Elucidating dynamics and mechanism of cyclic bioreaction networks using topologically-equivalent electrical circuits

A novel methodology is established to convert a set of elementary chemical reactions into topologically-equivalent electrical circuits. The circuit analog is then simulated to elucidate the dynamics of complex cyclic bionetworks. The pyramidal reaction network catalyzed by the universal enzyme dihydrofolate reductase – which has important pharmacological and medical relevance in connection with cancer therapy – is used to illustrate the application of our model. The finite number of mechanisms, sub-cycles, or graphs constituting the cyclic network are analyzed, their contribution to the overall steady-state reaction rate determined, and the most probable mechanism is identified. The developed methodology is elegant, modular, and permits representation and visualization of network structure and topology at a glance. It can handle linear and nonlinear kinetics/rate laws, does not require simplifying assumptions such as use of the quasi-steady-state/Bodenstein approximation or the absence of nonlinear kinetic steps in the intermediates, and is suitable for coupling and integration with other flux-based reaction models.