Citation: Giorgos Minas, David A Rand. Parameter sensitivity analysis for biochemical reaction networks[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3965-3987. doi: 10.3934/mbe.2019196
[1] | J-T Hwang, E. P. Dougherty, S. Rabitz, et al., The Green's function method of sensitivity analysis in chemical kinetics, J. Chem. Phys., 69 (1978), 5180–5191. |
[2] | J. Stelling, U. Sauer, Z. Szallasi, et al., Robustness of Cellular Functions, Cell, 118 (2004), 675–685. |
[3] | R. N. Gutenkunst, J. J. Waterfall, F. P. Casey, et al., Universally Sloppy Parameter Sensitivities in Systems Biology Models, PLoS Comput. Biol., 3 (2007), e189. |
[4] | M. B. Elowitz, A. J. Levine, E. D. Siggia, et al., Stochastic Gene Expression in a Single Cell,Science, 297 (2002), 1183–1186. |
[5] | J. K. Kim and J. C. Marioni, Inferring the kinetics of stochastic gene expression from single-cell RNA-sequencing data, Genome. Biol., 14 (2013), R7. |
[6] | F. Wimmers, N. Subedi, N. van Buuringen, et al., Single-cell analysis reveals that stochasticity and paracrine signaling control interferon-alpha production by plasmacytoid dendritic cells, Nature Commun., 9 (2018), 3317. |
[7] | S. Plyasunov and A. P. Arkin, Efficient stochastic sensitivity analysis of discrete event systems, J. Comput. Phys., 221 (2007), 724–738. |
[8] | D. F. Anderson, An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains, SIAM J. Numer. Anal. 50 (2012), 2237–2258. |
[9] | E. S. Wolf and D. F. Anderson, A finite difference method for estimating second order parameter sensitivities of discrete stochastic chemical reaction networks, J. Chem. Phys., 137 (2012), 224112. |
[10] | A. Gupta, M. Rathinam and M. Khammash, Estimation of parameter sensitivities for stochastic reaction networks using tau-leap simulations, SIAM J. Numer. Anal., 56 (2014), 1134–1167. |
[11] | P. Bauer and S. Engblom, Sensitivity estimation and inverse problems in spatial stochastic models of chemical kinetics, Numerical Mathematics and Advanced Applications: ENUMATH 2013, A. AbdulleandS.DeparisandD.KressnerandF.NobileandM.Picasso(eds), 103(2015), 519–527. |
[12] | A. Gupta and M. Khammash, Sensitivity Analysis for Multiscale Stochastic Reaction Networks Using Hybrid Approximations, Bull. Math. Biol., (2018), 1–38. |
[13] | D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), 2340–2361. |
[14] | N. G. van Kampen, Stochastic Processes in Physics and Chemistry, Third Edition, Amsterdam: Elsevier. Boston and London: Elsevier; 2007. |
[15] | Y. Cao, D. T. Gillespie and L. R. Petzold, Efficient step size selection for the tau-leaping simulation method, J. Chem. Phys., 124 (2006), 044109. |
[16] | D. T. Gillespie, The chemical Langevin equation, J. Chem. Phys., 113 (2000), 297–306. |
[17] | M. Scott, B. Ingalls and M. Kærn, Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks, Chaos, 16 (2006), 026107. |
[18] | R. Grima, Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems, Phys. Rev. E., 92 (2015), 042124. |
[19] | M. Komorowski, B. Finkenstädt, C. V. Harper, et al., Bayesian inference of biochemical kinetic parameters using the linear noise approximation, BMC Bioinform., 10 (2009), 343. |
[20] | B. Finkenstädt, D. J. Woodcock, M. Komorowski, et al., Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data, Ann. Appl. Stat., 7 (2013), 1960–1982. |
[21] | V. Stathopoulos and M. A. Girolami, Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation, Philos. Transact. A Math. Phys. Eng. Sci., 371 (2013), 20110541. |
[22] | P. Fearnhead, V. Giagos and C. Sherlock, Inference for reaction networks using the linear noise approximation Biometrics, 70 (2014), 457–466. |
[23] | M. Komorowski, M. J. Costa, D. A. Rand, et al., Sensitivity, robustness, and identifiability in stochastic chemical kinetics models P. Natl. Acad. Sci. USA, 108 (2011), 8645–8650. |
[24] | K. Tomita, T. Ohta and H. Tomita, Irreversible Circulation and Orbital Revolution: Hard Mode Instability in Far-from-Equilibrium Situation, Prog. Theor. Phys., 52 (1974), 1744–1765. |
[25] | R. P. Boland, T. Galla and A. J. McKane. How limit cycles and quasi-cycles are related in systems with intrinsic noise, J. Stat. Mech., 09 (2008), P09001. |
[26] | Y. Ito and K. Uchida, Formulas for intrinsic noise evaluation in oscillatory genetic networks, J. Theor. Biol., 267 (2010), 223–234. |
[27] | G. Minas and D. A. Rand, Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference, PLoS Comput. Biol., 13 (2017), e1005676. |
[28] | D. A. Rand, Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law, J. R. Soc. Interface, 5 (2008), S59–S69. |
[29] | I. Prigogine and R. Lefever, Symmetry Breaking Instabilities in Dissipative Systems. II., J. Chem. Phys., 48 (1968), 1695–1700. |
[30] | D. Gonze, J. Halloy, J. C. Leloup, et al., Stochastic model for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour, CR Biol., 326 (2003), 189–203. |
[31] | T. M. Cover and J. A. Thomas, Elements of information theory (Wiley Series in Telecommunications and Signal Processing), 2nd edition, Wiley-Interscience New York, NY, USA, 2006. |
[32] | R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991. |
[33] | D. T. Gillespie, A rigorous derivation of the chemical master equation, Physica A, 188 (1992), 404–425. |
[34] | D. T. Gillespie, The chemical Langevin equation, J. Chem. Phys. , 113 (2000), 297–306. |
[35] | D. F. Anderson and T. G. Kurtz, Continuous Time Markov Chain Models for Chemical Reaction Networks, in Design and Analysis of Biomolecular Circuits: Engineering Approaches to Systems and Synthetic Biology (eds. H. Koeppl, G. Setti, M. di Bernardo, D. Densmore) New York: Springer (2011). |
[36] | T. G. Kurtz, Limit Theorems for Sequences of Jump Markov Processes Approximating Ordinary Differential Processes, J. Appl. Probab., 8 (1971), 344–356. |
[37] | T. G. Kurtz, Approximation of Population Processes, Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics. 36 (1981). |
[38] | A. Gupta and M. Khammash, An efficient and unbiased method for sensitivity analysis of stochastic reaction networks, J. R. Soc. Interface, 11 (2014), 20140979. |
[39] | E. W. J. Wallace, D. T. Gillespie, K. R. Sanft, et al., Linear noise approximation is valid over limited times for any chemical system that is sufficiently large, IET Syst. Biol., 6 (2012), 102–115. |
[40] | T. Philipp, M. Hannes and R. Grima, How reliable is the linear noise approximation of gene regulatory networks? BMC Genomics, 14, S5. |