Exact solution for the Anisotropic Ornstein-Uhlenbeck process

Area of Science:

• Biophysics
• Statistical Mechanics
• Cell Biology

Background:

• Active-Matter models often use overdamped dynamics with constant speed and random direction, sometimes including noise for diffusive motion.
• Ornstein-Uhlenbeck processes use Langevin dynamics for velocity, predicting non-diffusive short-time motion.
• Migrating cells exhibit short-time diffusive behavior and gradual speed variations at longer timescales.

Purpose of the Study:

• To develop a unified model that explains both short-time diffusive and long-time speed variation regimes observed in migrating cells.
• To address the limitations of existing isotropic models that cannot reconcile these different temporal behaviors.
• To provide a theoretically robust framework for comparing simulations and experiments in cell migration studies.

Main Methods:

• Analytical solution of an Anisotropic Ornstein-Uhlenbeck process for polarized particles.
• Incorporation of Langevin dynamics for movement along the polarization direction.
• Inclusion of a Wiener process for displacement in the orthogonal direction.

Main Results:

• The proposed model analytically describes particle movement that is diffusive at short timescales and exhibits velocity variations at longer timescales.
• This anisotropic approach successfully bridges the gap between models suitable for short-time diffusion and those for long-time speed dynamics.
• A method is proposed to account for finite-precision effects in both experimental and simulation data.

Conclusions:

• The Anisotropic Ornstein-Uhlenbeck process offers a unified theoretical framework for modeling cell migration dynamics.
• This model provides a robust method for comparing dimensionless simulations with experimentally measured cell movement.
• The findings facilitate more accurate and comparable analyses of biological particle and cell motility.