The development of cDNA microarray technology has made it possible to simultaneously monitor the expression status of thousands of genes. A natural use for this vast amount of information would be to try and figure out inter-gene relationships by studying the gene expression patterns across different experimental conditions and to build Gene Regulatory Networks from these data. In this thesis, we study some of the issues involved in Genetic Regulatory Networks. One of them is to discover and elucidate multivariate logical predictive relations among gene expressions and to demonstrate how these logical relations based on coarse quantization closely reflect corresponding relations in the continuous data. The other issue involves construction of synthetic Probabilistic Boolean Networks with particular attractor structures. These synthetic networks help in testing of various algorithms like Bayesian Connectivity based approach for design of Probabilistic Boolean Networks.

The development of cDNA microarray technology has made it possible to simultaneously monitor the expression status of thousands of genes. A natural use for this vast amount of information would be to try and figure out inter-gene relationships by studying the gene expression patterns across different experimental conditions and to build Gene Regulatory Networks from these data. In this thesis, we study some of the issues involved in Genetic Regulatory Networks. One of them is to discover and elucidate multivariate logical predictive relations among gene expressions and to demonstrate how these logical relations based on coarse quantization closely reflect corresponding relations in the continuous data. The other issue involves construction of synthetic Probabilistic Boolean Networks with particular attractor structures. These synthetic networks help in testing of various algorithms like Bayesian Connectivity based approach for design of Probabilistic Boolean Networks.

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This dissertation attempts to answer some of the vital questions involved in the genetic regulatory networks: inference, optimization and robustness of the mathe- matical models. Network inference constitutes one of the central goals of genomic signal processing. When inferring rule-based Boolean models of genetic regulations, the same values of predictor genes can correspond to di®erent values of the target gene because of inconsistencies in the data set. To resolve this issue, a consistency-based inference method is developed to model a probabilistic genetic regulatory network, which consists of a family of Boolean networks, each governed by a set of regulatory functions. The existence of alternative function outputs can be interpreted as the result of random switches between the constituent networks. This model focuses on the global behavior of genetic networks and re°ects the biological determinism and stochasticity. When inferring a network from microarray data, it is often the case that the sample size is not su±ciently large to infer the network fully, such that it is neces- sary to perform model selection through an optimization procedure. To this end, the network connectivity and the physical realization of the regulatory rules should be taken into consideration. Two algorithms are developed for the purpose. One algo- rithm ¯nds the minimal realization of the network constrained by the connectivity, and the other algorithm is mathematically proven to provide the minimally connected network constrained by the minimal realization. Genetic regulatory networks are subject to modeling uncertainties and perturba- tions, which brings the issue of robustness. From the perspective of network stability, robustness is desirable; however, from the perspective of intervention to exert in- °uence on network behavior, it is undesirable. A theory is developed to study the impact of function perturbations in Boolean networks: It ¯nds the exact number of a®ected state transitions and attractors, and predicts the new state transitions and robust/fragile attractors given a speci¯c perturbation. Based on the theory, one algorithm is proposed to structurally alter the network to achieve a more favorable steady-state distribution, and the other is designed to identify function perturbations that have caused changes in the network behavior, respectively.

Technology, nowadays, has given us huge computational potential, but computer sciences have major problems tapping into this pool of resources. One of the main issues is how to program and design distributed systems. Biology has solved this issue about half a billion years ago, during the Cambrian explosion: the evolution of multicellularity. The evolution of multicellularity allowed cells to differentiate and so divide different tasks to different groups of cells; this combined with evolution gives us a very good example of how massively parallel distributed computational system can function and be “programmed”. However, the evolution of multicellularity is not very well understood, and most traditional methodologies used in evolutionary theory are not apt to address and model the whole transition to multicellularity. In this thesis I develop and argue for new computational artificial life methodologies for the study of the evolution of multicellularity that are able to address the whole transition, give new insights, and complement existing methods. I argue that these methodologies should have three main characteristics: accessible across scientific disciplines, have potentiality for complex behaviour, and be easy to analyse. To design models, which possess those characteristics, I developed a model of genetic regulatory networks (GRNs) that control artificial cells, which I have used in multiple evolutionary experiments. The first experiment was designed to present some of the engineering problems of evolving multicelled systems (applied to graph-colouring), and to perfect my artificial cell model. The two subsequent experiments demonstrate the characteristics listed above: one model based on a genetic algorithm with an explicit two-level fitness function to evolve multicelled cooperative patterning, and one with freely evolving artificial cells that have evolved some multicelled cooperation as evidenced by novel measures, and has the potential to evolve multicellularity. These experiments show how artificial life models of evolution can discover and investigate new hypotheses and behaviours that traditional methods cannot.

<p>In this thesis several random Boolean networks are simulated. Both completely computer generated network and models for biological networks are simulated. Several different tools are used to gain knowledge about the robustness. These tools are Derrida plots, noise analysis and mean probability for canalizing rules. Some simulations on how entropy works as an indicator on if a network is robust are also included. The noise analysis works by measuring the hamming distance between the state of the network when noise is applied and when no noise is applied. For many of the simulated networks two types of rules are applied: nested canalizing and flat distributed rules. The computer generated networks consists of two types of networks: scale-free and ER-networks. One of the conclusions in this report is that nested canalizing rules are often more robust than flat distributed rules. Another conclusion is that the mean probability for canalizing rules has, for flat distributed rules, a very dominating effect on if the network is robust or not. Yet another conclusion is that the probability distribution for indegrees, for flat distributed rules, has a strong effect on if a network is robust due to the connection between the probability distribution for indegrees and the mean probability for canalizing rules.</p>

All high-level living organisms are made of small cell units, containing DNA, RNA, genes, proteins etc. Genes are important components of the cells and it is necessary to understand the inter-gene relations, in order to comprehend, predict and ultimately intervene in the cells’ dynamics. Genetic regulatory networks (GRN) represent the gene interactions that dictate the cell behavior. Translational genomics aims to mathematically model GRNs and one of the main goals is to alter the networks’ behavior away from undesirable phenotypes such as cancer. The mathematical framework that has been often used for modeling GRNs is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks with perturbation, BNp. This dissertation uses BNps, to model gene regulatory networks with an intent of designing stationary control policies (CP) for the networks to shift their dynamics toward more desirable states. Markov Chains (MC) are used to represent the PBNs and stochastic control has been employed to find stationary control policies to affect steady-state distribution of the MC. However, as the number of genes increases, it becomes computationally burdensome, or even infeasible, to derive optimal or greedy intervention policies. This dissertation considers the problem of modeling and intervening in large GRNs. To overcome the computational challenges associated with large networks, two approaches are proposed: first, a reduction mapping that deletes genes from the network; and second, a greedy control policy that can be directly designed on large networks. Simulation results show that these methods achieve the goal of controlling large networks by shifting the steady-state distribution of the networks toward more desirable states. Furthermore, a new inference method is used to derive a large 17-gene Boolean network from microarray experiments on gastrointestinal cancer samples. The new algorithm has similarities to a previously developed well-known inference method, which uses seed genes to grow subnetworks, out of a large network; however, it has major differences with that algorithm. Most importantly, the objective of the new algorithm is to infer a network from a seed gene with an intention to derive the Gene Activity Profile toward more desirable phenotypes. The newly introduced reduction mappings approach is used to delete genes from the 17-gene GRN and when the network is small enough, an intervention policy is designed for the reduced network and induced back to the original network. In another experiment, the greedy control policy approach is used to directly design an intervention policy on the large 17-gene network to beneficially change the long-run behavior of the network. Finally, a novel algorithm is developed for selecting only non-isomorphic BNs, while generating synthetic networks, using a method that generates synthetic BNs, with a prescribed set of attractors. The goal of the new method described in this dissertation is to discard isomorphic networks.

In this thesis several random Boolean networks are simulated. Both completely computer generated network and models for biological networks are simulated. Several different tools are used to gain knowledge about the robustness. These tools are Derrida plots, noise analysis and mean probability for canalizing rules. Some simulations on how entropy works as an indicator on if a network is robust are also included. The noise analysis works by measuring the hamming distance between the state of the network when noise is applied and when no noise is applied. For many of the simulated networks two types of rules are applied: nested canalizing and flat distributed rules. The computer generated networks consists of two types of networks: scale-free and ER-networks. One of the conclusions in this report is that nested canalizing rules are often more robust than flat distributed rules. Another conclusion is that the mean probability for canalizing rules has, for flat distributed rules, a very dominating effect on if the network is robust or not. Yet another conclusion is that the probability distribution for indegrees, for flat distributed rules, has a strong effect on if a network is robust due to the connection between the probability distribution for indegrees and the mean probability for canalizing rules.

A basic issue for translational genomics is to model gene interactions via gene regulatory networks (GRNs) and thereby provide an informatics environment to derive and study effective interventions eradicating the tumor. In this dissertation, we present two different approaches to intervention methods in cancer-related GRNs. Decisions regarding possible interventions are assumed to be made at every state transition of the network. To account for dosing constraints, a model for the sequence of treatment windows is considered, where treatments are allowed only at the beginning of each treatment cycle followed by a recovery phase. Due to biological variabilities within tumor cells, the action period of an antitumor drug can vary among a population of patients. That is, a treatment typically has a random duration of action. We propose a unified approach to such intervention models for any Markovian GRN governing the tumor. To accomplish this, we place the problem in the general framework of partially controlled decision intervals with infinite horizon discounting cost. We present a methodology to devise optimal intervention policies for synthetically generated gene regulatory networks as well as a mutated mammalian cell-cycle network. As a different approach, we view the phenotype as a characterization of the long- run behavior of the Markovian GRN and desire interventions that optimally move the probability mass from undesirable to desirable states. We employ a linear programming approach to formulate the maximal shift problem, that is, optimization is directly based on the amount of shift. Moreover, the same basic linear programming structure is used for a constrained optimization, where there is a limit on the amount of mass that may be shifted to states that are not directly undesirable relative to the pathology of interest, but which bear some perceived risk. We demonstrate the performance of optimal policies on synthetic networks as well as two real GRNs derived from the metastatic melanoma and mammalian cell cycle. These methods, as any effective cancer treatment must, aim to carry out their actions rapidly and with high efficiency such that a very large percentage of tumor cells die or shift into a state where they stop proliferating.