Abstract
Modern experimental methods such as flow cytometry and fluorescence in-situ hybridization (FISH) allow the measurement of cell-by-cell molecule numbers for RNA, proteins and other substances for large numbers of cells at a time, opening up new possibilities for the quantitative analysis of biological systems. Of particular interest is the study of biological reaction systems describing processes such as gene expression, cellular signalling and metabolism on a molecular level. It is well established that many of these processes are inherently stochastic [1,2,3] and that deterministic approaches to their study can fail to capture properties essential for our understanding of these systems [4, 5]. Despite recent technological and conceptual advances, modelling and inference for stochastic models of reaction networks remains challenging due to additional complexities not present in the deterministic case. The Chemical Master Equation (CME) [6] in particular, while frequently used to model many types of reaction networks, is difficult to solve exactly, and parameter inference in practice often relies on a variety of approximation schemes whose accuracy can vary widely and unpredictably depending on the context [6,7,8].
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References
Elowitz, M.B.: Stochastic gene expression in a single cell. Science 297(5584), 1183–1186 (2002)
Choi, P.J., Cai, L., Frieda, K., Xie, X.S.: A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322(5900), 442–446 (2008)
Kiviet, D.J., Nghe, P., Walker, N., Boulineau, S., Sunderlikova, V., Tans, S.J.: Stochasticity of metabolism and growth at the single-cell level. Nature 514(7522), 376–379 (2014)
Morton-Firth, C.J., Bray, D.: Predicting temporal fluctuations in an intracellular signalling pathway. J. Theor. Biol. 192(1), 117–128 (1998)
McAdams, H.H., Arkin, A.: It’s a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 15(2), 65–69 (1999)
van Kampen, N.: Stochastic Processes in Physics and Chemistry, 3rd edn. Elsevier, Amsterdam (2007)
Cao, Z., Grima, R.: Linear mapping approximation of gene regulatory networks with stochastic dynamics. Nat. Commun. 9(1), 3305 (2018)
Schnoerr, D., Sanguinetti, G., Grima, R.: Comparison of different moment-closure approximations for stochastic chemical kinetics. J. Chem. Phys. 143(18), 185101 (2015)
Zechner, C., et al.: Moment-based inference predicts bimodality in transient gene expression. Proc. Nat. Acad. Sci. 109(21), 8340–8345 (2012)
Ruess, J., Lygeros, J.: Moment-based methods for parameter inference and experiment design for stochastic biochemical reaction networks. ACM Trans. Model. Comput. Simul. 25(2), 8:1–8:25 (2015)
Fröhlich, F., Thomas, P., Kazeroonian, A., Theis, F.J., Grima, R., Hasenauer, J.: Inference for stochastic chemical kinetics using moment equations and system size expansion. PLOS Comput. Biol. 12(7), e1005030 (2016)
Cinquemani, E.: Identifiability and reconstruction of biochemical reaction networks from population snapshot data. Processes 6(9), 136 (2018)
Marguerat, S., Schmidt, A., Codlin, S., Chen, W., Aebersold, R., Bähler, J.: Quantitative analysis of fission yeast transcriptomes and proteomes in proliferating and quiescent cells. Cell 151(3), 671–683 (2012)
Schnoerr, D., Sanguinetti, G., Grima, R.: Validity conditions for moment closure approximations in stochastic chemical kinetics. J. Chem. Phys. 141(8), 084103 (2014)
Schilling, C., Bogomolov, S., Henzinger, T.A., Podelski, A., Ruess, J.: Adaptive moment closure for parameter inference of biochemical reaction networks. Biosystems 149, 15–25 (2016)
Neuert, G., Munsky, B., Tan, R.Z., Teytelman, L., Khammash, M., Oudenaarden, A.V.: Systematic identification of signal-activated stochastic gene regulation. Science 339(6119), 584–587 (2013)
Munsky, B., Li, G., Fox, Z.R., Shepherd, D.P., Neuert, G.: Distribution shapes govern the discovery of predictive models for gene regulation. Proc. Nat. Acad. Sci. 115(29), 7533–7538 (2018)
Villani, C.: Optimal Transport: Old and New. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (2009). https://doi.org/10.1007/978-3-540-71050-9
Peyré, G., Cuturi, M.: Computational optimal transport. Found. Trends Mach. Learn. 11(5–6), 355–607 (2019)
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)
Shahrezaei, V., Swain, P.S.: Analytical distributions for stochastic gene expression. Proc. Nat. Acad. Sci. 105(45), 17256–17261 (2008)
Cao, Z., Grima, R.: Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data. J. Roy. Soc. Interface 16(153), 20180967 (2019)
Leclercq, F.: Bayesian optimisation for likelihood-free cosmological inference. Phys. Rev. D 98(6), 063511 (2018)
Tanaka, R., Iwata, H.: Bayesian optimization for genomic selection: a method for discovering the best genotype among a large number of candidates. Theor. Appl. Genet. 131(1), 93–105 (2018)
Bortolussi, L., Sanguinetti, G.: Learning and designing stochastic processes from logical constraints. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 89–105. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40196-1_7
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This work was supported in part by the EPSRC Centre for Doctoral Training in Data Science, funded by the UK Engineering and Physical Sciences Research Council (grant EP/L016427/1) and the University of Edinburgh.
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Öcal, K., Grima, R., Sanguinetti, G. (2019). Wasserstein Distances for Estimating Parameters in Stochastic Reaction Networks. In: Bortolussi, L., Sanguinetti, G. (eds) Computational Methods in Systems Biology. CMSB 2019. Lecture Notes in Computer Science(), vol 11773. Springer, Cham. https://doi.org/10.1007/978-3-030-31304-3_24
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