Accounting for extrinsic variability in the estimation of stochastic rate constants

International Journal of Robust and Nonlinear Control

Volumn 22, Issue 10, 2012, Pages 1103-1119

  Koeppl, Heinz ^a   Zechner, Christoph ^a   Ganguly, Arnab ^a   Pelet, Serge ^a   Peter, Matthias ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Bayesian estimation; cell to cell variability; MAPK Hog1 signaling pathway; mass conservation; stochastic chemical kinetics

Indexed keywords

BAYESIAN ESTIMATIONS; BAYESIAN INFERENCE; CELL CYCLE; CELL VOLUME; CELL-TO-CELL VARIABILITY; CELLULAR EVENTS; EXPERIMENTAL DATA; EXTRINSIC FACTORS; ISOGENIC CELLS; MASS CONSERVATION; MOLECULAR NOISE; NOISE SOURCE; PARAMETER INFERENCE; POST-TRANSCRIPTIONAL PROCESS; SIGNALING PATHWAYS; STATISTICAL INFORMATION; STOCHASTIC KINETICS; STOCHASTICITY; TRANSCRIPTIONAL ACTIVATIONS; TWO SOURCES;

BAYESIAN NETWORKS; CELL CULTURE; CELL PROLIFERATION; INFERENCE ENGINES; KINETICS; RATE CONSTANTS; STOCHASTIC SYSTEMS;

CELLS;

EID: 84861650075     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.2804     Document Type: Article

References (37)

1. Altschuler SJ, Wu LF,. Cellular heterogeneity: do differences make a difference. Cell 2010; 141: 559-563.
2. Rao C, Wolf D, Arkin A,. Control, exploitation and tolerance of intracellular noise. Nature 2002; 420: 231-237.
3. Elowitz MB, Levine AJ, Siggia ED, Swain PS,. Stochastic gene expression in a single cell. Science 2002; 297: 1183-1186.
4. Blake WJ, Kearns N, Cantor CR, Collins JJ,. Noise in eukaryotic gene expression. Nature 2003; 442: 633-637.
5. Paliwal S, Iglesias P, Campell K, Hilioti Z, Groisman A, Levchenko A,. MAPK-mediated bimodal gene expression and adaptive gradient sensing in yeast. Nature 2007; 446: 46-51.
6. Pelet S, Rudolf F, Nadal-Ribelles M, deNadal E, Posas F, Peter M,. Transient activation of the HOG MAPK pathway regulates bimodal gene expression. Science 2011; 332 (6030): 732-735. DOI: 10.1126/science.1198851.
7. McQuarrie DA,. Stochastic approach to chemical kinetics. Journal of Applied Probability 1967; 4 (3): 413-478.
8. Colman-Lerner A, Gordon A, Serra E, Chin T, Resnekov O, Endy D, Pesce G, Brent R,. Regulated cell-to-cell variation in a cell-fate decision system. Nature 2005; 437 (29): 699-502.
9. Raser JM, O'Shear EK,. Control of stochasticity in eukaryotic gene expression. Science 2004; 304: 1811-1814.
10. Yanagida T, Ishii Y, (eds). Single-molecule dynamics in life science. Wiley-VCH: Weinheim, 2009.
11. Raj A, van Oudenaarden A,. Single-molecule approaches to stochastic gene expression. Annual Review of Biophysics 2009; 38: 255-270.
12. Boys RJ, Wilkinson DJ, Kirkwood TBL,. Bayesian inference for a discretely observed stochastic kinetic model. Statistics and Computing 2008; 18 (2): 125-135.
13. Reinker S, Altman RM, Timmer J,. Parameter estimation in stochastic biochemical reactions. IEE Proceedings-Systems Biology 2006; 153 (4): 168-178.
14. Golightly A, Wilkinson DJ,. Bayesian inference for nonlinear multivariate diffusion models observed with error. Computational Statistics & Data Analysis 2008; 83: 1891-1901.
15. Wang Y, Christley S, Mjolsness E, Xie X,. Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent. BMC Systems Biology 2010; 4 (1): 99. DOI: 10.1186/1752-0509-4-99.
16. Ruttor A, Sanguinetti G, Opper M,. Approximate inference for stochastic reaction processes. In Learning and Inference in Computational Systems Biology. The MIT Press: Cambridge, MA, 2009 189-205.
17. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MPH,. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface 2009; 6 (31): 187-2022.
18. Rachev ST,. Probability metrics and the stability of stochastic models, Probability and Mathematical Statistics. Wiley: New York, 1991.
19. Thorsley D, Klavins E,. Model reduction of stochastic processes using Wasserstein pseudometrics. Proceedings of the American Control Conference, Seattle, Washington, USA, 2008; 1374-1381.
20. Koeppl H, Setti G, Mangia M, Petrov T, Pelet S, Peter M,. Probability metrics to calibrate stochastic chemical kinetics. IEEE Symposium on Circuits and Systems, Paris, France, 2010; 541-544.
21. Hasenauer J, Waldherr S, Radde N, Doszczak M, Allgoewer F,. A maximum likelihood estimator for parameter distributions in heterogeneous cell populations. Procedia Computer Science 2010; 1: 1655-1663.
22. Wilkinson DJ,. Stochastic Modelling for Systems Biology (Chapman & Hall/CRC Mathematical & Computational Biology), 1st edn. Chapman and Hall/CRC: London, UK, 2006.
23. Anderson DF, Ganguly A, Kurtz TG,. Error analysis of tau-leap simulation methods. Annals of Applied Probability 2011; 21 (6): 2226-2262.
24. Anderson DF, Kurtz TG,. Continuous time Markov chain models for chemical reaction networks. In Design and Analysis of Biomolecular Circuits. Springer: New York City, 2011 3-42.
25. Hastings WK,. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57 (1): 97-109. DOI: 10.1093/biomet/57.1.97.
26. Hohmann S, Krantz M, Nordlander B,. Yeast osmoregulation. Methods in Enzymology 2007; 428: 29-45.
27. Capaldi AP, Kaplan T, Liu Y, Habib N, Regev A, Friedman N, O'Shea EK,. Structure and function of a transcriptional network activated by the MAPK Hog1. Nature Genetics 2008; 40 (11): 1300-1306.
28. Schaber J, Adrover MA, Eriksson E, Pelet S, Petelenz-Kurdziel E, Klein D, Posas F, Goksör M, Peter M, Hohmann S, et al., Biophysical properties of saccharomyces cerevisiae and their relationship with HOG pathway activation. European Biophysics Journal 2010; 39 (11): 1547-1556.
29. deNadal E, Posas F,. Multilayered control of gene expression by stress-activated protein kinases. The EMBO Journal 2010; 29 (1): 4-13.
30. Gillespie DT,. A rigorous derivation of the chemical master equation. Physica A 1992; 188: 404-425.
31. Bishop CM,. Pattern Recognition and Machine Learning (Information Science and Statistics), 1st ed. 2006. corr. 2nd printing edn., Springer: New York City, 2007.
32. Anderson DF,. A modified next reaction method for simulating chemical systems with time dependent propensities and delays. Journal of Chemical Physics Dez 2007; 127 (21): 214-107.
33. Furusawa C, Suzuki T, Kashiwagi A, Yomo T, Kaneko K,. Ubiquity of log-normal distributions in intra-cellular reaction dynamics. Biophysics 2005; 1: 25-31.
34. Beal MJ,. Variational algorithms for approximate Bayesian inference. PhD Thesis, Gatsby Computational Neuroscience Unit, University College London, 2003.
35. Neath RC, Jones GL,. Variable-at-a-time implementations of Metropolis-Hastings. Technical Report, University of Minnesota, School of Statistics, 2009.
36. Chib S, Greenberg E,. Understanding the Metropolis-Hastings algorithm. The American Statistician 1995; 49 (4): 327-335.
37. Kay SM,. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (v. 1), 1st edn. Prentice Hall: Upper Saddle River, NJ, 1993.