Mesoscopic dynamic Monte Carlo simulations of fluctuating fluid membrane shaping in biological processes: a review

Plasma membranes not only serve as physical barriers to separate the cell or organelle from extracellular or intracellular environments, but also play important roles in many cellular processes, e.g., cell adhesion, cell migration, endocytosis as well as membrane budding, whose correct executions rely on locally highly curved membrane shaping. Mechanically, these membranes are soft fluid interfaces exhibiting extremely dynamic remodeling processes in response to mechanobiological stimulus from their surrounding complex intra/extra-membranous circumstances containing thermal fluctuations, protein binding, protein-protein interaction on the membrane surface forming protein superstructures and active cytoskeletal networks. Correlating these dynamic membrane shaping involving characteristic membrane mechanical properties with cellular functions is essential to improving fundamental understandings in cell physiology and cell biomechanics. The challenge here is to explicitly describe the dynamics of membrane remodeling under the complex biological situations. Interestingly, the developed mesoscopic Monte Carlo (MC) method has the capacity to concurrently capture the elasticity and fluidity of fluid membranes well on large time and length scales, as well as to successfully reproduce fluctuating membrane morphology as observed in experiments. In this review, we focus on this mesoscopic MC method used to depict the thermodynamics of fluctuating fluid membranes and further explore how diverse biophysical factors drive large membrane curvature generation. We also discuss the current efforts of the roles of membrane morphology on the regulation of biological processes on the basis of this mesoscopic MC method, provide the insights into the known biomechanical mechanisms of effect of membrane shape on cellular functions, and point out the potential opportunities where this mesoscopic dynamic MC method can be modified to investigate more intricate biological processes, such as membrane fusion and adhesion.