Optimal Intervention Methods for Markovian Gene Regulatory Networks

A central problem in translational medicine is to provide a framework for deriving and studying effective intervention methods to elicit desired steady-state behavior for a gene regulatory network of interest with Markovian dynamics. Heretofore, two rather different external control approaches have been taken. The first optimizes a subjectively defined cost function while modeling treatment constraints; therefore, desirable shift of the steady-state mass is a by-product. The second approach, on the other hand, focuses solely on the steady-state behavior of the network and provides the maximal shift achievable. Although both approaches are optimal with respect to their objectives, the choice of which to use depends on the treatment goals.

Dynamical Analysis of Drug Efficacy and Mechanism of Action Using GFP Reporters

To the development of effective cancer drug, it is necessary to, first, identify drugs and their possible combinations that could exert desired control over the type of cancer being considered; second, have a drug testing method that allows one to assess the variety of responses that can be provoked by drugs. To facilitate such an experiment-modeling-experiment cycle for drug development, a method based on the dynamical systems of pathways is presented. It involves a three-state experimental design: (1) formulate an oncologic pathway model of relevant cancer; (2) perturb the pathways with the drugs of known effects on components of the pathways of interest; and (3) measure process activity indicators at various points on cell populations. To evaluate the drug response in a high-throughput manner, a green fluorescent protein reporter-based technology has been developed. The authors apply the dynamical approach to several issues in the context of colon cancer cell lines.

Why Are Multiple Regulators Required for Transcription of Each Gene?

The human genome has been proposed to contain numerous regions called “consensus sequences” that are recognized by DNA-binding proteins required for gene expression. Results obtained with a computer simulation showed that: (1) all random sequences consisting of less than 15 base pairs were present in the human genome, and (2) consensus sequences reported to date were found in an artificial genome created randomly by a computer. These results suggest that conserved sequences consisting of more than 15 base pairs are required for accurate gene expression. No consensus sequence consisting of more than 15 base pairs has been identified to date. Thus, the co-association of multiple proteins bound side by side is required for appropriate gene expression because the total number of conserved sequences can exceed 15, whereas the binding of a single protein has no physiological role because its consensus sequence is present randomly in the human genome.

Structural Intervention and External Control for Markovian Regulatory Network Models

In order to derive system-based methods to control dynamic behavior of biological systems of interest for future gene-based intervention therapeutics, two basic categories of intervention strategies have been studied based on the Markov chain theory and Markov decision processes: Structural intervention by function perturbation and external control based on state perturbation. The chapter reviews the existing network analysis and control methods in these two categories and discusses their extensions for more robust and clinically relevant intervention strategies considering collateral damages from intervention.

Inference of Gene Regulatory Networks by Topological Prior Information and Data Integration

The inference of Gene Regulatory Networks (GRNs) is a very challenging problem which has attracted increasing attention since the development of high-throughput sequencing and gene expression measurement technologies. Many models and algorithms have been developed to identify GRNs using mainly gene expression profile as data source. As the gene expression data usually has limited number of samples and inherent noise, the integration of gene expression with several other sources of information can be vital for accurately inferring GRNs. For instance, some prior information about the overall topological structure of the GRN can guide inference techniques toward better results. In addition to gene expression data, recently biological information from heterogeneous data sources have been integrated by GRN inference methods as well. The objective of this chapter is to present an overview of GRN inference models and techniques with focus on incorporation of prior information such as, global and local topological features and integration of several heterogeneous data sources.

Computational Inference of Gene Regulation from Whole-Transcriptome Analysis of Early Embryos

To ensure totipotency of new zygotes, immediately after fertilization, two gametes activate genetic and epigenetic processes that highly interplay and lead to sequential waves of gene expression. Since the first report of fertilization a hundred years ago, a long-standing question to what factors govern the dramatic transcriptional changes remains elusive. Recently, significant advances in biological experiment technology and computational methodology have taken place in understanding of the regulatory dynamics during fertilization. This chapter provides an overview of the recent progress in characterizing mammalian fertilization, and focuses on the computational methods applicable to the inference of regulation for understanding early embryo development. In particular, this chapter introduces the linear regression modeling and log-linear graphical modeling to identify potential key regulators in the higher-order conditional distribution where statistical paradox often occurs.

Relationships between Models of Genetic Regulatory Networks with Emphasis on Discrete State Stochastic Models

Genetic Regulatory Networks (GRNs) represent the interconnections between genomic entities that govern the regulation of gene expression. GRNs have been represented by various types of mathematical models that capture different aspects of the biological system. This chapter discusses the relationships among the most commonly used GRN models that can enable effective integration of diverse types of sub-models. A detailed model in the form of stochastic master equation is described, followed by it coarse-scale and deterministic approximations in the form of Probabilistic Boolean Networks and Ordinary Differential Equation models respectively.

Prioritize Transcription Factor Binding Sites for Multiple Co-Expressed Gene Sets Based on Lasso Multinomial Regression Models

Computational prediction of cis-regulatory elements for a set of co-expressed genes based on sequence analysis provides an overwhelming volume of potential transcription factor binding sites. It presents a challenge to prioritize a set of functional transcription factors and their binding sites on the regulatory regions of the target genes that are relevant to the gene expression study. A novel approach based on the use of lasso multinomial regression models is proposed to address this problem. We examine the ability of the lasso models using a time-course microarray data obtained from a comprehensive study of gene expression profiles in skin and mucosal in mouse over all stages of wound healing.

Modeling Stochastic Gene Regulatory Networks Using Direct Solutions of Chemical Master Equation and Rare Event Sampling

Stochasticity plays important roles in many biological networks. A fundamental framework for studying the full stochasticity is the Discrete Chemical Master Equation (dCME). Under this framework, the combination of copy numbers of molecular species defines the microstate of the molecular interactions in the network. The probability distribution over these microstates provide a full description of the properties of a stochastic molecular network. However, it is challenging to solve a dCME. In this chapter, we will first discuss how to derive approximation methods including Fokker-Planck equation and the chemical Langevin equation from the dCME. We also discuss the widely used stochastic simulation method. After that, we focus on the direct solutions to the dCME. We first discuss the Finite State Projection (FSP) method, and then introduce the recently developed finite buffer method (fb-dCME) for directly solving both steady state and time-evolving probability landscape of dCME. We show the advantages of the fb-dCME method using two realistic gene regulatory networks.