Stochastic S-system modeling of gene regulatory network

Abstract Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli.

[1]  Suresh Kumar Poovathingal,et al.  Global parameter estimation methods for stochastic biochemical systems , 2010, BMC Bioinformatics.

[3]  E. O. Voit,et al.  Biochemical systems analysis of genome-wide expression data , 2000, Bioinform..

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

[5]  I. Shmulevich,et al.  Deterministic and stochastic models of genetic regulatory networks. , 2009, Methods in enzymology.

[6]  P J Goss,et al.  Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Hitesh Mistry,et al.  Stochastic Modeling of Gene Regulatory Networks , 2007 .

[8]  Takanori Ueda,et al.  Inference of Genetic Network Using the Expression Profile Time Course Data of Mouse P19 Cells , 2002 .

[9]  K. Burrage,et al.  Stochastic models for regulatory networks of the genetic toggle switch. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Tianhai Tian,et al.  Stochastic models for inferring genetic regulation from microarray gene expression data , 2010, Biosyst..

[11]  A. Goldbeter,et al.  Robustness of circadian rhythms with respect to molecular noise , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[12]  M. Groudine,et al.  Enhancers increase the probability but not the level of gene expression. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Ahsan Raja Chowdhury,et al.  An improved method to infer Gene Regulatory Network using S-System , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[14]  A. Arkin,et al.  Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. , 1998, Genetics.

[15]  Kwang-Hyun Cho,et al.  Inferring gene regulatory networks from temporal expression profiles under time-delay and noise , 2007, Comput. Biol. Chem..

[16]  N. Noman.  A memetic algorithm for reconstructing gene regulatory networks from expression profile , 2007 .

[17]  Tianhai Tian,et al.  Implicit Taylor methods for stiff stochastic differential equations , 2001 .

[18]  Aurélien Mazurie,et al.  Gene networks inference using dynamic Bayesian networks , 2003, ECCB.

[19]  Cheng-Fa Cheng,et al.  Robust stability of stochastic delayed genetic regulatory networks , 2014, 2014 CACS International Automatic Control Conference (CACS 2014).

[20]  Xuan Vinh Nguyen,et al.  Adaptive regulatory genes cardinality for reconstructing genetic networks , 2012, 2012 IEEE Congress on Evolutionary Computation.

[21]  Jinde Cao,et al.  Robust stability of genetic regulatory networks with distributed delay , 2008, Cognitive Neurodynamics.

[22]  Xiaoxin Liao,et al.  Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic , 2010, Cognitive Neurodynamics.

[23]  M Wahde,et al.  Coarse-grained reverse engineering of genetic regulatory networks. , 2000, Bio Systems.

[24]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

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

[26]  E. Cox,et al.  Real-Time Kinetics of Gene Activity in Individual Bacteria , 2005, Cell.

[27]  Linda R. Petzold,et al.  Stochastic modelling of gene regulatory networks , 2005 .

[28]  A. Goldbeter.  A model for circadian oscillations in the Drosophila period protein (PER) , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[29]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[30]  D. Bernardo,et al.  A Yeast Synthetic Network for In Vivo Assessment of Reverse-Engineering and Modeling Approaches , 2009, Cell.

[31]  K. F. Tipton,et al.  Biochemical systems analysis: A study of function and design in molecular biology , 1978 .

[32]  D. Bennett,et al.  Differentiation in mouse melanoma cells: Initial reversibility and an on-off stochastic model , 1983, Cell.

[33]  Linda R. Petzold,et al.  Improved leap-size selection for accelerated stochastic simulation , 2003 .

[34]  M. Savageau.  Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[35]  David M. Rocke,et al.  A Model for Measurement Error for Gene Expression Arrays , 2001, J. Comput. Biol..

[36]  Y. Tu,et al.  Quantitative noise analysis for gene expression microarray experiments , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[37]  Xuan Vinh Nguyen,et al.  Incorporating time-delays in S-System model for reverse engineering genetic networks , 2013, BMC Bioinformatics.

[38]  Zhengxia Wang,et al.  Robust stability of stochastic delayed genetic regulatory networks , 2014, Cognitive Neurodynamics.

[39]  Masaru Tomita,et al.  Dynamic modeling of genetic networks using genetic algorithm and S-system , 2003, Bioinform..

[40]  Jan Walleczek,et al.  Self-Organized Biological Dynamics and Nonlinear Control , 2006 .

[41]  D. Wilkinson.  Stochastic modelling for quantitative description of heterogeneous biological systems , 2009, Nature Reviews Genetics.

[42]  U. Alon,et al.  Assigning numbers to the arrows: Parameterizing a gene regulation network by using accurate expression kinetics , 2002, Proceedings of the National Academy of Sciences of the United States of America.