Non-Markovian data-driven modeling of single-cell motility.

Area of Science:

• Biophysics
• Cell Biology
• Statistical Mechanics

Background:

• Cell migration is crucial for biological processes, including cancer metastasis.
• Previous models often simplified cell motility, neglecting complex memory effects.
• Understanding single-cell behavior requires accounting for non-Markovian dynamics.

Purpose of the Study:

• To model human breast cancer cell trajectories using a non-Markovian Langevin equation.
• To develop a data-driven approach for extracting memory functions from cell migration data.
• To investigate the physical mechanisms underlying cell persistence and regulation.

Main Methods:

• Modeling cell trajectories with a non-Markovian Langevin equation incorporating an arbitrary memory function.
• Extracting the memory function directly from experimental trajectory data.
• Formulating a generalized, exactly solvable cell migration model based on the extracted memory.

Main Results:

• Single-cell velocity distributions are Gaussian, while averaged distributions show non-Gaussian behavior.
• A linear memory model accurately describes cell motility, encompassing various random walk behaviors.
• Cell memory exhibits time-delayed, single-exponential negative friction, indicative of regulatory feedback.
• Negative friction was found to generate long-timescale persistence in cell migration.

Conclusions:

• The data-driven approach provides unbiased, single-cell comparisons of migration dynamics.
• Negative friction is a key factor driving persistent cell migration, differentiating it from simple random walks.
• The study reveals a regulatory feedback mechanism controlling cell migration and highlights the nonequilibrium nature of cell motion.