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Langevin Equation in Heterogeneous Landscapes: How to Choose the Interpretation
Adrian Pacheco-Pozo1, Michał Balcerek2, Agnieszka Wyłomanska2
1Department of Electrical and Computer Engineering and School of Biomedical Engineering, <a href="https://ror.org/03k1gpj17">Colorado State University</a>, Fort Collins, Colorado 80523, USA.
Physical Review Letters
|August 23, 2024
Summary
The Langevin equation models particle diffusion. We present a method to uniquely interpret its solutions in complex, non-homogeneous environments using single-particle tracking data.
Area of Science:
- Physics
- Physical Chemistry
- Biophysics
Background:
- The Langevin equation models single-particle diffusion.
- Non-unique solutions arise in non-homogeneous environments due to stochastic integral interpretations.
- Aqueous two-phase systems and biological condensates are examples of such environments.
Purpose of the Study:
- To analyze particle diffusion in non-homogeneous environments using the Langevin equation.
- To evaluate key diffusion metrics: mean, mean square displacement, and particle distribution.
- To provide a method for selecting the correct interpretation parameter for stochastic integrals.
Main Methods:
- Analytical evaluation of diffusion in multi-phase systems.
- Calculation of mean, mean square displacement, and particle distribution.
- Analysis of the variance of time-averaged mean-square displacements.
Main Results:
- Derived analytical results for particle diffusion in non-homogeneous systems.
- Quantified diffusion behavior including mean, mean square displacement, and distribution.
- Established a framework for choosing the interpretation parameter.
Conclusions:
- The choice of stochastic integral interpretation is crucial for unique Langevin equation solutions in complex media.
- Single-particle tracking experiments can be used to determine the appropriate interpretation parameter.
- This work offers a quantitative approach to understanding diffusion in heterogeneous biological and chemical systems.
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