ExPA

ExPA computes extreme pathways to generate all possible steady-state flux maps of biochemical reaction networks by characterizing the convex basis of the null space of the stoichiometric matrix.

Key Features:

• Convex Basis Vectors: ExPA identifies extreme pathways that define the convex basis vectors for characterizing the null space of the stoichiometric matrix.
• Steady-state Flux Maps: ExPA generates the set of possible steady-state flux distributions implied by the extreme pathways.
• Insight into Metabolic Networks: Analysis of extreme pathways provides information on physiological and functional states of metabolic networks in silico.
• Computational Efficiency: To address exponential growth in the number of extreme pathways with network size, ExPA uses an estimating function that relates the logarithm of the number of extreme pathways to R, the incoming (d^{-i}) and outgoing (d^{+i}) degrees of each reaction, and the clustering coefficient (c_i) for each active reaction.
• Estimation Accuracy: The estimating function typically predicts the number of extreme pathways within an order of magnitude of the actual count.

Scientific Applications:

• Characterizing Metabolic Networks: ExPA provides comprehensive sets of possible flux distributions to elucidate the functional capabilities and limitations of metabolic networks.
• Predictive Modeling: ExPA supports simulation of physiological states and prediction of how changes in network topology or reaction activity affect system behavior.
• Network Analysis: The estimating function enables preliminary assessments of ExPA feasibility and guides further detailed network investigations.

Methodology:

ExPA analyzes the stoichiometric matrix using linear algebra and graph theory to compute extreme pathways and applies an estimating function that correlates the logarithm of the number of extreme pathways with R, d^{-i}, d^{+i}, and c_i.