
Mathematical Biosciences and Engineering, 2019, 16(5): 39653987. doi: 10.3934/mbe.2019196.
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Parameter sensitivity analysis for biochemical reaction networks
1 School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
2 Mathematics Institute & Zeeman Institute for Systems Biology and Infectious Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK
Received: , Accepted: , Published:
Special Issues: Mathematical Methods in the Biosciences
Keywords: parameter sensitivity analysis; reaction networks; oscillation; molecular biology
Citation: Giorgos Minas, David A Rand. Parameter sensitivity analysis for biochemical reaction networks. Mathematical Biosciences and Engineering, 2019, 16(5): 39653987. doi: 10.3934/mbe.2019196
References:
 1. JT 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 singlecell RNAsequencing data, Genome. Biol., 14 (2013), R7.
 6. F. Wimmers, N. Subedi, N. van Buuringen, et al., Singlecell analysis reveals that stochasticity and paracrine signaling control interferonalpha 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 tauleap 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 tauleaping 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, Linearnoise approximation and the chemical master equation agree up to secondorder 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 FarfromEquilibrium Situation, Prog. Theor. Phys., 52 (1974), 1744–1765.
 25. R. P. Boland, T. Galla and A. J. McKane. How limit cycles and quasicycles 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, Longtime 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, WileyInterscience 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.
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