A phase field model with stochastic input simulates cellular gradient sensing, morphodynamics, and fidelity of haptotaxis
- 1Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina, United States of America
Abstract
Haptotaxis is an understudied form of directed cell migration in which movements are biased by gradients of immobilized ligands. For example, fibroblasts and other mesenchymal cells sense and respond to gradients of extracellular matrix (ECM) composition, which is relevant during tissue morphogenesis and repair. As a step towards understanding how haptotactic gradients spatially bias cell adhesion, intracellular signal transduction, and cytoskeletal dynamics, we formulated a phase field model of whole-cell migration, in which the occupancy of potential adhesion sites changes stochastically with time. With careful assignment of parameter values, the model predicts significant haptotactic bias for adhesion-site gradient steepness of a few percent across the cell. We then used the model to predict how the cell’s removal of surface-bound ECM ligand (as observed in experiment) and/or the presence of a competing, chemotactic gradient influence(s) haptotactic fidelity. An emergent principle is that gains in directional persistence naturally offset losses of directional bias, at the cost of greater cell-to-cell heterogeneity of the response. In the case of orthogonally oriented gradients, this offset manifests as a remarkable robustness of the multi-cue response. Author summary: Cell movements in and among tissues are essential for a host of normal processes in animals, including development of an embryo, immune responses, and wound healing. Cell movements require specific adhesive interactions with the surrounding extracellular matrix or with other cells and are orchestrated/biased by chemical cues of different types. Both soluble and immobile factors guide migration. For instance, variations in matrix composition represent a key immobile factor. To gain insight and generate testable predictions about this process, we developed a novel modeling framework in which discrete adhesion sites are switched on and off with certain probabilities, coupled with a model of the cellular dynamics. Adhesions near the cell periphery promote force generation both directly and through an activator molecule. With appropriate parameter values, the model yields cell shape changes and cell migration ‘behavior’ that are similar to those observed in experiments. By applying variations of our model, we predict how 1) a cell’s removal of the protein from the surface, or 2) a competing migration cue, influences the directed migration response.
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BibTeX
@article{koelbl2026phase,
title = {{A phase field model with stochastic input simulates cellular gradient sensing, morphodynamics, and fidelity of haptotaxis}},
author = {Joseph M. Koelbl and Hector M. Apodaca and Jason M. Haugh},
journal = {PLOS Computational Biology},
year = {2026},
month = sep,
doi = {10.1371/journal.pcbi.1014726},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014726},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A phase field model with stochastic input simulates cellular gradient sensing, morphodynamics, and fidelity of haptotaxis
AU - Joseph M. Koelbl
AU - Hector M. Apodaca
AU - Jason M. Haugh
PY - 2026
DA - 2026/09/09
JO - PLOS Computational Biology
DO - 10.1371/journal.pcbi.1014726
UR - https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014726
AB - Haptotaxis is an understudied form of directed cell migration in which movements are biased by gradients of immobilized ligands. For example, fibroblasts and other mesenchymal cells sense and respond to gradients of extracellular matrix (ECM) composition, which is relevant during tissue morphogenesis and repair. As a step towards understanding how haptotactic gradients spatially bias cell adhesion, intracellular signal transduction, and cytoskeletal dynamics, we formulated a phase field model of whole-cell migration, in which the occupancy of potential adhesion sites changes stochastically with time. With careful assignment of parameter values, the model predicts significant haptotactic bias for adhesion-site gradient steepness of a few percent across the cell. We then used the model to predict how the cell’s removal of surface-bound ECM ligand (as observed in experiment) and/or the presence of a competing, chemotactic gradient influence(s) haptotactic fidelity. An emergent principle is that gains in directional persistence naturally offset losses of directional bias, at the cost of greater cell-to-cell heterogeneity of the response. In the case of orthogonally oriented gradients, this offset manifests as a remarkable robustness of the multi-cue response. Author summary: Cell movements in and among tissues are essential for a host of normal processes in animals, including development of an embryo, immune responses, and wound healing. Cell movements require specific adhesive interactions with the surrounding extracellular matrix or with other cells and are orchestrated/biased by chemical cues of different types. Both soluble and immobile factors guide migration. For instance, variations in matrix composition represent a key immobile factor. To gain insight and generate testable predictions about this process, we developed a novel modeling framework in which discrete adhesion sites are switched on and off with certain probabilities, coupled with a model of the cellular dynamics. Adhesions near the cell periphery promote force generation both directly and through an activator molecule. With appropriate parameter values, the model yields cell shape changes and cell migration ‘behavior’ that are similar to those observed in experiments. By applying variations of our model, we predict how 1) a cell’s removal of the protein from the surface, or 2) a competing migration cue, influences the directed migration response.
SN - 1553-7358
ER -