Team:Freiburg Bioware/Modeling

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<h1>Modeling</h1>
<h1>Modeling</h1>
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For the modeling part we considered three main parts:
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<br><br>
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<h2>Introduction</h2>
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<p style="text-align:justify;">
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Our modeling part consists of two main parts:
<ul>
<ul>
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<li>the virus production  
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<li>The mathematical modeling of <a href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Virus_Production"><b>virus production</b></a> and <a href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Virus_Infection"><b>infection</b></a> based on a model of ordinary differential equations (ODE).
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<li>the infection of a target cell
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<li>The modeling of the <a href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Structure_Modeling"><b>three dimensional structure</b></a> of the virus capsid based on X-ray crystallography data.
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<li>the therapy
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</ul>
</ul>
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For the first two models we assumed reactions according to the law of mass action to create a model of ordinary differential equations (ODE).
 
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<br><br>
 
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<h2>Model for Virus Production</h2>
 
<br>
<br>
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<h3>Reaction Scheme</h3>
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The first model describes the dynamic behavior of the virus production in terms of the law of mass action (Sidorenko & Reichl 2004). Therefore the temporal changes in concentrations of titrated plasmids, synthesized proteins, replicated single-stranded DNA and formed virus capsids and finally concentration of viral particles are simulated using MathWorks® MATLAB R2010b.<br>
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Reducing the complexity of virus production we divide the cell into three compartments: the <b>extracellular matrix</b> (all quantities with the index <i>ext</i>), the <b>cytoplasm</b> (<i>cyt</i>) and the <b>nucleus</b> (<i>nuc</i>). Four plasmids are transfected - the plasmid coding for the <b>helper proteins</b> (<i>helper</i>), the <b>gene of interest</b> (<i>goi</i>) and two types of plasmids coding for the <b>capsid proteins</b> (<i>capwt</i> [wild type], <i>capmod</i> [modified]).<br>
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Virus infection is modeled in a similar way but receptor binding has to be considered (Gurevich 2004). Starting with a given concentration of infectious virus particles, complexes with dimerized receptors emerge which can be internalized to the cytoplasm and transduction takes place.<br>
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The plasmids are transported into the nucleus where gene expression is initiated. Processed mRNA is transported into the cytoplasm and <b>proteins</b> (<i>phelper</i>, <i>pcapwt</i>, <i>pcapmod</i>) are produced. Containing a nuclear localization sequence proteins are relocated into the nucleus where capsid assembly occurs. The viral capsid is compose of 60 subunits of viral coat proteins. Titration of the two plasmids coding for the capsid proteins leads to virus surfaces with different ratios of wild type and modified capsid proteins.<br>
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The third part follows a different approach: X-ray crystallography data (Xie et al. 2002) has been used to reproduce the three dimensional structure of the virus. The resulting 3D visualization is obtained by using the open source software PyMOL (Schrödinger 2010).<br>
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The gene of interest is replicated by cellular polymerases and <b>single stranded DNA</b> (<i>ssDNA</i>) is encapsidated into the preformed <b>capsids</b> (<i>capsid</i>) forming infectious <b>viral particles</b> (<i>V</i>).<br>
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<br>
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Finally the recombinant viruses are released into the extracellular matrix and can be harvested for transduction.
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Click on the pictures below to get to the corresponding modeling pages!
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</p>
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<table>
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<tbody>
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<tr>
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<br><br>
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<td halign="center" valign="top" width="300">
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<a
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href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Virus_Production">
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<h3>Virus Production Model</h3></a>
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<br>
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<center>
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<div style="text-align: center;"><a
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<img width="733" height="966" src="https://static.igem.org/mediawiki/2010/b/b8/Freiburg10_VirusProduction01.png" alt="Reaction scheme for the virus production" />
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href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Virus_Production"><img
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</center>
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src="https://static.igem.org/mediawiki/2010/c/c0/Freiburg10_VirusProductionLogo.png"
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<br><br>
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alt="Virus Production Modeling" width="300"></a></div>
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<h3>Reduced Reaction Scheme</h3>
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</td>
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Even the coarse model for virus production would still consist of 24 ODEs containing 35 parameters i.e. rate constants. Taking into account the linearity of the law of mass action (LMA) we can neglect the fast reactions and for this reason reduce the model to the rate limiting step.
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<td halign="center" valign="top" width="290">
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<a
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href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Virus_Infection">
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<h3>Virus Infection Model</h3></a>
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<br>
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<br><br>
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<div style="text-align: center;"><a
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href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Virus_Infection"><img
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<center>
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src="https://static.igem.org/mediawiki/2010/1/1e/Freiburg10_VirusInfectionLogo.png"
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<img width="733" height="643" src="https://static.igem.org/mediawiki/2010/6/68/Freiburg10_VirusProduction02.png" alt="reduced reaction scheme for the virus production" />
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alt="Virus Infection Modeling" width="300"></a></div>
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</center>
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</td>
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<td halign="center" valign="top" width="290">
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<br><br>
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<a
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<h3>Differential Equations</h3>
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href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Structure_Modeling">
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<center>
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<h3>Structure Modeling</h3></a>
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<img width="739" height="899" src="https://static.igem.org/mediawiki/2010/2/24/Freiburg10_VirusProduction03.png" alt="Reaction scheme for the virus production" />
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<br>
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</center>
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<br><br>
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<h3>Simulation</h3>
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<br><br>
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<h3>Results and Discussion</h3>
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<br><br>
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<h2>Model for Virus Infection</h2>
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-
<br><br>
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<h3>Reaction Scheme</h3>
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<center>
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<img width="359" height="335" src="https://static.igem.org/mediawiki/2010/9/90/Freiburg10_VirusInfection01.png" alt="Reaction scheme for the virus production" />
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-
</center>
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-
<br><br>
+
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<h3>Reduced Reaction Scheme</h3>
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-
<center>
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<img width="359" height="227" src="https://static.igem.org/mediawiki/2010/8/83/Freiburg10_VirusInfection02.png" alt="Reaction scheme for the virus production" />
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</center>
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<br><br>
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<center>
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<img width="429" height="134" src="https://static.igem.org/mediawiki/2010/3/3f/Freiburg10_VirusInfection03.png" alt="Reaction scheme for the virus production" />
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</center>
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<br><br>
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-
 
+
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<h3>Differential Equations</h3>
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-
<center>
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<img width="655" height="314" src="https://static.igem.org/mediawiki/2010/8/85/Freiburg10_VirusInfection04.png" alt="Reaction scheme for the virus production" />
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</center>
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-
<br><br>
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<center>
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<img width="800" height="285" src="https://static.igem.org/mediawiki/2010/8/84/Freiburg10_VirusInfection05.png" alt="Reaction scheme for the virus production" />
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</center>
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 +
<div style="text-align: center;"><a
 +
href="https://2010.igem.org/Team:Freiburg_Bioware/Modeling/Structure_Modeling"><img
 +
src="https://static.igem.org/mediawiki/2010/2/24/Freiburg10_rot250trans.gif"
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alt="Structure Modeling" width="250"></a></div>
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</td>
 +
</tr>
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</tbody>
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</table>
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<br>
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<br>
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<h2>References</h2>
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<br>
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<h3>Mathematical Modeling</h3>
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<ul>
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<li>Bartlett, J.S., Wilcher, R. & Samulski, R.J., 2000. Infectious entry pathway of adeno-associated virus and adeno-associated virus vectors. Journal of virology, 74(6), pp.2777-85. Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=111768&tool=pmcentrez&rendertype=abstract.
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<li>Culshaw, R. V., Ruan, S., & Webb, G. (2003). A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. Journal of mathematical biology, 46(5), 425-44. Springer Berlin / Heidelberg. doi: 10.1007/s00285-002-0191-5.
 +
<li>Endres, D., & Zlotnick, A. (2002). Model-Based Analysis of Assembly Kinetics for Virus Capsids or Other Spherical Polymers. Biophysical Journal, 83(2), 1217-1230. Elsevier. doi: 10.1016/S0006-3495(02)75245-4.
 +
<li>Friedman, A. (2006). Cancer Models and Their Mathematical Analysis. Cancer, 246, 223- 246.
 +
<li>Gurevich, K. G. (2004). Application of methods of identifying receptor binding models and analysis of parameters. Theoretical biology & medical modelling, 1, 11. doi: 10.1186/1742-4682-1-11.
 +
<li>Johnston, I. G., Louis, A. A., & Doye, J. P. K. (2010). Modelling the self-assembly of virus capsids. Journal of Physics: Condensed Matter, 22(10), 104101. doi: 10.1088/0953-8984/22/10/104101.
 +
<li>Komarova, N. L., & Wodarz, D. (2010). ODE models for oncolytic virus dynamics. Journal of Theoretical Biology, 263(4), 530-543. Elsevier. doi: 10.1016/j.jtbi.2010.01.009.
 +
<li>Moradpour, D., Penin, F., & Rice, C. M. (2007). Replication of hepatitis C virus. Nature, 5(June), 453-463. doi: 10.1038/nrmicro1645.
 +
<li>Novozhilov, A. S., Berezovskaya, F. S., Koonin, E. V., & Karev, G. P. (2006). Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models. Biology direct, 1, 6. doi: 10.1186/1745-6150-1-6.
 +
<li>Seisenberger, G. et al., 2001. Real-time single-molecule imaging of the infection pathway of an adeno-associated virus. Science (New York, N.Y.), 294(5548), pp.1929-32. Available at: http://www.ncbi.nlm.nih.gov/pubmed/11729319.
 +
<li>Sidorenko, Y., & Reichl, U. (2004). Structured Model of Influenza Virus Replication in MDCK Cells. Biotechnology and Bioengineering, 88, 1-14. doi: 10.1002/bit.20096.
 +
<li>Sweeney, B., Zhang, T., & Schwartz, R. (2008). Exploring the Parameter Space of Complex Self-Assembly through Virus Capsid Models. Biophysical Journal, 94(3), 772-783. Elsevier. doi: 10.1529/biophysj.107.107284.
 +
<li>Tao, Y., & Guo, Q. (2005). The competitive dynamics between tumor cells, a replication-competent virus and an immune response. Journal of mathematical biology, 51(1), 37-74. doi: 10.1007/s00285-004-0310-6.
 +
<li>Wu, J T, Byrne, H. M., Kirn, D H, & Wein, L M. (2001). Modeling and analysis of a virus that replicates selectively in tumor cells. Bulletin of mathematical biology, 63(4), 731-68. doi: 10.1006/bulm.2001.0245.
 +
<li>Wu, Joseph T, Kirn, David H, & Wein, Lawrence M. (2004). Analysis of a three-way race between tumor growth, a replication-competent virus and an immune response. Bulletin of mathematical biology, 66(4), 605-25. doi: 10.1016/j.bulm.2003.08.016.
 +
<li>Zlotnick, Adam. (1997). To Build a Virus Capsid. Journal of molecular biology.
 +
</ul>
 +
<br>
 +
<h3>Structure Modeling</h3>
 +
<ul>
 +
<li>Schrödinger, L., 2010. The {PyMOL} Molecular Graphics System, Version~1.3r1.
 +
<li>Xie, Q. et al., 2002. The atomic structure of adeno-associated virus (AAV-2), a vector for human gene therapy. Proceedings of the National Academy of Sciences of the United States of America, 99(16), pp.10405-10. Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=124927&tool=pmcentrez&rendertype=abstract.
 +
<li>Xie, Q. et al., 2003. Structure determination of adeno-associated virus 2: three complete virus particles per asymmetric unit. Acta Crystallographica Section D Biological Crystallography, 59(6), pp.959-970. Available at: http://scripts.iucr.org/cgi-bin/paper?S0907444903005675.
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</ul>
</html>
</html>
{{:Team:Freiburg_Bioware/Footer}}
{{:Team:Freiburg_Bioware/Footer}}

Latest revision as of 01:24, 28 October 2010

Modeling



Introduction

Our modeling part consists of two main parts:


The first model describes the dynamic behavior of the virus production in terms of the law of mass action (Sidorenko & Reichl 2004). Therefore the temporal changes in concentrations of titrated plasmids, synthesized proteins, replicated single-stranded DNA and formed virus capsids and finally concentration of viral particles are simulated using MathWorks® MATLAB R2010b.
Virus infection is modeled in a similar way but receptor binding has to be considered (Gurevich 2004). Starting with a given concentration of infectious virus particles, complexes with dimerized receptors emerge which can be internalized to the cytoplasm and transduction takes place.
The third part follows a different approach: X-ray crystallography data (Xie et al. 2002) has been used to reproduce the three dimensional structure of the virus. The resulting 3D visualization is obtained by using the open source software PyMOL (Schrödinger 2010).

Click on the pictures below to get to the corresponding modeling pages!

Virus Production Model
Virus Production Modeling

Virus Infection Model
Virus Infection Modeling

Structure Modeling
Structure Modeling


References


Mathematical Modeling

  • Bartlett, J.S., Wilcher, R. & Samulski, R.J., 2000. Infectious entry pathway of adeno-associated virus and adeno-associated virus vectors. Journal of virology, 74(6), pp.2777-85. Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=111768&tool=pmcentrez&rendertype=abstract.
  • Culshaw, R. V., Ruan, S., & Webb, G. (2003). A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. Journal of mathematical biology, 46(5), 425-44. Springer Berlin / Heidelberg. doi: 10.1007/s00285-002-0191-5.
  • Endres, D., & Zlotnick, A. (2002). Model-Based Analysis of Assembly Kinetics for Virus Capsids or Other Spherical Polymers. Biophysical Journal, 83(2), 1217-1230. Elsevier. doi: 10.1016/S0006-3495(02)75245-4.
  • Friedman, A. (2006). Cancer Models and Their Mathematical Analysis. Cancer, 246, 223- 246.
  • Gurevich, K. G. (2004). Application of methods of identifying receptor binding models and analysis of parameters. Theoretical biology & medical modelling, 1, 11. doi: 10.1186/1742-4682-1-11.
  • Johnston, I. G., Louis, A. A., & Doye, J. P. K. (2010). Modelling the self-assembly of virus capsids. Journal of Physics: Condensed Matter, 22(10), 104101. doi: 10.1088/0953-8984/22/10/104101.
  • Komarova, N. L., & Wodarz, D. (2010). ODE models for oncolytic virus dynamics. Journal of Theoretical Biology, 263(4), 530-543. Elsevier. doi: 10.1016/j.jtbi.2010.01.009.
  • Moradpour, D., Penin, F., & Rice, C. M. (2007). Replication of hepatitis C virus. Nature, 5(June), 453-463. doi: 10.1038/nrmicro1645.
  • Novozhilov, A. S., Berezovskaya, F. S., Koonin, E. V., & Karev, G. P. (2006). Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models. Biology direct, 1, 6. doi: 10.1186/1745-6150-1-6.
  • Seisenberger, G. et al., 2001. Real-time single-molecule imaging of the infection pathway of an adeno-associated virus. Science (New York, N.Y.), 294(5548), pp.1929-32. Available at: http://www.ncbi.nlm.nih.gov/pubmed/11729319.
  • Sidorenko, Y., & Reichl, U. (2004). Structured Model of Influenza Virus Replication in MDCK Cells. Biotechnology and Bioengineering, 88, 1-14. doi: 10.1002/bit.20096.
  • Sweeney, B., Zhang, T., & Schwartz, R. (2008). Exploring the Parameter Space of Complex Self-Assembly through Virus Capsid Models. Biophysical Journal, 94(3), 772-783. Elsevier. doi: 10.1529/biophysj.107.107284.
  • Tao, Y., & Guo, Q. (2005). The competitive dynamics between tumor cells, a replication-competent virus and an immune response. Journal of mathematical biology, 51(1), 37-74. doi: 10.1007/s00285-004-0310-6.
  • Wu, J T, Byrne, H. M., Kirn, D H, & Wein, L M. (2001). Modeling and analysis of a virus that replicates selectively in tumor cells. Bulletin of mathematical biology, 63(4), 731-68. doi: 10.1006/bulm.2001.0245.
  • Wu, Joseph T, Kirn, David H, & Wein, Lawrence M. (2004). Analysis of a three-way race between tumor growth, a replication-competent virus and an immune response. Bulletin of mathematical biology, 66(4), 605-25. doi: 10.1016/j.bulm.2003.08.016.
  • Zlotnick, Adam. (1997). To Build a Virus Capsid. Journal of molecular biology.

Structure Modeling

  • Schrödinger, L., 2010. The {PyMOL} Molecular Graphics System, Version~1.3r1.
  • Xie, Q. et al., 2002. The atomic structure of adeno-associated virus (AAV-2), a vector for human gene therapy. Proceedings of the National Academy of Sciences of the United States of America, 99(16), pp.10405-10. Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=124927&tool=pmcentrez&rendertype=abstract.
  • Xie, Q. et al., 2003. Structure determination of adeno-associated virus 2: three complete virus particles per asymmetric unit. Acta Crystallographica Section D Biological Crystallography, 59(6), pp.959-970. Available at: http://scripts.iucr.org/cgi-bin/paper?S0907444903005675.

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