<i>In Silico</i> optimization of time-dependent motility and proliferation control for wound closure: a hybrid Fisher–KPP and force-based agent model

Wound healing is a coordinated process of cell migration and proliferation, and computational modeling can replace laborious experiments by predicting outcomes under varied conditions. We develop a hybrid in silico model that couples a Fisher–KPP reaction–diffusion equation with a force-based agent-based model (ABM) to simulate wound closure. The continuum PDE captures overall cell-density dynamics, while the discrete ABM explicitly represents individual cells with short-range repulsion and adhesion forces. We first used a digitized literature control curve as an approximate calibration benchmark and then performed independent validation on a public replicate-level MDCK time-lapse wound-healing dataset using leave-one-replicate-out evaluation. On the independent dataset, the hybrid model achieved slightly lower mean hold-out error than Fisher–KPP in both control and HGF/SF conditions, although the improvement was modest rather than statistically decisive. In silico experiments further demonstrate that sustained control can accelerate wound closure substantially relative to baseline, whereas short priming inputs yield only modest improvements. A vector-field analysis of the wound front indicates that leading-edge agents initially migrate rapidly into the void and then decelerate as crowding and adhesion constraints increase, consistent with collective migration behavior. Parameter mapping reveals a sharp threshold in closure efficacy: only sufficiently strong and long-lasting control achieves full wound closure within 48 h, whereas weaker or shorter inputs lead to incomplete closure. Importantly, the control signal is treated as an abstract, dimensionless input that modulates effective motility, proliferation rate, and protrusive forcing rather than any single physical therapy modality. This study therefore provides a general computational framework for studying how time-dependent modulation of motility and proliferation can shift tissue dynamics across critical wound-closure thresholds.