Curvature inducing macroion condensation driven shape changes of fluid vesicles

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.

Conformations of a charged vesicle interacting with an oppositely charged particle

Endocytotic and exocytotic processes are usually studied using particle-vesicle systems in theory, but most of them are electroneutral. Nevertheless, charged particle-vesicle systems are much closer to real biological systems. Therefore, wrapping behaviors of a negatively charged vesicle wrapping a positively charged particle are systematically investigated by a series of 2D dynamical simulations in this article. The competition between the elastic bending energy and the electrostatic energy dictates the vesicle configuration and charge distribution. It is found that only for intermediate charge concentrations and small particle sizes a vesicle can completely engulf the particle. When the charge density is high, the interaction between vesicle and particle is unexpectedly weakened by both the hardening effect of the charged membrane and the effective-transportation-frozen effect of the charged components. When the particle is strongly charged, multi-layer folding conformations are observed. These studies may provide important insights into mechanism of endocytotic and exocytotic processes in biological systems.