THE UNDERLYING PATHWAY STRUCTURE OF BIOCHEMICAL REACTION NETWORKS

Bioinformatics is yielding extensive, and in some cases complete, gene tic and biochemical information about individual cell types and cellul ar processes, providing the composition of living cells and the molecu lar structure of its components. These components together perform int egrated cellular functions that now need to be analyzed. In particular , the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how t he mass balance constraints that govern the function of biochemical re action networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reactio n networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix, The null space is span ned by a finite number of basis vectors. We present an algorithm for t he synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the correspond ing biochemical reaction network In other words, all possible flux dis tributions achievable by a defined set of biochemical reactions are re presented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defin ed biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic d efinition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochem ical processes. Additionally, this new conceptual framework will be im portant in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function.