This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Hidden Markov Model for Transcriptional Regulation in Single Cells
January-March 2006 (vol. 3 no. 1)
pp. 57-71
ASCII Text
x 
 
John Goutsias, "A Hidden Markov Model for Transcriptional Regulation in Single Cells," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 57-71, January-March, 2006.
 
 
BibTex
x
 
@article{ 10.1109/TCBB.2006.2,
author = {John Goutsias},
title = {A Hidden Markov Model for Transcriptional Regulation in Single Cells},
journal ={IEEE/ACM Transactions on Computational Biology and Bioinformatics},
volume = {3},
number = {1},
issn = {1545-5963},
year = {2006},
pages = {57-71},
doi = {http://doi.ieeecomputersociety.org/10.1109/TCBB.2006.2},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE/ACM Transactions on Computational Biology and Bioinformatics
TI - A Hidden Markov Model for Transcriptional Regulation in Single Cells
IS - 1
SN - 1545-5963
SP57
EP71
EPD - 57-71
A1 - John Goutsias,
PY - 2006
KW - Hidden Markov models
KW - Monte Carlo simulation
KW - stochastic biochemical systems
KW - stochastic dynamical systems
KW - transcriptional regulation
KW - transcriptional regulatory systems.
VL - 3
JA - IEEE/ACM Transactions on Computational Biology and Bioinformatics
ER -
 
We discuss several issues pertaining to the use of stochastic biochemical systems for modeling transcriptional regulation in single cells. By appropriately choosing the system state, we can model transcriptional regulation by a hidden Markov model (HMM). This opens the possibility of using well-known techniques for the statistical analysis and stochastic control of HMMs to mathematically and computationally study transcriptional regulation in single cells. Unfortunately, in all but a few simple cases, analytical characterization of the statistical behavior of the proposed HMM is not possible. Moreover, analysis by Monte Carlo simulation is computationally cumbersome. We discuss several techniques for approximating the HMM by one that is more tractable. We employ simulations, based on a biologically relevant transcriptional regulatory system, to show the relative merits and limitations of various approximation techniques and provide general guidelines for their use.

[1] M.V. Karamouzis, V.G. Gorgoulis, and A.G. Papavassiliou, “Transcription Factors and Neoplasia: Vistas in Novel Drug Design,” Clinical Cancer Research, vol. 8, pp. 949-961, 2002.
[2] L. Hood, J.R. Heath, M.E. Phelps, and B. Lin, “Systems Biology and New Technologies Enable Predictive and Preventive Medicine,” Science, vol. 306, pp. 640-643, 2004.
[3] M. Ptashne and A. Gann, Genes & Signals. Cold Spring Harbor, N.Y.: Cold Spring Harbor Laboratory Press, 2002.
[4] H. Lodish, A. Berk, P. Matsudaira, C.A. Kaiser, M. Krieger, M.P. Scott, S.L. Zipursky, and J. Darnell, Molecular Cell Biology, fifth ed. New York: W.H. Freeman and Company, 2003.
[5] D. Endy and R. Brent, “Modelling Cellular Behaviour,” Nature, vol. 409, pp. 391-395, 2001.
[6] H. Kitano, “Computational Systems Biology,” Nature, vol. 420, pp. 206-210, 2002.
[7] J. Goutsias and S. Kim, “A Nonlinear Discrete Dynamical Model for Transcriptional Regulation: Construction and Properties,” Biophysical J., vol. 86, pp. 1922-1945, 2004.
[8] C.V. Rao, D.M. Wolf, and A.P. Arkin, “Control, Exploitation and Tolerance of Intracelluar Noise,” Nature, vol. 420, pp. 231-237, 2002.
[9] J.M. Raser and E.K. O'Shea, “Control of Stochasticity in Eukaryotic Gene Expression,” Science, vol. 304, pp. 1811-1814, 2004.
[10] J.M. Levsky and R.H. Singer, “Gene Expression and the Myth of the Average Cell,” Trends in Cell Biology, vol. 13, no. 1, pp. 4-6, 2003.
[11] H.H. McAdams and A. Arkin, “Stochastic Mechanisms in Gene Expression,” Proc. Nat'l Academy of Science, vol. 94, pp. 814-819, 1997.
[12] H.H. McAdams and A. Arkin, “It's a Noisy Business! Genetic Regulation at the Nanomolar Scale,” Trends in Genetics, vol. 15, no. 2, pp. 65-69, 1999.
[13] N. Fedoroff and W. Fontana, “Small Numbers of Big Molecules,” Science, vol. 297, pp. 1129-1131, 2002.
[14] M.B. Elowitz, A.J. Levine, E.D. Siggia, and P.S. Swain, “Stochastic Gene Expression in a Single Cell,” Science, vol. 297, pp. 1183-1186, 2002.
[15] W.J. Ewens and G.R. Grant, Statistical Methods in Bioinformatics: An Introduction. New York: Springer, 2001.
[16] M. Ptashne, A Genetic Switch: Phage Lambda Revisited, third ed. Cold Spring Harbor, N.Y.: Cold Spring Harbor Laboratory Press, 2004.
[17] N.G. vanKampen, Stochastic Processes in Physics and Chemistry. Amsterdam: Elsevier, 1992.
[18] D.T. Gillespie, “A Rigorous Derivation of the Chemical Master Equation,” Physica A, vol. 188, pp. 404-425, 1992.
[19] D.T. Gillespie, “The Chemical Langevin Equation,” J. Chemical Physics, vol. 113, no. 1, pp. 297-306, 2000.
[20] E.L. Haseltine and J.B. Rawlings, “Approximate Simulation of Coupled Fast and Slow Reactions for Stochastic Chemical Kinetics,” J. Chemical Physics, vol. 117, no. 15, pp. 6959-6969, 2002.
[21] S. Karlin and H.M. Taylor, A First Course in Stochastic Processes, second ed. San Diego, Calif.: Academic Press, 1975.
[22] S. Karlin and H.M. Taylor, A Second Course in Stochastic Processes. San Diego, Calif.: Academic Press, 1981.
[23] A. Papoulis and S.U. Pillai, Probability, Random Variables and Stochastic Processes, fourth ed. New York: McGraw-Hill, 2002.
[24] R. Heinrich and S. Schuster, The Regulation of Cellular Systems. New York: Chapman & Hall, 1996.
[25] J. Goutsias, “Quasiequilibrium Approximation of Fast Reaction Kinetics in Stochastic Biochemical Systems,” J. Chemical Physics, vol. 122, 184102, 2005.
[26] D.T. Gillespie, “Exact Stochastic Simulation of Coupled Chemical Reactions,” J. Physical Chemistry, vol. 81, no. 25, pp. 2340-2361, 1977.
[27] J.S. Liu, Monte Carlo Strategies in Scientific Computing. New York: Springer-Verlag, 2001.
[28] D.T. Gillespie, “General Method for Numerically Simulating Stochastic Time Evolution of Coupled-Chemical Reactions,” J. Computational Physics, vol. 22, pp. 403-434, 1976.
[29] M.A. Gibson and J. Bruck, “Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels,” J. Physical Chemistry A, vol. 104, pp. 1876-1889, 2000.
[30] D.T. Gillespie, “Approximate Accelerated Stochastic Simulation of Chemically Reacting Systems,” J. Chemical Physics, vol. 115, no. 4, pp. 1716-1733, 2001.
[31] D.T. Gillespie and L.R. Petzold, “Improved Leap-Size Selection for Accelerated Stochastic Simulation,” J. Chemical Physics, vol. 119, no. 16, pp. 8229-8234, 2003.
[32] M. Rathinam, L.R. Petzold, Y. Cao, and D.T. Gillespie, “Stiffness in Stochastic Chemically Reacting Systems: The Implicit Tau-Leaping Method,” J. Chemical Physics, vol. 119, no. 24, pp. 12784-12794, 2003.
[33] Y. Cao, H. Li, and L. Petzold, “Efficient Formulation of the Stochastic Simulation Algorithm for Chemically Reacting Systems,” J. Chemical Physics, vol. 121, no. 9, pp. 4059-4067, 2004.
[34] T. Tian and K. Burrage, “Bionomial Leap Methods for Simulating Stochastic Chemical Kinetics,” J. Chemical Physics, vol. 121, no. 21, pp. 10356-10364, 2004.
[35] A. Chatterjee, D.G. Vlachos, and M.A. Katsoulakis, “Binomial Distribution Based $\tau$ -Leap Accelerated Stochastic Simulation,” J. Chemical Physics, vol. 122, 024112, 2005.
[36] Y. Cao, D.T. Gillespie, and L.R. Petzold, “Avoiding Negative Populations in Explicit Poisson Tau-Leaping,” J. Chemical Physics, vol. 123, 054104, 2005.
[37] D.J. Higham, “An Algebraic Introduction to Numerical Simulation of Stochastic Differential Equations,” SIAM Rev., vol. 43, no. 3, pp. 525-546, 2001.
[38] J. Hasty, J. Pradines, M. Dolnik, and J.J. Collins, “Noise-Based Switches and Amplifiers for Gene Expression,” Proc. Nat'l Academy of Science, vol. 97, no. 5, pp. 2075-2080, 2000.
[39] E.M. Ozbudak, M. Thattai, I. Kurtser, A.D. Grossman, and A. van Oudenaarden, “Regulation of Noise in the Expression of a Single Gene,” Nature Genetics, vol. 31, pp. 69-73, 2002.
[40] J.R. Pirone and T.C. Elston, “Fluctuations in Transcription Factor Binding Can Explain the Graded and Binary Responses Observed in Inducible Gene Expression,” J. Theoretical Biology, vol. 226, pp. 111-121, 2004.
[41] R. Steuer, “Effects of Stochastisity in Models of the Cell Cycle: From Quantized Cycle Times to Noise-Induced Oscillations,” J. Theoretical Biology, vol. 228, pp. 293-301, 2004.
[42] M.L. Simpson, C.D. Cox, and G.S. Sayler, “Frequency Domain Chemical Langevin Analysis of Stochasticity in Gene Transcriptional Regulation,” J. Theoretical Biology, vol. 229, pp. 383-394, 2004.
[43] J. Elf and M. Ehrenberg, “Fast Evaluation of Fluctuations in Biochemical Networks with the Linear Noise Approximation,” Genome Research, vol. 13, pp. 2475-2484, 2003.
[44] R. Tomioka, H. Kimura, T.J. Kobayashi, and K. Aihara, “Multivariate Analysis of Noise in Genetic Regulatory Networks,” J. Theoretical Biology, vol. 229, pp. 501-521, 2004.
[45] C.V. Rao and A.P. Arkin, “Stochastic Chemical Kinetics and the Quasi-Steady-State Assumption: Application to the Gillespie Algorithm,” J. Chemical Physics, vol. 118, no. 11, pp. 4999-5010, 2003.
[46] Y. Cao, D.T. Gillespie, and L.R. Petzold, “The Slow-Scale Stochastic Simulation Algorithm,” J. Chemical Physics, vol. 122, 014116, 2005.
[47] G. Parisi, Statistical Field Theory. Redwood City, Calif.: Addison-Wesley, 1988.
[48] J.J. Binney, N.J. Dowrick, A.J. Fisher, and M.E. J. Newman, The Theory of Critical Phenomena: An Introduction to the Renormalization Group. Oxford, U.K.: Oxford Univ. Press, 1992.

Index Terms:
Hidden Markov models, Monte Carlo simulation, stochastic biochemical systems, stochastic dynamical systems, transcriptional regulation, transcriptional regulatory systems.
Citation:
John Goutsias, "A Hidden Markov Model for Transcriptional Regulation in Single Cells," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 57-71, Jan.-March 2006, doi:10.1109/TCBB.2006.2
Usage of this product signifies your acceptance of the Terms of Use.