Difference between revisions of "Team:UI Indonesia/Model"
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<h6><b>Table 5.</b>HB-EGF Receptor Properties</h6> | <h6><b>Table 5.</b>HB-EGF Receptor Properties</h6> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/d/d4/T--UI_Indonesia--modelling15.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/d/d4/T--UI_Indonesia--modelling15.png" width="300"></img> |
<br> | <br> | ||
<h6><b>Table 6.</b>Association and Dissociation Constants of HB-EGF Receptor.</h6> | <h6><b>Table 6.</b>Association and Dissociation Constants of HB-EGF Receptor.</h6> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/1/11/T--UI_Indonesia--modelling16.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/1/11/T--UI_Indonesia--modelling16.png" width="300"></img> |
<br> | <br> | ||
<h6><b>Table 7.</b>Association and Dissociation Response Unit and Concentration of Natural Diphtheria Toxin and HB-EGF Binding.</h6> | <h6><b>Table 7.</b>Association and Dissociation Response Unit and Concentration of Natural Diphtheria Toxin and HB-EGF Binding.</h6> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/c/ce/T--UI_Indonesia--modelling17.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/c/ce/T--UI_Indonesia--modelling17.png" width="500"></img> |
<br> | <br> | ||
<h6><b>Table 8.</b>Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin Based on Concentration.</h6> | <h6><b>Table 8.</b>Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin Based on Concentration.</h6> | ||
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<br> | <br> | ||
<h6><b>Table 10.</b>Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time</h6> | <h6><b>Table 10.</b>Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time</h6> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/9/91/T--UI_Indonesia--modelling23.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/9/91/T--UI_Indonesia--modelling23.png" width="400"></img> |
<br> | <br> | ||
<h5>The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:</h5> | <h5>The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:</h5> | ||
<br> | <br> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/c/c3/T--UI_Indonesia--modelling24.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/c/c3/T--UI_Indonesia--modelling24.png" width="700"></img> |
<br> | <br> | ||
<h5>Our team formulated models (based on utilization of <i>Polymath 6.0</i> software) based on that with trial and error fit to the data, and the best fitted model would be:</h5> | <h5>Our team formulated models (based on utilization of <i>Polymath 6.0</i> software) based on that with trial and error fit to the data, and the best fitted model would be:</h5> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/5/52/T--UI_Indonesia--modelling25.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/5/52/T--UI_Indonesia--modelling25.png" width="700"></img> |
<br> | <br> | ||
| − | <img src ="https://static.igem.org/mediawiki/2018/0/00/T--UI_Indonesia--modelling26.png" width=" | + | <img src ="https://static.igem.org/mediawiki/2018/0/00/T--UI_Indonesia--modelling26.png" width="500"></img> |
<h6><b>Figure 10.</b>The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)</h6> | <h6><b>Figure 10.</b>The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)</h6> | ||
<br> | <br> | ||
Revision as of 08:21, 16 October 2018
MODELLING
Structural Modelling
Chimera Combination
Our first steps in modelling the subsequent parts of Finding Diphthy iGEM-UI 2018 in silico is by
constructing all 3D models via I-Tasser server.1,2,3 The extension of the product file is .pdb, that
could be read by the server. The chimera molecules which we need to predict their modelling are HB-EGF/TAR
(Heparin Binding Epidermal Growth Factor- TAR chemotaxis), CheA signalling protein, Che-Y signalling protein,
LuxAB dimerized luciferase subunits, and eYFP (enhanced yellow fluorescent protein), as well as DiphTox
(modified diphtheria exotoxin). Since CheA and CheY are required to be linked with LuxB or eYFP,
we have cited one of the universal linker, that is ‘GGGSGGGGSGGGGSG’ peptides, according to Sun S et al.
In choosing the best combination, we use FoldX option via YASARA molecules viewer
to calculate the ∆G of each molecule, searching for the smallest free energy
(regarding its stability in vivo). All those sequences are also submitted to
I-Tasser server for projecting their 3D models qualitatively. The following
results would conclude that our cytoplasmic signalling combinations are
CheY-eYFP and LuxB-CheA.
Table 1. Specific Gibbs Energy within Each Protein Combination.
Combination
∆G
LuxB-CheY
58.15 kcal/mol
LuxB-CheA
1355.46 kcal/mol
CheY-eYFP
36.48 kcal/mol
CheA-eYFP
36.48 kcal/mol
Characterisation or purification of those proteins would promote the usage
of His-tag; therefore, insertion of His-tag inside the sequence is essential.
To ensure the slightest change of tertiary structures of each protein,
we would need to find out the secondary structure and surface accesibility
via NetSurfP ver. 1.1 analyser (http://www.cbs.dtu.dk/services/NetSurfP/).
We would insert His-tag sequence in either no available specific protein
domain or the coiled secondary structure of protein to minimize any
interruptions. Here is our DiphTox data from NetSurfP server.Result from the NetSurf server, we choose C-terminus side,
because it most likely turns/coils around (indicated by
has high number on the most right column is closest to 1),
and it is freely exposed (indicated by most left column has E alphabet)
Table 2. Coiling probability of DipThox’s specific domain.
Class assignment
Amino acid
Amino acid
number
Probability
for Coil
B
I
54
0.223
E
K
55
0.669
E
S
56
0.994
Performing structural similarity between original molecule and
the one inserted with His-tag sequence have been done by MUSTANG
server that built in via YASARA molecule viewer.5 The output would be
distance calculation between interacting atoms called RMSD
(Root-mean-square deviation). Following tables are summaries of the
molecular similarity analysis. From the data that described above, all the combinations are acceptable,
except LuxA, since its possible combination has high RMSD. The threshold
is relative, but several literatures define the RMSD value of 2 as
threshold for structure similarity.5,6,7
Table 1. RMSD Calculation within Several Protein Linked with His-tag.
Similarities between
RMSD
LuxA with LuxA + His
2.203 Å
LuxC with LuxC + His
0.985 Å
LuxD with LuxD + His
0.1777 Å
LuxE with LuxE + His
0.800
CheY-eYFP with CheY-eYFP+his
0.108 Å
eYFP with eYFP + His
0.315 Å
CheA with CheA + His
0.134 Å
HB-EGF/Tar Receptor Modelling
In HB-EGF, the part that serves as binding domain for diphtheria exotoxin
predominantly located in the extracellular environment. Therefore,
the domain, expands between 20th – 160th amino acid, was selected from
natural HB-EGF protein. On the other hand, the Tar domain that are
functions to establish intracellular chemotactic signalling includes
NdeI cutting-site (around 257th amino acid) until the utmost C-terminal
of the protein (the 553rd amino acid).8-11 By those factors, our team also
selected Tar domains involving the 1st – 33rd and 191st –
553rd amino acid as part of chimeric protein.
Figure 1. The selected segment of Tar protein. The functional
intracellular domain of Tar is shown as yellow box, blue box is
transmembrane domain and orange box is periplasmic domain. Selected Tar
domain expands from 1st -33rd amino acids and 191st -553rd amino acids.
Modification of binding domain is located between 33rd – 191st amino acids
Our team have predicted the HB-EGF/Tar protein orientation in the
Escherichia coli membrane. For this purpose, server TMHMM and OPM Membrane,
are utilized to predict protein orientation.12,13 Conceptual hypothesis
about the chimera protein is that it should begin its orientation of
C-terminus in cytoplasm, then continued to fold into transmembrane and
extracellular sites, as well as re-folding towards cytoplasm.
Figure 2. The graph above explains the result of HB-EGF/Tar
orientation, which began from C-terminus (left) to N-terminus (right).12
Y-axis pictured the possibility of nth amino acid on protein located somewhere
between transmembrane (red part), intracellular (blue line), and
extracellular (pink line). There is also a diagram located above the graph
that represent the most possible location of each domain (with elongated box).
From the results, it could be concluded that the protein was oriented
as expected in the hypothesis. Therefore, the usage of chimera protein is
predicted to be functional anatomically.
![]()
Figure 3.Molecular comparation of HB-EGF native protein (left)
with the HB-EGF/Tar fusion (right).13,14 The pink-coloured
domain is intracellularly located as the N-terminus, yellow-coloured
domain for the transmembrane one. Then, purple-coloured could be a sign
as the extracellular domain, finally folding into transmembrane and back
to cytoplasm with orange-coloured and cyan-coloured domain respectively.
After deciding sequence combination of amino acids in modelled chimera
HB-EGF/Tar protein, analyzing the interaction of both fusion protein and
diphtheria exotoxin is extremely important to ensure functional
ligand-receptor system. The basic concept of interaction modelling is
that the protein will be bound to each other well if it causes the
‘environment’ energy (termed by E parameter; calculated by formula below)
being lowered down. In this part, our team sent the respective sequence to
ClusPro website for further analyzing.15
E = 0.4Erep + -0.40Eatt + 600Eelec + 1.00EDARS
Note: Erep and Eattr denote as repulsive and attractive contributions
to the van der Waals interaction energy. Additionally, Eelec means an
electrostatic energy that occur during both protein interaction. EDARS
is a pairwise structure-based potential constructed by the Decoys of
the Reference State (DARS) approach, and it primarily represents
desolvation contributions, i.e., the free energy change due to the
removal of the water molecules from the interface.15
Table 4. Comparation of E parameter of native and chimera protein of HB-EGF interacted with DiphTox.
HB-EGF
Protein
Median Energy (kcal/mol)
Lowest Energy (kcal/mol)
Native
-944.3
-994.3
Chimera
858.2
934.4
Figure 5.HB-EGF natural receptor and DiphTox 3D interaction modelling result.
The result of interaction modelling is quantified as energy score based on
the formula above. Referring to figure 4 and 5, we might expect that the
DiphTox (cyan) would bind to both native and chimeric HB-EGF receptor that
are both located in the extracellular (green). It is indicated by higher
energy score of interaction between chimeric HB-EGF/Tar receptor-DiphTox
than that of to HB-EGF natural receptor-DiphTox (Table 4). This means
that the chimeric receptor could bind towards DiphTox as good
(or even better) than the original one.
Beside the cell’s ability to detect toxin, our team also need to ensure
the signaling machine works well. Our team also modelled the interaction
between LuxA dan LuxB (that we fused with CheA). From figure 6 and 7,
we might expect that both proteins are still able to interact normally
after combining them with FRET unit (CheA or CheY protein).
Table 5. Comparation of E parameter of native and His-tagged protein of LuxB-CheA.
LuxAB
Median Energy (kcal/mol)
Lowest Energy (kcal/mol)
Native
-1515.4.3
-1553.2
Chimera
-1220.9
-1290.7
Figure 6.LuxA and LuxB-CheA (LuxAB-CheA) 3D interaction modelling result.
Figure 7..LuxA and LuxB 3D interaction modelling result.
Kinetical Modelling
In synthesizing any designed system of engineered protein, one must able to oversee and predict regarding its performance and behaviour. In analysing the protein, one can apply principles of mathematics and engineering in doing so. Reaction kinetics study can be largely described as the study of reactions regarding their performance such as rates, effects of various variables, etc. In this report, the kinetics of the designed protein will be evaluated based on existing literature. Mass transportation principle, such as Langmuir-Hill or Michaelis-Menten equation, will be loosely applied and adequately correlated for the resulting models. Mathematical models and non-linear regression will play roles for the protein. Out team hopes that this mathematical modelling analysis for the protein will shed a new perspective for the synthesized protein’s function and enlighten some parts of our project.
Qualitative Overview
Figure 1. The figure above describes the event of diphtheria toxin initial binding to the HB-EGF receptors in human epithelial cells. Attached toxin will inhibit protein synthesis and result in apoptosis.
Figure 2. The figure above describes the difference between the chimeric protein performance’s regarding of its reaction with diphtheria toxin.
Thus, in overseeing the entire performance, it can be divided into three parts:
- HB-EGF binding to the diphtheria toxin
- TAR protein’s binding performance
- Reaction rates of the auto-phosphorylation process
Quantitative Overview
In calculating reaction rates of either association or dissociation rate, the following mathematical equations are applied:
The surface concentration Gamma (G), for a protein can be calculated by the following formula (3): One Response Unit (RU) in the Blacore 2000/3000 machine corresponds to a surface coverage of 10-6 g m-2 for a typical protein. A 100 kDa protein generating a response of 1000 RU, corresponds to a surface coverage of 10-8 moles m-2.
Formulas:
Response unit, which is the symbol for reaction rates’ response that are given directly by the response machine will first be converted into gamma (surface concentration), which will then be converted into concentration of complex with the following formula:
Therefore, reaction rates can be calculated with following formula:
The formula is synthesized by following the mass-transportation-based reaction rates, which is based on chemical kinetics of the reaction’s constituent.
HB-EGF Receptor Activity
Part I: Association and Dissociation Rates Based on Time
This part of analysis is mainly referenced to an article by Brooke et.al. [1], in which they model binding of immobilized HB-EGF with diphtheria toxin response unit versus time, which will be shown below:
Figure 3.Binding of DT to immobilized hHB-EGF. The first arrow represents the start of the injection of DT over the immobilized hHB-EGF. The arrow with a ball represents the end of the DT injection and the beginning of the flow running buffer. From the bottom curve to the top curve, the respective binding curves for DT of 400 nM, 500 nM, 600 nM, 700 nM, 800 nM and 1 μM concentrations are shown. The number ①, ②, and ③ represent the baseline of running buffer, the association phase of the binding of DT to hHB-EGF, and the dissociation phase of the release of DT from hHB-EGF, respectively, RU, resonance units. This figure shows a representative experiment (use Materials and Methods).
Therefore, the prediction of both association rates and dissociation rates are shown below, by comparing our chimeric protein’s kinetics with literature, the x axis represents time, while the y axis represents response in Response Unit (RU).
- Association Rates
Table 1.HB-EGF Receptor Properties
Table 2.Calculation Table of Diphtheria Toxin and HB-EGF Association Rate
Therefore, the data regression will be plotted as below:
Figure 4.Association Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 5.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
- Dissociation Rates
Table 3.HB-EGF Receptor Properties
Table 4.Calculation Table of Diphtheria Toxin and HB-EGF Dissociation Rate
Therefore, the data regression will be plotted as below:
Figure 6.Dissociation Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 7.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
Part II: Rates Based on Concentration
The figure/literature used is still the same as the association/dissociation rates above; therefore, by remodelling and regressing the data based on the literature, one can predict the association and dissociation rates on certain times, with the concentration of the toxin as the independent variable, which is shown at the interactive Excel with this interface:
Table 5.HB-EGF Receptor Properties
Table 6.Association and Dissociation Constants of HB-EGF Receptor.
Table 7.Association and Dissociation Response Unit and Concentration of Natural Diphtheria Toxin and HB-EGF Binding.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin Based on Concentration.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin.
Figure 8.The Regression Graph for Response Unit vs Toxin Concentration
The programmed Excel will calculate the reaction rates just by inserting desired concentration.
Part III: Effects of pH and Temperature
- Effects of pH
Based on throughout literature review, the closest thing for binding of diphtheria toxin is for Vero Cells [2], which is shown below:
Based on graph above, it can be assumed that the best temperature for diphtheria binding is 4°C. Assumed that the chosen temperature is 4°C, the regression model for said temperature for graph of time versus reaction rate, is shown below (at toxin concentration of 0.06 μM). All of the data and assumption are based on journal.
Table 10.Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time
The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:
Our team formulated models (based on utilization of Polymath 6.0 software) based on that with trial and error fit to the data, and the best fitted model would be:
Figure 10.The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)
- Effects of Temperature
Reference :
- J Yang, R Yan, A Roy, D Xu, J Poisson, Y Zhang. The I-TASSER Suite: Protein structure and function prediction. Nature Methods, 12: 7-8 (2015)
- A Roy, A Kucukural, Y Zhang. I-TASSER: a unified platform for automated protein structure and function prediction. Nature Protocols, 5: 725-738 (2010)
- Y Zhang. I-TASSER server for protein 3D structure prediction. BMC Bioinformatics, vol 9, 40 (2008)
- Sun, S., Yang, X., Wang, Y., Shen, X., 2016. In Vivo Analysis of Protein–Protein Interactions with Bioluminescence Resonance Energy Transfer (BRET): Progress and Prospects. International Journal of Molecular Sciences 17, 1704. https://doi.org/10.3390/ijms17101704
- MUSTANG: A multiple structural alignment algorithm Konagurthu AS, Whisstock JC, Stuckey PJ, Lesk AM (2006) Proteins 64,559-574
- Bordogna, A., Pandini, A., Bonati, L., 2010. Predicting the accuracy of protein-ligand docking on homology models. Journal of Computational Chemistry 32, 81–98. https://doi.org/10.1002/jcc.21601
- Carugo, O., 2003. How root-mean-square distance (r.m.s.d.) values depend on the resolution of protein structures that are compared. Journal of Applied Crystallography 36, 125–128. https://doi.org/10.1107/s0021889802020502
- Kanchan, K., Linder, J., Winkler, K., Hantke, K., Schultz, A. and Schultz, J. (2009). Transmembrane Signaling in Chimeras of the Escherichia coli Aspartate and Serine Chemotaxis Receptors and Bacterial Class III Adenylyl Cyclases. Journal of Biological Chemistry, 285(3), pp.2090-2099.
- Ward, S., Delgado, A., Gunsalus, R. and Manson, M. (2002). A NarX-Tar chimera mediates repellent chemotaxis to nitrate and nitrite. Molecular Microbiology, 44(3), pp.709-719.
- Melchers, L. S., Regensburg-Tuïnk, T. J., Bourret, R. B., Sedee, N. J., Schilperoort, R. A. and Hooykaas, P. J. (1989). Membrane topology and functional analysis of the sensory protein VirA of Agrobacterium tumefaciens. The EMBO Journal, 8(7), pp.1919-1925.
- Weerasuriya, S., Schneider, B. M. and Manson, M. D. (1998). Chimeric Chemoreceptors in Escherichia coli: Signaling Properties of Tar-Tap and Tap-Tar Hybrids. Journal of Bacteriology, 180(4), pp.914-920.
- Cbs.dtu.dk. (2018). TMHMM Server, v. 2.0. [online] Available at: http://www.cbs.dtu.dk/services/TMHMM/ [Accessed 22 Jul. 2018].
- Lomize M.A., Pogozheva I,D, Joo H., Mosberg H.I., Lomize A.L. OPM database and PPM web server: resources for positioning of proteins in membranes. Nucleic Acids Res., 2012, 40(Database issue):D370-6
- Kelley LA et al. (2015). The Phyre2 web portal for protein modeling, prediction and analysis. Nature Protocols 10, pp.845-858
- Kozakov D, Hall DR, Xia B, Porter KA, Padhorny D, Yueh C, Beglov D, Vajda S. The ClusPro web server for protein-protein docking. Nature Protocols.2017 Feb;12(2):255-278 ; pdf
- Kozakov D, Beglov D, Bohnuud T, Mottarella S, Xia B, Hall DR, Vajda, S. How good is automated protein docking? Proteins: Structure, Function, and Bioinformatics, 2013 Aug ; pdf
- Kozakov D, Brenke R, Comeau SR, Vajda S. PIPER: An FFT-based protein docking program with pairwise potentials. Proteins. 2006 Aug 24; pdf
- Comeau SR, Gatchell DW, Vajda S, Camacho CJ. ClusPro: an automated docking and discrimination method for the prediction of protein complexes.Bioinformatics. 2004 Jan 1; pdf
- Comeau SR, Gatchell DW, Vajda S, Camacho CJ. ClusPro: a fully automated algorithm for protein-protein docking Nucleic Acids Research. 2004 Jul 1; pdf
- Högbom, M., Eklund, M., Nygren, P. Å., & Nordlund, P. (2003). Structural basis for recognition by an in vitro evolved affibody. Proceedings of the National Academy of Sciences, 100(6), 3191-3196.
- 2015.igem.org. (2018). Team:Stockholm/Description - 2015.igem.org. [online] Available at: https://2015.igem.org/Team:Stockholm/Description [Accessed 22 Jul. 2018].
Table 1. Specific Gibbs Energy within Each Protein Combination.
| Combination | ∆G |
|---|---|
| LuxB-CheY | 58.15 kcal/mol |
| LuxB-CheA | 1355.46 kcal/mol |
| CheY-eYFP | 36.48 kcal/mol |
| CheA-eYFP | 36.48 kcal/mol |
Table 2. Coiling probability of DipThox’s specific domain.
| Class assignment | Amino acid | Amino acid |
Probability |
|---|---|---|---|
| B | I | 54 |
0.223 |
| E | K | 55 |
0.669 |
| E | S | 56 |
0.994 |
Table 1. RMSD Calculation within Several Protein Linked with His-tag.
Similarities between |
RMSD |
|---|---|
| LuxA with LuxA + His | 2.203 Å |
| LuxC with LuxC + His | 0.985 Å |
| LuxD with LuxD + His | 0.1777 Å |
| LuxE with LuxE + His | 0.800 |
| CheY-eYFP with CheY-eYFP+his | 0.108 Å |
| eYFP with eYFP + His | 0.315 Å |
| CheA with CheA + His | 0.134 Å |
Figure 2. The graph above explains the result of HB-EGF/Tar
orientation, which began from C-terminus (left) to N-terminus (right).12
Y-axis pictured the possibility of nth amino acid on protein located somewhere
between transmembrane (red part), intracellular (blue line), and
extracellular (pink line). There is also a diagram located above the graph
that represent the most possible location of each domain (with elongated box).
From the results, it could be concluded that the protein was oriented
as expected in the hypothesis. Therefore, the usage of chimera protein is
predicted to be functional anatomically.
![]()
Figure 3.Molecular comparation of HB-EGF native protein (left)
with the HB-EGF/Tar fusion (right).13,14 The pink-coloured
domain is intracellularly located as the N-terminus, yellow-coloured
domain for the transmembrane one. Then, purple-coloured could be a sign
as the extracellular domain, finally folding into transmembrane and back
to cytoplasm with orange-coloured and cyan-coloured domain respectively.
After deciding sequence combination of amino acids in modelled chimera
HB-EGF/Tar protein, analyzing the interaction of both fusion protein and
diphtheria exotoxin is extremely important to ensure functional
ligand-receptor system. The basic concept of interaction modelling is
that the protein will be bound to each other well if it causes the
‘environment’ energy (termed by E parameter; calculated by formula below)
being lowered down. In this part, our team sent the respective sequence to
ClusPro website for further analyzing.15
E = 0.4Erep + -0.40Eatt + 600Eelec + 1.00EDARS
Note: Erep and Eattr denote as repulsive and attractive contributions
to the van der Waals interaction energy. Additionally, Eelec means an
electrostatic energy that occur during both protein interaction. EDARS
is a pairwise structure-based potential constructed by the Decoys of
the Reference State (DARS) approach, and it primarily represents
desolvation contributions, i.e., the free energy change due to the
removal of the water molecules from the interface.15
Table 4. Comparation of E parameter of native and chimera protein of HB-EGF interacted with DiphTox.
HB-EGF
Protein
Median Energy (kcal/mol)
Lowest Energy (kcal/mol)
Native
-944.3
-994.3
Chimera
858.2
934.4
Figure 5.HB-EGF natural receptor and DiphTox 3D interaction modelling result.
The result of interaction modelling is quantified as energy score based on
the formula above. Referring to figure 4 and 5, we might expect that the
DiphTox (cyan) would bind to both native and chimeric HB-EGF receptor that
are both located in the extracellular (green). It is indicated by higher
energy score of interaction between chimeric HB-EGF/Tar receptor-DiphTox
than that of to HB-EGF natural receptor-DiphTox (Table 4). This means
that the chimeric receptor could bind towards DiphTox as good
(or even better) than the original one.
Beside the cell’s ability to detect toxin, our team also need to ensure
the signaling machine works well. Our team also modelled the interaction
between LuxA dan LuxB (that we fused with CheA). From figure 6 and 7,
we might expect that both proteins are still able to interact normally
after combining them with FRET unit (CheA or CheY protein).
Table 5. Comparation of E parameter of native and His-tagged protein of LuxB-CheA.
LuxAB
Median Energy (kcal/mol)
Lowest Energy (kcal/mol)
Native
-1515.4.3
-1553.2
Chimera
-1220.9
-1290.7
Figure 6.LuxA and LuxB-CheA (LuxAB-CheA) 3D interaction modelling result.
Figure 7..LuxA and LuxB 3D interaction modelling result.
Kinetical Modelling
In synthesizing any designed system of engineered protein, one must able to oversee and predict regarding its performance and behaviour. In analysing the protein, one can apply principles of mathematics and engineering in doing so. Reaction kinetics study can be largely described as the study of reactions regarding their performance such as rates, effects of various variables, etc. In this report, the kinetics of the designed protein will be evaluated based on existing literature. Mass transportation principle, such as Langmuir-Hill or Michaelis-Menten equation, will be loosely applied and adequately correlated for the resulting models. Mathematical models and non-linear regression will play roles for the protein. Out team hopes that this mathematical modelling analysis for the protein will shed a new perspective for the synthesized protein’s function and enlighten some parts of our project.
Qualitative Overview
Figure 1. The figure above describes the event of diphtheria toxin initial binding to the HB-EGF receptors in human epithelial cells. Attached toxin will inhibit protein synthesis and result in apoptosis.
Figure 2. The figure above describes the difference between the chimeric protein performance’s regarding of its reaction with diphtheria toxin.
Thus, in overseeing the entire performance, it can be divided into three parts:
- HB-EGF binding to the diphtheria toxin
- TAR protein’s binding performance
- Reaction rates of the auto-phosphorylation process
Quantitative Overview
In calculating reaction rates of either association or dissociation rate, the following mathematical equations are applied:
The surface concentration Gamma (G), for a protein can be calculated by the following formula (3): One Response Unit (RU) in the Blacore 2000/3000 machine corresponds to a surface coverage of 10-6 g m-2 for a typical protein. A 100 kDa protein generating a response of 1000 RU, corresponds to a surface coverage of 10-8 moles m-2.
Formulas:
Response unit, which is the symbol for reaction rates’ response that are given directly by the response machine will first be converted into gamma (surface concentration), which will then be converted into concentration of complex with the following formula:
Therefore, reaction rates can be calculated with following formula:
The formula is synthesized by following the mass-transportation-based reaction rates, which is based on chemical kinetics of the reaction’s constituent.
HB-EGF Receptor Activity
Part I: Association and Dissociation Rates Based on Time
This part of analysis is mainly referenced to an article by Brooke et.al. [1], in which they model binding of immobilized HB-EGF with diphtheria toxin response unit versus time, which will be shown below:
Figure 3.Binding of DT to immobilized hHB-EGF. The first arrow represents the start of the injection of DT over the immobilized hHB-EGF. The arrow with a ball represents the end of the DT injection and the beginning of the flow running buffer. From the bottom curve to the top curve, the respective binding curves for DT of 400 nM, 500 nM, 600 nM, 700 nM, 800 nM and 1 μM concentrations are shown. The number ①, ②, and ③ represent the baseline of running buffer, the association phase of the binding of DT to hHB-EGF, and the dissociation phase of the release of DT from hHB-EGF, respectively, RU, resonance units. This figure shows a representative experiment (use Materials and Methods).
Therefore, the prediction of both association rates and dissociation rates are shown below, by comparing our chimeric protein’s kinetics with literature, the x axis represents time, while the y axis represents response in Response Unit (RU).
- Association Rates
Table 1.HB-EGF Receptor Properties
Table 2.Calculation Table of Diphtheria Toxin and HB-EGF Association Rate
Therefore, the data regression will be plotted as below:
Figure 4.Association Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 5.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
- Dissociation Rates
Table 3.HB-EGF Receptor Properties
Table 4.Calculation Table of Diphtheria Toxin and HB-EGF Dissociation Rate
Therefore, the data regression will be plotted as below:
Figure 6.Dissociation Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 7.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
Part II: Rates Based on Concentration
The figure/literature used is still the same as the association/dissociation rates above; therefore, by remodelling and regressing the data based on the literature, one can predict the association and dissociation rates on certain times, with the concentration of the toxin as the independent variable, which is shown at the interactive Excel with this interface:
Table 5.HB-EGF Receptor Properties
Table 6.Association and Dissociation Constants of HB-EGF Receptor.
Table 7.Association and Dissociation Response Unit and Concentration of Natural Diphtheria Toxin and HB-EGF Binding.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin Based on Concentration.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin.
Figure 8.The Regression Graph for Response Unit vs Toxin Concentration
The programmed Excel will calculate the reaction rates just by inserting desired concentration.
Part III: Effects of pH and Temperature
- Effects of pH
Based on throughout literature review, the closest thing for binding of diphtheria toxin is for Vero Cells [2], which is shown below:
Based on graph above, it can be assumed that the best temperature for diphtheria binding is 4°C. Assumed that the chosen temperature is 4°C, the regression model for said temperature for graph of time versus reaction rate, is shown below (at toxin concentration of 0.06 μM). All of the data and assumption are based on journal.
Table 10.Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time
The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:
Our team formulated models (based on utilization of Polymath 6.0 software) based on that with trial and error fit to the data, and the best fitted model would be:
Figure 10.The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)
- Effects of Temperature
Reference :
- J Yang, R Yan, A Roy, D Xu, J Poisson, Y Zhang. The I-TASSER Suite: Protein structure and function prediction. Nature Methods, 12: 7-8 (2015)
- A Roy, A Kucukural, Y Zhang. I-TASSER: a unified platform for automated protein structure and function prediction. Nature Protocols, 5: 725-738 (2010)
- Y Zhang. I-TASSER server for protein 3D structure prediction. BMC Bioinformatics, vol 9, 40 (2008)
- Sun, S., Yang, X., Wang, Y., Shen, X., 2016. In Vivo Analysis of Protein–Protein Interactions with Bioluminescence Resonance Energy Transfer (BRET): Progress and Prospects. International Journal of Molecular Sciences 17, 1704. https://doi.org/10.3390/ijms17101704
- MUSTANG: A multiple structural alignment algorithm Konagurthu AS, Whisstock JC, Stuckey PJ, Lesk AM (2006) Proteins 64,559-574
- Bordogna, A., Pandini, A., Bonati, L., 2010. Predicting the accuracy of protein-ligand docking on homology models. Journal of Computational Chemistry 32, 81–98. https://doi.org/10.1002/jcc.21601
- Carugo, O., 2003. How root-mean-square distance (r.m.s.d.) values depend on the resolution of protein structures that are compared. Journal of Applied Crystallography 36, 125–128. https://doi.org/10.1107/s0021889802020502
- Kanchan, K., Linder, J., Winkler, K., Hantke, K., Schultz, A. and Schultz, J. (2009). Transmembrane Signaling in Chimeras of the Escherichia coli Aspartate and Serine Chemotaxis Receptors and Bacterial Class III Adenylyl Cyclases. Journal of Biological Chemistry, 285(3), pp.2090-2099.
- Ward, S., Delgado, A., Gunsalus, R. and Manson, M. (2002). A NarX-Tar chimera mediates repellent chemotaxis to nitrate and nitrite. Molecular Microbiology, 44(3), pp.709-719.
- Melchers, L. S., Regensburg-Tuïnk, T. J., Bourret, R. B., Sedee, N. J., Schilperoort, R. A. and Hooykaas, P. J. (1989). Membrane topology and functional analysis of the sensory protein VirA of Agrobacterium tumefaciens. The EMBO Journal, 8(7), pp.1919-1925.
- Weerasuriya, S., Schneider, B. M. and Manson, M. D. (1998). Chimeric Chemoreceptors in Escherichia coli: Signaling Properties of Tar-Tap and Tap-Tar Hybrids. Journal of Bacteriology, 180(4), pp.914-920.
- Cbs.dtu.dk. (2018). TMHMM Server, v. 2.0. [online] Available at: http://www.cbs.dtu.dk/services/TMHMM/ [Accessed 22 Jul. 2018].
- Lomize M.A., Pogozheva I,D, Joo H., Mosberg H.I., Lomize A.L. OPM database and PPM web server: resources for positioning of proteins in membranes. Nucleic Acids Res., 2012, 40(Database issue):D370-6
- Kelley LA et al. (2015). The Phyre2 web portal for protein modeling, prediction and analysis. Nature Protocols 10, pp.845-858
- Kozakov D, Hall DR, Xia B, Porter KA, Padhorny D, Yueh C, Beglov D, Vajda S. The ClusPro web server for protein-protein docking. Nature Protocols.2017 Feb;12(2):255-278 ; pdf
- Kozakov D, Beglov D, Bohnuud T, Mottarella S, Xia B, Hall DR, Vajda, S. How good is automated protein docking? Proteins: Structure, Function, and Bioinformatics, 2013 Aug ; pdf
- Kozakov D, Brenke R, Comeau SR, Vajda S. PIPER: An FFT-based protein docking program with pairwise potentials. Proteins. 2006 Aug 24; pdf
- Comeau SR, Gatchell DW, Vajda S, Camacho CJ. ClusPro: an automated docking and discrimination method for the prediction of protein complexes.Bioinformatics. 2004 Jan 1; pdf
- Comeau SR, Gatchell DW, Vajda S, Camacho CJ. ClusPro: a fully automated algorithm for protein-protein docking Nucleic Acids Research. 2004 Jul 1; pdf
- Högbom, M., Eklund, M., Nygren, P. Å., & Nordlund, P. (2003). Structural basis for recognition by an in vitro evolved affibody. Proceedings of the National Academy of Sciences, 100(6), 3191-3196.
- 2015.igem.org. (2018). Team:Stockholm/Description - 2015.igem.org. [online] Available at: https://2015.igem.org/Team:Stockholm/Description [Accessed 22 Jul. 2018].
E = 0.4Erep + -0.40Eatt + 600Eelec + 1.00EDARS
Table 4. Comparation of E parameter of native and chimera protein of HB-EGF interacted with DiphTox.
HB-EGF
Protein
Median Energy (kcal/mol)
Lowest Energy (kcal/mol)
Native
-944.3
-994.3
Chimera
858.2
934.4
Figure 5.HB-EGF natural receptor and DiphTox 3D interaction modelling result.
The result of interaction modelling is quantified as energy score based on
the formula above. Referring to figure 4 and 5, we might expect that the
DiphTox (cyan) would bind to both native and chimeric HB-EGF receptor that
are both located in the extracellular (green). It is indicated by higher
energy score of interaction between chimeric HB-EGF/Tar receptor-DiphTox
than that of to HB-EGF natural receptor-DiphTox (Table 4). This means
that the chimeric receptor could bind towards DiphTox as good
(or even better) than the original one.
Beside the cell’s ability to detect toxin, our team also need to ensure
the signaling machine works well. Our team also modelled the interaction
between LuxA dan LuxB (that we fused with CheA). From figure 6 and 7,
we might expect that both proteins are still able to interact normally
after combining them with FRET unit (CheA or CheY protein).
Table 5. Comparation of E parameter of native and His-tagged protein of LuxB-CheA.
LuxAB
Median Energy (kcal/mol)
Lowest Energy (kcal/mol)
Native
-1515.4.3
-1553.2
Chimera
-1220.9
-1290.7
Figure 6.LuxA and LuxB-CheA (LuxAB-CheA) 3D interaction modelling result.
Figure 7..LuxA and LuxB 3D interaction modelling result.
Kinetical Modelling
In synthesizing any designed system of engineered protein, one must able to oversee and predict regarding its performance and behaviour. In analysing the protein, one can apply principles of mathematics and engineering in doing so. Reaction kinetics study can be largely described as the study of reactions regarding their performance such as rates, effects of various variables, etc. In this report, the kinetics of the designed protein will be evaluated based on existing literature. Mass transportation principle, such as Langmuir-Hill or Michaelis-Menten equation, will be loosely applied and adequately correlated for the resulting models. Mathematical models and non-linear regression will play roles for the protein. Out team hopes that this mathematical modelling analysis for the protein will shed a new perspective for the synthesized protein’s function and enlighten some parts of our project.
Qualitative Overview
Figure 1. The figure above describes the event of diphtheria toxin initial binding to the HB-EGF receptors in human epithelial cells. Attached toxin will inhibit protein synthesis and result in apoptosis.
Figure 2. The figure above describes the difference between the chimeric protein performance’s regarding of its reaction with diphtheria toxin.
Thus, in overseeing the entire performance, it can be divided into three parts:
- HB-EGF binding to the diphtheria toxin
- TAR protein’s binding performance
- Reaction rates of the auto-phosphorylation process
Quantitative Overview
In calculating reaction rates of either association or dissociation rate, the following mathematical equations are applied:
The surface concentration Gamma (G), for a protein can be calculated by the following formula (3): One Response Unit (RU) in the Blacore 2000/3000 machine corresponds to a surface coverage of 10-6 g m-2 for a typical protein. A 100 kDa protein generating a response of 1000 RU, corresponds to a surface coverage of 10-8 moles m-2.
Formulas:
Response unit, which is the symbol for reaction rates’ response that are given directly by the response machine will first be converted into gamma (surface concentration), which will then be converted into concentration of complex with the following formula:
Therefore, reaction rates can be calculated with following formula:
The formula is synthesized by following the mass-transportation-based reaction rates, which is based on chemical kinetics of the reaction’s constituent.
HB-EGF Receptor Activity
Part I: Association and Dissociation Rates Based on Time
This part of analysis is mainly referenced to an article by Brooke et.al. [1], in which they model binding of immobilized HB-EGF with diphtheria toxin response unit versus time, which will be shown below:
Figure 3.Binding of DT to immobilized hHB-EGF. The first arrow represents the start of the injection of DT over the immobilized hHB-EGF. The arrow with a ball represents the end of the DT injection and the beginning of the flow running buffer. From the bottom curve to the top curve, the respective binding curves for DT of 400 nM, 500 nM, 600 nM, 700 nM, 800 nM and 1 μM concentrations are shown. The number ①, ②, and ③ represent the baseline of running buffer, the association phase of the binding of DT to hHB-EGF, and the dissociation phase of the release of DT from hHB-EGF, respectively, RU, resonance units. This figure shows a representative experiment (use Materials and Methods).
Therefore, the prediction of both association rates and dissociation rates are shown below, by comparing our chimeric protein’s kinetics with literature, the x axis represents time, while the y axis represents response in Response Unit (RU).
- Association Rates
Table 1.HB-EGF Receptor Properties
Table 2.Calculation Table of Diphtheria Toxin and HB-EGF Association Rate
Therefore, the data regression will be plotted as below:
Figure 4.Association Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 5.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
- Dissociation Rates
Table 3.HB-EGF Receptor Properties
Table 4.Calculation Table of Diphtheria Toxin and HB-EGF Dissociation Rate
Therefore, the data regression will be plotted as below:
Figure 6.Dissociation Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 7.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
Part II: Rates Based on Concentration
The figure/literature used is still the same as the association/dissociation rates above; therefore, by remodelling and regressing the data based on the literature, one can predict the association and dissociation rates on certain times, with the concentration of the toxin as the independent variable, which is shown at the interactive Excel with this interface:
Table 5.HB-EGF Receptor Properties
Table 6.Association and Dissociation Constants of HB-EGF Receptor.
Table 7.Association and Dissociation Response Unit and Concentration of Natural Diphtheria Toxin and HB-EGF Binding.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin Based on Concentration.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin.
Figure 8.The Regression Graph for Response Unit vs Toxin Concentration
The programmed Excel will calculate the reaction rates just by inserting desired concentration.
Part III: Effects of pH and Temperature
- Effects of pH
Based on throughout literature review, the closest thing for binding of diphtheria toxin is for Vero Cells [2], which is shown below:
Based on graph above, it can be assumed that the best temperature for diphtheria binding is 4°C. Assumed that the chosen temperature is 4°C, the regression model for said temperature for graph of time versus reaction rate, is shown below (at toxin concentration of 0.06 μM). All of the data and assumption are based on journal.
Table 10.Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time
The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:
Our team formulated models (based on utilization of Polymath 6.0 software) based on that with trial and error fit to the data, and the best fitted model would be:
Figure 10.The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)
- Effects of Temperature
Reference :
- J Yang, R Yan, A Roy, D Xu, J Poisson, Y Zhang. The I-TASSER Suite: Protein structure and function prediction. Nature Methods, 12: 7-8 (2015)
- A Roy, A Kucukural, Y Zhang. I-TASSER: a unified platform for automated protein structure and function prediction. Nature Protocols, 5: 725-738 (2010)
- Y Zhang. I-TASSER server for protein 3D structure prediction. BMC Bioinformatics, vol 9, 40 (2008)
- Sun, S., Yang, X., Wang, Y., Shen, X., 2016. In Vivo Analysis of Protein–Protein Interactions with Bioluminescence Resonance Energy Transfer (BRET): Progress and Prospects. International Journal of Molecular Sciences 17, 1704. https://doi.org/10.3390/ijms17101704
- MUSTANG: A multiple structural alignment algorithm Konagurthu AS, Whisstock JC, Stuckey PJ, Lesk AM (2006) Proteins 64,559-574
- Bordogna, A., Pandini, A., Bonati, L., 2010. Predicting the accuracy of protein-ligand docking on homology models. Journal of Computational Chemistry 32, 81–98. https://doi.org/10.1002/jcc.21601
- Carugo, O., 2003. How root-mean-square distance (r.m.s.d.) values depend on the resolution of protein structures that are compared. Journal of Applied Crystallography 36, 125–128. https://doi.org/10.1107/s0021889802020502
- Kanchan, K., Linder, J., Winkler, K., Hantke, K., Schultz, A. and Schultz, J. (2009). Transmembrane Signaling in Chimeras of the Escherichia coli Aspartate and Serine Chemotaxis Receptors and Bacterial Class III Adenylyl Cyclases. Journal of Biological Chemistry, 285(3), pp.2090-2099.
- Ward, S., Delgado, A., Gunsalus, R. and Manson, M. (2002). A NarX-Tar chimera mediates repellent chemotaxis to nitrate and nitrite. Molecular Microbiology, 44(3), pp.709-719.
- Melchers, L. S., Regensburg-Tuïnk, T. J., Bourret, R. B., Sedee, N. J., Schilperoort, R. A. and Hooykaas, P. J. (1989). Membrane topology and functional analysis of the sensory protein VirA of Agrobacterium tumefaciens. The EMBO Journal, 8(7), pp.1919-1925.
- Weerasuriya, S., Schneider, B. M. and Manson, M. D. (1998). Chimeric Chemoreceptors in Escherichia coli: Signaling Properties of Tar-Tap and Tap-Tar Hybrids. Journal of Bacteriology, 180(4), pp.914-920.
- Cbs.dtu.dk. (2018). TMHMM Server, v. 2.0. [online] Available at: http://www.cbs.dtu.dk/services/TMHMM/ [Accessed 22 Jul. 2018].
- Lomize M.A., Pogozheva I,D, Joo H., Mosberg H.I., Lomize A.L. OPM database and PPM web server: resources for positioning of proteins in membranes. Nucleic Acids Res., 2012, 40(Database issue):D370-6
- Kelley LA et al. (2015). The Phyre2 web portal for protein modeling, prediction and analysis. Nature Protocols 10, pp.845-858
- Kozakov D, Hall DR, Xia B, Porter KA, Padhorny D, Yueh C, Beglov D, Vajda S. The ClusPro web server for protein-protein docking. Nature Protocols.2017 Feb;12(2):255-278 ; pdf
- Kozakov D, Beglov D, Bohnuud T, Mottarella S, Xia B, Hall DR, Vajda, S. How good is automated protein docking? Proteins: Structure, Function, and Bioinformatics, 2013 Aug ; pdf
- Kozakov D, Brenke R, Comeau SR, Vajda S. PIPER: An FFT-based protein docking program with pairwise potentials. Proteins. 2006 Aug 24; pdf
- Comeau SR, Gatchell DW, Vajda S, Camacho CJ. ClusPro: an automated docking and discrimination method for the prediction of protein complexes.Bioinformatics. 2004 Jan 1; pdf
- Comeau SR, Gatchell DW, Vajda S, Camacho CJ. ClusPro: a fully automated algorithm for protein-protein docking Nucleic Acids Research. 2004 Jul 1; pdf
- Högbom, M., Eklund, M., Nygren, P. Å., & Nordlund, P. (2003). Structural basis for recognition by an in vitro evolved affibody. Proceedings of the National Academy of Sciences, 100(6), 3191-3196.
- 2015.igem.org. (2018). Team:Stockholm/Description - 2015.igem.org. [online] Available at: https://2015.igem.org/Team:Stockholm/Description [Accessed 22 Jul. 2018].
Table 4. Comparation of E parameter of native and chimera protein of HB-EGF interacted with DiphTox.
HB-EGF |
Median Energy (kcal/mol) |
Lowest Energy (kcal/mol) |
|---|---|---|
| Native | -944.3 |
-994.3 |
| Chimera | 858.2 |
934.4 |
Table 5. Comparation of E parameter of native and His-tagged protein of LuxB-CheA.
LuxAB |
Median Energy (kcal/mol) |
Lowest Energy (kcal/mol) |
|---|---|---|
| Native | -1515.4.3 |
-1553.2 |
| Chimera | -1220.9 |
-1290.7 |
In synthesizing any designed system of engineered protein, one must able to oversee and predict regarding its performance and behaviour. In analysing the protein, one can apply principles of mathematics and engineering in doing so. Reaction kinetics study can be largely described as the study of reactions regarding their performance such as rates, effects of various variables, etc. In this report, the kinetics of the designed protein will be evaluated based on existing literature. Mass transportation principle, such as Langmuir-Hill or Michaelis-Menten equation, will be loosely applied and adequately correlated for the resulting models. Mathematical models and non-linear regression will play roles for the protein. Out team hopes that this mathematical modelling analysis for the protein will shed a new perspective for the synthesized protein’s function and enlighten some parts of our project.
Qualitative Overview
Figure 1. The figure above describes the event of diphtheria toxin initial binding to the HB-EGF receptors in human epithelial cells. Attached toxin will inhibit protein synthesis and result in apoptosis.
Figure 2. The figure above describes the difference between the chimeric protein performance’s regarding of its reaction with diphtheria toxin.
Thus, in overseeing the entire performance, it can be divided into three parts:
- HB-EGF binding to the diphtheria toxin
- TAR protein’s binding performance
- Reaction rates of the auto-phosphorylation process
Quantitative Overview
In calculating reaction rates of either association or dissociation rate, the following mathematical equations are applied:
The surface concentration Gamma (G), for a protein can be calculated by the following formula (3): One Response Unit (RU) in the Blacore 2000/3000 machine corresponds to a surface coverage of 10-6 g m-2 for a typical protein. A 100 kDa protein generating a response of 1000 RU, corresponds to a surface coverage of 10-8 moles m-2.
Formulas:
Response unit, which is the symbol for reaction rates’ response that are given directly by the response machine will first be converted into gamma (surface concentration), which will then be converted into concentration of complex with the following formula:
Therefore, reaction rates can be calculated with following formula:
The formula is synthesized by following the mass-transportation-based reaction rates, which is based on chemical kinetics of the reaction’s constituent.
HB-EGF Receptor Activity
Part I: Association and Dissociation Rates Based on Time
This part of analysis is mainly referenced to an article by Brooke et.al. [1], in which they model binding of immobilized HB-EGF with diphtheria toxin response unit versus time, which will be shown below:
Figure 3.Binding of DT to immobilized hHB-EGF. The first arrow represents the start of the injection of DT over the immobilized hHB-EGF. The arrow with a ball represents the end of the DT injection and the beginning of the flow running buffer. From the bottom curve to the top curve, the respective binding curves for DT of 400 nM, 500 nM, 600 nM, 700 nM, 800 nM and 1 μM concentrations are shown. The number ①, ②, and ③ represent the baseline of running buffer, the association phase of the binding of DT to hHB-EGF, and the dissociation phase of the release of DT from hHB-EGF, respectively, RU, resonance units. This figure shows a representative experiment (use Materials and Methods).
Therefore, the prediction of both association rates and dissociation rates are shown below, by comparing our chimeric protein’s kinetics with literature, the x axis represents time, while the y axis represents response in Response Unit (RU).
- Association Rates
Table 1.HB-EGF Receptor Properties
Table 2.Calculation Table of Diphtheria Toxin and HB-EGF Association Rate
Therefore, the data regression will be plotted as below:
Figure 4.Association Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 5.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
- Dissociation Rates
Table 3.HB-EGF Receptor Properties
Table 4.Calculation Table of Diphtheria Toxin and HB-EGF Dissociation Rate
Therefore, the data regression will be plotted as below:
Figure 6.Dissociation Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 7.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
Table 1.HB-EGF Receptor Properties
Table 2.Calculation Table of Diphtheria Toxin and HB-EGF Association Rate
Therefore, the data regression will be plotted as below:
Figure 4.Association Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 5.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
Table 3.HB-EGF Receptor Properties
Table 4.Calculation Table of Diphtheria Toxin and HB-EGF Dissociation Rate
Therefore, the data regression will be plotted as below:
Figure 6.Dissociation Response of Diphtheria Toxin towards HB-EGF Receptor.
Figure 7.Reaction Rate of Diphtheria Toxin towards HB-EGF Receptor.
Part II: Rates Based on Concentration
The figure/literature used is still the same as the association/dissociation rates above; therefore, by remodelling and regressing the data based on the literature, one can predict the association and dissociation rates on certain times, with the concentration of the toxin as the independent variable, which is shown at the interactive Excel with this interface:
Table 5.HB-EGF Receptor Properties
Table 6.Association and Dissociation Constants of HB-EGF Receptor.
Table 7.Association and Dissociation Response Unit and Concentration of Natural Diphtheria Toxin and HB-EGF Binding.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin Based on Concentration.
Table 8.Calculation of Binding Reaction Rate of HB-EGF and Diphtheria Toxin.
Figure 8.The Regression Graph for Response Unit vs Toxin Concentration
The programmed Excel will calculate the reaction rates just by inserting desired concentration.
Part III: Effects of pH and Temperature
- Effects of pH
Based on throughout literature review, the closest thing for binding of diphtheria toxin is for Vero Cells [2], which is shown below:
Based on graph above, it can be assumed that the best temperature for diphtheria binding is 4°C. Assumed that the chosen temperature is 4°C, the regression model for said temperature for graph of time versus reaction rate, is shown below (at toxin concentration of 0.06 μM). All of the data and assumption are based on journal.
Table 10.Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time
The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:
Our team formulated models (based on utilization of Polymath 6.0 software) based on that with trial and error fit to the data, and the best fitted model would be:
Figure 10.The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)
- Effects of Temperature
Based on throughout literature review, the closest thing for binding of diphtheria toxin is for Vero Cells [2], which is shown below:
Based on graph above, it can be assumed that the best temperature for diphtheria binding is 4°C. Assumed that the chosen temperature is 4°C, the regression model for said temperature for graph of time versus reaction rate, is shown below (at toxin concentration of 0.06 μM). All of the data and assumption are based on journal.
Table 10.Concentration Counts of Diphtheria Toxin and HB-EGF Complex versus Time
The proposed model will follow arbitrary model based on Hill-Langmuir model, which is:
Our team formulated models (based on utilization of Polymath 6.0 software) based on that with trial and error fit to the data, and the best fitted model would be:
Figure 10.The Estimated Graphs for DT-Vero Cells Binding (Auth’s Personal Data)
- J Yang, R Yan, A Roy, D Xu, J Poisson, Y Zhang. The I-TASSER Suite: Protein structure and function prediction. Nature Methods, 12: 7-8 (2015)
- A Roy, A Kucukural, Y Zhang. I-TASSER: a unified platform for automated protein structure and function prediction. Nature Protocols, 5: 725-738 (2010)
- Y Zhang. I-TASSER server for protein 3D structure prediction. BMC Bioinformatics, vol 9, 40 (2008)
- Sun, S., Yang, X., Wang, Y., Shen, X., 2016. In Vivo Analysis of Protein–Protein Interactions with Bioluminescence Resonance Energy Transfer (BRET): Progress and Prospects. International Journal of Molecular Sciences 17, 1704. https://doi.org/10.3390/ijms17101704
- MUSTANG: A multiple structural alignment algorithm Konagurthu AS, Whisstock JC, Stuckey PJ, Lesk AM (2006) Proteins 64,559-574
- Bordogna, A., Pandini, A., Bonati, L., 2010. Predicting the accuracy of protein-ligand docking on homology models. Journal of Computational Chemistry 32, 81–98. https://doi.org/10.1002/jcc.21601
- Carugo, O., 2003. How root-mean-square distance (r.m.s.d.) values depend on the resolution of protein structures that are compared. Journal of Applied Crystallography 36, 125–128. https://doi.org/10.1107/s0021889802020502
- Kanchan, K., Linder, J., Winkler, K., Hantke, K., Schultz, A. and Schultz, J. (2009). Transmembrane Signaling in Chimeras of the Escherichia coli Aspartate and Serine Chemotaxis Receptors and Bacterial Class III Adenylyl Cyclases. Journal of Biological Chemistry, 285(3), pp.2090-2099.
- Ward, S., Delgado, A., Gunsalus, R. and Manson, M. (2002). A NarX-Tar chimera mediates repellent chemotaxis to nitrate and nitrite. Molecular Microbiology, 44(3), pp.709-719.
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