Fractional reversible chemical kinetics: Time-Driven Monte Carlo method and application to enzyme conformational dynamics
Year: 2026
Type: preprint
Abstract: In this work, we present a fractional framework for reversible two-state chemical kinetics derived from the Continuous-Time Random Walk (CTRW) formalism with Mittag-Leffler waiting-time distributions. This derivation provides a microscopic basis for the fractional kinetic equations governed by the Caputo derivative. An exact analytical solution is obtained, yielding closed-form expressions for the time evolution of the state populations. To the best of our knowledge, a time-driven Monte Carlo algorithm is developed for the first time to simulate the irreversible underlying non-Markovian stochastic dynamics governed by a system of Caputo fractional differential equations. The proposed framework is applied to the conformational dynamics of the TbQSOX enzyme, whose relaxation exhibits power-law behavior. The fractional model accurately reproduces the experimental kinetics, providing an estimate of the fractional order $α= 0.22$, which is consistent with the observed anomalous dynamics.
Source: arXiv (Cornell University)
Institution: Universidade Federal de Alfenas
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223878314