Statistical-Mechanical Model

The model minimizes Helmholtz free energy as a function of order parameters for three transitions. For PT1, increasing substrate stiffness lowers interaction energy and favors stress-fiber formation. For PT2, larger numbers of stress fibers make alignment easier under the same force conditions. For PT3, high binding-protein concentration stabilizes aggregated fibers. The model treats local cellular regions as two-dimensional square lattices under constant volume, temperature, and particle or fiber number assumptions.