Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper. 1

We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and differences between different types of RBNs with the aid of a public software laboratory we developed. Particularly, we find that the point attractors are independent of the updating scheme, and that RBNs are more different depending on their determinism or non-determinism rather than depending on their synchronicity or asynchronicity. We also show a way of mapping non-synchronous deterministic RBNs into synchronous RBNs. Our results are important for justifying the use of specific types of RBNs for modelling natural phenomena.

Biological development is a remarkably complex process. A single cell, in an appropriate environment, contains su#cient information to generate a variety of di#erentiated cell types, whose spatial and temporal dynamics interact to form detailed morphological patterns. While several di#erent physical and chemical processes play an important role in the development of an organism, the locus of control is the cell's gene regulatory network.

Evolution depends on the possibility of successfully exploring fitness landscapes via mutation and recombination. With these search procedures, exploration is difficult in ”rugged” fitness landscapes, where small mutations can drastically change functionalities in an organism. Random Boolean networks (RBNs), being general models, can be used to explore theories of how evolution can take place in rugged landscapes; or even change the landscapes. In this paper, we study the effect that redundant nodes have on the robustness of RBNs. Using computer simulations, we have found that the addition of redundant nodes to RBNs increases their robustness. We conjecture that redundancy is a way of ”smoothing ” fitness landscapes. Therefore, redundancy can facilitate evolutionary searches. However, too much robustness could reduce the rate of adaptation of an evolutionary process.

Abstract This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary cellular automata. We provide formulae for the probability of finding a node in state 1 at a time t for the class of Asynchronous Random Boolean Networks (ARBN) in which only one node is updated at every time step, and for the class of Generalized ARBNs (GARBN) in which a random number of nodes can be updated at each time point. We use simulation methods to generate consecutive states of the network for both the real system and the models under the various schemes. The results match well. We study the dynamics of the models through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show, both theoretically and by example, that the ARBNs generate an ordered behavior regardless of the updating scheme used, whereas the GARBNs have behaviors that range from order to chaos depending on the type of random variable used to determine the number of nodes to be updated and the parameter combinations. 1.

Abstract — A Kauffman network is an abstract model of gene regulatory networks. Each gene is represented by a vertex. An edge from one vertex to another implies that the former gene regulates the latter. Statistical features of Kauffman networks match the characteristics of living cells. The number of cycles in the network’s state space, called attractors, corresponds to the number of different cell types. The attractor’s length corresponds to the cell cycle time. The sensitivity of attractors to different kinds of disturbances, modeled by changing a network connection, the state of a vertex, or the associated function, reflects the stability of the cell to damage, mutations and virus attacks. In order to evaluate attractors, their number and lengths have to be computed. This problem is the major open problem related to Kauffman networks. Available algorithms can only handle networks with less than a hundred vertices. The number of genes in a cell is often larger. In this paper, we present a set of efficient algorithms for computing attractors in large Kauffman networks. The resulting software package is hoped to be of assistance in understanding the principles of gene interactions and discovering a computing scheme operating on these principles. I.

Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little attention paid to the dynamical role of a feedback loop, which is a circular chain of interactions between Boolean variables. We note that such feedback loops are ubiquitously found in various biological systems as multiple coupled structures and they are often the primary cause of complex dynamics. In this article, we investigate the relationship between the multiple coupled feedback loops and the dynamics of Boolean networks. We show that networks have a larger proportion of basins corresponding to fixed-point attractors as they have more coupled positive feedback loops, and a larger proportion of basins for limit-cycle attractors as they have more coupled negative feedback loops.

As with most of the graduate students close to finish their thesis, I waited until the very last minute to write this section. And while it may seem as a sign of laziness, it represents maybe the most difficult episode of the entire work. There are so many people to thank that I’m sure I will forget some. Anyway, here I go: First of all, I would like to thank my advisor Dr. J. Carson Meredith. His orientation, unwavering support, and especially, his infinite patience were essential during the course of this work. I have never met anybody with more broad-ranging knowledge and interests. I have to say that his enthusiasm to custom build every single piece of equipment needed in our lab is contagious and makes you feel it is possible to do everything you want to do, you just have to try. I would like to thank all the members of the thin-film and colloid research group. To Joe-Lahai Sormana, the best yahoo pool “runner-up ” I’ve ever seen, thanks for all the laughs and “free ” entertainment provided during these years, although I still believe you should not consider a professional singer career. Krishna Tej Marla whose impressive physical insight is only matched by his affinity for chemical potentials, and that alone is

Background: Microarray technologies have become common tools in biological research. As a result, a need for effective computational methods for data analysis has emerged. Numerous different algorithms have been proposed for analyzing the data. However, an objective evaluation of the proposed algorithms is not possible due to the lack of biological ground truth information. To overcome this fundamental problem, the use of simulated microarray data for algorithm validation has been proposed. Results: We present a microarray simulation model which can be used to validate different kinds of data analysis algorithms. The proposed model is unique in the sense that it includes all the steps that affect the quality of real microarray data. These steps include the simulation of biological ground truth data, applying biological and measurement technology specific error models, and finally simulating the microarray slide manufacturing and hybridization. After all these steps are taken into account, the simulated data has realistic biological and statistical characteristics. The applicability of the proposed model is demonstrated by several examples. Conclusion: The proposed microarray simulation model is modular and can be used in different

this document may be downloaded from: http://www.itee.uq.edu.au/nic/ accs-grn/modelling-grns.pdf Overview This document provides an overview of approaches to the modelling of genetic regulatory networks, with an emphasis on techniques from complex systems