The interact...

Interactions between different genes become more and more important in understanding how they collectively make cells, tissues, organisms, even form a biological system. This gives rise to genetic regulatory networks. Mathematical models and computational methods are widely used to analyze them recently. Probabilistic Boolean network is one proposed to model such systems incorporating uncertainty. Evolution of the system is according to the transition probability matrix. Steady-state (long run behavior) analysis is a key aspect in studying the dynamics of genetic regulatory networks. In this paper, an efficient method to construct the sparse transition probability matrix is proposed, and the power method based on the sparse matrix-vector multiplication is applied to compute the steady-state probability distribution. Such methods provide a tool for us to study the sensitivity of the steady-state distribution to influence of input genes, gene connections and Boolean networks. Simulation results based on a real network are given to illustrate the method and to demonstrate th