Construction of Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix: A Maximum Entropy Rate Approach (East Asian Journal on Applied Mathematics, 2018)
Modeling genetic regulatory networks is an important problem in genomicresearch. Boolean Networks (BNs) and their extensions Probabilistic Boolean Networks(PBNs) have been proposed for modeling genetic regulatory interactions. In a PBN, itssteady-state distribution gives very important information about the long-run behaviorof the whole network. However, one is also interested in system synthesis which requiresthe construction of networks. The inverse problem is ill-posed and challenging, as theremay be many networks or no network having the given properties, and the size of theproblem is huge. The construction of PBNs from a given transition-probability matrixand a given set of BNs is an inverse problem of huge size. We propose a maximumentropy approach for the above problem. Newton’s method in conjunction with theConjugate Gradient (CG) method is then applied to solving the inverse problem. Weinvestigate the convergence rate of the proposed method. Numerical examples are alsogiven to demonstrate the effectiveness of our proposed method.
Keywords: Boolean networks; conjugate gradient method; genetic regulatory networks; inverse problem; Markov chains; Newton's method; probabilistic Boolean networks; transition-probability matrix.