Quantitative Treatments for Explaining the Mechanism and Kinetics of Catalytic Electron Transfers in Murburn Processes, Particularly Involving Heme Enzymes Like (Per)oxidases and P450s

The seminal Michaelis-Menten theorization for biological catalysis was based on "transition state" (TS), involving the formation of a topologically complementary substrate (S) and enzyme (E) complex (ES) at the "active site" of the latter. Rudolph Marcus put forth the theory of outer sphere electron transfer (ET) in a "donor-acceptor" TS complex, which was seen as a foundational framework for understanding ET reactions in chemical systems. Although these two theories are quite robust, the active site treatment of Michaelis-Menten may not be relevant in promiscuous/nonspecific xenobiotic-metabolizing redox enzymes, and Marcus theory's applicability to biological ET (BET) systems can be limited in interfacial protein-protein interactions. Herein, the "mathematical" necessity to venture beyond the "active site constraints" of interpreting redox enzyme kinetics and BETs is established first with fresh data. Also, (i) the classical explanation vouching for active site binding and protein-protein complexation-based BET in xenobiotic metabolism (mediated at the endoplasmic reticulum membranes of hepatocytes) and oxidative phosphorylation (multiprotein machinery at mitochondrial cristae) is demonstrated to be untenable, and (ii) tangible/viable murburn models were proposed in lieu. Therefore, toward the imperative goal of arriving at quantitative expressions correlating the parameters/variables involved, the foundational considerations of murburn ET and murzyme catalysis in simple heme systems are presented, with some assumptions/constraints. While some derivations are from ab initio considerations, others are heuristic/empirical, often needing experimental fitting. The linear time-course profiles of ET (substrate depletion) and the biphasic substrate-dependent (product formation) are well fit with the newly derived expressions. A mechanistic comparison of the murburn model vis-à-vis the longstanding P450cam explanation for drug/xenobiotic metabolism is also provided.