Abstract
By building kinetic models of biological networks one may advance the development of new modeling approaches while gaining insights into the biology. We focus here on building a stochastic kinetic model for the intracellular growth of vesicular stomatitis virus (VSV), a well-studied virus that encodes five genes. The essential network of VSV reactions creates challenges to stochastic simulation owing to (i) delayed reactions associated with transcription and genome replication, (ii) production of large numbers of intermediate proteins by translation, and (iii) the presence of highly reactive intermediates that rapidly fluctuate in their intracellular levels. We address these issues by developing a hybrid implementation of the model that combines a delayed stochastic simulation algorithm (DSSA) with Langevin equations to simulate the reactions that produce species in high numbers. Further, we employ a quasi-steady-state approximation (QSSA) to overcome the computational burden of small time steps caused by highly reactive species. The simulation is able to capture experimentally observed patterns of viral gene expression. Moreover, the simulation suggests that early levels of a low-abundance species, VSV L mRNA, play a key role in determining the production level of VSV genomes, transcripts, and proteins within an infected cell. Ultimately, these results suggest that stochastic gene expression contribute to the distribution of virus progeny yields from infected cells.
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References
Abraham, G., Banerjee, A.K., 1976. Sequential transcription of the genes of vesicular stomatitis virus. Proc. Natl. Acad. Sci. USA 73(5), 1504–1508.
Arkin, A., Ross, J., McAdams, H., 1998. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149(4), 1633–1648.
Ball, L.A., White, C.N., 1976. Order of transcription of genes of vesicular stomatitis virus. Proc. Natl. Acad. Sci. USA 73(2), 442–446.
Barr, J.N., Whelan, S.P.J., Wertz, G.W., 2002. Transcriptional control of the RNA-dependent RNA polymerase of vesicular stomatitis virus. Biochim. Biophys. Acta, Gene Struct. Expr. 1577(2), 337–353.
Barrio, M., Burrage, K., Leier, A., Tian, T., 2006. Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation. PLoS Comput. Biol. 2(9), e117.
Bratsun, D., Volfson, D., Tsimring, L.S., Hasty, J., 2005. Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. USA 102(41), 14593–14598.
Delbrück, M., 1940. Statistical fluctuations in autocatalytic reactions. J. Chem. Phys. 8, 120–124.
Delbrück, M., 1945. The burst size distribution in the growth of bacterial viruses (bacteriophages). J. Bact. 50, 131–135.
E, W., Liu, D., Vanden-Eijnden, E., 2005. Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J. Chem. Phys. 123, 194107.
Flanagan, E.B., Ball, L.A., Wertz, G.W., 2000. Moving the glycoprotein gene of vesicular stomatitis virus to promoter-proximal positions accelerates and enhances the protective immune response. J. Virol. 74(17), 7895–7902.
Gillespie, D.T., 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434.
Gillespie, D.T., 1992. A rigorous derivation of the chemical master equation. Physica A 188, 404–425.
Gillespie, D.T., 2000. The chemical Langevin equation. J. Chem. Phys. 113(1), 297–306.
Goutsias, J., 2005. Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 122(18), 184102.
Griffith, M., Courtney, T., Peccoud, J., Sanders, W., 2006. Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network. Bioinformatics 22(22), 2782–2789.
Haseltine, E.L., Rawlings, J.B., 2002. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117(15), 6959–6969.
Iverson, L.E., Rose, J.K., 1981. Localized attenuation and discontinuous synthesis during vesicular stomatitis virus transcription. Cell 23(2), 477–484.
Janssen, J.A.M., 1989. The elimination of fast variables in complex chemical reactions. II. Mesoscopic level (reducible case). J. Stat. Phys. 57(1/2), 171–185.
Lim, K., Lang, T., Lam, V., Yin, J., 2006. Model-based design of growth-attenuated viruses. PLoS Comput. Biol. 2(9), e116.
Mastny, E.A., Haseltine, E.L., Rawlings, J.B., 2007. Two classes of quasi-steady-state model reductions for stochastic kinetics. J. Chem. Phys. 127(9), 094106.
Rao, C.V., Arkin, A.P., 2003. Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys. 118(11), 4999–5010.
Rose, J., Whitt, M., 2001. Rhabdoviridae: The viruses and their replication. In: Knipe, D., Howley, P. (Eds.), Fields Virology, vol. 1, 4th edn. pp. 1221–1244. Lippincot Williams & Wilkins, Philadelphia.
Salis, H., Kaznessis, Y., 2005a. Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 122(5), 054103.
Salis, H., Kaznessis, Y., 2005b. An equation-free probabilistic steady-state approximation: Dynamic application to the stochastic simulation of biochemical reaction networks. J. Chem. Phys. 123, 214106.
Samant, A., Vlachos, D.G., 2005. Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm. J. Chem. Phys. 123, 144114.
Samant, A., Ogunnaike, B., Vlachos, D., 2007. A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks. BMC Bioinf. 8(1), 175.
Simonsen, C.C., Batt-Humphries, S., Summers, D., 1979. RNA synthesis of vesicular stomatitis virus-infected cells: In vivo regulation of replication. J. Virol. 31(1), 124–132.
Spirin, A., 1986. Ribosome Structure and Protein Biosysthesis. Benjamin/Cummings, Redwood City.
Srivastava, R., You, L., Summers, J., Yin, J., 2002. Stochastic vs. deterministic modeling of intracellular viral kinetics. J. Theor. Biol. 218, 309–321.
van Kampen, N.G., 1992. Stochastic Processes in Physics and Chemistry, 2nd edn. Elsevier, Amsterdam.
Villarreal, L.P., Breindl, M., Holland, J.J., 1976. Determination of molar ratios of vesicular stomatitis virus induced RNA species in BHK21 cells. Biochemistry 15(8), 1663–1667.
Weinberger, L.S., Burnett, J.C., Toettcher, J.E., Arkin, A.P., Schaffer, D.V., 2005. Stochastic gene expression in a lentiviral positive-feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity. Cell 122(2), 169–182.
Werner, M., 1991. Kinetic and thermodynamic characterization of the interaction between Q beta-replicase and template RNA molecules. Biochemistry 30(24), 5832–5838.
Zhu, Y., Yongky, A., Yin, J., 2009. Growth of an RNA virus in single cells reveals a broad fitness distribution. Virology 385(1), 39–46.
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Hensel, S.C., Rawlings, J.B. & Yin, J. Stochastic Kinetic Modeling of Vesicular Stomatitis Virus Intracellular Growth. Bull. Math. Biol. 71, 1671–1692 (2009). https://doi.org/10.1007/s11538-009-9419-5
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DOI: https://doi.org/10.1007/s11538-009-9419-5