In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.

Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to the dynamic case, and show how to search for structure when some of the variables are hidden. Finally, we examine two applications where such a technology might be useful: predicting and classifying dynamic behaviors, and learning causal orderings in biological processes. We provide empirical results that demonstrate the applicability of our methods in both domains. 1

Recently, there has been much interest in reverse engineering genetic networks from time series data. In this paper, we show that most of the proposed discrete time models — including the boolean network model [Kau93, SS96], the linear model of D’haeseleer et al. [DWFS99], and the nonlinear model of Weaver et al. [WWS99] — are all special cases of a general class of models called Dynamic Bayesian Networks (DBNs). The advantages of DBNs include the ability to model stochasticity, to incorporate prior knowledge, and to handle hidden variables and missing data in a principled way. This paper provides a review of techniques for learning DBNs. Keywords: Genetic networks, boolean networks, Bayesian networks, neural networks, reverse engineering, machine learning. 1

ABSTRACT Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

In this paper, we review the qualitative tools developed by our group for the analysis of regulatory networks. Focusing on the dynamical and biological roles of feedback circuits, this method can be applied in the context of both logical and differential formalisms. This approach already led to several interesting results about the relation between the network structure and the corresponding dynamical properties. In particular, it could be shown that at least one positive regulatory circuit is necessary to generate multistationarity (i.e., alternative states of gene expression), whereas at least one negative circuit is necessary to generate a stable oscillatory behavior. Applications to the analysis of complex gene networks, as well as to the synthesis of regulatory models to account for global expression data are discussed.

Motivation: Genetic networks regulate key processes in living cells. Various methods have been suggested to reconstruct network architecture from gene expression data. However, most approaches are based on qualitative models that provide only rough approximations of the underlying events, and lack the quantitative aspects that are critical for understanding the proper function of biomolecular systems. Results: We present fine-grained dynamical models of gene transcription and develop methods for reconstructing them from gene expression data within the framework of a generative probabilistic model. Unlike previous works, we employ quantitative transcription rates, and simultaneously estimate both the kinetic parameters that govern these rates, and the activity levels of unobserved regulators that control them. We apply our approach to expression data sets from yeast and show that we can learn the unknown regulator activity profiles, as well as the binding affinity parameters. We also introduce a novel structure learning algorithm, and demonstrate its power to accurately reconstruct the regulatory network from those data sets.

The following two matters should be resolved for biosimulation tools in order to be accepted by users in biology/medicine; (1) Remove issues which are irrelevant to biological importance, and (2) Allow users to represent biopathways intuitively and understand/manage easily the details of representation and simulation mechanism. From these criteria, we firstly define a novel notion of Petri net called hybrid functional Petri net (HFPN). Then, we introduce a software tool, Genomic Object Net, for representing and simulating biopathways, which we have developed by employing the architecture of HFPN. In order to show the effectiveness of Genomic Object Net for representing and simulating biopathways, we show some typical biopathway modelings related to gene regulation (switching mechanism of λ phage, circadian rhythm of Drosophila, lacoperon regulatory mechanism of E. coli), metabolic pathway (glycolitic pathway), and signal transduction (Fas ligand induced apoptosis)), which cover the basic aspects in biopathways. The software is available to academic users from

A major current challenge is to understand the design principles of gene regulation networks. It is therefore of interest to study the properties of regulatory structures, or “motifs”, that occur frequently

Motivation: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to recover a complex functional network from biologically reasonable simulated data.

Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinite-dimensional linear ordinary differential equations (ODEs), which can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the master equation; a decaying-dimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. 1