Combining Agent-Based Models with Stochastic Differential Equations for Gene Regulatory Networks

Mathematical models in systems biology can use quantitative techniques to study the integrated behaviors of biological systems in macro level. Agent-based modeling provides a qualitative framework, focusing on how each individual molecule behaves in micro level. We are motivated to combine their features together to describe the gene regulatory networks, in particular the emergence of macro phenomena from micro interactions. An agent-based model will be well defined as general as possible, including of many agents of various molecular species interacting in it. The mathematical premises, which are grounded in the micro behaviors of agents, can derive the chemical master equations and the stochastic differential equations for modeling the integrated behaviors of systems in macro level. Combing agent-based models with stochastic differential equations affords a more complete perspective on gent regulatory networks. In addition, the sources and magnitudes of deterministic dynamics and random noises are explicitly characterized.

[1]  Eberhard O Voit,et al.  Models-of-data and models-of-processes in the post-genomic era. , 2002, Mathematical biosciences.

[2]  P. Woolf,et al.  A fuzzy logic approach to analyzing gene expression data. , 2000, Physiological genomics.

[3]  Joshua M. Epstein,et al.  Generative Social Science: Studies in Agent-Based Computational Modeling (Princeton Studies in Complexity) , 2007 .

[4]  Cheng-Yan Kao,et al.  A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae , 2005, Bioinform..

[5]  Adriana Climescu-Haulica,et al.  A stochastic differential equation model for transcriptional regulatory networks , 2007, BMC Bioinformatics.

[6]  Eric Bonabeau,et al.  Agent-based modeling: Methods and techniques for simulating human systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Jiri Vohradsky,et al.  Nonlinear differential equation model for quantification of transcriptional regulation applied to microarray data of Saccharomyces cerevisiae , 2006, Nucleic acids research.

[8]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[9]  Terence Hwa,et al.  Extracting transcriptional events from temporal gene expression patterns during Dictyostelium development , 2002, Bioinform..

[10]  D. Gillespie.  The chemical Langevin equation , 2000 .

[11]  Nir Friedman,et al.  Inferring quantitative models of regulatory networks from expression data , 2004, ISMB/ECCB.