Matrix mechanics couple contractility to metabolic adaptation in cancer cells

Cells dynamically regulate their morphology, contractility, and metabolism in response to the mechano-chemical properties of their microenvironment. Here, we show matrix stiffness and ligand density jointly govern the bioenergetics of contractile cells through a nonequilibrium active chemo-mechanical model built around a newly introduced cellular metabolic potential. This concept links ATP hydrolysis to mechanosensitive signaling, quantifies the energetic cost of stress fiber assembly, and determines mechanically stable states. The metabolic potential enables quantitative prediction of cell contractility, morphology, and ATP consumption in different stiffness 2D and 3D environments, and we find quantitative agreement with experimental measurements in MDA-MB-231 breast cancer cells. The model further predicts activation of AMPK accompanies increased energetic demands in stiffer microenvironments which we experimentally validate and correlate with increased mitochondrial membrane potential, glucose uptake, and intracellular ATP levels. Together, these findings establish a predictive quantitative framework linking mechanosensitive control of cell shape and contractility to actomyosin-dependent ATP consumption and AMPK-mediated energy replenishment. STATEMENT OF SIGNIFICANCE: While it is well established that extracellular matrix stiffness alters cell shape, contractility, and signaling, how these cues quantitatively integrate with cellular energy homeostasis in diseases such as cancer remains unclear. In this work, we establish a framework connecting extracellular mechanics, actomyosin organization, and intracellular energy regulation into a single energetic principle governing cell behavior. We show that mechanical environments reshape the cellular energy budget, driving cells toward morphologies and contractile states that balance energetic demand with metabolic supply. This perspective reframes mechanotransduction not simply as a signaling cascade, but as a process fundamentally constrained by energy economics, providing new insight into how cancer cells navigate mechanically heterogeneous tissues, with implications for invasion, metastasis, and therapeutic targeting of mechano-metabolic vulnerabilities.