Computational studies of metabolism aim to systematically analyze the metabolic behaviour of biological systems in different conditions. Genome-scale metabolic network models (GEMs) capture the connection between elements of the network by applying stoichiometric balances while taking into account gene-protein-reaction associations. Several methods have already been developed for the analysis of these models. These methods are mainly used to optimize a single or combination of objective functions subject to different constraints. In this thesis, we have summarized the optimization methods and objective functions by classifying them based on biological and mathematical features. Particularly, we suggest reformulations to convert some of the complex optimization classes to simpler ones. One of the reformulations is the conversion of mixed-integer linear fractional programming (MILFP) to mixed-integer linear programming (MILP). We show that this conversion is useful in studying coupling relationships in thermodynamically constrained metabolic network models. Coupling determines how different components of the network such as metabolites or reactions are interrelated. Particularly, flux Coupling Analysis (FCA) is a method for evaluating the dependencies between metabolic reactions. In FCA, two reactions are considered as coupled if the activity of one, constrains the activity of the other. So far, FCA has been used for analyzing metabolic reactions in flux-balanced models. In this work, we developed a new formulation, Thermodynamic Flux Coupling Analysis (TFCA), which calculates flux couplings of metabolic models that are subjected to thermodynamic constraints. With TFCA, we show that adding thermodynamic constraints can significantly change the coupling relationship of reactions of the network. Moreover, we show that calculating coupling relations helps in reducing the number of combinations of bidirectional reactions (BDRs), which in turn will facilitate the analysis of the metabolic network. In addition to proposing several mathematical reformulations to gain global optimality, we also addressed the issue of finding the proper cellular objective function in different conditions of cellular metabolism. This is not always straight-forward, since the metabolic activities of some organisms are not well-characterized, e.g., metabolism of dormancy phase in some bacteria and parasites. In this thesis, we studied the metabolic behaviour of dormant malaria parasite using genome-scale model of Plasmodium falciparum. We examined known and novel objective functions and scored them based on the model’s consistency with experimental gene expression data. Our results suggested that minimizing energy dissipation can best describe the metabolic activities of the malaria parasites in the dormancy phase. In the last chapter, we focus on studying another poorly characterized metabolic system that is the process of iron reduction in Clostridium acetobutylicum. Research has shown that this organism can reduce Fe(III), but the mechanism behind this reduction is yet to be identified. In this thesis, we analyzed the metabolism of C. acetobutylicum using its reconstructed genome-scale metabolic network model and experimental transcriptomics data in the presence or absence of Fe(III). By performing several computational studies, we suggested that NAD(P) is involved in the reduction of iron and is the potential physiological electron donor to Fe(III).