[Paper Review] A stochastic modeling framework for single cell migration: coupling contractility and focal adhesions

Aydar Uatay|arXiv (Cornell University)|Oct 26, 2018

Cellular Mechanics and InteractionsBiochemistry, Genetics and Molecular Biology87 references3 citations

TL;DR

This paper presents a minimal stochastic modeling framework for single cell migration by coupling deterministic actomyosin contractility with stochastic focal adhesion dynamics, resulting in a piecewise deterministic Markov process that reproduces experimentally observed behaviors such as anomalous diffusion, tactic migration, and contact guidance. The model captures the intrinsic randomness of cell motility through mechanistically grounded adhesion kinetics rather than assuming Gaussian noise.

ABSTRACT

The interaction of the actin cytoskeleton with cell-substrate adhesions is necessary for cell migration. While the trajectories of motile cells have a stochastic character, investigations of cell motility mechanisms rarely elaborate on the origins of the observed randomness. Here, guided by a few fundamental attributes of cell motility, we construct a minimal stochastic cell migration model from ground-up. The resulting model couples a deterministic actomyosin contractility mechanism with stochastic cell-substrate adhesion kinetics, and yields a well-defined piecewise deterministic process. Numerical simulations reproduce several experimentally observed results, including anomalous diffusion, tactic migration, and contact guidance. This work provides a basis for the development of cell-cell collision and population migration models.

Motivation & Objective

• To develop a minimal, mechanistically grounded stochastic model of single cell migration that captures experimentally observed random trajectories.
• To explain the origins of stochasticity in cell motility not as external noise but as arising from stochastic adhesion dynamics.
• To integrate deterministic contractility with stochastic adhesion events into a well-defined piecewise deterministic process.
• To reproduce key experimental phenomena such as superdiffusive displacement, contact guidance, and tactic migration without assuming Gaussian noise.
• To establish a foundation for modeling cell-cell collisions and population-level migration in future work.

Proposed method

• The model uses a piecewise deterministic Markov process framework, where deterministic motion (driven by actomyosin contractility) alternates with stochastic adhesion events.
• Adhesion dynamics are modeled through a continuous-time Markov jump process with rates derived from mechanobiological principles, not assumed distributions.
• The transition rates for adhesion (de)assembly are based on local mechanical and biochemical signals, including Rho GTPase activity and substrate strain.
• Numerical simulations use a hybrid algorithm combining ODE integration for deterministic phases with stochastic event timing via rejection sampling and interpolation of adhesion rates.
• Interpolation methods (forward, backward, average, linear) are used to approximate time-integrated adhesion rates during deterministic phases for accurate event time prediction.
• The transition measure for adhesion events is sampled using the Vose Alias Method to efficiently draw from the discrete distribution of possible reaction types.

Experimental results

Research questions

• RQ1 How can stochastic cell migration trajectories emerge from the interplay between deterministic contractility and stochastic adhesion dynamics?
• RQ2 Can a minimal mechanistic model reproduce experimentally observed non-Gaussian motility patterns such as superdiffusion and contact guidance?
• RQ3 What is the role of focal adhesion kinetics in generating the randomness observed in single cell migration?
• RQ4 How can a piecewise deterministic process be constructed to accurately model the full cycle of cell migration with minimal assumptions?
• RQ5 Can this framework serve as a foundation for modeling collective cell migration and cell-cell interactions?

Key findings

• The model successfully reproduces anomalous diffusion, with squared displacement scaling superlinearly over time, consistent with experimental observations in migrating cells.
• Tactic migration toward external cues is captured through asymmetric contractility and adhesion dynamics, even in the absence of directional guidance cues.
• Contact guidance—alignment of cell migration along substrate topographical cues—is accurately reproduced by coupling adhesion kinetics to local substrate geometry.
• The model generates non-Gaussian, persistent random walks with long-range correlations, reflecting the true stochastic nature of cell motility.
• Numerical simulations confirm that the piecewise deterministic process framework allows for efficient and accurate simulation of cell migration with minimal computational overhead.
• The framework provides a mathematically consistent and biologically grounded basis for extending to multicellular systems, including cell-cell collisions and population-level migration.