Mathematical Modeling of Cell Migration and Motility Dynamics

Mathematical modeling of cell migration and motility dynamics employs theoretical, computational and data-driven approaches to dissect how individual cells and multicellular assemblies navigate complex environments. Core frameworks include continuum descriptions, such as reaction–diffusion and advection–diffusion equations, stochastic differential equations capturing random fluctuations, and discrete or phase-field models that resolve evolving cell shapes and interfaces. Active matter theories treat cells as internally driven fluids or gels, accounting for forces generated by actin polymerisation, myosin contractility and adhesion dynamics. Recent advances in imaging, microfabrication and single-cell tracking yield large datasets that inform parameter inference and validate model predictions. Integration of machine learning with mechanistic models enables the discovery of governing equations directly from experimental observations, revealing how molecular noise, environmental heterogeneity and cell–cell interactions give rise to emergent migration patterns. These quantitative insights are pivotal for understanding wound healing, immune surveillance, developmental morphogenesis and metastatic dissemination, as well as for designing biomimetic materials and high-throughput drug screening platforms.

Research from Nature Portfolio

Recent studies have uncovered a reversible switching between fast and slow migration modes in keratocyte cells by correlating three-dimensional lamellipodium morphology with intracellular diffusion dynamics. Deformation of the lamellipodium and molecular crowding at the front are shown to regulate migration speed and directional steering. A simplified physical model has been introduced that represents crawling cells as droplets of active polar fluid with spatially localised treadmilling and uniform contractility. This minimal framework reproduces a spectrum of cell shapes and motility regimes observed in vitro, supporting the view that autonomous physical mechanisms underlie persistent movement without continuous regulatory input. Another work employs a phase-field description of multiple interacting deformable cells, demonstrating that inelastic collisions and adhesion coupling alone can drive spontaneous alignment and the emergence of coherently migrating multicellular clusters, offering mechanistic insight into collective invasion and tissue repair.

Mathematical Modeling of Cell Migration and Motility Dynamics publication trend

The graph below shows the total number of articles in mathematical modeling of cell migration and motility dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Lamellipodium: A flat, sheet-like protrusion at the leading edge of a migrating cell, driven by a branched network of polymerising actin filaments.

Phase-field model: A diffuse-interface computational method that represents cell boundaries and internal variables using continuous fields to simulate shape changes and motility.

Active polar fluid: A theoretical representation of a cell as a fluid with oriented internal forces, capturing self-generated propulsion from cytoskeletal activity.

Stochastic differential equation: A mathematical expression that incorporates random noise terms to model the unpredictable components of cell movement.

Machine learning inference: The use of algorithms to extract governing equations or model parameters directly from experimental data without predefined functional forms.

References

1. Learning dynamical models of single and collective cell migration: a review. Reports on Progress in Physics (2024).
2. Switch of cell migration modes orchestrated by changes of three-dimensional lamellipodium structure and intracellular diffusion. Nature Communications (2023).
3. A minimal physical model captures the shapes of crawling cells. Nature Communications (2015).
4. Collisions of deformable cells lead to collective migration. Scientific Reports (2015).
5. Effects of Adhesion Dynamics and Substrate Compliance on the Shape and Motility of Crawling Cells. PLOS ONE (2013).
6. Biologically-informed neural networks guide mechanistic modeling from sparse experimental data. PLOS Computational Biology (2020).