scholarly journals GPU-Accelerated Steady-State Computation of Large Probabilistic Boolean Networks

2016 ◽  
pp. 50-66 ◽  
Author(s):  
Andrzej Mizera ◽  
Jun Pang ◽  
Qixia Yuan
Keyword(s):  
Steady State ◽  
Boolean Networks ◽  
Probabilistic Boolean Networks

scholarly journals Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks

2003 ◽  
Vol 4 (6) ◽  
pp. 601-608 ◽  
Author(s):  
Ilya Shmulevich ◽  
Ilya Gluhovsky ◽  
Ronaldo F. Hashimoto ◽  
Edward R. Dougherty ◽  
Wei Zhang
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Markov Chains ◽  
Regulatory Networks ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Long Run ◽  
Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.

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