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<h1 class="text-wall-heading">Modeling</h1> | <h1 class="text-wall-heading">Modeling</h1> | ||
<div class="text-wall-area-box"> | <div class="text-wall-area-box"> | ||
− | <h2 class="text-wall-area-box-heading"> | + | <h2 class="text-wall-area-box-heading">Mathematical model</h2> |
<div class="scroll-area"> | <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> | <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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<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> | <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> | ||
<p></p> | <p></p> | ||
− | <h1>Mass Action Equations</h1 | + | <h1>Mass Action Equations</h1> |
<p></p> | <p></p> | ||
<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> | <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> | ||
<p> | <p> | ||
− | + | <div class="image-container"> | |
− | </ | + | <img src="https://static.igem.org/mediawiki/2018/6/6d/T--Vilnius-Lithuania--_Fig1_Edinburgh_Model.png"/> |
− | <strong>Fig. 1</strong> Mass Action Equations for Protein Expression | + | <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> | <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> | ||
</p> | </p> | ||
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<p>The model uses a set of differential equations:</p> | <p>The model uses a set of differential equations:</p> | ||
<P> | <P> | ||
− | + | <div class="image-container"> | |
− | </ | + | <img src="https://static.igem.org/mediawiki/2018/2/2e/T--Vilnius-Lithuania--_Fig2_Edinburgh_Model.png"/> |
− | <strong>Fig. 2</strong> System of differential equations for BamA kinetics | + | <p><strong>Fig. 2</strong> System of differential equations for BamA kinetics</p> |
+ | </div> | ||
<p></p> | <p></p> | ||
<h1>Determination of the System Values</h1> | <h1>Determination of the System Values</h1> | ||
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<li>pRSETb with lgA - 2490.8 kDa</li> | <li>pRSETb with lgA - 2490.8 kDa</li> | ||
</ol> | </ol> | ||
− | <p>Knowledge that 1 ng equals to 6. | + | <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> | <p>Tab. 1 Number of plasmids present for a particular number of ng of DNA added</p> | ||
<table> | <table> | ||
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<td>2.361*10<sup>17</sup></td> | <td>2.361*10<sup>17</sup></td> | ||
</tr> <tr> | </tr> <tr> | ||
− | <td><strong>pRSETb with IgA</strong | + | <td><strong>pRSETb with IgA</strong></td> |
<td></td> | <td></td> | ||
</tr> <tr> | </tr> <tr> | ||
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</table> | </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> | <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"> | |
− | </ | + | |
− | <strong>Fig. 3</strong>Minimum, maximum and average levels of mRNAs and protein for BamA, OmpA and lgA | + | <p><strong>Fig. 3</strong> Minimum, maximum and average levels of mRNAs and protein for BamA, OmpA and lgA</p></div> |
<p></p> | <p></p> | ||
− | <strong>Tab. 3</strong>Average, minimum and maximum number of protein molecules after 2 hours | + | <strong>Tab. 3</strong>Average, minimum and maximum number of protein molecules after 2 hours |
− | <thead> | + | <table><thead> |
<tr> | <tr> | ||
<th><strong>Protein</strong></th> | <th><strong>Protein</strong></th> | ||
− | <th><Strong>Number of molecules</ | + | <th><Strong>Number of molecules</strong></th> |
</tr> | </tr> | ||
</thead> | </thead> | ||
<tbody> | <tbody> | ||
− | |||
<tr> | <tr> | ||
− | <td><strong>Average</strong>< | + | <td><strong>Average</strong></td> |
<td></td> | <td></td> | ||
</tr> <tr> | </tr> <tr> | ||
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<td>3.44*10<sup>21</sup></td> | <td>3.44*10<sup>21</sup></td> | ||
</tr> <tr> | </tr> <tr> | ||
− | <td><strong>Minimum</strong | + | <td><strong>Minimum</strong></td> |
<td></td> | <td></td> | ||
+ | </tr> | ||
<tr> | <tr> | ||
<td>BamA</td> | <td>BamA</td> | ||
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<tr> | <tr> | ||
− | <td><strong>Maximum</strong | + | <td><strong>Maximum</strong></td> |
<td></td> | <td></td> | ||
+ | </tr> | ||
<tr> | <tr> | ||
<td>BamA</td> | <td>BamA</td> | ||
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<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>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> | <p></p> | ||
− | <h1>Sensitivity Analysis</h1 | + | <h1>Sensitivity Analysis</h1> |
<p></p> | <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> | <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> |
− | <strong>Fig. 4 </strong>FAST sensitivity analysis of BamA | + | |
<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>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> | <p></p> | ||
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<p></p> | <p></p> | ||
<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, <a href="https://2018.igem.org/Team:Vilnius-Lithuania/Description"> | + | <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>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 | + | <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’ | + | <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. | 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> | </p> | ||
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<p> | <p> | ||
− | </p><p>Sequence of particular fusion protein was built <a href="http://parts.igem.org/Part:BBa_K2622029"> BBa_K2622029.</p> | + | </p><p>Sequence of particular fusion protein was built <a href="http://parts.igem.org/Part:BBa_K2622029"> BBa_K2622029</a>.</p> |
<p> | <p> | ||
<div class="image-container"> | <div class="image-container"> | ||
<img src="https://static.igem.org/mediawiki/2018/1/1c/T--Vilnius-Lithuania--Fig1_Groningen.png"/> | <img src="https://static.igem.org/mediawiki/2018/1/1c/T--Vilnius-Lithuania--Fig1_Groningen.png"/> | ||
− | <p><strong>Fig 1</strong> Sequence scheme of Lpp_OmpA and Anti_GFP nanobody fusion protein. </p> | + | <p><strong>Fig. 1</strong> Sequence scheme of Lpp_OmpA and Anti_GFP nanobody fusion protein. </p> |
</div> | </div> | ||
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</p> | </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. | + | <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> | <p> | ||
<div class="image-container"> | <div class="image-container"> | ||
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</section> | </section> | ||
<section class="design_subsections"> | <section class="design_subsections"> | ||
− | + | <h1 id="COMSOL_model">COMSOL model</h1> | |
− | + | <div class="third_level_links"> | |
− | + | <a href="#Edinburgh_model">Edinburgh model</a> | |
− | + | <a href="#Groeningen_model">Groeningen model</a> | |
− | + | <a href="#COMSOL_model">COMSOL model</a> | |
− | + | <a href="#Thermo_Switches_model">Thermo Switches model</a> | |
− | + | </div> | |
− | + | <div> | |
− | + | <h1>Background</h1> | |
− | + | <h2>Phase-field modeling overview</h2> | |
− | + | <p>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<sub>i</sub> , where i = A, B, C, and the variable is equal to 1 in the phase i and 0 outside.</p> | |
− | + | <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 | ||
+ | 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)</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 | ||
+ | 2% 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, | ||
+ | 130–141 (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> | ||
<section class="design_subsections"> | <section class="design_subsections"> | ||
− | + | <h1 id="Thermo_Switches_model">Thermo Switches model</h1> | |
− | + | <div class="third_level_links"> | |
− | + | <a href="#Edinburgh_model">Edinburgh model</a> | |
− | + | <a href="#Groeningen_model">Groeningen model</a> | |
− | + | <a href="#COMSOL_model">COMSOL model</a> | |
− | + | <a href="#Thermo_Switches_model">Thermo Switches model</a> | |
− | + | </div> | |
− | + | <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 liposome IVTT system. | |
− | + | </p> | |
− | + | <p> | |
− | + | 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. | |
− | + | </P> | |
− | + | <p></p> | |
− | + | <h2>Concept of the Model</h2> | |
− | + | <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> | ||
</div> | </div> |
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