In the vast majority of physiological processes, lipid membranes and their relative proteins are the fundamental actors controlling the mechanics of the phenomena. The fluid lipid bilayer acts as a boundary for the cell and as a support for membrane proteins. It represents the stage for all life-related processes involving signal trafficking, compounds adsorption, environmental sensing, cell-cell interactions, and cell¿s reproduction and death. The ability of the membrane to deform and remodel its shape is crucial in all the aforementioned scenarios, and it is often driven by the curvature-inducing proteins crowding the cell¿s surface. This project aims at shedding light on the complex multiscale phenomenon of protein aggregation on the bilayer, usually driven by direct protein-protein potentials and, more interestingly, curvature-mediated long-range interactions. Implementing a suitable phase field model for proteins and lipids interactions, it will be possible to numerically investigate the underlying physics of these systems.
Proteins' interactions with lipid membranes are involved in complex multiscale mechanics, where local molecular phenomenology strictly controls the mesoscale behavior of the bilayer. The protein action locally deforms the elastic membrane and a curvature-mediated aggregation mechanism guides the protein clustering and coating on it. The innovative content of this project aims at filling the gap between molecular dynamics models describing the nanoscale relevant physics and the mesoscale remodeling observed experimentally. Coarse grained methods are actually constrained to relatively small systems (~100nm [1]) with some strong approximations and without the possibility to observe second order effects like external hydrodynamics and long-time phenomena. Furthermore, curvature-driven aggregation of proteins strongly depends on the geometry and elasticity of the bilayer (both locally and in long-range interactions), thus calling for a proper continuous elastic description. Following the ideas of Canham and Helfrich [2], several analytical and sharp interface approaches tried to reproduce the mutual action of protein insertions on the membrane, but very limited results have been obtained due to the small deformations hypothesis and lack of protein orientation dependence. A major change in perspective has been introduced considering the specific mechanical signature of each protein with the surrounding lipid surface [3], but strong numerical limitations still prohibit an extensive use of such techniques.
Phase field methods have the right ingredients to overcome the aforementioned problems and spontaneous curvature models have been used to take into account the diffused overall deformation induced by protein concentration on the membrane [4]. However, to the best of our knowledge, no phase field model has ever been proposed in order to include the action or interaction of distinct membrane proteins.
The PI has already addressed the needed characteristics of the additional free energy term describing the effects of an external force field onto the membrane. Other than that, the force field has been linked to a moving point standing for the protein center of mass, thus enabling proteins mobility. Recovering the right structure and intensity of the force fields stands as a direct connection between the phase field mesoscale mechanics and the world of molecular dynamics simulations. By analyzing different compounds, it would be possible to infer some fundamental protein aggregation modes. The following steps towards a full description of protein-induced membrane remodeling consist in augmenting the size of numerically solvable systems and introducing direct protein interactions, external hydrodynamics, and thermal fluctuations effects.
The outcomes of this research project will shed new light on the possibilities of phase field approaches and on the tightly coupled mechanics of protein clusters and lipid membranes.
[1] Voth, G.A. et al. Linear aggregation of proteins on the membrane as a prelude to membrane remodeling. Pnas 2013.
[2] Helfrich, W. Elastic properties of lipid bilayers: theory and possible experiments. Zeitschrift für Naturforschung C 1973.
[3] Himani, A. et al. Revisiting the curvature-mediated interactions between proteins in biological membranes. Soft matter 2016.
[4] Hernandez-Machado, A. et al. The dynamics of shapes of vesicle membranes with time dependent spontaneous curvature. PloS ONE 2020.