Abstract
Chemical reactions in small-volume reactors such as biological cells are highly variable due to the stochastic collision events of the small number of molecules. To analyze and design these stochastic biomolecular reactions, computational tools have been developed based on rigorous mathematical foundations. This paper reviews fundamental theory and computational tools for the modeling, analysis, and design of stochastic biomolecular systems. Specifically, we first review the governing equation of the stochastic kinetics using the first principle modeling. Then, three computational approaches are introduced for simulating and/or analyzing the governing equation.
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Carter, A.H.: Classical and Statistical Thermodynamics. Pearson Education International, Upper Saddle River (2001)
Dowdy, G.R., Barton, P.I.: Bounds on stochastic chemical kinetic systems at steady state. J. Chem. Phys. 148(8), 084106 (2018)
Dowdy, G.R., Barton, P.I.: Dynamic bounds on stochastic chemical kinetic systems using semidefinite programming. J. Chem. Phys. 149(7), 074103 (2018)
Eldar, A., Elowitz, M.B.: Functional roles for noise in genetic circuits. Nature 467(2), 167–173 (2010)
Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S.: Stochastic gene expression in a single cell. Science 297(5584), 1183–1186 (2002)
Gardner, T.S., Cantor, C.R., Collins, J.J.: Construction of a genetic toggle switch in Escherichia coli. Nature 403(6767), 339–342 (2000)
Ghusinga, K.R., Vargas-Garcia, C.A., Lamperski, A., Singh, A.: Exact lower and upper bounds on stationary moments in stochastic biochemical systems. Phys. Biol. 14(4), 04LT01 (2017)
Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22(4), 403–434 (1976)
Gillespie, D.T.: A rigorous derivation of the chemical master equation. Physica A 188(1–3), 404–425 (1992)
Hsiao, V., Hori, Y., Rothemund, P.W.K., Murray, R.M.: A population-based temporal logic gate for timing and recording chemical events. Mol. Syst. Biol. 12, 869 (2016)
Kuntz, J., Thomas, P., Stan, G.-B., Barahona, M.: Bounding the stationary distributions of the chemical master equation via mathematical programming. J. Chem. Phys. 151(3), 034109 (2019)
Lakatos, E., Ale, A., Kirk, P.D.W., Stumpf, M.P.H.: Multivariate moment closure techniques for stochastic kinetic models. J. Chem. Phys. 143(9), 094107 (2015)
Lasserre, J.-B., Prieto-Rumeau, T.: SDP vs. LP relaxations for the moment approach in some performance evaluation problems. Stochastic Models 20(4), 439–456 (2014)
McAdams, H.H., Arkin, A.: Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94(3), 814–819 (1997)
Niederholtmeyer, H., Sun, Z., Hori, Y., Yeung, E., Verpoorte, A., Murray, R.M., Maerkl, S.J.: Rapid cell-free forward engineering of novel genetic ring oscillators. eLife 4, e09771 (2015)
Raj, A., van Oudenaarden, A.: Stochastic gene expression and its consequences. Cell 135(2), 216–226 (2008)
Raser, J.M., O’Shea, E.K.: Noise in gene expression: origins, consequences and control. Science 309(5743), 2010–2013 (2005)
Sakurai, Y., Hori, Y.: A convex approach to steady state moment analysis for stochastic chemical reactions. In: Proceedings of IEEE Conference on Decision and Control, pp. 1206–1211 (2017)
Sakurai, Y., Hori, Y.: Optimization-based synthesis of stochastic biocircuits with statistical specifications. J. R. Soc. Interface 15(138), 20170709 (2018)
Sakurai, Y., Hori, Y.: Bounding transient moments of stochastic chemical reactions. IEEE Control Syst. Lett. 3(2), 290–295 (2019)
Singh, A., Hespanha, J.P.: Lognormal moment closures for biochemical reactions. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 2063–2068 (2006)
Singh, A., Hespanha, J.P.: A derivative matching approach to moment closure for the stochastic logistic model. Bull. Math. Biol. 69(6), 1909–1925 (2007)
Singh, A., Hespanha, J.P.: Approximate moment dynamics for chemically reacting systems. IEEE Trans. Autom. Control 56(2), 414–418 (2011)
Smith, H.L.: Monotone dynamical system: an introduction to the theory of com-petitive and cooperative systems. American Mathematical Society, Providence (1995)
Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11–12, 625–653 (1999)
Toh, K.C., Todd, M.J., Tütüncü, R.H.: SDPT3—a Matlab software package for semidefinite programming, version 1.3. Optim. Methods Softw. 11, 545–581 (1999)
Zhao, Y.-B., Kim, J., Hespanha, J.P.: Hybrid moment computation algorithm for biochemical reaction networks. In: Proceedings of IEEE Conference on Decision and Control, pp. 1693–1698 (2010)
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Hori, Y. Modeling and Analysis of Stochastic Reaction Kinetics in Biomolecular Systems. New Gener. Comput. 38, 367–377 (2020). https://doi.org/10.1007/s00354-020-00095-y
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DOI: https://doi.org/10.1007/s00354-020-00095-y