Phase-field model with stochastic adhesion reproduces haptotaxis and predicts when cells maintain directional fidelity

# Overview

This study presents a phase-field model of whole-cell migration that explicitly represents discrete potential adhesion sites whose occupancy switches on and off stochastically. The adhesion dynamics are coupled to an intracellular activator and to mechanics that control protrusion and retraction. The authors calibrate parameters to produce cell shapes and behaviors comparable to experimental observations of mesenchymal cells such as fibroblasts.

# Model design and rationale

# Main findings

• Haptotactic sensitivity: With careful parameter assignment the model produces a measurable directional bias (haptotaxis) when the adhesion-site occupancy gradient across the cell is just a few percent. That is, shallow gradients of immobilized ligand can suffice to bias migration.

• Ligand removal: The model was used to predict how a cell's own removal of surface-bound ECM ligand—an effect observed experimentally—affects haptotactic fidelity. The framework allows exploration of dynamic substrate changes and how they alter adhesive cues over time.

• Competing cues and multi-cue integration: Introducing a competing chemotactic gradient changes fidelity. An emergent principle in these simulations is a tradeoff between directional bias and directional persistence: gains in persistence can offset losses in instantaneous bias, yielding continued net alignment with a cue but increasing variability between cells.

• Robustness under orthogonal cues: When chemotactic and haptotactic gradients are orthogonally oriented, the persistence–bias tradeoff leads to a robust multi-cue response: cells maintain directed movement despite competing directional information.

# Predictions and experimental implications

The model makes several testable predictions suitable for experimental follow-up:

• Even small spatial differences in adhesive ligand density (a few percent across a cell) should produce measurable haptotactic bias if adhesion and signaling parameters fall within realistic ranges.

• Increasing directional persistence (for example by modulating intracellular signaling that stabilizes protrusions) can preserve net migration direction when external bias weakens, but this will increase heterogeneity in single-cell responses within a population.

# Practical takeaways

• Modeling adhesion as discrete stochastic events is sufficient to reproduce key aspects of haptotactic sensing and morphodynamics.

• Experiments aiming to quantify haptotaxis should consider measuring both instantaneous bias and persistence, because persistence can mask changes in bias at the population level.

# Availability and resources

The authors have provided Python code on GitHub for reproducing and extending the simulations, enabling direct comparison between model predictions and experimental data.