Delayed Extracellular Matrix Negative Feedback Contributes to Nascent Adhesion Dynamics: Mathematical Modeling and Analysis

Abstract

AO_SCPLOWBSTRACTC_SCPLOWCell migration, both in vivo and in vitro, is a complex process governed by mechano-chemical interactions between cells and the extracellular matrix (ECM). These interactions, mediated by cell membrane receptors called integrins, involve bidirectional signaling between the intracellular actin cytoskeleton and the ECM. Integrins bind with cytoplasmic proteins to form adhesion complexes of varying sizes and maturity, which play crucial roles in cellular processes such as cell migration. Among these complexes are nascent adhesions-the smallest and earliest observable structures that emerge within the lamellipodium and are associated with rapid cell motility. While other adhesion types have been extensively studied, the mechanisms regulating nascent adhesions remain poorly understood. Here, we develop a mathematical model describing the bidirectional signaling between the actin cytoskeleton and ECM that controls nascent adhesion dynamics. Our framework employs a system of delay differential equations to capture the temporal coupling between actin polymerization-driven adhesion formation and force-dependent ECM displacement. The model demonstrates that nascent adhesions, initiated by actin polymerization, exert forces on the ECM, whose delayed displacement provides negative feedback that limits adhesion growth. Numerical simulations reveal that this delayed ECM feedback mechanism reproduces the characteristic lifetime and dynamics of nascent adhesions, with quantitative agreement with experimental observations. Our results suggest that delayed ECM negative feedback is a key regulator of nascent adhesion turnover, providing new insights into the spatiotemporal control of cell migration.