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Recent developments in automation and novel experimental techniques have led to the accumulation of vast amounts of biological data and the emergence of numerous databases to store the wealth of information. Consequentially, bioinformatics have drawn considerable attention, accompanied by the development of a plethora of tools for the analysis of biological data. DNA microarrays constitute a prominent example of a high-throughput experimental technique that has required substantial contribution of bioinformatics tools. Following its popularity there is an on-going effort to integrate gene expression with other types of data in a common analytical approach. Pathway based microarray analysis seeks to facilitate microarray data in conjunction with biochemical pathway data and look for a coordinated change in the expression of genes constituting a pathway. However, it has been observed that genes in a pathway may show variable expression, with some appearing activated while others repressed. This thesis aims to add some contribution to pathway based microarray analysis and assist the interpretation of such observations, based on the fact that in all organisms a substantial number of genes take part in more than one biochemical pathway. It explores the hypothesis that the expression of such genes represents a net effect of their contribution to all their constituent pathways, applying statistical and data mining approaches. A heuristic search methodology is proposed to manipulate the pathway contribution of genes to follow underlying trends and interpret microarray results centred on pathway behaviour. The methodology is further refined to account for distinct genes encoding enzymes that catalyse the same reaction, and applied to modules, shorter chains of reactions forming sub-networks within pathways. Results based on various datasets are discussed, showing that the methodology is promising and may assist a biologist to decipher the biochemical state of an organism, in experiments where pathways exhibit variable expression.

In this thesis, we study two fundamental problems that arise in the modeling of stochastic systems: (i) Validation of stochastic models against behavioral specifications such as temporal logics, and (ii) Discovery of kinetic parameters of stochastic biochemical models from behavioral specifications. We present a new Bayesian algorithm for Statistical Model Checking of stochastic systems based on a sequential version of Jeffreys’ Bayes Factor test. We argue that the Bayesian approach is more suited for application do- mains like systems biology modeling, where distributions on nuisance parameters and priors may be known. We prove that our Bayesian Statistical Model Checking algorithm terminates for a large subclass of prior probabilities. We also characterize the Type I/II errors associated with our algorithm. We experimentally demonstrate that this algorithm is suitable for the analysis of complex biochemical models like those written in the BioNetGen language. We then argue that i.i.d. sampling based Statistical Model Checking algorithms are not an effective way to study rare behaviors of stochastic models and present another Bayesian Statistical Model Checking algorithm that can incorporate non-i.i.d. sampling strategies. We also present algorithms for synthesis of chemical kinetic parameters of stochastic biochemical models from high level behavioral specifications. We consider the setting where a modeler knows facts that must hold on the stochastic model but is not confident about some of the kinetic parameters in her model. We suggest algorithms for discovering these kinetic parameters from facts stated in appropriate formal probabilistic specification languages. Our algorithms are based on our theoretical results characterizing the probability of a specification being true on a stochastic biochemical model. We have applied this algorithm to discover kinetic parameters for biochemical models with as many as six unknown parameters.