Thermodynamic Consistency and Kinetic Mechanism of a Complex Reaction Pathway by Analysis of Its Constituent Cyclic Networks

The complete set of thermodynamically consistent sub-cyclic routes that produce a net positive reaction flux in the dihydrofolate reductase (DHFR) network is identified by a novel approach based on the theory of graphs. The net positive flux cycles that yield the minimal set of linearly independent rate equations ("mechanisms") are then selected. The steady-state flux (reaction rate) through these constituent sub-cycles is quantified, and the sub-cycle that generates the maximum flux is identified as the most probable mechanism of the pathway. This analysis is performed for both wild-type and mutant Escherichia coli DHFR systems. The graph-theoretical method of visualization of networks developed here should prove to be a useful tool for elucidating the kinetic mechanism complex cyclic reaction networks.