Quantum mechanical justification for induced fit model conformational changes in allosteric enzymes based on the quantum perturbation theory and Davydov’s soliton theory

Abstract

We develop a refined quantum framework for the induced-fit model of allosteric enzymes incorporating vibrational exciton (Davydov’s soliton) dynamics and open-system perturbation theory. Using realistic biochemical parameters, we numerically evaluate the excitation conditions and find that under normal assumptions the quantum excitation energy remains orders of magnitude below the threshold needed to drive a stable soliton. This implies that classical Davydov conditions alone are insufficient for enzyme catalysis on sub-nanosecond timescales. To address this, we identify additional factors – multi-state energy accumulation and strong quantum-coherent processes – that could plausibly enhance the effect. We discuss model limitations (e.g., idealized 1D protein chain, neglect of dissipation) and the validity of our assumptions. By modeling allosteric enzymes as quantum multi-particle systems, we represent substrate-induced structural changes as Hamiltonian deformations and calculate transition probabilities and interaction energies that correlate with enzymatic accuracy or error. While Davydov’s soliton offers an appealing formalism, our calculations indicate they are insufficient under naïve parameter choices. Under standard parameters, this mechanism alone is not sufficient and requires auxiliary mechanisms. We present conditions (e.g., multi-state accumulation, enhanced coupling) under which solitonic behaviour might emerge, and propose experiments/simulations to validate these scenarios. This work bridges biophysical mechanisms with quantum mechanics, offering a novel perspective on enzymatic function at the quantum level. Finally, we situate our model within the broader context of macro-quantum effects (quantum coherence, tunneling, superradiance) known in biology, arguing that while Davydov’s soliton remains speculative, related quantum phenomena (e.g., proton tunneling) are well-supported in enzymatic systems.