Mechanics of the bilayer membrane play an important role in many biological and bioengineering problems such as cell-substrate and cell-nanomaterial interactions. In this work, we study the effect of thermal fluctuation and the substrate elasticity on the cell membrane-substrate adhesion. We model the adhesion of a fluctuating membrane on an elastic substrate as a two-step reaction comprised of the out-of-plane membrane fluctuation and the receptor-ligand binding. The equilibrium closed bond ratio as a function of substrate rigidity was computed by developing a coupled Fourier space Brownian dynamics and Monte Carlo method. The simulation results show that there exists a crossover value of the substrate rigidity at which the closed bond ratio is maximal.
Keywords: Brownian dynamics; Fourier transform; Monte Carlo; cell membrane; fluctuation.