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Mathematical modeling of collective cell migration in wound healing

Creative Commons 'BY' version 4.0 license
Abstract

The collective migration of keratinocytes during wound healing requires both the generation and transmission of mechanical forces for individual cellular locomotion and the coordination of movement across cells. Leader cells along the wound edge transmit mechanical and biochemical cues to ensuing follower cells, ensuring their coordinated direction of migration across multiple cells. Despite the observed importance of mechanical cues in leader cell formation and in controlling coordinated directionality of cell migration, the underlying biophysical mechanisms remain elusive. The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during the reepithelialization of wounds. Here, through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1’s contributions to collective migration. Time-lapse microscopy reveals that PIEZO1 activity inhibits leader cell formation at the wound edge. To probe the relationship between PIEZO1 activity, leader cell formation and inhibition of reepithelialization, we developed an integrative 2D continuum model of wound closure that links observations at the single cell and collective cell migration scales. Through numerical simulations and subsequent experimental validation, we found that coordinated directionality plays a key role during wound closure and is inhibited by upregulated PIEZO1 activity. We propose that PIEZO1-mediated retraction suppresses leader cell formation which inhibits coordinated directionality between cells during collective migration. We also extended the model to include two distinct cell types, each governed by its own set of equations and parameters, interacting through cell-cell adhesion, volume-filling effects, and wound edge retraction. Simulations with various cell mixtures reveal that mutually repulsive cells promote wound closure more effectively than homogeneous populations, with the promotion level amplified by mixture heterogeneity. Additionally, simulations show that cells with higher PIEZO1 activity are generally less represented among edge cells, correlating with wound edge retraction. Through the study of this extended model, we comprehensively explored the roles of cell-cell interactions and heterogeneity in collective cell migration involving PIEZO1 mixtures.

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