The underlying pathway structure of biochemical reaction networks

Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated 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 the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the 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 corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally, this new conceptual framework will be important in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function.

Inputs to directionally selective simple cells in macaque striate cortex

It is clear that the initial analysis of visual motion takes place in the striate cortex, where directionally selective cells are found that respond to local motion in one direction but not in the opposite direction. Widely accepted motion models postulate as inputs to directional units two or more cells whose spatio-temporal receptive fields (RFs) are approximately 90° out of phase (quadrature) in space and in time. Simple cells in macaque striate cortex differ in their spatial phases, but evidence is lacking for the varying time delays required for two inputs to be in temporal quadrature. We examined the space-time RF structure of cells in macaque striate cortex and found two subpopulations of (nondirectional) simple cells, some that show strongly biphasic temporal responses, and others that are weakly biphasic if at all. The temporal impulse responses of these two classes of cells are very close to 90° apart, with the strongly biphasic cells having a shorter latency than the weakly biphasic cells. A principal component analysis of the spatio-temporal RFs of directionally selective simple cells shows that their RFs could be produced by a linear combination of two components; these two components correspond closely in their respective latencies and biphasic characters to those of strongly biphasic and weakly biphasic nondirectional simple cells, respectively. This finding suggests that the motion system might acquire the requisite temporal quadrature by combining inputs from these two classes of nondirectional cells (or from their respective lateral geniculate inputs, which appear to be from magno and parvo lateral geniculate cells, respectively).