Boolean Models of Genomic Regulatory Networks: Reduction Mappings, Inference, and External Control

Ivan Ivanov

doi:10.2174/138920209789177584

Abstract

Computational modeling of genomic regulation has become an important focus of systems biology and genomic signal processing for the past several years. It holds the promise to uncover both the structure and dynamical properties of the complex gene, protein or metabolic networks responsible for the cell functioning in various contexts and regimes. This, in turn, will lead to the development of optimal intervention strategies for prevention and control of disease. At the same time, constructing such computational models faces several challenges. High complexity is one of the major impediments for the practical applications of the models. Thus, reducing the size/complexity of a model becomes a critical issue in problems such as model selection, construction of tractable subnetwork models, and control of its dynamical behavior. We focus on the reduction problem in the context of two specific models of genomic regulation: Boolean networks with perturbation (BNP) and probabilistic Boolean networks (PBN). We also compare and draw a parallel between the reduction problem and two other important problems of computational modeling of genomic networks: the problem of network inference and the problem of designing external control policies for intervention/altering the dynamics of the model.

Highlights

One can think of a Gene Regulatory Network (GRN) as a network of relations among strands of DNA and the regulatory activities associated with those genes [1]
Because every probabilistic Boolean networks (PBN) is a collection of individual BNs endowed with a probability structure and gene mutation probability, we focus on reduction mappings for Boolean networks
The reduction problem in its very general formulation emphasizes the role of constraints in the process of designing reduction mappings for probabilistic Boolean networks

Summary

INTRODUCTION

One can think of a Gene Regulatory Network (GRN) as a network of relations among strands of DNA (genes) and the regulatory activities associated with those genes [1]. The two interpretations of the attractors in the Boolean network model are complementary to each other: for a given cell type, different functional states exist and are determined by Boolean Models of Genomic Regulatory Networks the collective gene activity. The infinite-horizon intervention strategies have been studied using stochastic control combined with dynamic programming algorithms This approach has led to finding of stationary control policies that affect the steady-state distribution of a given PBN? Without loss of generality one can assume that the gene x is the leftmost gene in the states' binary representations, i.e. x1 = x and s = [x, x2,..., xn ] , and the desirable states correspond to the value x = 0 With this assumption, the probability transition matrix P of the Markov chain representing the PBN can be written as. Is a sub-optimal one it can approximate well the optimal control policy which being a solution to the Bellman optimality equation is a stationary one [23, 26, 27]

REDUCTION MAPPINGS FOR PBN

The Reduction Problem

Reduction and Inference

Reduction and Control

Findings

CONCLUSIONS