Emergent material properties and shape transformations of fluctuating membranes with adhered proteins

Many processes that occur at biological membranes have been shown to be remarkable displays of molecular coordination and shape transformation. Despite the apparent complexity of these processes, investigations of simplified systems have successfully characterized many ways that these materials can self-organize. Such studies established that proteins may either bend membranes by binding to them along curved structural domains or by inserting into them asymmetrically. One recent study, however, showed that generic clusters of small membrane-adhered proteins that lack these features can nevertheless remodel membranes into highly curved shapes.In this manuscript we use theoretical and computational methods of statistical mechanics to elucidate how a driving force for membrane curvature emerges from the steric effects among such adhered proteins. First, we develop a basic thermodynamic model of the experimental system referenced above, considering the energetic penalty of membrane bending for simple shapes while also introducing the 2-dimensional pressure of the adhered protein layer. We show that increasing the curvature of the underlying membrane effectively increases the area of the adhered protein layer, lowering the associated pressure and entropically stabilizing the composite system at nonzero curvatures. To generate quantitative predictions of curvature as a function of adhered protein concentration, we model the protein layer as a hard disk fluid and compare these results to experimental data. We also use overdamped Langevin dynamics simulations, again considering only volume excluding interactions among proteins, to observe shape transformations and fluctuations of such systems in more complex morphologies. We extend our thermodynamic model to show that cylindrical curvature becomes more stable than spherical curvature at protein densities higher than some critical value. This critical value becomes smaller as membrane area increases, which supports experimental observations and explains why tubules are unstable in simulated systems, which are much smaller. The development of a molecular simulation model for this research was a significant effort, and we discuss this implementation in some detail. We build upon a coarse-grained model previously developed in our research group, however we modify its original functional forms to be smoothly varying and thus stable for dynamical integrators. We also develop consistent coarse-grained models for adhered proteins and for a second lipid type. We then discuss extensions developed for future studies, methods of analysis, and relaxation time scaling for cylindrical configurations.Finally, we show how the adhered protein layer effectively renormalizes the original material properties of the underlying membrane. We begin by theoretically analyzing our composite membrane-protein system in the regime of small but nonzero curvature fluctuations. This analysis yields a form identical to the standard free energy of a bare membrane but with effective expressions for the bending rigidity, surface tension, and spontaneous curvature that are dependent on the density of adhered proteins. As protein density increases, the effective bending rigidity and spontaneous curvature reduces until the system can become unstable. We support these predictions with molecular simulation calculations of the type discussed earlier. These results exemplify the ideas discussed at the start of this manuscript, demonstrating how the emergent characteristics of seemingly complex membranes can sometimes be remarkably folded back into the basic physics of these soft materials. Moreover, since a membrane attachment region alone is sufficient for protein clusters to produce the results presented throughout this work, these results could characterize a new and general way that proteins modify and sculpt membranes during various essential cellular processes.