Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models

PLoS ONE

Volumn 7, Issue 8, 2012, Pages

  Kügler, Philipp ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; MATHEMATICAL PHENOMENA; MOMENT FITTING; NONLINEAR SYSTEM; STOCHASTIC MODEL; UNCERTAINTY;

ALGORITHMS; COMPUTER SIMULATION; DIMERIZATION; KINETICS; MODELS, BIOLOGICAL; SIGNAL TRANSDUCTION; STOCHASTIC PROCESSES; SYSTEMS BIOLOGY; TUMOR SUPPRESSOR PROTEIN P53;

EID: 84864988006     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0043001     Document Type: Article

References (64)

1. Chen WW, Niepel M, Sorger PK, ((2010)) Classic and contemporary approaches to modeling biochemical reactions. Genes & Development 24:: 1861--1875.
2. Wilkinson JD (2012) Stochastic modelling for systems biology. Chapman & Hall/CRC, 2nd edition.
3. Munsky B, Khammash M, ((2006)) The finite state projection algorithm for the solution of the chemical master equation. Journal of Chemical Physics 124:: 044104.
4. Gillespie DT, ((1977)) Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81:: 2340--2361.
5. Gillespie D, ((2000)) The chemical langevin equation. Journal of Chemical Physics 113:: 297--306.
6. Van Kampen NG (2007) Stochastic Processes in Physics and Chemistry. Amsterdam: North Holland.
7. Engl HW, Hanke M, Neubauer A (1996) Regularization of Inverse Problems. Dordrecht: Kluwer.
8. Kaipio J, Somersalo E (2004) Statistical and Computational Inverse Problems. Dordrecht: Springer.
9. Isakov V (2006) Inverse Problems for Partial Differential Equations, volume 127 of Applied Mathematical Sciences. Springer.
10. Bishwal JPN (2008) Parameter Estimation in Stochastic Differential Equations. Springer.
11. Pepperkok R, Ellenberg J, ((2006)) High-throughput fluorescence microscopy for systems biology. Nature Reviews Molecular Cell Biology 7:: 690--696.
12. Shen H, Nelson G, Nelson DE, Kennedy S, Spiller DG, et al. ((2006)) Automated tracking of gene expression in individual cells and cell compartments. Journal of the Royal Society Interface 3:: 787--794.
13. Moles CG, Pedro Mendes P, Banga JR, ((2003)) Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Research 13:: 2467--2474.
14. Engl HW, Flamm C, Kügler P, Lu J, Müller S, et al. ((2009)) Inverse problems in systems biology. Inverse Problems 25:: 123014.
15. Rodriguez-Fernandez M, Egea JA, Banga JR (2006) Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics 7.
16. Golightly A, Wilkinson DJ, ((2008)) Bayesian inference for stochastic kinetic models using a diffusion approximation. Biometrics 61:: 781--788.
17. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MPH, ((2009)) Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface 6:: 187--202.
18. Lecca P, Palmisano A, Priami C (2009) Deducing chemical reaction rate constants and their regions of confidence from noisy measurements of time series of concentration. Computer Modelling and Simulation, 2009 UKSIM '09 11th International Conference on: 200-205.
19. Komorowski M, Finkenstädt B, Harper CV, Rand DA (2009) Bayesian inference of biochemical kinetic parameters using the linear noise approximation. BMC Bioinformatics 10.
20. Poovathingal SK, Gunawan R (2010) Global parameter estimation methods for stochastic biochemical systems. BMC Bioinformatics 11.
21. Lillacci G, Khammash M (2010) Parameter estimation and model selection in computational biology. PLoS Computational Biology 6.
22. Sun X, Jin L, Xiong M (2008) Extended kalman filter for estimation of parameters in nonlinear state space models of biochemical networks. PLoS ONE 3.
23. Fey D, Findeisen R, Bullinger E (2008) Parameter estimation in kinetic reaction models using nonlinear observers is facilitated by model extensions. 17th IFAC World Congress. 313-318.
24. Jaqaman K, Danuser G, ((2006)) Linking data to models: data regression. Nature Reviews Molecular Cell Biology 7:: 813--819.
25. Gillespie C (2008). Parameter estimation using moment closure methods. Video lecture. Available: http://www.videolectures.net.
26. Brown KS, Sethna JP (2003) Statistical mechanical approaches to models with many poorly known parameters. Physical Review E 68.
27. Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR,et al. (2007) Universally sloppy parameter sensitivities in systems biology models. PLoS Computational Biology 3.
28. Anguelova M, Cedersund G, Johansson M, Franzen CJ, Wennberg B, ((2007)) Conservation laws and unidentifiability of rate expressions in biochemical models. IET Systems Biology 1:: 230--237.
29. Audoly S, Bellu G, D'Angio L, Saccomani MP, Cobelli C, ((2001)) Global identifiability of nonlinear models of biological systems. IEEE Transactions on Biomedical Engineering 48:: 55--65.
30. Ashyraliyev M, Jaeger J, Blom JG (2008) Parameter estimation and determinability analysis applied to drosophila gap gene circuits. BMC Systems Biology 2.
31. Komorowski M, Costab MJ, Rand DA, Stumpf MPH, ((2011)) Sensitivity, robustness, and identifiability in stochastic chemical kinetics models. PNAS 108:: 8645--8650.
32. Bandara S, Schlder JP, Eils R, Bock HG, Meyer T, ((2009)) Optimal experimental design for parameter estimation of a cell signaling model. PLoS Comput Biol 5:: e1000558.
33. Wu JQ, Pollard TD, ((2005)) Counting cytokinesis proteins globally and locally in fission yeast. Science 310:: 310--314.
34. Wu JQ, McCormick CD, Pollard TD (2008) Counting proteins in living cells by quantitative fluorescence microscopy with internal standards. In: Correia JJ, Detrich HW, editors, Biophysical Tools for Biologists, Volume Two: In Vivo Techniques, Academic Press, volume 89 of Methods in Cell Biology. 253-273.
35. Ferguson ML, Le Coq D, Jules M, Aymerich S, Radulescu O, et al. ((2012)) Reconciling molecular regulatory mechanisms with noise patterns of bacterial metabolic promoters in induced and repressed states. Proceedings of the National Academy of Sciences 109:: 155--160.
36. Kivioja T, Vähärautio A, Karlsson K, Bonke M, Enge M, et al. ((2012)) Counting absolute numbers of molecules using unique molecular identifiers. Nature Methods 9:: 72--74.
37. Lee CH, Kyeong-Hun Kim KH, Kim P, ((2009)) A moment closure method for stochastic reaction networks. Journal of Chemical Physics 130:: 813--819.
38. Engblom S, ((2006)) Computing the moments of high dimensional solutions of the master equation. Applied Mathematics and Computation 180:: 498--515.
39. Gillespie CS, ((2009)) Moment-closure approximations for mass-action models. IET Systems Biology 3:: 52--58.
40. Milner P, Gillespie CS, Wilkinson DJ, ((2011)) Moment closure approximations for stochastic kinetic models with rational rate laws. Mathematical Biosciences 231:: 99--104.
41. Singh A, Hespanha JP, ((2011)) Approximate moment dynamics for chemically reaction systems. IEEE Transactions on Automatic Control 56:: 414--418.
42. Mathworks T (2010) Matlab version 7.10.0.499 (r2010a). Available: http://www.mathworks.com.
43. Nocedal J, Wright SJ (2006) Numerical Optimization. Springer.
44. Kaltenbacher B, Neubauer A, Scherzer O (2008) Iterative Regularization Methods for Nonlinear Problems. Berlin, New York: de Gruyter.
45. Goutte C, Hansen LK, ((1997)) Regularization with a pruning prior. Neural Networks 10:: 1053--1059.
46. Bruckstein AM, Donoho DL, Elad M, ((2009)) From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review 51:: 34--81.
47. Lai MJ, ((2010)) On sparse solution of underdetermined linear systems. Journal of Concrete and Applicable Mathematics 8:: 296--327.
48. Engl HW, Flamm C, Kügler P, Lu J, Müller S, et al. ((2009)) Inverse problems in systems biology. Inverse Problems 25:: 123014.
49. Kügler P, Gaubitzer E, Müller S, ((2009)) Parameter identification for chemical reaction systems using sparsity enforcing regularization: a case study for the chlorite-iodide reaction. The Journal of Physical Chemistry A 113:: 2775--2785.
50. Kügler P (2012) A sparse update method for solving underdetermined systems of nonlinear equations applied to the manipulation of biological signaling pathways. SIAM Journal on Applied Mathematics.
51. Kang K, Goldsman D, ((1990)) The correlation between mean and variance estimators in computer simulation. IIE Transactions 22:: 15--23.
52. Seber GAF, Wild CJ (2003) Nonlinear Regression. Wiley.
53. Liese F, Vajda I, ((2006)) On divergences and informations in statistics and information theory. Information Theory, IEEE Transactions on 52:: 4394--4412.
54. Wackerly DD, Mendenhall W, Scheaffer RL (2008) Mathematical Statistics with Applications. Cengage Learning.
55. Grima R, Thomas P, Straube AV, ((2011)) How accurate are the nonlinear chemical fokker-planck and chemical langevin equations? The Journal of Chemical Physics 135:: 084103.
56. Grima R, ((2012)) A study of the accuracy of moment-closure approximations for stochastic chemical kinetics. The Journal of Chemical Physics 136:: 154105.
57. Aldridge BB, Burke JM, Lauffenburger DA, Sorger PK, ((2006)) Physicochemical modelling of cell signalling pathways. Nature Cell Biology 8:: 1195--1203.
58. Ross SM (2010) Introduction to Probability Models. Academic Press.
59. Matis TI, Guardiola IG (2010) Achieving moment closure through cumulant neglect. The Mathematica Journal 12.
60. Bartholomay AF, ((1958)) On the linear birth and death processes of biology as markoff chains. Bulletin of Mathematical Biophysics 20:: 97--118.
61. Geva-Zatorsky N, Rosenfeld N, Itzkovitz S, Milo R, Sigal A, et al. (2006) Oscillations and variability in the p53 system. Molecular Systems Biology 2.
62. Tabachnick BG, Fidell LS (2006) Using Multivariate Statistics. Allyn & Bacon.
63. Hair JF, Black WC, Babin BJ, Anderson RE (2009) Multivariate Data Analysis. Prentice Hall.
64. Schäfer J, Strimmer K, ((2005)) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology 4:: 99--104.