Steady-state analysis of probabilistic Boolean networks

Abstract This paper investigates steady-state distributions of probabilistic Boolean networks via cascading aggregation. Under this approach, the problem is converted to computing least square solutions to several corresponding equations. Two necessary and sufficient conditions for the existence of the steady-state distributions for probabilistic Boolean networks are given firstly. Secondly, an algorithm for finding the steady-state distributions of probabilistic probabilistic Boolean networks is given. Finally, a numerical example is given to show the effectiveness of the proposed method.

[1]  Zhao Jing,et al.  Observability of probabilistic Boolean networks , 2015, 2015 34th Chinese Control Conference (CCC).

[2]  Wang Yuzhen,et al.  Optimal finite-horizon control problem of context-sensitive probabilistic Boolean networks with perturbation , 2012, Proceedings of the 31st Chinese Control Conference.

[3]  Edward R. Dougherty,et al.  Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks , 2003, Comparative and functional genomics.

[4]  Dianjing Guo,et al.  A new multiple regression approach for the construction of genetic regulatory networks , 2010, Artif. Intell. Medicine.

[5]  Yuzhen Wang,et al.  Further results on feedback stabilization control design of Boolean control networks , 2017, Autom..

[6]  Yang Liu,et al.  Controllability of probabilistic Boolean control networks based on transition probability matrices , 2015, Autom..

[7]  James Lam,et al.  Stability and Stabilization of Boolean Networks With Stochastic Delays , 2019, IEEE Transactions on Automatic Control.

[8]  Wai-Ki Ching,et al.  A semi-tensor product approach for Probabilistic Boolean Networks , 2014, 2014 8th International Conference on Systems Biology (ISB).

[9]  Daizhan Cheng,et al.  Control of Large-Scale Boolean Networks via Network Aggregation , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Zhiqiang Li,et al.  Partial stability of probabilistic Boolean network , 2014, The 26th Chinese Control and Decision Conference (2014 CCDC).

[11]  Daizhan Cheng,et al.  Block Decoupling of Boolean Control Networks , 2019, IEEE Transactions on Automatic Control.

[12]  M. Ng,et al.  Control of Boolean networks: hardness results and algorithms for tree structured networks. , 2007, Journal of theoretical biology.

[13]  Michael K. Ng,et al.  An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks , 2007, Bioinform..

[14]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[15]  Michael K. Ng,et al.  On construction of stochastic genetic networks based on gene expression sequences , 2005, Int. J. Neural Syst..

[16]  Daizhan Cheng,et al.  On controllability and stabilizability of probabilistic Boolean control networks , 2012, Science China Information Sciences.

[17]  Ranadip Pal,et al.  Context-Sensitive Probabilistic Boolean Networks: Steady-State Properties, Reduction, and Steady-State Approximation , 2010, IEEE Transactions on Signal Processing.

[18]  Lijun Zhang,et al.  Controllability of probabilistic Boolean control networks with time-variant delays in states , 2013, 52nd IEEE Conference on Decision and Control.

[19]  Jianwei Xia,et al.  Controllability decomposition of dynamic-algebraic Boolean control networks , 2018, Int. J. Control.

[20]  Richard Banks,et al.  Modelling and Analysing Genetic Networks: From Boolean Networks to Petri Nets , 2006, CMSB.

[21]  Satoru Miyano,et al.  Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data. , 2004 .

[22]  Diana Marculescu,et al.  Tractable Learning and Inference for Large-Scale Probabilistic Boolean Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

[24]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[25]  Jinde Cao,et al.  Synchronization Analysis of Master-Slave Probabilistic Boolean Networks , 2015, Scientific Reports.

[26]  Jianlong Qiu,et al.  Synchronization for the Realization-Dependent Probabilistic Boolean Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Gang Feng,et al.  Stability and $l_1$ Gain Analysis of Boolean Networks With Markovian Jump Parameters , 2017, IEEE Transactions on Automatic Control.

[28]  Jongrae Kim,et al.  Aggregation Algorithm Towards Large-Scale Boolean Network Analysis , 2013, IEEE Transactions on Automatic Control.