Construction, analysis and assessment of relevance of an algebraic model for a class of biochemical networks

Abstract

The intracellular milieu presents a complex physicochemical environment where molecular redundancy prevails and infra-threshold perturbations are integrated by biochemical networks. The pathways that result from these interactions are complex and will result in a plethora of signalling cascades. The stoichiometry number matrix for a biochemical network is a suitable way to represent the interactions between various molecular species under baseline conditions and in response to stimuli. Here, we model a class of biochemical networks with a set of constrained, reaction-centric, stoichiometry equivalent and degenerate matrices. The matrices exhibit a many-to-one surjection with the null space and form a semigroup with respect to addition. The parameters for these studies are the probable dissociation constants and will be used to derive several network- and reaction-specific metrics. These will describe the class of modelled biochemical networks both, at the level of a single network and as a unit. The model is extendible and can be used to perturb a biochemical network by introducing a finite number of extraneous reactions and then comparing pairs of like-reactions. The theoretical assertions presented are complemented by detailed computational analyses of the hexose monophosphate shunt, urea cycle and folate metabolism in humans. The model provides a theoretically sound basis to interrogate the effects of molecular redundancy and perturbations in the genesis and regulation of complex biochemical function. The model is theoretically sound, mathematically rigorous, readily testable, biochemically relevant, easily parameterizable and can be used to compare biochemical networks under differing intracellular conditions, both, between cells and across taxa.