Fractional reversible chemical kinetics: Time-Driven Monte Carlo method and application to enzyme conformational dynamics
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.
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BibTeX
@misc{lemes2026fractional,
title = {{Fractional reversible chemical kinetics: Time-Driven Monte Carlo method and application to enzyme conformational dynamics}},
author = {Nelson H. T. Lemes and Higor V. M. Ferreira},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33652},
eprint = {2610.33652},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33652},
}
RIS
TY - UNPB
TI - Fractional reversible chemical kinetics: Time-Driven Monte Carlo method and application to enzyme conformational dynamics
AU - Nelson H. T. Lemes
AU - Higor V. M. Ferreira
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33652
UR - https://arxiv.org/abs/2610.33652
AB - 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.
ER -