Boolean networks are coarse-grained models of the regulatory dynamics that controls the survival and proliferation of a living cell. The dynamics is time- and state-discrete. This Boolean abstraction assumes that small differences in concentration levels are irrelevant; and the binary distinction of a low or a high concentration of each biomolecule is sufficient to capture the dynamics. In this work, we briefly introduce the gene regulatory models, where with the advent of system-specific Boolean models, new conceptual questions and analytical and numerical challenges arise. In particular, the response of the system to external intervention presents a novel area of research. Thus first we investigate how to quantify a node\\\''s individual impact on dynamics in a more detailed manner than an averaging against all eligible perturbations. Since each node now represents a specific biochemical entity, it is the subject of our interest. The prediction of nodes\\\'' dynamical impacts from the model may be compared to the empirical data from biological experiments. Then we develop a hybrid model that incorporates both continuous and discrete random Boolean networks to compare the reaction of the dynamics against small as well as flip perturbations in different regimes. We show that the chaotic behaviour disappears in high sensitive Boolean ensembles with respect to continuous small fluctuations in contrast to the flipping. Finally, we discuss the role of distributing delays in stabilizing of the Boolean dynamics against noise. These studies are expected to trigger additional experiments and lead to improvement of models in gene regulatory dynamics.

Modeling complex gene interacting systems as Boolean networks lead to a significant simplification of computational investigation. This can be achieved by discretization of the expression level to ON or OFF states and classifying the interactions to inhibitory and activating. In this respect, Boolean functions are responsible for the evolution of the binary elements of the Boolean networks. In this thesis, we investigate the mostly used Boolean functions in modeling gene regulatory networks. Moreover, we introduce a new type of function with strong inhibitory namely the veto function. Our computational and analytic studies on the verity of the networks capable of constructing the same State Transition Graph lead to define a new concept namely the “degeneracy” of Boolean functions. We further derive analytically the sensitivity of the Boolean functions to perturbations. It turns out that the veto function forms the most robust dynamics. Furthermore, we verify the applicability of veto function to model the yeast cell cycle networks. In particular, we show that in an intracellular signal transduction network [Helikar et al, PNAS (2008)], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. The statistics of the connections of the functional networks are studied in detail. Finally, we look at a different scale of biological phenomena using a binary model. We propose a simple correlation-based model to describe the pattern formation of Fly eye. Specifically, we model two different procedures of Fly eye formation, and provide a generic approach for Fly eye simulation.

<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.

Understanding the mechanisms of gene regulation in the field of systems biology is a very important issue. With the development of bio-information technology, we can capture large quantities of gene¡¦s expression data from DNA microarray data. In order to discover the relationship of gene regulation, the simulation of gene regulatory networks have been proposed. Among these simulations methods, the S-system model is the most widely used in non-linear differential equations. It can simulate the dynamic behavior of gene regulatory networks and gene expression, but can¡¦t explain the structure and orientation of gene regulatory networks. Therefore, we propose a Boolean knowledge-based approach to assist the S-system modeling of gene regulatory networks. In this study, we derive the positive and negative regulatory relationships between genes from the regulation of S-system parameters, and use the structure of Boolean networks as our knowledge base. According to the results of the experiment, we can verify our assumptions for the regulation of the S-system parameters, and also has a better understanding of the regulatory relationship between genes.

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.

abstract: Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level. / Dissertation/Thesis / Ph.D. Computer Science 2013

With the transition from single-core to multi-core computing and CMOS technology reaching its physical limits, new computing architectures which are scalable, robust, and low-power are required. A promising alternative to conventional computing architectures are Cellular Automata (CA) networks and Random Boolean Networks (RBN), where simple computational nodes combine to form a network that is capable of performing a larger computational task. It has previously been shown that RBNs can offer superior characteristics over mesh networks in terms of robustness, information processing capabilities, and manufacturing costs while the locally connected computing elements of a CA network provide better scalability and low average interconnect length. This study presents a low level hardware analysis of these architectures using a framework which generates the HDL code and netlist of these networks for various network parameters. The HDL code and netlists are then used to simulate these new computing architectures to estimate the latency, area and power consumed when implemented on silicon and performing a pre-determined computation. We show that for RBNs, information processing is faster compared to a CA network, but CA networks are found to a have lower and better distribution of power dissipation than RBNs because of their regular structure. A well-established task to determine the latency of operation for these architectures is presented for a good understanding of the effect of non-local connections in a network. Programming the nodes for this purpose is done externally using a novel self-configuration algorithm requiring minimal hardware. Configuration for RBNs is done by sending in configuration packets through a randomly chosen node. Logic for identifying the topology for the network is implemented for the nodes in the RBN network to enable compilers to analyze and generate the configuration bit stream for that network. On the other hand, the configuration of the CA network is done by passing in configuration data through the inputs on one of the sides of the cell array and shifting it into the network. A study of the overhead of the network configuration and topology identification mechanisms are presented. An analysis of small-world networks in terms of interconnect power and information propagation capability has been presented. It has been shown that small-world networks, whose randomness lies between that of completely regular and completely irregular networks, are realistic while providing good information propagation capability. This study provides valuable information to help designers make decisions for various performance parameters for both RBN and CA networks, and thus to find the best design for the application under consideration.

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