Defining the free-energy landscape of curvature-inducing proteins on membrane bilayers

Abstract

Curvature-sensing and curvature-remodeling proteins, such as Amphiphysin, Epsin, and Exo70, are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors; they aggregate to membrane regions matching their intrinsic curvature; as well as induce curvature in cell membranes to stabilize emergent high curvature, nonspherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test particle (or field) insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane—in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of thermal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer membranes.

Curvature–undulation coupling as a basis for curvature sensing and generation in bilayer membranes

“…To quantify the dependence of bilayer curvature on protein density, we carried out simulations with one, four, or eight coarse-grained ENTH domains according to the methods used in previous simulations of ENTH (35) and Exo70 (27). We adhere these proteins to a bare bilayer containing a total of 12,800 lipids at a 4:1 composition of DOPC and DOPS at a spacing of roughly 15 nm.…”

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

“…Recently, Tourdot et al [322] introduced and compared three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. Specifically, they showed the utility of the Widom-test-particle/field insertion methodology in computing the excess chemical potential associated with curvature-inducing proteins on the membrane and in tracking the onset of morphological transitions on the membrane at elevated protein density.…”

Phenomenology Based Multiscale Models as Tools to Understand Cell Membrane and Organelle Morphologies

“…[27] to compute surface quantifiers on the triangulated surface. In general, the value of the spontaneous curvature at a vertex is determined as, $$H_{0,v}=\sum _{v=1}^N{C}_0\mathcal{F}(v,v^{\prime }),$$ where C 0 denotes the magnitude of the induced curvature and $\mathcal{F}(v,v^{\prime })$ denotes the functional form of the contribution of the curvature contribution at vertex v′ due to a curvature field at vertex v ; see references [21, 28–31] for various forms of $\mathcal{F}(v,v^{\prime })$ in different contexts.…”

“…(2). Details of the formulation and the simulation techniques, including methods to characterize the isotropic curvature field for ENTH domains, can be found in references [13, 21, 30, 31, 82], and these methods are equally applicable to non-isotropic curvactants. In this section, we present an alternative treatment for anisotropic-curvature inducing proteins by treating the spontaneous curvature as an in-plane nematic field.…”

“…al. [13, 31] to study the thermodynamic stability of the membrane conformations remodeled by isotropic curvature inducing proteins. These techniques can also be readily extended to understand the stability of the various conformations observed for the nematic membrane.…”