Least Squares Estimation in Stochastic Biochemical Networks

Bulletin of Mathematical Biology

Volumn 74, Issue 8, 2012, Pages 1938-1955

  Rempala, Grzegorz A ^a  

^a MEDICAL COLLEGE OF GEORGIA   (United States)

Author keywords

Biochemical network; Density dependent Markov jump process; Law of mass action; Least squares estimation; Reverse engineering; Stochastic trajectory

Indexed keywords

ARTICLE; CHEMICAL MODEL; GENE REGULATORY NETWORK; KINETICS; LONG INTERSPERSED REPEAT; REGRESSION ANALYSIS; STATISTICS;

GENE REGULATORY NETWORKS; KINETICS; LEAST-SQUARES ANALYSIS; LONG INTERSPERSED NUCLEOTIDE ELEMENTS; MODELS, CHEMICAL; STOCHASTIC PROCESSES;

EID: 84864026649     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-012-9744-y     Document Type: Article

References (32)

1. Andersson, H., & Britton, T. (2000). Lecture notes in statistics: Vol. 151. Stochastic epidemic models and their statistical analysis (1st ed.). Berlin: Springer.
2. Arkin, A., Shen, P., & Ross, J. (1997). A test case of correlation metric construction of a reaction pathway from measurements. Science, 277, 1275-1279.
3. Bain, A., & Crişan, D. (2008). Fundamentals of stochastic filtering (Vol. 60). Berlin: Springer.
4. Baker, S. M., Schallau, K., & Junker, B. H. (2010). Comparison of different algorithms for simultaneous estimation of multiple parameters in kinetic metabolic models. J. Integr. Bioinform., 7(3).
5. Ball, K., Kurtz, T., Popovic, L., & Rempala, G. (2006). Asymptotic analysis of multiscale approximations to reaction networks. Ann. Appl. Probab., 16(4), 1925-1961.
6. Billingsley, P. (1999). Convergence of probability measures (Vol. 316). New York: Wiley-Interscience.
7. Blanchard, S. C., Kim, H. D., Gonzalez, R. L. J., Puglisi, J. D., & Chu, S. (2004). trna dynamics on the ribosome during translation. Proc. Natl. Acad. Sci. USA, 101(35), 12893-12898.
8. Choi, B., & Rempala, G. A. (2012). Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling. Biostatistics, 13(1), 153-165.
9. Ethier, S. N., & Kurtz, T. G. (1986). Wiley series in probability and mathematical statistics: probability and mathematical statistics: Markov processes. New York: Wiley. Characterization and convergence.
10. Finkenstädt, B., Heron, E. A., Komorowski, M., Edwards, K., Tang, S., Harper, C. V., Davis, J. R. E., White, M. R. H., Millar, A. J., & Rand, D. A. (2008). Reconstruction of transcriptional dynamics from gene reporter data using differential equations. Bioinformatics, 24(24), 2901-2907.
11. Gillespie, D. T. (1992). A rigorous derivation of the chemical master equation. Physica A, 188, 404-425.
12. Kim, J., Craciun, G., Pantea, C., & Rempala, G. (2011). Statistical model for biochemical networks inference. Commun. Stat., Simul. Comput. doi: 10. 1080/03610918. 2011. 633200.
13. Komorowski, M., Costa, M. J., Rand, D. A., & Stumpf, M. P. H. (2011). Sensitivity, robustness, and identifiability in stochastic chemical kinetics models. Proc. Natl. Acad. Sci. USA, 108(21), 8645-8650.
14. Kurtz, T. G. (1972). The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys., 57(7), 2976-2978.
15. Kurtz, T. G. (1981). Approximation of discontinuous processes by continuous processes. In L. Arnold & R. Lefever (Eds.), Proceedings, Bielefeld conf on stochastic nonlinear systems in physics, chemistry and biology (pp. 22-35). Berlin: Springer.
16. Marbach, D., Prill, R. J., Schaffter, T., Mattiussi, C., Floreano, D., & Stolovitzky, G. (2010). Revealing strengths and weaknesses of methods for gene network inference. Proc. Natl. Acad. Sci. USA, 107(14), 6286-6291.
17. Margolin, A. A., & Califano, A. (2007). Theory and limitations of genetic network inference from microarray data. Ann. N. Y. Acad. Sci., 1115, 51-72.
18. Masters, J. R. (2002). Hela cells 50 years on: the good, the bad and the ugly. Nat. Rev. Cancer, 2(4), 315-319.
19. McQuarrie, D. A. (1967). Stochastic approach to chemical kinetics. J. Appl. Probab., 4, 413-478.
20. Perez, O. D., Krutzik, P. O., & Nolan, G. P. (2004). Flow cytometric analysis of kinase signaling cascades. Methods Mol. Biol., 263, 67-94.
21. Raue, A., Becker, V., Klingmüller, U., & Timmer, J. (2010). Identifiability and observability analysis for experimental design in nonlinear dynamical models. Chaos, 20(4), 045105.
22. Rempala, G. A., Ramos, K. S., & Kalbfleisch, T. (2006). A stochastic model of gene transcription: an application to l1 retrotransposition events. J. Theor. Biol., 242(1), 101-116.
23. Rempala, G. A., Ramos, K. S., Kalbfleisch, T., & Teneng, I. (2007). Validation of a mathematical model of gene transcription in aggregated cellular systems: application to l1 retrotransposition. J. Comput. Biol., 14(3), 85-95.
24. Samoilov, M., Arkin, A., & Ross, J. (2001). On the deduction of chemical reaction pathways from measurements of time series of concentrations. Chaos, 11(1), 108-114.
25. Sassaman, D., Dombroski, B., Moran, J., Kimberland, M., Naas, T., DeBerardinis, T., Gabriel, A., Swergold, G., & Kazazian, S. Jr. (1997). Many human l1 elements are capable of retrotransposition. Nat. Genet., 16, 37-43.
26. Transtrum, M. K., Machta, B. B., & Sethna, J. P. (2011). Geometry of nonlinear least squares with applications to sloppy models and optimization. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., 83(3 Pt 2), 036701.
27. Wheeler, D. A., Srinivasan, M., Egholm, M., Shen, Y., Chen, L., McGuire, A., He, W., Chen, Y.-J., Makhijani, V., Roth, G. T., Gomes, X., Tartaro, K., Niazi, F., Turcotte, C. L., Irzyk, G. P., Lupski, J. R., Chinault, C., Song, X.-z., Liu, Y., Yuan, Y., Nazareth, L., Qin, X., Muzny, D. M., Margulies, M., Weinstock, G. M., Gibbs, R. A., & Rothberg, J. M. (2008). The complete genome of an individual by massively parallel DNA sequencing. Nature, 452(7189), 872-876.
28. Wilkinson, D. J. (2009). Stochastic modelling for quantitative description of heterogeneous biological systems. Nat. Rev. Genet., 10(2), 122-133.
29. Wood, S. N. (2010). Statistical inference for noisy nonlinear ecological dynamic systems. Nature, 466(7310), 1102-1104.
30. Yoon, J., & Deisboeck, T. S. (2009). Investigating differential dynamics of the mapk signaling cascade using a multi-parametric global sensitivity analysis. PLoS ONE, 4(2), e4560.
31. Zacharof, A. I., & Butler, A. P. (2004). Stochastic modelling of landfill leachate and biogas production incorporating waste heterogeneity. Model formulation and uncertainty analysis. Waste Manag., 24(5), 453-462.
32. Zamir, E., & Bastiaens, P. I. H. (2008). Reverse engineering intracellular biochemical networks. Nat. Chem. Biol., 4(11), 643-647.