Phenotype Heterogeneity Warrants Trizonal Feedback between Intracellular Contractility and Extracellular stiffening

The intricate interplay between actomyosin contractility and extracellular matrix (ECM) strain stiffening is pivotal in cancer invasion. Despite the admitted impact of such feedback, current models are inadequate in predicting the largely overlapping ranges of cell shapes and their corresponding motility levels at intermediate ranges of collagen density. To address this gap, we introduce a free energy-based, trizonal model for cell shape transition under ECM stiffening, which delineates two distinct and one overlapping motility zones entitled with their implications for cancer progression: a low-motility zone with minimal invasiveness, a high-motility zone indicative of significantly invasive cells, and a mesoregion which harbors cells at crossroads of both states. This model integrates critical factors influencing the bidirectional interaction between the cell and ECM, thereby offering a deeper grasp of cancer cell behavior. Our findings reveal that the combined effects of ECM strain stiffening and cellular contractility are key drivers of cell population heterogeneity and invasiveness. This model goes beyond existing paradigms by accurately determining the optimal cell elongation at matrix-driven steady-state equilibrium, factoring in collagen density, contractility density, stress polarization, membrane-cortical tension, and integrin dynamics through the lens of total free energy minimization. The models predictive capability is further validated against measured cell shapes from histological sections. Altogether, this research not only bridges a crucial knowledge gap, but also provides a robust computational framework for predicting and replicating cell shape transitions observed in human functional tissue assays, thereby enhancing our ability to understand and potentially combat cancer invasion. SignificanceECM stiffening is crucial in prompting metastatic phenotypes, with the interaction between cell contractility and ECM stiffening heavily influenced by cell motility level and reflected in distinct cell shapes [1-3]. This research introduces a free-energy-based model that, based on sound physics, not only distinguishes among different cell populations by their motility levels, but also truly replicates the recently observed trizonal cell response to ECM stiffness. This predictive model, validated by experiment, bridges a critical gap in our understanding of cellular dynamics in cancer progression, offering profound insight into the physical concepts driving these complex interactions. Thereupon, this work provides a powerful computational tool, potentially leading to new strategies in diagnosing and treating cancer by targeting specific cell behavioral traits and interactions within the tumor microenvironment.