</sup> proteins per minute </li>
+        </ol>
+<p></p>
+<h1>Starting Conditions</h1>
+<p></p>
+<p>In order to examine the eﬀects of higher initial mass of BamA RNA, 6 diﬀerent values were screened over (Tab.  2). Assuming that addition of RNA in IVTT system is between 1 and 5 µg, the masses of sense and antisense strands of BamA in kDa [6] are 830.382 and 820.8, respectively, and conversion is 1 µg = 6.022∗10<sup>20</sup> kDa, the number of RNA molecules added can be calculated using the formula µgadded∗(6.022∗10<sup>20</sup>/((830.382+820.8)/2)).</p>
+<p></p>
+<strong>Tab. 2</strong> Initial BamA mRNA
+<table>
+        <thead>
+         <tr>
+          <th><strong>RNA added (µg)</strong></th>
+          <th><Strong>RNA added (molecules)</Strong></th>
+         </tr>
+        </thead>
+        <tbody>
+             </tr>
+         <tr>
+            <td>0</td>
+            <td>0</td>
+         </tr> <tr>
+                <td>1</td>
+            <td>7.29*10<sup>17</sup></td>
+       </tr> <tr>
+                <td>2</td>
+            <td>1.46*10<sup>18</sup></td>
+        </tr> <tr>
+                <td>3</td>
+            <td>2.19*10<sup>18</sup></td>
+        </tr>  <tr>
+                <td>4</td>
+            <td>2.92*10</td>
+        </tr>  <tr>
+                <td>5</td>
+            <td>3.65*10<sup>18</sup></td>
+        </tr>
+        </tbody>
+       </table>
+       <p>The primary aim of this model was to identify parameters leading to rapidly-achieved and consistently high levels of BamA under conditions of co-expression of BamA, OmpA, and lgA. Prior to this it was important to identify particular parameters leading to these conditions and to examine some general trends. The number of molecules of mRNA and protein for each average, minimum and maximum plot and each of BamA, OmpA, and lgA after 2 hours were calculated (Fig.  3) and summarized (Tab.  3).</p>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/6/6d/T--Vilnius-Lithuania--_Fig3.1_Edinburgh_Model.png"></div>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/9/94/T--Vilnius-Lithuania--_Fig3.2_Edinburgh_Model.png">
+<p><strong>Fig. 3</strong> Minimum, maximum and average levels of mRNAs and protein for BamA, OmpA and lgA</p></div>
+<p></p>
+<strong>Tab. 3</strong>Average, minimum and maximum number of protein molecules after 2 hours
+<table><thead>
+        <tr>
+         <th><strong>Protein</strong></th>
+         <th><Strong>Number of molecules</strong></th>
+        </tr>
+       </thead>
+       <tbody>
+        <tr>
+           <td><strong>Average</strong></td>
+           <td></td>
+        </tr> <tr>
+               <td>BamA</td>
+           <td>2.8*10<sup>20</sup></td>
+       </tr> <tr>
+               <td>OmpA</td>
+           <td>2.78*10<sup>21</sup></td>
+       </tr> <tr>
+               <td>IgA</td>
+           <td>3.44*10<sup>21</sup></td>
+       </tr>  <tr>
+               <td><strong>Minimum</strong></td>
+           <td></td>
+</tr>
+           <tr>
+                <td>BamA</td>
+            <td>1.95*10<sup>18</sup></td>
+       </tr> <tr>
+                <td>OmpA</td>
+            <td>2.13*10<sup>19</sup></td>
+        </tr> <tr>
+                <td>IgA</td>
+            <td>2.63*10<sup>19</sup></td>
+        </tr>
+        <tr>
+                <td><strong>Maximum</strong></td>
+            <td></td>
+</tr>
+            <tr>
+                 <td>BamA</td>
+             <td>1.28*10<sup>21</sup></td>
+        </tr> <tr>
+                 <td>OmpA</td>
+             <td>1.28*10<sup>22</sup></td>
+         </tr> <tr>
+                 <td>IgA</td>
+             <td>1.58*10<sup>22</sup></td>
+         </tr>
+       </tbody>
+      </table>
+<p>In average, minimum, and maximum cases the protein expression of OmpA, lgA, and BamA follows the same trend which is unaﬀected by ﬂuctuations of mRNA level. Each protein is expressed at a rate primarily proportional to its length and to a magnitude primarily dependent on the mass of available DNA.</p>
+<p></p>
+<h1>Sensitivity Analysis</h1>
+<p></p>
+<p>Fourier Amplitude Sensitivity Testing (FAST) indices represent the proportion of the output variance of the model attributable  to a particular variable and its interactions. Focusing on BamA expression as the protein of interest, total order FAST sensitivity indices were calculated using the BamA protein level each 20 minutes as the model output (Fig.  4).</p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/4/4b/T--Vilnius-Lithuania--_Fig4_Edinburgh_Model.png">
+<p><strong>Fig. 4 </strong>FAST sensitivity analysis of BamA</p></div>
+<p>As it can be seen from the graph, number of BamA plasmid copies contributes most to output variance over the whole time span. Also, BamA mRNA degradation rate is considerably faster than BamA degradation rate - with mRNA halﬂife of the order of minutes and protein halﬂife of the order of hours - hence the greater FAST index.</p>
+<p></p>
+<h1>Conclusions</h1>
+<p></p>
+<p>Prior to starting the wet lab experiments, we had hypothesized that the addition of mRNA into our system would ensure that BamA folded and inserted into liposome membrane more efficiently, thus enhancing the expression of OmpA and IgA. Therefore it was decided to purify BamA mRNA and add it to the reaction mixture as a template instead of DNA as we assumed that skipping the transcription step would increase protein synthesis rate. After creating a mathematical model that calculated the necessity of mRNA addition to IVTT system, we were able to generate a more efficient transcription-translation system in which we used both the purified BamA mRNA and DNA. This model clearly revealed that using both mRNA and plasmid DNA in our system was essential as BamA mRNA did increase the rate of protein expression while this eﬀect was proportional to the mass of initial DNA. However, after experimenting in the wet lab, we chose to use purified BamA as it was desired to reach higher expression yields of membrane proteins and it proved to be more effective as BamA mRNA degradation rate was considerably faster than BamA protein degradation rate. </p>
+<p></p>
+<H2>References</H2>
+<p>
+        <ol>
+        <li>Gu, Y. et al. Structural basis of outer membrane protein insertion by the BAM complex. Nature 531, 64-69 (2016).</li>
+        <li>Biolabs, N. PURExpress® In Vitro Protein Synthesis Kit | NEB. International.neb.com (2018). at < https://international.neb.com/</li>
+        <li>Philips, R. What is faster, transcription or translation?. Book.bionumbers.org (2018). at <http://book.bionumbers.org/></li>
+        <li>Exponential decay. En.wikipedia.org (2018). Accession: at <https://en.wikipedia.org/wiki/Exponential_decay></li>
+        <li>Bachmair, A., Finley, D. & Varshavsky, A. In vivo half-life of a protein is a function of its amino-terminal residue. Science 234, 179-186 (1986).</li>
+        <li>RNA Molecular Weight Calculator | AAT Bioquest. Aatbio.com (2018). Accession: at <https://www.aatbio.com/tools/calculate-RNA-molecular-weight-mw></https:></li>
+    </ol>
+</p>
     </div>
 </section>
@@ Line 502: / Line 296: @@
       <h1>Background</h1>
 <p></p>
-     <p>During the past several decades, display systems have been successfully implemented in linking the genotype to phenotype of particular proteins. While some of these systems naturally occur in nature, some are artificially created in laboratory. Overall, the display systems have been widely used for protein research. For a brief overview of these systems, click here "Kristina". </p>
+<p>
+                                  <img src="https://static.igem.org/mediawiki/2018/a/a7/T--Vilnius-Lithuania--Groningen-Transparent.png">
+</p>
+     <p>During the past several decades, display systems have been successfully implemented in linking the genotype to phenotype of particular proteins. While some of these systems naturally occur in nature, some are artificially created in laboratory. Overall, the display systems have been widely used for protein research. For a brief overview of these systems, <a href="https://2018.igem.org/Team:Vilnius-Lithuania/Description">
+click here</a>.</p>
 <p>One of the nearest future applications of SynDrop is liposome surface display. It stands out from the other display methods as it has fully controllable settings of an experiment such as the optimized interior composition for synthesis and adjusted exterior configuration for protein folding. Unlike cells, liposomes are free of unnecessary cross-talk and biological noise. Additionally, high-throughput production of liposomes might reduce the experimental time substantially.</p>
-<p>To achieve this goal, we chose a prokaryotic membrane protein - OmpA (Outer membrane protein A) - it was successfully used as a membrane protein which enables the display of a fused globular protein in prokaryotes1. In our case, we wanted to demonstrate two different proteins: scFv with affinity to vaginolysin2 and camelid nanobody, capable to interact with a GFP molecule3 . These membrane proteins were chosen to mimic targets of current display systems.</p>
+<p>To achieve this goal, we chose a prokaryotic membrane protein - OmpA (Outer membrane protein A) - it was successfully used as a membrane protein which enables the display of a fused globular protein in prokaryotes<sup>1</sup>. In our case, we wanted to demonstrate two different proteins: scFv with affinity to vaginolysin<sup>2</sup> and camelid nanobody, capable to interact with a GFP molecule<sup>3</sup> . These membrane proteins were chosen to mimic targets of current display systems.</p>
-<p>In nature, OmpA surface display system flips the selective protein from the inside of the living organism to the outside of its’ surface4. By achieving this in liposomes, the bottom-up approach would allow us to understand the mechanism and relevant components of the flipping process.
+<p>In nature, OmpA surface display system flips the selective protein from the inside of the living organism to the outside of its’ surface<sup>4</sup>. By achieving this in liposomes, the bottom-up approach would allow us to understand the mechanism and relevant components of the flipping process.
      For this reason, we decided to model a simple system with few variables to evaluate the activity of the fusion protein containing OmpA and Anti_GFP - it seemed like a good starting point to investigate well characterized parts. This is where molecular dynamics GROMACS package came in handy. GROMACS is a powerful open-sourced tool to build simulations of protein folding and lipids interactions. With a huge help from iGEM team Groningen molecular thermodynamics model with GROMACS was built.
      </p>
@@ Line 512: / Line 311: @@
 <p>
-</p><p>Sequence of particular fusion protein was built BBa_K2622029."Kristina"</p>
+</p><p>Sequence of particular fusion protein was built <a href="http://parts.igem.org/Part:BBa_K2622029"> BBa_K2622029</a>.</p>
 <p>
-   Fig. 1
+                <div class="image-container">
-</p>
+                                  <img src="https://static.igem.org/mediawiki/2018/1/1c/T--Vilnius-Lithuania--Fig1_Groningen.png"/>
-<strong>Fig. 1</strong>Sequence scheme of Lpp_OmpA and Anti_GFP nanobody fusion protein.
+                                  <p><strong>Fig. 1</strong> Sequence scheme of Lpp_OmpA and Anti_GFP nanobody fusion protein. </p>
+                </div>
 <p>Next, the fusion protein was constructed. The sequences of OmpA and anti-GFP (PDB: 3OGO) were joined exactly where they will be fused according to the DNA sequence using PyMOL (Fig. 2). To start, the structure of OmpA (PDB: 1QJP) had to be reconstructed as parts of it are missing in the crystal structure. This was achieved using the “modeler” software, a python module for homology modeling. The same structure was used as the reference structure and so the filled in structure only serves to complete the molecule.</p>
@@ Line 522: / Line 323: @@
 </p>
-<p>GFP was also coarse grained using martinize and inserted in the system containing the fusion protein and the DOPC bilayer, after which the system was solvated with regular water beads. 150mM equivalence of NaCl was added to neutralize the system. For both coarse grained structures, an elastic network was applied with a cutoff of 0.5nm such that the beta-barrels of the proteins are maintained.</p>
+<p>GFP was also coarse grained using martinize and inserted in the system containing the fusion protein and the DOPC bilayer, after which the system was solvated with regular water beads. 150 mM equivalence of NaCl was added to neutralize the system. For both coarse grained structures, an elastic network was applied with a cutoff of 0.5 nm such that the beta-barrels of the proteins are maintained.</p>
 <p>
-    Fig. 2
+        <div class="image-container">
+                          <img src="https://static.igem.org/mediawiki/2018/7/75/T--Vilnius-Lithuania--Fig2_Groningen.png"/>
+                          <p><strong>Fig 2</strong> The molecular system. Left image represents  the fused Lpp_OmpA+anti_GFP inserted to a DOPC lipid bilayer while the coarse grained structure of GFP is presented on the right. </p>
 </p>
-<strong>Fig. 2</strong> The molecular system. Left image represents  the fused Lpp_OmpA+anti_GFP inserted to a DOPC lipid bilayer while the coarse grained structure of GFP is presented on the right.
+</div>
 <p>To set up a calculation, the system having the simplest and least variables containing configuration was chosen:</p>
@@ Line 538: / Line 340: @@
          Common parameters for martini were used for minimization and equilibration, and the model was setup to run for about 10 microseconds with berendsen temperature coupling and Parrinello-Rahman pressure coupling. The system runs at 300 K and a pressure of 1 bar.
      </p>
-     <p>The building process is documented on the project’s github page "Kristina"</p>
+     <p>The building process is documented on the project’s <a href="http://parts.igem.org/Part:BBa_K2622029">
+        github page
+      </a>
      <H1>Results</H1>
@@ Line 544: / Line 349: @@
          <p>Binding between anti-GFP and GFP was visualized over time in Fig. 3 to validate that the model functions as expected. Fig. 3 shows that binding occurs after roughly 1 ms and is quite strong as expected.
          </p>
-    </p>
+        <p>
-<p>
+                <div class="image-container">
-    Fig. 3
+                                  <img src="https://static.igem.org/mediawiki/2018/2/27/T--Vilnius-Lithuania--Fig3_Groningen.png"/>
-</p>
+                                  <p><strong>Fig 3</strong> Distance between GFP and anti-GFP measured over time. Strong binding occurs over roughly 1 ms of simulation. </p>
-<strong>Fig. 3</strong>Distance between GFP and anti-GFP measured over time. Strong binding occurs over roughly 1 ms of simulation.
+        </p>
+        </div>
 <p>The Root Mean Square Deviation (RMSD) was computed over time using GROMACS and plotted in Fig. 4 to show OmpA unfolding over time. The entire event takes place over a time scale of roughly 1 ms.</p>
 <p>
-    Fig. 4
+        <div class="image-container">
+                <img src="https://static.igem.org/mediawiki/2018/2/2b/T--Vilnius-Lithuania--Fig4_Groningen.png"/>
+                <p><strong>Fig 4</strong> OmpA unfolding visualized over time by computing the Root Mean Square Deviation from the starting conformation. Unfolding occurs roughly over a time scale of 1 ms. </p>
 </p>
-<strong>Fig. 4</strong>OmpA unfolding visualized over time by computing the Root Mean Square Deviation from the starting conformation. Unfolding occurs roughly over a time scale of 1 ms.
+</div>
 <p>Due to a strong tendency to shield charged residues within the remaining barrel structure from interacting with apolar lipids tails, a part of the transmembrane OmpA stays anchored in the lipid bilayer Fig. 5. The figure shows clearly that red and blue (charged) side chains are kept within the remnants of the beta barrel and only apolar and slightly polar side chains are exposed to the lipid environment.</p>
 <p>Another observation is that the end of the unfolded beta-barrel is sticking out of the membrane, and contains many charged side chains as well, while the boundary between this part and the transmembrane domain is quite apolar. Overall this structure gives the impression to be still highly stable, but perhaps less stable than the native beta-barrel, anchored in the lipid bilayer.</p>
 <p>
-    Fig. 5
+        <div class="image-container">
+                <img src="https://static.igem.org/mediawiki/2018/5/56/T--Vilnius-Lithuania--Fig5_Groningen.png"/>
+                <p><strong>Fig 5</strong> Van der Waals representation of the side chains of OmpA in the membrane. The membrane is represented by dashed lines. The protein backbone is colored in magenta. White beads represent non-polar side chains, green beads represent polar side chains (of varying polarity, there are 5 different levels of polarity in Martini and they are all colored green), blue beads represent positively charged side chains and red beads represent negatively charged side chains. </p>
 </p>
-<Strong>Fig. 5</Strong> Van der Waals representation of the side chains of OmpA in the membrane. The membrane is represented by dashed lines. The protein backbone is colored in magenta. White beads represent non-polar side chains, green beads represent polar side chains (of varying polarity, there are 5 different levels of polarity in Martini and they are all colored green), blue beads represent positively charged side chains and red beads represent negatively charged side chains.
+</div>
 <p>As this large scale conformational change should have a large effect on the behaviour of the protein, the angle between OmpA and the membrane normal was measured over time. To visualize trends in the data, a running average was calculated with a window of 100 frames. Fig 6. shows that this angle oscillates stably around 84.9 degrees. However after 10 ms of simulation, the angle suddenly shifts to 84 degrees. This could be an indication that the usual right-angle of OmpA is perhaps not so stable in the new conformation this fusion protein adopts.
 </p>
 <p>
-    Fig. 6
-</p>
+        <div class="image-container">
-<strong>Fig. 6</strong>Angle between OmpA and membrane normal, running average over time. The angle oscillates stably around 84.9 then suddenly drops to 84.
+                <img src="https://static.igem.org/mediawiki/2018/6/62/T--Vilnius-Lithuania--Fig6_Groningen.png"/>
-<p>Under the assumption that the fusion protein indeed retains this conformation, the unfolding beta-barrel and subsequent stable anchoring in the membrane is a novel insight. As the system is meant to function as a display mechanism for soluble proteins binding to it, it is likely that this change in conformation contributes to this mechanism. It is hypothesized that the protein-ligand complex flips across the lipid bilayer entirely to function as a display system, generally assisted by chaperone proteins. Since the angle between OmpA and the membrane normal becomes more acute over the time scale of the simulation, unfolding of the beta-barrel structure may contribute to OmpA flipping over the lipid bilayer to display its ligand.
+                <p><strong>Fig 6</strong> Angle between OmpA and membrane normal, running average over time. The angle oscillates stably around 84.9 then suddenly drops to 84.
-</p>
+                    <p>Under the assumption that the fusion protein indeed retains this conformation, the unfolding beta-barrel and subsequent stable anchoring in the membrane is a novel insight. As the system is meant to function as a display mechanism for soluble proteins binding to it, it is likely that this change in conformation contributes to this mechanism. It is hypothesized that the protein-ligand complex flips across the lipid bilayer entirely to function as a display system, generally assisted by chaperone proteins. Since the angle between OmpA and the membrane normal becomes more acute over the time scale of the simulation, unfolding of the beta-barrel structure may contribute to OmpA flipping over the lipid bilayer to display its ligand.
-<p>Fig. 7 shows the starting and final structures of the OmpA-anti-GFP fusion protein. Note that Fig. 7 shows that the structure is still a beta-barrel, however the fusion to anti-GFP abolishes a part of the beta-sheet in the barrel, resulting in a disruption of the beta-barrel structure shown in Figure 7B. Despite of this however, the fusion protein remains stably anchored in the membrane.
+                    </p>
+</div>
 </p>
 <p>
-    Fig. 7
+        <div class="image-container">
-</p>
+                <img src="https://static.igem.org/mediawiki/2018/d/da/T--Vilnius-Lithuania--Fig7_Groningen.png"/>
-<strong>Fig. 7</strong> A. OmpA-anti-GFP fusion structure at the start of the simulation represented on the left. OmpA is colored in green, anti-GFP is colored in red. Martini elastic bonds are colored in orange. Membrane position is indicated with dashed lines. B. Fusion protein after 10ms of simulation. GFP is colored in blue.
+                <p><strong>Fig 7</strong> A. OmpA-anti-GFP fusion structure at the start of the simulation represented on the left. OmpA is colored in green, anti-GFP is colored in red. Martini elastic bonds are colored in orange. Membrane position is indicated with dashed lines. B. Fusion protein after 10ms of simulation. GFP is colored in blue.
-<p>
+                </p>
+</div>
-</p>
 <H1>Conclusions</H1></p>
@@ Line 612: / Line 430: @@
 </section>
 <section class="design_subsections">
-   <h1 id="COMSOL_model">COMSOL model</h1>
+    <h1 id="COMSOL_model">COMSOL model</h1>
-   <div class="third_level_links">
+    <div class="third_level_links">
-      <a href="#Edinburgh_model">Edinburgh model</a>
+        <a href="#Edinburgh_model">Edinburgh model</a>
-      <a href="#Groeningen_model">Groeningen model</a>
+        <a href="#Groeningen_model">Groeningen model</a>
-      <a href="#COMSOL_model">COMSOL model</a>
+        <a href="#COMSOL_model">COMSOL model</a>
-      <a href="#Thermo_Switches_model">Thermo Switches model</a>
+        <a href="#Thermo_Switches_model">Thermo Switches model</a>
-   </div>
+    </div>
-   <div>
+    <div>
-      Lorem ipsum dolor, sit amet consectetur adipisicing elit. Esse beatae assumenda eaque ex recusandae pariatur sunt soluta modi facere laborum exercitationem odio iure magnam obcaecati quos voluptatibus placeat, ratione harum!
+        <h1>Background</h1>
-      Provident, maxime ipsum veniam, rerum facere ad vero fugit ipsa natus recusandae sit voluptatum architecto laudantium vitae necessitatibus! Nesciunt illum porro sint odio sequi reprehenderit. Sint eligendi ex impedit recusandae!
+        <h2>Phase-field modeling overview</h2>
-      Alias obcaecati impedit iure recusandae quas asperiores tempore sint, consectetur veniam provident iste nulla fugit velit aliquam expedita, assumenda repellat dolorem dolore! Sit quis dolorem ad pariatur repellat reiciendis officiis.
+        <p>Phase-field models are mathematical models used for solving interfacial problems. They are based on the
-      Asperiores molestiae eos quo inventore recusandae quae placeat delectus, natus sint. Ullam quas culpa nobis exercitationem omnis animi velit, deleniti fugit! Sapiente aperiam sit minima nostrum, rerum quae laudantium vero?
+            generalized free-energy functional approach (lattice Boltzmann), meaning that the system evolution is
-      Qui blanditiis, excepturi veritatis eaque temporibus voluptate maxime facere laborum voluptatem rerum ex a ipsum voluptatibus tempore, saepe sunt omnis nostrum sint? Voluptatum facilis omnis ea accusantium explicabo magnam architecto!
+            driven by the minimisation of free energy. Important thing to note is that sharp fluid interfaces in the
-      Repellendus incidunt doloremque, a cum voluptates esse officia quia veniam architecto. Quibusdam deserunt nulla, dolore perspiciatis accusantium ad aliquam voluptatem iste iure, quae minus ipsa voluptates, sit voluptatum consequatur tempora?
+            models are replaced by a thin transition region where the interfacial forces are distributed in a smooth
-      Architecto impedit in repellendus, quo dolorum sequi voluptatum omnis maxime perspiciatis aspernatur obcaecati sint iusto tenetur praesentium labore. Natus eveniet quaerat recusandae dignissimos nam sed distinctio quos fugiat aliquid eligendi.
+            manner. This provides model an easy treatment of topological variations at the interface1. In order to
-      Molestias inventore nobis minus aspernatur recusandae asperiores excepturi ipsam voluptas quos, quae voluptatem voluptatibus vero veniam dolores fuga aliquid neque ut dolorem beatae cum temporibus tempora? Iure expedita debitis corrupti.
+            describe phases in numerical form, equations use phase variables ϕ. In three-phase systems, phase variables
-      Quae quam earum impedit laborum, nobis aspernatur fugit enim consequuntur provident laboriosam obcaecati doloremque ipsam quis modi quos ratione ipsum beatae? Voluptas, debitis eum! Dolorem accusantium et rem. Veniam, dicta!
+            are described as ϕ<sub>i</sub> , where i = A, B, C, and the variable is equal to 1 in the phase i and 0 outside.</p>
-      Sequi aut, eos id nemo maiores iste! Dicta cum eos, incidunt aperiam voluptate facilis vero vel deleniti inventore accusantium cupiditate saepe dolore atque quisquam voluptates aliquam amet a! Hic, consectetur.
+        <p>Typically used phase-field models for two and three phase fluid systems couple fourth order nonlinear
-    </div>
+            advection-diffusion equations, called Cahn-Hilliard equations, which represent the evolution of the phase
+            variables with the Navier-Stokes equations for the fluid motion<sup>2</sup> . Equations (1), (2) and (3) form the
+            traditional Cahn-Hilliard equation, and Eq. (4) is Navier-Stokes equation - both of them are used in our
+            calculations on COMSOL</p>
+        <p> <img src="https://static.igem.org/mediawiki/2018/f/fe/T--Vilnius-Lithuania--dv_eq1_Model.png">
+        </p>
+        <p> <img src="https://static.igem.org/mediawiki/2018/f/fe/T--Vilnius-Lithuania--dv_eq2_Model.png">
+        </p>
+        <p> <img src="https://static.igem.org/mediawiki/2018/c/c8/T--Vilnius-Lithuania--dv_eq3_Model.png">
+        </p>
+        <p> <img src="https://static.igem.org/mediawiki/2018/f/fb/T--Vilnius-Lithuania--dv_eq4_Model.png">
+        </p>
+        <p>M<sub>0</sub> is the mobility tuning parameter that determines the relaxation time of interface and the time scale of
+            diffusion in C-H equation. It should be noted, that interfacial diffusion (the Gibbs-Thomson effect) is
+            inevitable in phase phase field method because the diffusion term is used in the right side of Eq. (1). Due
+            to this, prolonged simulations of our system result in spheres diffusing and constantly changing their size
+            (Fig. 1). Because of that, we have chosen to analyze only the first few spheres formed in every simulation
+            as their size proved to be most accurate.</p>
+        <p>ϵ (interface thickness parameter) is also an important parameter as it defines the width of transition
+            between phases and affects both the surface tension force and the relaxation time of interface. Usually it
+            is compared to the characteristic length of the system and must be chosen small enough to depict interface
+            changes accurately, yet too small of a thickness shall cause instabilities in calculations.</p>
+        <p>Most of the time the model can be described with several dimensionless parameters, such as capillary number
+            calculated for the continuous phase, Ca =μ<sub>c</sub>v<sub>c</sub>/γ, the Reynolds number Re =ρv<sub>c</sub>L/μ<sub>c</sub>, the viscosity ratio
+            λ=μ<sub>d</sub>/μ<sub>c</sub>, and the flow rate ratio Q=v<sub>d</sub>/v<sub>c</sub><sup>3</sup>. In our model Reynolds number is small (Re < 1) and does not
+                influence droplet size, so we mainly focus on Ca, λ and Q and consider the influence of the latter two
+                on the liposome formation. </p> <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/e/ed/T--Vilnius-Lithuania--dv_fig1a_Model.gif">
+    </div>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/9/99/T--Vilnius-Lithuania--dv_fig1b_Model.gif"></div>
+    <strong>Fig. 1</strong> Visual comparison of modeled and real life liposome formation process. A slight diffusion
+    is observed in a model due to the diffusion term in C-H equations, which makes long simulations unreliable. In the
+    plot, phase variables A, B and C have values of 1 (blue), 2 (green) and 3 (red) respectively.
+    <p></p>
+    <H2>Geometry</H2>
+    <p>Since the microfluidic devices were designed by ourselves, we were able to extract the exact geometry from the
+        CAD file. The part that interested us was the junction at which all of three phases contacted and started
+        forming droplets (Fig. 2). However, we then proceeded to minimize the geometry (Fig. 3) in order to reduce the
+        computation times and improve solution qualities: </p>
+    <p>
+        <ol>
+            <li>
+                <p>Device height was greater than our largest expected droplets, so 2D model was sufficient;</p>
+            </li>
+            <li>
+                <p>Since our devices were technically perfectly symmetrical, it was more efficient to do calculations
+                    for only half of it and mirror the results;</p>
+            </li>
+            <li>
+                <p>Usually only the first few droplets need to be analyzed, so the length of post-junction part could
+                    be decreased;</p>
+            </li>
+            <li>
+                <p>Microchannels usually contain only one phase, so their length was not crucial.</p>
+            </li>
+        </ol>
+    </p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/a/a3/T--Vilnius-Lithuania--dv_fig2_Model.png"></div>
+    <strong>Fig. 2</strong> Original 3D junction geometry extracted from the CAD file. Because of its size, it is too
+    inefficient to simulate this whole piece of device.
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/6/6a/T--Vilnius-Lithuania--dv_fig3_Model.png"></div>
+    <strong>Fig. 3</strong> Minimized geometry with main measurements and boundaries described, used in all
+    simulations. The inflow rates of LO and OA phases are divided by 2, because their channels split into two in order
+    to press the stream of IA phase in junction.
+    <h2>Mesh</h2>
+    <p>For solving the model we used finite element method, which divides geometry into small mesh elements, where
+        partial differential equations are solved. Interface capturing method incorporated in it keeps the mesh fixed
+        and the boundary discontinuities are smeared out over the finite width ϵ <sup>3,4</sup>. To successfully capture interface
+        movement between different phases, mesh size should be small enough, but not too small, as every single element
+        adds more time to computing and quality of the results stops improving substantially at a certain point.</p>
+    <p>Most of the time we only control the size of mesh elements. For our channel domains a predefined normal sized
+        mesh was used, as they only contained one phase and interface problems did not occur there. For junction and
+        post-junction parts, a predefined extra fine mesh was used with maximum element size value set to 1µm, which is
+/10 size of a smallest expected droplet and also 1/10 of our characteristic length, which has been chosen to
+        be the width of horizontal IA channel (Fig. 4)</p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/6/68/T--Vilnius-Lithuania--dv_fig4_Model.png"></div>
+    <strong>Fig. 4</strong> Generated mesh used in all simulations. Refined grid in junction and post-junction helps
+    with realistic interface capturing.
+    <p></p>
+    <H2>Materials</H2>
+    <p>Our system consists of three different fluids: OA (Outer Aqueous), IA (Inner Aqueous) and LO (Lipid carrying
+        organic) phases. It should be noted that experiments have been carried with fluids of many different
+        compositions, but here we use only one for each. IA and OA phases are quite similar so for simplicity, we set
+        the same densities for both of them. It has a negligible influence on the results since in most microfluidic
+        configurations buoyancy-driven speeds are much smaller than the actual flow speeds <sup>3</sup>. Parameters and
+        compositions of materials are shown in Tab. 1.</p>
+    <strong>Tab. 1</strong> Main parameters of our fluid system. To simplify the system and approximate the viscosity
+    closest to reality, only the content of glycerol, octanol and water was taken into account.
+    <table>
+        <thead>
+            <tr>
+                <th><strong>Phase</strong></th>
+                <th><Strong>Density ρ(kg/m<sup>3</sup>) </Strong></th>
+                <th><Strong>Dynamic viscosity µ (Pa*s)</Strong></th>
+                <th><Strong>Real composition</Strong></th>
+            </tr>
+        </thead>
+        <tbody>
+            </tr>
+            <tr>
+                <td>OA</td>
+                <td>1000</td>
+                <td>0.00119</td>
+                <td>Pure<var>frex</var> custom buffer and surfactant (treated as 7% glycerol and 93% water)</td>
+            </tr>
+            <tr>
+                <td>IA</td>
+                <td>1000</td>
+                <td>0.00115</td>
+                <td>Pure<var>frex</var> IVTT reaction mixture (treated as 6% glycerol and 94% water)</td>
+            </tr>
+            <tr>
+                <td>LO</td>
+                <td>830</td>
+                <td>0.00736</td>
+                <td> 98% octanol
+% lipids
+                </td>
+            </tr>
+        </tbody>
+    </table>
+<p></p>
+    <h1>Description of the System</h1>
+    <p>Fig. 3 shows our flow focusing model configuration with boundaries specified. There is one main inlet for IA
+        phase, and two for each LO and OA phases on the left side. On the right side, there is an outlet with outflow
+        pressure set to p = 0. For laminar flow, wall condition is set to no slip, which states that the flow velocity
+        at the walls is always v = 0 and it gives a good approximation of the whole system.</p>
+    <p>In experimental set-up, we coat the OA channels, junction and post-junction with PVA to make it hydrophilic,
+        contrary to hydrophobic PDMS, which is the material of which the microfluidic devices are made. This provides a
+        good setting for liposome formation<sup>5</sup>, and we take that into account by adjusting contact angles at the wetted
+        walls for ternary phase field node. With respect to model limitations, all the
+        contact angles in IA and LO channels are set to 90 degrees. In the coated side, we assume phase OA has a
+        perfect wetting condition on the channel walls against both IA and LO phases, while the contact angle between
+        the latter two is set at 30 degrees.
+    </p>
+    <p>The aforementioned interface thickness parameter ϵ is set to 1.4 µm as it is the lowest stable value regarding
+        our mesh and mobility tuning parameter, though it is more than enough to accurately depict the results of
+        simulations. Surface tension is another important aspect to be considered and it is set to σ = 0.0085 N/m,
+        which is an interfacial tension between octanol and water <sup>6</sup>, for all three interfaces between phases (<strong>See
+            Limitations</strong>).</p>
+    <p>In order to make our model as realistic as possible, several other parameters are taken from a single baseline
+        wet lab experiment with similar materials and geometry as mentioned before.</p>
+    <p>Flow rates are transformed into flow velocities for COMSOL and calculated as described in Tab. 2.</p>
+    <strong>Tab. 2</strong> Specifications of baseline set-up fluid flows.
+    <table>
+        <thead>
+            <tr>
+                <th><strong>Channel</strong></th>
+                <th><Strong>Inlet area(µm<sup>2</sup>) ρ(kg/m<sup>3</sup>) </Strong></th>
+                <th><Strong>Flow rate(µL/h)</Strong></th>
+                <th><Strong>Flow velocity (m/s)</Strong></th>
+            </tr>
+        </thead>
+        <tbody>
+            </tr>
+            <tr>
+                <td>OA</td>
+                <td>273</td>
+                <td>240</td>
+                <td>0.244</td>
+            </tr>
+            <tr>
+                <td>LO</td>
+                <td>157</td>
+                <td>14.57</td>
+                <td>0.0258</td>
+            </tr>
+            <tr>
+                <td>IA</td>
+                <td>193</td>
+                <td>11.36</td>
+                <td>0.0164</td>
+            </tr>
+        </tbody>
+    </table>
+    <p>Mobility parameter in this model is crucial. As its value becomes higher, droplet size in micro-channel
+        increases. This can be explained by the parameters’ mathematical function - raising values causes the increase
+        in interface relaxation time, meaning the diffusion gets stronger as well <sup>1</sup>. So we have compared
+        the numerical and experimental results of liposome synthesis (Fig. 5) and approximated our characteristic
+        mobility tuning parameter to be M<sub>0</sub> = 2E-12 m<sup>3</sup>>/s. The diameter of the droplet with this
+        value was 12.1µm, which is a close match to the real size.
+    </p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/d/d9/T--Vilnius-Lithuania--dv_fig5a_Model.png"></div>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/4/4a/T--Vilnius-Lithuania--dv_fig5b_Model.png"></div>
+    <strong>Fig. 5</strong> A comparison between a modeled baseline experiment and actual view of the junction. Both of
+    them produce vesicles of around 12 µm, though slight variations occur in real setting due to unsteady flow caused
+    by micro-pumps. Results of both systems concur well enough to assume that our model setup is reliable and close to
+    reality.
+    <p></p>
+    <h1>Results</h1>
+    <h2>Parametric sweeps and example of liposome radius calculation</h2>
+    <p>In order to investigate how our system depends on certain parameters, we have performed parametric sweeps on
+        every one of these parameters separately. By doing so, COMSOL Multiphysics resolved our model with every
+        parametric value specified automatically and stored the results under a single node.
+        To find out the size of the liposomes, the first fully formed droplet was taken and 2D cut line data set was
+        created going through the middle of the sphere in y-axis direction (Fig. 6). Next, the variation of phase
+        variable C (which stands for our IA phase) was extracted from the data set and results were depicted in graphs.
+        The exact point of phase edge for all studies performed has been assumed as ϕc = 0.5.</p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/5/59/T--Vilnius-Lithuania--dv_fig6_Model.png"></div>
+    <strong>Fig. 6</strong> An example of data sets analysed (yellow line in Fig.). One fully formed sphere for every
+    parametric sweep step was measured by extracting ϕc values from similar linear data sets.
+    <p></p>
+    <h2>Liposome size dependence on viscosity ratio λ </h2>
+    <p>First of all, the impact of IA and OA phase viscosity ratio ( λ = µ<sub>IA</sub>/µ<sub>OA</sub>) was
+        investigated. Studies suggest, that increasing λ also increases the generated droplet size <sup>7</sup>. Though the
+        changes are more significant in high capillary numbers, where droplet formation is driven by viscosity. In our
+        case, the capillary number was relatively small (Ca ≈ 0.034), so the flow was more surface tension-dominated.
+        The simulation was run with a set of different OA phase dynamic viscosity values (Tab. 3) and results are
+        presented in Fig. 7 and Fig. 8.</p>
+    <strong>Tab. 3</strong> Values of OA phase dynamic viscosity used for parametric sweep; µ<sub>IA</sub> = 0.00115
+    Pa*s.
+    <table>
+        <thead>
+            <tr>
+                <th><strong>No.</strong></th>
+                <th><Strong>OA dynamic viscosity µ<sub>OA</sub> (Pa*s)
+                    </Strong></th>
+                <th><Strong>Viscosity ratio λ</Strong></th>
+            </tr>
+        </thead>
+        <tbody>
+            <tr>
+                <td>1</td>
+                <td>0.00050</td>
+                <td>2.300</td>
+            </tr>
+            <tr>
+                <td>2</td>
+                <td>0.00119</td>
+                <td>0.966</td>
+            </tr>
+            <tr>
+                <td>3</td>
+                <td>0.00130</td>
+                <td>0.885</td>
+            </tr>
+            <tr>
+                <td>4</td>
+                <td>0.00150</td>
+                <td>0.767</td>
+            </tr>
+            <tr>
+                <td>5</td>
+                <td>0.00200</td>
+                <td>0.575</td>
+            </tr>
+            <tr>
+                <td>6</td>
+                <td>0.00300</td>
+                <td>0.383</td>
+            </tr>
+            <tr>
+                <td>7</td>
+                <td>0.00800</td>
+                <td>0.144</td>
+            </tr>
+        </tbody>
+    </table>
+    <p></p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/7/74/T--Vilnius-Lithuania--dv_fig7_Model.png"></div>
+    <strong>Fig. 7</strong> Sphere radius dependency on viscosity ratio λ. Graph shows the simulated results of liposome
+    radius for every given viscosity parameter, which here are depicted as ratio between viscosities of IA and OA
+    phases. In our simulated range of parameters the radius varies from 5.08 µm to 6.75 µm.
+<p></p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/d/df/T--Vilnius-Lithuania--dv_fig8_Model.png"></div>
+    <strong>Fig. 8</strong> Sphere diameter dependence on viscosity ratio λ. Simplified graph shows that sphere size
+    increases linearly up until λ = 1 and viscosity regulation above this value results in less changes.
+    <p>As we see, droplet size increases almost linearly up to λ = 0.996, meaning that increasing viscosity of OA phase
+        leads to formation of smaller liposomes. However, it should be noted that by increasing viscosity in real life,
+        we may encounter other problems, such as impeded droplet formation or liposomes bursting due to differences in
+        osmotic pressure between inside and outside environments. Given these limitations, we can still effectively
+        control our liposome size in about 1µm range. <var>Thus, we can conclude that viscosity ratio, while having a
+            moderate effect, is still not a decisive parameter in vesicle size determination.</var></p>
+    <h2>Liposome size dependency on velocity ratio V</h2>
+    <p>Flow rates of our fluids were easiest and fastest to control as a parameter, so they certainly needed to be
+        studied more deeply. The flow of the continuous phase here was fixed, so the Capillary number could be
+        considered as a constant. Thus, only the flow rate of disperse IA phase was varied and the effect of flow rate
+        ratio (Q = Q<sub>IA</sub>/Q<sub>OA</sub>) could be assessed.
+        The simulation was run with a set of different IA phase flow velocity values (Tab. 4) and results are
+        presented in Fig. 9 and Fig. 10.
+    </p>
+    <strong>Tab. 4</strong> Values of IA phase flow velocities used for parametric sweep and reference flow rates and
+    ratios; v<sub>OA</sub>= 0.244 m/s, Q<sub>OA</sub>= 240µl/h.
+    <table>
+        <thead>
+            <tr>
+                <th><strong>No.</strong></th>
+                <th><Strong>
+                        IA flow velocity v<sub>IA</sub> (m/s)
+                    </Strong></th>
+                <th><Strong> IA flow rate Q<sub>IA</sub>(µl/h)</Strong></th>
+                <th><Strong>Flow rate ratio Q</Strong></th>
+            </tr>
+        </thead>
+        <tbody>
+            </tr>
+            <tr>
+                <td>1</td>
+                <td>0.0050</td>
+                <td>3.46</td>
+                <td>0.014</td>
+            </tr>
+            <tr>
+                <td>2</td>
+                <td>0.0100</td>
+                <td>6.93</td>
+                <td>0.029</td>
+            </tr>
+            <tr>
+                <td>3</td>
+                <td>0.0164</td>
+                <td>11.36</td>
+                <td>0.047</td>
+            </tr>
+            <tr>
+                <td>4</td>
+                <td>0.0500</td>
+                <td>34.63</td>
+                <td>0.144</td>
+            </tr>
+            <tr>
+                <td>5</td>
+                <td>0.0750</td>
+                <td>51.95</td>
+                <td>0.216</td>
+            </tr>
+            <tr>
+                <td>6</td>
+                <td>0.1000</td>
+                <td>69.27</td>
+                <td>0.289</td>
+            </tr>
+            <tr>
+                <td>7</td>
+                <td>0.2000</td>
+                <td>138.54</td>
+                <td>0.577</td>
+            </tr>
+        </tbody>
+    </table>
+    <p></p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/4/40/T--Vilnius-Lithuania--dv_fig9_Model.png"></div>
+    <strong>Fig. 9</strong> Sphere radius dependency on flow rate ratio Q. It should be noted that x-axis doesn’t start
+    from zero in order to distinguish between first three values. In comparison with λ, Q seems to affect liposome
+    radius at a greater magnitude. In our simulated range of parameters the radius varies from 6.05 µm to 8.56 µm.
+<p></p>
+    <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/8/80/T--Vilnius-Lithuania--dv_fig10_Model.png"></div>
+    <strong>Fig. 10</strong> Sphere diameter dependency on flow rate ratio Q. Simplified graph shows that liposome
+    diameter variation range is 5.5 µm in our configurations, which can be considered good enough for fine-tuning.
+    <p>Relying on the results we can safely assume, that liposome size depends directly on IA phase flow rate. However
+        studies suggest that this dependency is not linearly proportional because the droplet formation process is also
+        affected by the surface tension force and the dynamic energy equilibrium<sup>1</sup>. This seems to be true
+        considering given data.
+    </p>
+    <p>In contrary to dynamic viscosity ratio variation, flow rate ratio can be experimentally modified in a broad
+        range of values, meaning we can effectively synthesize liposomes from 12 µm to around 17 µm with our current
+        set-up. Nevertheless, we have found that when Q = 0.7, spheres cannot form anymore, as the OA phase cannot cut
+        the stream of IA phase and it transforms into a continuous flow (Fig. 11). Therefore, Q = 0.7 is the critical
+        value for liposome synthesis in our system. <var>In conclusion, the regulation of IA phase flow rate gives us
+            an effective and fast method to vary the size of our liposomes in a range of few micrometers.
+        </var> </p>
+    <div class="image-container"> <img src="https://static.igem.org/mediawiki/2018/4/49/T--Vilnius-Lithuania--dv_fig11_Model.png"></div>
+    <strong>Fig. 11</strong> Liposomes stop forming in our system when Q > 0.7, or V > 1 ( v<sub>IA</sub>/v<sub>OA</sub>).
+    It means that in given dimensions, these values are critical for vesicle formation.
+    <h2>Liposome size dependency on IA channel width <var>w</var></h2>
+    <p>While our goal has always been to attain cell-sized liposomes, which stretch from 5 µm to 30 µm, theoretically
+        we had yet only managed to produce 10 µm to around 17 µm sized vesicles by modifying dynamic viscosity and flow
+        rates of our fluids. It became clear that in order to expand this range, we had to start from the microfluidics
+        device design. Possibilities of the design are virtually infinite, but here we focused on the width of IA phase
+        channel, which we assumed to have the biggest impact on sphere size.
+    </p>
+    <p>In our model configuration, we have added an additional parameter w<sub>y</sub>, which is the width expansion of
+        the device parallel to the symmetry axis <strong>(See Geometry)</strong>. The simulation was run with a set of different wy
+        values (Tab. 5.) and results are present in Fig. 12 and Fig. 13</p>
+    <p></p>
+    <strong>Tab. 5</strong> Values of w<sub>y</sub> used for parametric sweep, the width of channels with parameter
+    applied and IA phase inflow velocities, which were varied in order to keep the flow rate constant.
+    <table>
+        <thead>
+            <tr>
+                <th><strong>No.</strong></th>
+                <th><Strong>w<sub>y</sub>(µm)</Strong></th>
+                <th><Strong>IA channel width (µm)</Strong></th>
+                <th><Strong>IA flow velocity v<sub>IA</sub>(m/s)</Strong></th>
+            </tr>
+        </thead>
+        <tbody>
+            </tr>
+            <tr>
+                <td>1</td>
+                <td>0</td>
+                <td>10</td>
+                <td>0.0164</td>
+            </tr>
+            <tr>
+                <td>2</td>
+                <td>0.5</td>
+                <td>11</td>
+                <td>0.0148</td>
+            </tr>
+            <tr>
+                <td>3</td>
+                <td>1</td>
+                <td>12</td>
+                <td>0.0135</td>
+            </tr>
+            <tr>
+                <td>4</td>
+                <td>1.5</td>
+                <td>13</td>
+                <td>0.0125</td>
+            </tr>
+            <tr>
+                <td>5</td>
+                <td>2</td>
+                <td>14</td>
+                <td>0.0116</td>
+            </tr>
+            <tr>
+                <td>6</td>
+                <td>2.5</td>
+                <td>15</td>
+                <td>0.0108</td>
+            </tr>
+        </tbody>
+    </table>
+    <p></p>
+    <div class="image-container"> <img src="https://static.igem.org/mediawiki/2018/5/5f/T--Vilnius-Lithuania--dv_fig12_Model.png"></div>
+    <strong>Fig. 12 </strong> Sphere radius dependency on IA channel width. Changes in IA channel width seem to cause
+    greatest impact to the output. By increasing it by 5µm, liposome radius grows by 2.86µm.
+    <p></p><div class="image-container"><img src="https://static.igem.org/mediawiki/2018/c/c2/T--Vilnius-Lithuania--dv_fig13_Model.png"></div>
+    <strong>Fig. 13</strong> Sphere diameter dependency on IA channel width. Simplified graph shows an explicit
+    tendency of liposome growth with increased width parameter. This implies that increasing or reducing the parameter
+    should affect our system in a highly predictable manner.
+    <p>As we can see, channel width has a huge impact on the size of liposomes. Even by keeping flow rates of all
+        phases the same, droplet radius variations depend solely on channel dimensions. We have tested channels from 10
+        µm to 15 µm, but other widths should also comply with given results and the only limit on minimal channel
+        dimensions could be the quality of photolithography used in production of microfluidic devices.<var>Using given
+            results we can now calculate the required width of the channel in order to produce liposomes of needed size
+            as well as synthesize them in whole range of 5-30 µm.
+        </var></p>
+    <p></p>
+    <h1>Conclusion</h1>
+    <p></p>
+    <p>From the simulations we’ve gained much invaluable information about liposome size determination <var>in silico</var>,
+        which led us to saving some of our most expensive reagents, such as Pure<var>frex</var> IVTT system. Also, we
+        could conclude that the system worked just as expected and it matched real life experiments surprisingly well.
+        All of the studied parameters affected liposome size to some extent, IA channel-junction width being the most
+        sensitive and effective, flow rate ratio being easiest to control for fine adjustments, while dynamic viscosity
+        ratio tuning may be used in tandem with flow rate regulation.</p>
+    <p></p>
+    <h1>Discussion</h1>
+    <p></p>
+    <p>Although we can choose from a vast selection of different parameter values to achieve needed results, there are
+        consequences to every change since microfluidics’ experiments are so delicate. For this reason, parameters for
+        every experiment should be properly evaluated in order to evade failed attempts and wasted materials. For
+        example, proper junction between all three phases sometimes might be so sensitive, that even slight variations
+        can disrupt the flow. In this case, it might be wiser to avoid extreme flow rate changes and design devices
+        with a bit different channel dimensions at first. Moreover, liposome velocity increases with IA phase flow
+        rate, so by colliding with each other in post-junction, risk of them bursting also increases. This is also the
+        case with viscosity changes because it may sometimes be hard to regulate dynamic viscosity ratio without
+        disrupting osmotic pressure. To conclude, every experiment should begin with selection of the right channel
+        design, while flow rate and viscosity regulation should only be used for fine-tuning</p>
+    <p></p>
+    <h1>Model Limitations</h1>
+    <p>Our model has some limitations. Due to the nature of phase-field model and minimal free energy principle, it
+        proved to be an invidious task to model liposomes exactly like in the real life. Since we cannot characterize
+        lipids and surfactants inside our materials to act as in reality, LO phase just forms a distinct sphere outside
+        of junction instead of surrounding the IA phase. </p>
+    <p>However, LO phase doesn’t impact the size of liposomes in any meaningful way and just needs to barely reach the
+        junction to subsequently form a pocket for inner fluid. So, in order to mimic the reality as best as possible,
+        we have made a few adjustments:</p>
+    <ul>
+        <li>The surface tension between IA and OA phases was set the same as LO and OA, to depict the interface
+            movement correctly.
+        </li>
+        <Li>While IA phase is hydrophilic, it was set as a fully de-wetting phase to form veracious droplets
+        </Li>
+    </ul>
+    <h2>References</h2>
+    <p>
+        <ol>
+            <li>Bai, F., He, X., Yang, X., Zhou, R. & Wang, C. Three dimensional phase-field investigation of droplet
+                formation in microfluidic flow focusing devices with experimental validation. Int. J. Multiph. Flow 93,
+–141 (2017).
+            </li>
+            <li>Kim, J. Phase-Field Models for Multi-Component Fluid Flows. Commun. Comput. Phys. 12, 613–661 (2012).</li>
+            <li>De Menech, M., Garstecki, P., Jousse, F. & Stone, H. A. Transition from squeezing to dripping in a
+                microfluidic T-shaped junction. J. Fluid Mech. 595, (2008).</li>
+            <li>Boyer, F., Lapuerta, C., Minjeaud, S., Piar, B. & Quintard, M. Cahn–Hilliard/Navier–Stokes Model for
+                the Simulation of Three-Phase Flows. Transp. Porous Media 82, 463–483 (2010).
+            </li>
+            <li>Deshpande, S., Caspi, Y., Meijering, A. E. C. & Dekker, C. Octanol-assisted liposome assembly on chip.
+                Nat. Commun. 7, 10447 (2016).</li>
+            <li>Demond, A. H. & Lindner, A. S. Estimation of interfacial tension between organic liquids and water.
+                Environ. Sci. Technol. 27, 2318–2331 (1993).
+            </li>
+            <li>Nekouei, M. & Vanapalli, S. A. Volume-of-fluid simulations in microfluidic T-junction devices:
+                Influence of viscosity ratio on droplet size. Phys. Fluids 29, 032007 (2017).
+            </li>
+        </ol>
+    </p>
+    </div>
 </section>
 <section class="design_subsections">
-   <h1 id="Thermo_Switches_model">Thermo Switches model</h1>
+        <h1 id="Thermo_Switches_model">Thermo Switches model</h1>
-   <div class="third_level_links">
+        <div class="third_level_links">
-      <a href="#Edinburgh_model">Edinburgh model</a>
+           <a href="#Edinburgh_model">Edinburgh model</a>
-      <a href="#Groeningen_model">Groeningen model</a>
+           <a href="#Groeningen_model">Groeningen model</a>
-      <a href="#COMSOL_model">COMSOL model</a>
+           <a href="#COMSOL_model">COMSOL model</a>
-      <a href="#Thermo_Switches_model">Thermo Switches model</a>
+           <a href="#Thermo_Switches_model">Thermo Switches model</a>
-   </div>
+        </div>
-   <div>
+        <div>
-      Lorem ipsum dolor, sit amet consectetur adipisicing elit. Esse beatae assumenda eaque ex recusandae pariatur sunt soluta modi facere laborum exercitationem odio iure magnam obcaecati quos voluptatibus placeat, ratione harum!
+            <h1>Background</h1>
-      Provident, maxime ipsum veniam, rerum facere ad vero fugit ipsa natus recusandae sit voluptatum architecto laudantium vitae necessitatibus! Nesciunt illum porro sint odio sequi reprehenderit. Sint eligendi ex impedit recusandae!
+            <p></p>
-      Alias obcaecati impedit iure recusandae quas asperiores tempore sint, consectetur veniam provident iste nulla fugit velit aliquam expedita, assumenda repellat dolorem dolore! Sit quis dolorem ad pariatur repellat reiciendis officiis.
+            <p>
-      Asperiores molestiae eos quo inventore recusandae quae placeat delectus, natus sint. Ullam quas culpa nobis exercitationem omnis animi velit, deleniti fugit! Sapiente aperiam sit minima nostrum, rerum quae laudantium vero?
+                    RNA thermometers are RNA-based genetic control tools that react to temperature changes <sup>1</sup>. Low temperatures keep the mRNA at a conformation that masks the ribosome binding site within the 5’ end untranslated region (UTR). Masking of the Shine-Dalgarno (SD) sequence restricts ribosome binding and subsequent protein-translation. Higher temperatures melt the hairpins of RNA secondary structure allowing the ribosomes to access SD sequence to initiate translation <sup>1</sup>. In terms of applicability of RNA thermometers in <var>in vitro</var> systems, they display certain advantages over ribo- or toehold switches: they do not require binding of a ligand, metabolite or trigger RNA to induce the conformational change <sup>2,3</sup>, therefore are especially compatible with liposome IVTT system.
-      Qui blanditiis, excepturi veritatis eaque temporibus voluptate maxime facere laborum voluptatem rerum ex a ipsum voluptatibus tempore, saepe sunt omnis nostrum sint? Voluptatum facilis omnis ea accusantium explicabo magnam architecto!
+            </p>
-      Repellendus incidunt doloremque, a cum voluptates esse officia quia veniam architecto. Quibusdam deserunt nulla, dolore perspiciatis accusantium ad aliquam voluptatem iste iure, quae minus ipsa voluptates, sit voluptatum consequatur tempora?
+            <p>
-      Architecto impedit in repellendus, quo dolorum sequi voluptatum omnis maxime perspiciatis aspernatur obcaecati sint iusto tenetur praesentium labore. Natus eveniet quaerat recusandae dignissimos nam sed distinctio quos fugiat aliquid eligendi.
+                    Although some acquirable and already tested thermoswitches can be found in literature <sup>1,4</sup>, the field is still particularly underexplored. Possibility to design countless synthetic thermoswitches corresponding to different temperatures and of varying structure, is facilitated by computational models and RNA bioinformatics approaches. Together with two pioneers in this field from Vienna University (see <a href="https://2018.igem.org/Team:Vilnius-Lithuania/Attributions">Attributions</a>), we have <var>de novo</var> designed six heat-inducible RNA thermometers previously never mentioned in any paper or literature review. Not only did they complement SynDrop, but also helped expanding the library of well characterized and widely-applicable biobricks.
-      Molestias inventore nobis minus aspernatur recusandae asperiores excepturi ipsam voluptas quos, quae voluptatem voluptatibus vero veniam dolores fuga aliquid neque ut dolorem beatae cum temporibus tempora? Iure expedita debitis corrupti.
+            </P>
-      Quae quam earum impedit laborum, nobis aspernatur fugit enim consequuntur provident laboriosam obcaecati doloremque ipsam quis modi quos ratione ipsum beatae? Voluptas, debitis eum! Dolorem accusantium et rem. Veniam, dicta!
+            <p></p>
-      Sequi aut, eos id nemo maiores iste! Dicta cum eos, incidunt aperiam voluptate facilis vero vel deleniti inventore accusantium cupiditate saepe dolore atque quisquam voluptates aliquam amet a! Hic, consectetur.
+            <h2>Concept of the Model</h2>
-   </div>
+            <p>
-</section>
+                    We have optimized the opening energy of the ribosome docking site, which is a stretch of 30 nucleotides starting at the beginning of the Shine-Dalgarno (SD) sequence downstream into the coding sequence. This region corresponds to the binding footprint of the assembled initiation ribosome and must be unfolded prior to the assembly of the ribosome machinery. The model optimized for that region to have a high opening energy (meaning low translation efficiency) at low temperatures and a low opening energy (high translation efficiency) at high temperatures. Opening energies were calibrated around the mean value of opening energies observed for all protein coding genes in E. coli. When designing custom synthetic RNA thermometers, it was important to take into account the upstream and downstream sequences of our constructs and to model different structures and sequences in order to select only the best ones for practical implementation. Therefore 10 designs for each construct was designed (see figures below) out of which only 1 was selected based on the computed plots of translation efficiency vs. temperature.
+            </p>
+            <p></p>
+            <h1>Results</h1>
+            <p></p>
+            <p>
+                    the model computed total 40 different thermoswitches for our composite parts, 10 for each:
+                    <ol>
+                        <li>
+                                Mstx-OmpA-GFP Nanobody;
+                        </li>
+                        <li>
+                                GFP Nanobody-Iga-Mstx;
+                        </li>
+                        <li>
+                                Mstx-OmpA-His;
+                        </li>
+                        <li>
+                                His-Iga-Mstx.
+                        </li>
+                    </ol>
+            </p>
+            <p>
+                    Only 1 design was selected based on the computed plots of translation efficiency vs. temperature.
+            </p>
+<div class="image-container">
+<img src="https://static.igem.org/mediawiki/2018/2/24/T--Vilnius-Lithuania--_Fig1_Modeling_RNAthermos.jpg">
+<p>
+                    <strong>Fig. 1</strong> Plots of translation efficiency vs. temperature. On the left hand side: plots of 10 modelled thermoswitches for Mstx-OmpA-GFP Nanobody. On the right hand side: plot of the selected thermoswitch to use with Mstx-OmpA-GFP Nanobody. RNA thermometer termed sw_6 displayed no artifacts, with near control-identical translation efficiency at high temperature and low efficiency at < 25 C.
+            </p></div>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/5/5e/T--Vilnius-Lithuania--_Fig2_Modeling_RNAthermos.jpg">
+<p>
+                    <strong>Fig. 2</strong> Plots of translation efficiency vs temperature. On the left hand side: plots of 10 modelled thermoswitches for GFP Nanobody-Iga-Mstx. On the right hand side: plot of the selected thermoswitch to use with GFP Nanobody-Iga-Mstx. RNA thermometer termed sw_5 displayed no artifacts, with relatively high translation efficiency at high temperature and largely lower efficiency at < 25 C.
+            </p></div>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/d/db/T--Vilnius-Lithuania--_Fig3_Modeling_RNAthermos.jpg">
+            <p>
+                    <strong>Fig. 3</strong> Plots of translation efficiency vs. temperature. On the left hand side: plots of 10 modelled thermoswitches for Mstx-OmpA-His. On the right hand side: plot of the selected thermoswitch to use with Mstx-OmpA-His. RNA thermometer termed sw_8 displayed no artifacts, with near control-identical translation efficiency at high temperature and low efficiency at < 25 C.
+            </p></div>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/b/b5/T--Vilnius-Lithuania--_Fig4_Modeling_RNAthermos.jpg">
+            <p>
+                    <strong>Fig. 4</strong> Plots of translation efficiency vs temperature. On the left hand side: plots of 10 modelled thermoswitches for His-Iga-Mstx. On the right hand side: plot of the selected thermoswitch to use with His-Iga-Mstx. RNA thermometer termed sw_4 displayed no artifacts, with relatively high translation efficiency at high temperature and largely lower efficiency at < 25 C.
+            </p></div>
+            <p>
+                    Thermoswitches were initially designed to appropriately melt and function at 37 C. Comparing the first curve in each plot which resembles the original sequence of our constructs without incorporated thermoswitch (control), it can be seen that novel designs show much stronger temperature dependence. However, they did not manage to achieve quite exact 37 C and displayed marginally lower translation efficiency than controls. Some sequences displayed artifacts that showed up as jumps in the efficiency plots. The believed reason was the usage of different SD sequences at low and high temperatures. For in vivo testing we selected designs that did not exhibit such jumps. Another interesting finding was that all thermoswitches designed for Iga protease bearing constructs showed a considerably lower efficiency of translation even at higher temperatures compared to OmpA bearing constructs, meaning that this characteristic was probably attributed to membrane protein structure and would be needed to be addressed in the future.
+            </p>
+            <p>
+                    The model was also applied to check the activity of thermoswitches that we have acquired from literature (see <a href="https://2018.igem.org/Team:Vilnius-Lithuania/Design">Design and Results</a>/<a href="https://2018.igem.org/Team:Vilnius-Lithuania/Design#RNA_Thermoswitches">RNA Thermoswitches</a>). Our model predicted fair, but viable switching effects for thermoswitch-GFP designs, which were later supported by in vivo measurements.
+            </p>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/6/63/T--Vilnius-Lithuania--_Fig5_Modeling_RNAthermos_NEW.png">
+            <p>
+                    <strong>Fig. 5</strong> Plots of translation efficiency vs. temperature of the “GJ” thermoswithes-GFP constructs. Thermoswitches GJ2, GJ3, GJ9, GJ10 display similarly fair translation efficiency at 37 C, except for GJ6, which displays notably higher translation efficiency. GJ thermoswitches significantly differ in their activity at lower temperatures, with GJ9 locking the transcription most tightly and GJ3 being the leakiest of all tested designs.
+            </p></div>
+            <p></p>
+            <h1>Model</h1>
+            <p></p>
+            <p>
+                    A simple in-silico translation-initiation potential model<sup>5</sup> to quantify the likelihood of in vitro translation of a given mRNA sequence from a series of interaction energy parameters at constant temperatures was developed. The model defines the translation-initiation potential σ as:
+            </p>
+<div class="image-container"><img src="https://static.igem.org/mediawiki/2018/7/7c/T--Vilnius-Lithuania--Fig_6_NEW_-RNA_thermoswiches.png
+">
+            <p><strong>Fig. 6</strong></p>
+            <p>
+                    where R is the Boltzmann constant, T the temperature, ΔE<sub>SD</sub> the hybridization energy between the SD and anti-SD sequences, ΔE<sub>tRNA</sub> the hybridization energy of the start codon and its respective anti-codon (i.e, the tRNA<sup>Met</sup>), and ΔE<sub>open</sub> the energy required to unfold the 30-nucleotide-long RDS. Here, ΔE<sub>SD</sub> and ΔE<sub>tRNA</sub> are constant since neither the SD nor the start codon are altered. Consequently, variations in σ are exclusively determined by ΔE<sub>open</sub>. Applying the model to the plasmids with our constructs bearing thermoswitches, enabled us to rationalize translation events, as translatable constructs consistently scored higher σ, or lower ΔE<sub>open</sub>, than non-translatable ones.
+            </p></div>
+            <p></p>
+            <h2>References</h2>
+            <p></p>
+            <ol>
+                <li>
+                        Neupert J, Karcher D, Bock R. Design of simple synthetic RNA thermometers for temperature-controlled gene expression in Escherichia coli. Nucleic Acids Res. [Internet]. Oxford University Press; 2008; 36:e124–e124.
+                </li>
+                <li>
+                        Narberhaus F, Waldminghaus T, Chowdhury S. RNA thermometers. FEMS Microbiol. Rev. [Internet]. Wiley/Blackwell (10.1111); 2006; 30:3–16.
+                </li>
+                <li>
+                        Storz G. An RNA thermometer. Genes Dev. [Internet]. Cold Spring Harbor Laboratory Press; 1999; 13:633–6.
+                </li>
+                <li>
+                        Sen S, Apurva D, Satija R, Siegal D, Murray RM. Design of a Toolbox of RNA Thermometers. ACS Synth. Biol. [Internet]. 2017; 6:1461–70.
+                </li>
+                <li>
+                        Zayni S, Damiati S, Moreno-Flores S, Amman F, Hofacker I, Ehmoser EK. Enhancing the cell-free expression of native membrane proteins by in-silico optimization of the coding sequence – an experimental study of the human voltage-dependent anion channel.ioRxiv [Internet]. Cold Spring Harbor Laboratory; 2018; 411694.
+                </li>
+            </ol>
+             </div>
+     </section>
 </div>
 </div>

Difference between revisions of "Team:Vilnius-Lithuania/Model"

Latest revision as of 13:51, 7 December 2018

Modeling

Mathematical model

Edinburgh model

The β-barrel Assembly Machinery Complex

Mass Action Equations

Ordinary Differential Equations

Determination of the System Values

Starting Conditions

Sensitivity Analysis

Conclusions

References

eXplaY

Background

Setup

Results

Conclusions

Discussion

References

COMSOL model

Background

Phase-field modeling overview

Geometry

Mesh

Materials

Description of the System

Results

Parametric sweeps and example of liposome radius calculation

Liposome size dependence on viscosity ratio λ

Liposome size dependency on velocity ratio V

Liposome size dependency on IA channel width w

Conclusion

Discussion

Model Limitations

References

Thermo Switches model

Background

Concept of the Model

Results

Model

References

Liposome size dependency on IA channel width `w`