Abstract
Cells regulate their shape and metabolic activity in response to the mechano-chemical properties of their microenvironment. To elucidate the impact of matrix stiffness and ligand density on the bioenergetics of mesenchymal cells, we developed a nonequilibrium, active chemo-mechanical model that accounts for the mechanical energy of the cell and matrix, chemical energy from ATP hydrolysis, interfacial energy, and mechano-sensitive regulation of stress fiber assembly through signaling. By integrating the kinetics and energetics of these processes, we define the cell "metabolic potential" that, when minimized, provides testable predictions of cell contractility, shape, and ATP consumption. Specifically, we show that the morphology of MDA-MB-231 breast cancer cells in 3D collagen changes from spherical to elongated to spherical with increasing matrix stiffness, which is consistent with experimental observations. On 2D hydrogels, our model predicts a hemispherical-to-spindle-to-disc shape transition with increasing gel stiffness. In both cases, we show that these shape transitions emerge from competition between the energy of ATP hydrolysis associated with increased contractility that drives cell elongation and the interfacial energy that favors a rounded shape. Furthermore, our model can predict how increased energy demand in stiffer microenvironments is met by AMPK activation, which is confirmed experimentally in both 2D and 3D microenvironments and found to correlate with the upregulation of mitochondrial potential, glucose uptake, and ATP levels, as well as provide estimates of changes in intracellular adenosine nucleotide concentrations with changing environmental stiffness. Overall, we present a framework for relating adherent cell energy levels and contractility through biochemical regulation of underlying physical processes. STATEMENT OF SIGNIFICANCE: Increasing evidence indicates that cellular metabolism is regulated by mechanical cues from the extracellular environment. Forces transmitted from the microenvironment activate mechanotransduction pathways in the cell, which trigger a cascade of biochemical events that impact cytoskeletal tension, cellular morphology and energy budget available to the cell. Using a nonequilibrium free energy-based theory, we can predict the ATP consumption, contractility, and shape of mesenchymal cancer cells, as well as how cells regulate energy levels dependent on the mechanosensitive metabolic regulator AMPK. The insights from our model can be used to understand the mechanosensitive regulation of metabolism during metastasis and tumor progression, during which cells experience dynamic changes in their microenvironment and metabolic state.