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IEPDYN: Integral-equation formalism of population dynamics
Kento Kasahara1, Ryo Okabe1, Chia-En A Chang2
1Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka, Toyonaka, Osaka 560-8531, Japan.
The Journal of Chemical Physics
|March 27, 2026
Summary
We introduce the integral-equation formalism of population dynamics (IEPDYN) to model distinct state changes. This method uses short molecular dynamics simulations for accurate, lag-time-independent kinetic analysis.
Area of Science:
- Physical Chemistry
- Computational Chemistry
- Chemical Physics
Background:
- Classical reaction dynamics theory describes state populations using the Liouville equation.
- Modeling transitions between configurational states requires understanding influx and efflux dynamics.
- Existing methods may suffer from lag-time dependence, limiting accuracy.
Purpose of the Study:
- To develop a novel integral-equation formalism of population dynamics (IEPDYN).
- To accurately describe population dynamics of distinct configurational states.
- To overcome limitations of lag-time dependence in kinetic analysis.
Main Methods:
- Formulated IEPDYN using a Markov approximation for state boundary crossings.
- Derived tractable integral equations for state populations.
- Employed short-timescale molecular dynamics (MD) simulations to compute time-dependent quantities.
Main Results:
- IEPDYN provides population dynamics on long timescales.
- Kinetic quantities derived from IEPDYN are independent of lag time.
- Applied IEPDYN to binding/unbinding kinetics (CH4/CH4, Na+/Cl-, crown ether/K+).
- IEPDYN time constants agree with brute-force MD simulations.
- IEPDYN reduced MD trajectory timescales by two orders of magnitude for crown ether/K+.
Conclusions:
- IEPDYN offers an accurate and efficient method for analyzing population dynamics.
- The approach overcomes lag-time dependence limitations.
- IEPDYN enables the study of complex binding/unbinding systems beyond brute-force MD capabilities.
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