Despite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results.

Various types of recurrent neural networks have been used as models for the regulatory relationships between genes. The neural network is trained on the data from micro-array techniques, each gene corresponds to a neuron in the network. The data from the micro-array technologies has numerous genes, but usually involves few samples, this makes the network heavily under-determined. In this work we will propose a method that can cope with the poorness of the data. We will use a Hopfield-type neural network to model the ontogenetic differentiation of female honeybees. A method that identifies the genes that determine the castes is proposed.

Despite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results.

<p>Various types of recurrent neural networks have been used as models for the regulatory relationships between genes. The neural network is trained on the data from micro-array techniques, each gene corresponds to a neuron in the network. The data from the micro-array technologies has numerous genes, but usually involves few samples, this makes the network heavily under-determined. In this work we will propose a method that can cope with the poorness of the data. We will use a Hopfield-type neural network to model the ontogenetic differentiation of female honeybees. A method that identifies the genes that determine the castes is proposed.</p>

<p>The arrival of microarray technology has produced a lot of expression profiles of genes. The amount of data now available is so huge that new alternate and efficient methods are needed to analyse it. One of the approaches that have been taken is the use of reverse engineering to build up a picture of how the genes are interacting, where one of the obstacles is the amount of calculations needed. Liang et al. (1998) introduced an algorithm called REVEAL, where reverse engineering with entropy and mutual information are used in an attempt to generate the rules of regulation in genetic networks.</p><p>In this dissertation it was investigated if it was possible to compliment the REVEAL algorithm with heuristics. The heuristic approach probed consists of setting a threshold on mutual information values, thereby dismissing combinations of input genes producing values below the threshold value as being non-relevant.</p><p>Four experiments were performed, where each consisted of a different combination of rule complexity, size of network and number of inputs per gene tested.</p><p>The findings of this study are that applying a threshold on mutual information is a realistic option that can reduce the number of calculations and also act as a filter that divides the important information from the irrelevant information. However this method has its limitations; since it is not known in advance where to place the threshold it will always be a chance that true connections fall below the threshold and therefore will be disregarded and not further analysed.</p>

The arrival of microarray technology has produced a lot of expression profiles of genes. The amount of data now available is so huge that new alternate and efficient methods are needed to analyse it. One of the approaches that have been taken is the use of reverse engineering to build up a picture of how the genes are interacting, where one of the obstacles is the amount of calculations needed. Liang et al. (1998) introduced an algorithm called REVEAL, where reverse engineering with entropy and mutual information are used in an attempt to generate the rules of regulation in genetic networks. In this dissertation it was investigated if it was possible to compliment the REVEAL algorithm with heuristics. The heuristic approach probed consists of setting a threshold on mutual information values, thereby dismissing combinations of input genes producing values below the threshold value as being non-relevant. Four experiments were performed, where each consisted of a different combination of rule complexity, size of network and number of inputs per gene tested. The findings of this study are that applying a threshold on mutual information is a realistic option that can reduce the number of calculations and also act as a filter that divides the important information from the irrelevant information. However this method has its limitations; since it is not known in advance where to place the threshold it will always be a chance that true connections fall below the threshold and therefore will be disregarded and not further analysed.

In this work three different approaches for deriving genetic association networks were tested. The three approaches were Pearson correlation, an algorithm based on the Boolean network approach and prior knowledge. Pearson correlation and the algorithm based on the Boolean network approach derived associations from gene expression data. In the third approach, prior knowledge from a known genetic network of a related organism was used to derive associations for the target organism, by using homolog matching and mapping the known genetic network to the related organism. The results indicate that the Pearson correlation approach gave the best results, but the prior knowledge approach seems to be the one most worth pursuing

Microarray experiments generate vast amounts of data that evidently reflect many aspects of the underlying biological processes. A major challenge in computational biology is to extract, from such data, significant information and knowledge about the complex interplay between genes/proteins. An analytical approach that has recently gained much interest is reverse engineering of genetic networks. This is a very challenging approach, primarily due to the dimensionality of the gene expression data (many genes, few time points) and the potentially low information content of the data. Bayesian networks (BNs) and its extension, dynamic Bayesian networks (DBNs) are statistical machine learning approaches that have become popular for reverse engineering. In the present study, a DBN learning algorithm was applied to gene expression data produced from experiments that aimed to study the etiology of necrotizing enterocolitis (NEC), a gastrointestinal inflammatory (GI) disease that is the most common GI emergency in neonates. The data sets were particularly challenging for the DBN learning algorithm in that they contain gene expression measurements for relatively few time points, between which the sampling intervals are long. The aim of this study was, therefore, to evaluate the applicability of DBNs when learning genetic networks for the NEC disease, i.e. from the above-mentioned data sets, and use biological knowledge to assess the hypothesized gene interactions. From the results, it was concluded that the NEC gene expression data sets were not informative enough for effective derivation of genetic networks for the NEC disease with DBNs and Bayesian learning.

<p>In this work three different approaches for deriving genetic association networks were tested. The three approaches were Pearson correlation, an algorithm based on the Boolean network approach and prior knowledge. Pearson correlation and the algorithm based on the Boolean network approach derived associations from gene expression data. In the third approach, prior knowledge from a known genetic network of a related organism was used to derive associations for the target organism, by using homolog matching and mapping the known genetic network to the related organism. The results indicate that the Pearson correlation approach gave the best results, but the prior knowledge approach seems to be the one most worth pursuing</p>

<p>Recent methods to infer genetic networks are based on identifying gene interactions by similarities in expression profiles. These methods are founded on the assumption that interacting genes share higher similarities in their expression profiles than non-interacting genes. In this dissertation this assumption is validated when using mutual information as a similarity measure. Three algorithms that calculate mutual information between expression data are developed: 1) a basic approach implemented with the histogram technique; 2) an extension of the basic approach that takes into consideration time delay between expression profiles; 3) an extension of the basic approach that takes into consideration that genes are regulated in a complex manner by multiple genes. In our experiments we compare the mutual information distributions for profiles of interacting and non-interacting genes. The results show that interacting genes do not share higher mutual information in their expression profiles than non-interacting genes, thus contradicting the basic assumption that similarity measures need to fulfil. This indicates that mutual information is not appropriate as similarity measure, which contradicts earlier proposals.</p>