Jakob Ruess
Skip Abstract Section
Abstract
Continuous-time Markov chains are commonly used in practice for modeling biochemical reaction networks in which the inherent randomness of the molecular interactions cannot be ignored. This has motivated recent research effort into methods for parameter inference and experiment design for such models. The major difficulty is that such methods usually require one to iteratively solve the chemical master equation that governs the time evolution of the probability distribution of the system. This, however, is rarely possible, and even approximation techniques remain limited to relatively small and simple systems. An alternative explored in this article is to base methods on only some low-order moments of the entire probability distribution. We summarize the theory behind such moment-based methods for parameter inference and experiment design and provide new case studies where we investigate their performance.
- M. Acar, J. Mettetal, and A. van Oudenaarden. 2008. Stochastic switching as a survival strategy in fluctuating environments. Nature Genetics 40, 2008, 471--475. DOI: http://dx.doi.org/10.1038/ng.110Google Scholar
Cross Ref
- A. Ale, P. Kirk, and M. Stumpf. 2013. A general moment expansion method for stochastic kinetic models. Journal of Chemical Physics 138, 2013, 174101. DOI: http://dx.doi.org/10.1063/1.4802475Google ScholarCross Ref
- A. Andreychenko, L. Mikeev, D. Spieler, and V. Wolf. 2011. Parameter identification for Markov models of biochemical reactions. In Proceedings of the 23rd International Conference on Computer Aided Verification (CAV’11). (2011), 83--98. DOI: http://dx.doi.org/10.1007/978-3-642-22110-1_8 Google ScholarDigital Library
- G. Balazsi, A. van Oudenaarden, and J. Collins. 2011. Cellular decision making and biological noise: From microbes to mammals. Cell 144, 2011, 910--925. DOI: http://dx.doi.org/10.1016/j.cell.2011.01.030Google Scholar
- A. Colman-Lerner, A. Gordon, E. Serra, T. Chin, O. Resnekov, D. Endy, G. Pesce, and R. Brent. 2005. Regulated cell-to-cell variation in a cell-fate decision system. Nature 437, 7059 (2005), 699--706. DOI: http://dx.doi.org/10.1038/nature03998Google ScholarCross Ref
- M. Elowitz, A. Levine, E. Siggia, and P. Swain. 2002. Stochastic gene expression in a single cell. Science 297, 5584 (2002), 1183--1186. DOI: http://dx.doi.org/10.1126/science.1070919Google Scholar
- S. Engblom. 2006. Computing the moments of high dimensional solutions of the master equation. Applied Mathematics and Computation 180, 2 (2006), 498--515. DOI: http://dx.doi.org/10.1016/j.amc.2005.12.032Google ScholarCross Ref
- G. Franceschini and S. Macchietto. 2008. Model-based design of experiments for parameter precision: State of the art. Chemical Engineering Science 63, 19 (2008), 4846--4872. DOI: http://dx.doi.org/10.1016/j.ces.2007.11.034Google ScholarCross Ref
- D. Gillespie. 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22, 4 (1976), 403--434. DOI: http://dx.doi.org/10.1016/0021-9991(76)90041-3Google ScholarCross Ref
- D. Gillespie. 1992. A rigorous derivation of the chemical master equation. Physica A 188, 1--3 (1992), 404--425. DOI: http://dx.doi.org/10.1016/0378-4371(92)90283-vGoogle ScholarCross Ref
- A. Gonzalez, J. Uhlendorf, J. Schaul, E. Cinquemani, G. Batt, and G. Ferrari-Trecate. 2013. Identification of biological models from single-cell data: A comparison between mixed-effects and moment-based inference. In Proceedings of the 12th European Control Conference.Google Scholar
- J. Goutsias and G. Jenkinson. 2013. Markovian dynamics on complex reaction networks. Physics Reports 529 (2013), 199--264. DOI: http://dx.doi.org/doi:10.1016/j.physrep.2013.03.004Google ScholarCross Ref
- C. Guet, A. Gupta, T. A. Henzinger, M. Mateescu, and A. Sezgin. 2012. Delayed continuous-time Markov chains for genetic regulatory circuits. In Proceedings of the 24th International Conference on Computer Aided Verification (CAV’12). 294--309. DOI: http://dx.doi.org/10.1007/978-3-642-31424-7_24 Google ScholarDigital Library
- D. Hagen, J. White, and B. Tidor. 2013. Convergence in parameters and predictions using computational experimental design. Interface Focus 3 (2013), 20130008. DOI: http://dx.doi.org/10.1098/rsfs.2013.0008Google ScholarCross Ref
- J. Hasenauer, V. Wolf, A. Kazeroonian, and F. Theis. 2014. Method of conditional moments (MCM) for the chemical master equation. Journal of Mathematical Biology 69, 3 (2013), 687--735. DOI: http://dx.doi.org/10.1007/s00285-013-0711-5Google ScholarCross Ref
- J. Hasty, J. Pradines, M. Dolnik, and J. Collins. 2000. Noise-based switches and amplifiers for gene expression. Proceedings of the National Academy of Sciences of the U.S.A. 97, 5 (2000), 2075--2080. DOI: http://dx.doi.org/10.1073/pnas.040411297Google ScholarCross Ref
- T. A. Henzinger, L. Mikeev, M. Mateescu, and V. Wolf. 2010. Hybrid numerical solution of the chemical master equation. Proceedings of the 8th International Conference on Computational Methods in Systems Biology (CMSB’10). ACM, New York, 55--65. DOI: http://dx.doi.org/10.1145/1839764.1839772 Google ScholarDigital Library
- J. Hespanha. 2006. StochDynTools - A MATLAB toolbox to compute moment dynamics for stochastic networks of bio-chemical reactions. Available at http://www.ece.ucsb.edu/∼hespanha/software.Google Scholar
- J. Hespanha. 2008. Moment closure for biochemical networks. In Proceedings of the 3rd International Symposium on Communications, Control and Signal Processing. 142--147. DOI: http://dx.doi.org/10.1109/ISCCSP.2008.4537208Google ScholarCross Ref
- A. Hindmarsh, P. Brown, K. Grant, S. Lee, R. Serban, D. Shumaker, and C. Woodward. 2005. SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software (TOMS) 31, 3 (2005), 363--396. DOI: http://dx.doi.org/10.1145/1089014.1089020 Google ScholarDigital Library
- A. Hjartarson, J. Ruess, and J. Lygeros. 2013. Approximating the solution of the chemical master equation by combining finite state projection and stochastic simulation. In Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC’13).Google Scholar
- W. Hunter, W. Hill, and T. Henson. 1969. Designing experiments for precise estimation of all or some of the constants in a mechanistic model. Canadian Journal of Chemical Engineering 47, 1 (1969), 76--80. DOI: http://dx.doi.org/10.1002/cjce.5450470114Google ScholarCross Ref
- C. Ko, Y. Yamada, D. Welsh, E. Buhr, A. Liu, E. Zhang, M. Ralph, S. Kay, D. Forger, and J. Takahashi. 2010. Emergence of noise-induced oscillations in the central circadian pacemaker. PLoS Biology 8 (2010), e1000513. DOI: http://dx.doi.org/10.1371/journal.pbio.1000513Google ScholarCross Ref
- M. Komorowski, M. Costa, D. Rand, and M. Stumpf. 2011. Sensitivity, robustness, and identifiability in stochastic chemical kinetics models. Proceedings of the National Academy of Sciences of the U.S.A. 108, 21 (2011), 8645--8650. DOI: http://dx.doi.org/10.1073/pnas.1015814108Google ScholarCross Ref
- P. Kügler. 2012. Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models. PLoS ONE 7, 8 (2012), e43001. DOI: http://dx.doi.org/10.1371/journal.pone.0043001Google ScholarCross Ref
- G. Lillacci and M. Khammash. 2013. The signal within the noise: Efficient inference of stochastic gene regulation models using fluorescence histograms and stochastic simulations. Bioinformatics 29, 18 (2013), 2311--2319. DOI: http://dx.doi.org/10.1093/bioinformatics/btt380Google ScholarCross Ref
- M. Mateescu, V. Wolf, F. Didier, and T. A. Henzinger. 2010. Fast adaptive uniformisation of the chemical master equation. IET Systems Biology 4, 6 (2010), 441--452. DOI: http://dx.doi.org/10.1049/iet-syb.2010.0005Google ScholarCross Ref
- H. McAdams and A. Arkin. 1997. Stochastic mechanisms in gene expression. Proceedings of the National Academy of Sciences of the U.S.A. 94, 3 (1997), 814--819.Google ScholarCross Ref
- F. Menolascina, M. di Bernardo, and D. di Bernardo. 2011. Analysis, design and implementation of a novel scheme for in-vivo control of synthetic gene regulatory networks. Automatica 47, 6 (2011), 1265--1270. Google ScholarDigital Library
- L. Mikeev and V. Wolf. 2012. Parameter estimation for stochastic hybrid models of biochemical reaction networks. In Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control. ACM, New York. (2012), 155--166. DOI: http://dx.doi.org/10.1145/2185632.2185657 Google ScholarDigital Library
- A. Milias-Argeitis, S. Summers, J. Stewart-Ornstein, I. Zuleta, D. Pincus, H. El-Samad, M. Khammash, and J. Lygeros. 2011. In silico feedback for in vivo regulation of a gene expression circuit. Nature Biotechnology 29 (2011), 1114--1116. DOI: http://dx.doi.org/10.1038/nbt.2018Google ScholarCross Ref
- B. Munsky and M. Khammash. 2006. The finite state projection algorithm for the solution of the chemical master equation. Journal of Chemical Physics 124 (2006), 044104. DOI: http://dx.doi.org/10.1063/1.2145882Google ScholarCross Ref
- B. Munsky, B. Trinh, and M. Khammash. 2009. Listening to the noise: Random fluctuations reveal gene network parameters. Molecular Systems Biology 5, 1 (2009), 318. DOI: http://dx.doi.org/10.1038/msb.2009.75Google ScholarCross Ref
- S. Poovathingal and R. Gunawan. 2010. Global parameter estimation methods for stochastic biochemical systems. BMC Bioinformatics 11, 1 (2010), 414--425. DOI: http://dx.doi.org/10.1186/1471-2105-11-414Google ScholarCross Ref
- L. Pronzato and E. Walter. 1985. Robust experimental design via stochastic approximation. Mathematical Biosciences 75 (1985), 103--120. DOI: http://dx.doi.org/10.1016/0025-5564(85)90068-9Google ScholarCross Ref
- J. Raser and E. O’Shea. 2005. Noise in gene expression: Origins, consequences, and control. Science 309, 5743 (2005), 2010--2013. DOI: http://dx.doi.org/10.1126/science.1105891Google Scholar
- J. Ruess and J. Lygeros. 2013. Identifying stochastic biochemical networks from single-cell population experiments: A comparison of approaches based on the Fisher information. In Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC’13).Google Scholar
- J. Ruess, A. Milias-Argeitis, and J. Lygeros. 2013. Designing experiments to understand the variability in biochemical reaction networks. Journal of the Royal Society Interface 10, 88 (2013), 20130588. DOI: http://dx.doi.org/10.1098/rsif.2013.0588Google ScholarCross Ref
- J. Ruess, A. Milias-Argeitis, S. Summers, and J. Lygeros. 2011. Moment estimation for chemically reacting systems by extended Kalman filtering. Journal of Chemical Physics 135 (2011), 165102. DOI: http://dx.doi.org/10.1063/1.3654135Google ScholarCross Ref
- M. Samoilov and A. Arkin. 2006. Deviant effects in molecular reaction pathways. Nature Biotechnology 24, 10 (2006), 1235--1240. DOI: http://dx.doi.org/10.1038/nbt1253Google ScholarCross Ref
- V. Shahrezaei, J. Ollivier, and P. Swain. 2008. Colored extrinsic fluctuations and stochastic gene expression. Molecular Systems Biology 4, 196 (2008). DOI: http://dx.doi.org/10.1038/msb.2008.31Google Scholar
- A. Singh and J. Hespanha. 2006. Lognormal moment closures for biochemical reactions. In Proceedings of the IEEE 45th Annual Conference on Decision and Control (CDC’06). 2063--2068. DOI: http://dx. doi.org/10.1109/CDC.2006.376994Google Scholar
- A. Singh and J. Hespanha. 2011. Approximate moment dynamics for chemically reacting systems. IEEE Transactions on Automatic Control 56, 2 (2011), 414--418. DOI: http://dx.doi.org/10.1109/TAC.2010. 2088631Google ScholarCross Ref
- T. Toni and B. Tidor. 2013. Combined model of intrinsic and extrinsic variability for computational network design with application to synthetic biology. PLoS Computational Biology 9 (2013), 3. DOI: http://dx.doi.org/10.1371/journal.pcbi.1002960Google ScholarCross Ref
- J. Uhlendorf, A. Miermont, T. Delaveau, G. Charvin, F. Fages, S. Bottani, G. Batt, and P. Hersen. 2012. Long-term model predictive control of gene expression at the population and single-cell levels. Proceedings of the National Academy of Sciences of the U.S.A. 109, 35 (2012), 14271--14276. DOI: http://dx.doi.org/10.1073/pnas.1206810109Google ScholarCross Ref
- D. Volfson, J. Marciniak, W. Blake, N. Ostroff, L. Tsimring, and J. Hasty. 2005. Origins of extrinsic variability in eukaryotic gene expression. Nature 439, 7078 (2005), 861--864. DOI: http://dx.doi.org/10.1038/nature04281Google ScholarCross Ref
- E. Walter and L. Pronzato. 1990. Qualitative and quantitative experiment design for phenomenological models—a survey. Automatica 26, 2 (1990), 195--213. DOI: http://dx.doi.org/10.1016/0005- 1098(90)90116-Y Google ScholarDigital Library
- P. Whittle. 1957. On the use of the normal approximation in the treatment of stochastic processes. Journal of the Royal Statistical Society Series B Statistical Methodology 19 (1957), 268--281.Google ScholarCross Ref
- V. Wolf, R. Goel, M. Mateescu, and T. A. Henzinger. 2010. Solving the chemical master equation using sliding windows. BMC Systems Biology 4 (2010), 42. DOI: http://dx.doi.org/10.1186/1752-0509-4-42Google ScholarCross Ref
- C. Zechner, J. Ruess, P. Krenn, S. Pelet, M. Peter, J. Lygeros, and H. Koeppl. 2012. Moment-based inference predicts bimodality in transient gene expression. Proceedings of the National Academy of Sciences of the U.S.A. 109, 21 (2012), 8340--8345. DOI: http://dx.doi.org/10.1073/pnas.1200161109Google ScholarCross Ref
- C. Zechner, M. Unger, S. Pelet, M. Peter, and H. Koeppl. 2014. Scalable inference of heterogeneous reaction kinetics from pooled single-cell recordings. Nature Methods 11, 2 (2014), 197--202. DOI: http://dx.doi.org/10.1038/nmeth.2794Google ScholarCross Ref
Index Terms
- Moment-Based Methods for Parameter Inference and Experiment Design for Stochastic Biochemical Reaction Networks
Recommendations
Parameter estimation for stochastic hybrid models of biochemical reaction networks
HSCC '12: Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and ControlThe dynamics of biochemical reaction networks can be accurately described by stochastic hybrid models, where we assume that large chemical populations evolve deterministically and continuously over time while small populations change through random ...
Metabolite and reaction inference based on enzyme specificities
Motivation: Many enzymes are not absolutely specific, or even promiscuous: they can catalyze transformations of more compounds than the traditional ones as listed in, e.g. KEGG. This information is currently only available in databases, such as the ...
Comments