Rates and Reversibilities in Interconnected Reaction Networks

Mathematical relations prescribing unidirectional forward and reverse rates originally derived based on single-path reaction sequences do not apply to interconnected reaction networks. The presence of branches in reaction networks, leading to alternative stable products, decreases unidirectional rates in reference to those calculated by single-path functional forms, as shown by simulated isotopic exchange rates, but impacts the unidirectional forward and reverse rates equally such that the functional form of effective reversibility remains unchanged. Regardless of stoichiometric numbers and network connectivity, the application of the pseudo-steady-state hypothesis on reactive intermediates in conjunction with consideration of unidirectional rates toward the product of interest and all alternative stable products results in mathematical expressions that accurately reflect simulated isotopic exchange rates. Further analyses based on kinetic resistance, a property akin to electrical resistance, illustrate the manifestation of nodal resistances in addition to the single-path kinetic resistance for interconnected reaction networks. The generalized formalism for assessing rates and reversibilities in interconnected networks derived herein enables us to demonstrate that unidirectional rates cannot be assessed solely from effective reversibilities and net rates of generation of stable species in such networks. However, isotopic exchange rates, under the condition that each elementary step in the overall reaction sequence forms a unique reactive intermediate that is consumed solely by the subsequent step, can be utilized to determine unidirectional rates and can serve to validate postulated reaction pathways in highly interconnected reaction networks (e.g., CO_x hydrogenation).