Combinatorial mathematical modelling approaches to interrogate rear retraction dynamics in 3D cell migration

Area of Science:

• Cell Biology
• Biophysics
• Mathematical Biology

Background:

• Cell migration in 3D environments relies on coordinated protrusion and retraction.
• Mechanisms of cell rear retraction are less understood than protrusion dynamics.
• Previous work identified caveolae mechanosensing and RhoA signaling in cell rear retraction.

Purpose of the Study:

• To investigate the dynamics of cell rear retraction using multiple mathematical modeling approaches.
• To generate testable hypotheses and predictions regarding cell rear dynamics.
• To compare the utility of Boolean logic, ODE, and stochastic modeling for studying cell signaling.

Main Methods:

• Employed three distinct mathematical modeling approaches: Boolean logic, deterministic kinetic ordinary differential equations (ODEs), and stochastic simulations.
• Utilized these models to simulate cell rear retraction dynamics in 3D extracellular matrix (ECM).
• Validated model predictions through experimental confirmation, including the role of CDK1.

Main Results:

• A multi-faceted modeling approach provided greater insight than single methods.
• ODE models offered plausible population-level predictions, while stochastic simulations mimicked single-cell behavior.
• Identified an unexpected role for CDK1 in cell rear retraction and predicted a 'set point' in stiffness gradients that promotes cell polarization.

Conclusions:

• Mathematical modeling, particularly a multi-approach strategy, is crucial for understanding complex biological systems like cell rear retraction.
• The study experimentally validated the role of CDK1 in rear retraction, a key finding from the modeling.
• A novel prediction suggests that specific local stiffness gradients act as a 'set point' to drive cell polarization and efficient migration.