This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Stochastic Gene Expression Modeling with Hill Function for Switch-Like Gene Responses
July-Aug. 2012 (vol. 9 no. 4)
pp. 973-979
Haseong Kim, Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
E. Gelenbe, Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
Gene expression models play a key role to understand the mechanisms of gene regulation whose aspects are grade and switch-like responses. Though many stochastic approaches attempt to explain the gene expression mechanisms, the Gillespie algorithm which is commonly used to simulate the stochastic models requires additional gene cascade to explain the switch-like behaviors of gene responses. In this study, we propose a stochastic gene expression model describing the switch-like behaviors of a gene by employing Hill functions to the conventional Gillespie algorithm. We assume eight processes of gene expression and their biologically appropriate reaction rates are estimated based on published literatures. We observed that the state of the system of the toggled switch model is rarely changed since the Hill function prevents the activation of involved proteins when their concentrations stay below a criterion. In ScbA-ScbR system, which can control the antibiotic metabolite production of microorganisms, our modified Gillespie algorithm successfully describes the switch-like behaviors of gene responses and oscillatory expressions which are consistent with the published experimental study.

[1] N. Friedman, M. Linial, I. Nachman, and D. Pe'er, "Using Bayesian Networks to Analyze Expression Data," J. Computational Biology, vol. 7, nos. 3/4, pp. 601-620, 2000.
[2] R. Opgen-Rhein and K. Strimmer, "Learning Causal Networks from Systems Biology Time Course Data: An Effective Model Selection Procedure for the Vector Autoregressive Process," BMC Bioinformatics, vol. 8, no. 2,article S3, 2007.
[3] H. McAdams and A. Arkin, "Stochastic Mechanisms in Gene Expression," Proc. Nat'l Academy of Sciences USA, vol. 94, no. 3, pp. 814-819, 1997.
[4] J. Paulsson, "Models of Stochastic Gene Expression," Physics of Life Rev., vol. 2, no. 2, pp. 157-175, 2005.
[5] E. Gelenbe, "Steady-State Solution of Probabilistic Gene Regulatory Networks," J. Physical Rev. E, vol. 76, p. 031903, 2007.
[6] H. Kim and E. Gelenbe, "Anomaly Detection in Gene Expression via Stochastic Models of Gene Regulatory Networks," BMC Genomics, vol. 10, no. Suppl 3, article S26, 2009.
[7] H. Maamar, A. Raj, and D. Dubnau, "Noise in Gene Expression Determines Cell Fate in Bacillus Subtilis," Science, vol. 317, no. 5837, pp. 526-529, 2007.
[8] A. Eldar and M. Elowitz, "Functional Roles for Noise in Genetic Circuits," Nature, vol. 467, no. 7312, pp. 167-173, 2010.
[9] J. Wang, L. Xu, and E. Wang, "Potential Landscape and Flux Framework of Nonequilibrium Networks: Robustness, Dissipation, and Coherence of Biochemical Oscillations," Proc. Nat'l Academy of Sciences USA, vol. 105, no. 34, pp. 12271-12276, 2008.
[10] J. Chahine, R. Oliveira, V. Leite, and J. Wang, "Configuration-Dependent Diffusion Can Shift the Kinetic Transition State and Barrier Height of Protein Folding," Proc. Nat'l Academy of Sciences USA, vol. 104, no. 37, pp. 14646-14651, 2007.
[11] P. Ao, "Global View of Bionetwork Dynamics: Adaptive Landscape," J. Genetics and Genomics, vol. 36, no. 2, pp. 63-73, 2009.
[12] D. Nevozhay, R. Adams, K. Murphy, K. Josić, and G. Balázsi, "Negative Autoregulation Linearizes the Dose-Response and Suppresses the Heterogeneity of Gene Expression," Proc. Nat'l Academy of Sciences USA, vol. 106, no. 13, pp. 5123-5128, 2009.
[13] D. Gillespie, "Stochastic Simulation of Chemical Kinetics," Ann. Rev. Physical Chemistry, vol. 58, pp. 35-55, 2007.
[14] V. Shahrezaei and P. Swain, "Analytical Distributions for Stochastic Gene Expression," Proc. Nat'l Academy of Sciences USA, vol. 105, no. 45, pp. 17256-17261, 2008.
[15] T. Gardner, C. Cantor, and J. Collins, "Construction of a Genetic Toggle Switch in Escherichia Coli," Nature, vol. 403, pp. 339-342, 2000.
[16] S. Mehra, S. Charaniya, E. Takano, and W. Hu, "A Bistable Gene Switch for Antibiotic Biosynthesis: The Butyrolactone Regulon in Streptomyces coelicolor," PLoS One, vol. 3, no. 7, p. e2724, 2008.
[17] M. Thattai and A. van Oudenaarden, "Intrinsic Noise in Gene Regulatory Networks," Proc. Nat'l Academy of Sciences USA, vol. 98, no. 15, pp. 8614-8619, 2001.
[18] L. Cai, N. Friedman, and X. Xie, "Stochastic Protein Expression in Individual Cells at the Single Molecule Level," Nature, vol. 440, no. 7082, pp. 358-362, 2006.
[19] D. Bratsun, D. Volfson, L. Tsimring, and J. Hasty, "Delay-Induced Stochastic Oscillations in Gene Regulation," Proc. Nat'l Academy of Sciences USA, vol. 102, no. 41, pp. 14593-14598, 2005.
[20] N. Marianayagam, M. Sunde, and J. Matthews, "The Power of Two: Protein Dimerization in Biology," Trends in Biochemical Sciences, vol. 29, no. 11, pp. 618-625, 2004.
[21] N. Buchler, U. Gerland, and T. Hwa, "Nonlinear Protein Degradation and the Function of Genetic Circuits," Proc. Nat'l Academy of Sciences USA, vol. 102, no. 27, pp. 9559-9564, 2005.
[22] D. Wilkinson, Stochastic Modelling for Systems Biology. Chapman and Hall/CRC, 2006.
[23] D. Goeddel, D. Yansura, and M. Caruthers, "Binding of Synthetic Lactose Operator DNAs to Lactose Repressors," Proc. Nat'l Academy of Sciences USA, vol. 74, no. 8, pp. 3292-3296, 1977.
[24] P. Smolen, D. Baxter, and J. Byrne, "Modeling Circadian Oscillations with Interlocking Positive and Negative Feedback Loops," J. Neuroscience, vol. 21, no. 17, pp. 6644-6656, 2001.
[25] N. Buchler, U. Gerland, and T. Hwa, "Nonlinear Protein Degradation and the Function of Genetic Circuits," Proc. Nat'l Academy of Sciences USA, vol. 102, no. 27, pp. 9559-9564, 2005.
[26] H. De Jong, "Modeling and Simulation of Genetic Regulatory Systems: A Literature Review," J. Computational Biology, vol. 9, no. 1, pp. 67-103, 2002.
[27] E. Takano, T. Nihira, Y. Hara, J. Jones, C. Gershater, Y. Yamada, and M. Bibb, "Purification and Structural Determination of SCB1, a $\gamma$ -Butyrolactone that Elicits Antibiotic Production in Streptomyces Coelicolor A3 (2)," J. Biological Chemistry, vol. 275, no. 15, pp. 11010-11016, 2000.
[28] E. Takano, H. Kinoshita, V. Mersinias, G. Bucca, G. Hotchkiss, T. Nihira, C. Smith, M. Bibb, W. Wohlleben, and K. Chater, "A Bacterial Hormone(the SCB 1) Directly Controls the Expression of a Pathway-Specific Regulatory Gene in the Cryptic Type I Polyketide Biosynthetic Gene Cluster of Streptomyces Coelicolor," Molecular Microbiology, vol. 56, no. 2, pp. 465-479, 2005.
[29] T. Perkins and P. Swain, "Strategies for Cellular Decision-Making," Molecular Systems Biology, vol. 5, no. 1, pp. 326-341, 2009.
[30] H. Kim and E. Gelenbe, "G-Networks Based Two Layer Stochastic Modeling of Gene Regulatory Networks with Post-Translational Processes," Interdisciplinary Bio Central, vol. 3, pp. 1-8, 2011.
[31] E. Gelenbe and R. Muntz, "Probabilistic Models of Computer Systems Part I (Exact Results)," Acta Informatica, vol. 7, no. 1, pp. 35-60, 1976.
[32] E. Gelenbe, "Diffusion Approximations: Waiting Times and Batch Arrivals," Acta Informatica, vol. 12, pp. 285-303, 1979.
[33] E. Gelenbe and R. Schassberger, "Stability of Product form G-Networks," Probability in the Eng. and Informational Sciences, vol. 6, no. 3, pp. 271-276, 1992.
[34] E. Gelenbe, "G-Networks with Signals and Batch Removal," Probability in the Eng. and Informational Sciences, vol. 7, no. 3, pp. 335-342, 1993.
[35] E. Gelenbe and A. Labed, "G-Networks with Multiple Classes of Signals and Positive Customers," European J. Operational Research, vol. 108, no. 2, pp. 293-305, 1998.
[36] E. Gelenbe and J. Fourneau, "Random Neural Networks with Multiple Classes of Signals," Neural Computation, vol. 11, no. 4, pp. 953-963, 1999.
[37] E. Gelenbe, "Network of Interacting Synthetic Molecules in Equilibrium," Proc. Royal Soc. A (Math. and Physical Sciences), vol. 464, pp. 2219-2228, 2008.
[38] E. Gelenbe, "Genetic Algorithms with Analytical Solution," Proc. First Ann. Conf. Genetic Programming, pp. 437-443, 1996.
[39] E. Gelenbe, "Search in Unknown Random Environments," Physical Rev. E, vol. 82, no. 6, p. 061112, 2010.

Index Terms:
stochastic processes,biochemistry,cellular biophysics,genetics,microorganisms,molecular biophysics,proteins,oscillatory expressions,stochastic gene expression modeling,Hill function,switch-like gene response,Gillespie algorithm,biologically appropriate reaction rates,toggled switch model,proteins,ScbA-ScbR system,antibiotic metabolite production,microorganisms,Proteins,Mathematical model,Switches,Stochastic processes,Gene expression,Equations,Degradation,Gillespie algorithm.,Stochastic gene expression modeling,gene regulatory networks,switch-like gene responses
Citation:
Haseong Kim, E. Gelenbe, "Stochastic Gene Expression Modeling with Hill Function for Switch-Like Gene Responses," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 4, pp. 973-979, July-Aug. 2012, doi:10.1109/TCBB.2011.153
Usage of this product signifies your acceptance of the Terms of Use.