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

Abstract

We present coarse-grained molecular dynamics simulations of the epsin N-terminal homology domain interacting with a lipid bilayer and demonstrate a rigorous theoretical formalism and analysis method for computing the induced curvature field in varying concentrations of the protein in the dilute limit. Our theory is based on the description of the height-height undulation spectrum in the presence of a curvature field. We formulated an objective function to compare the acquired undulation spectrum from the simulations to that of the theory. We recover the curvature field parameters by minimizing the objective function even in the limit where the protein-induced membrane curvature is of the same order as the amplitude due to thermal undulations. The coupling between curvature and undulations leads to significant predictions: (i) Under dilute conditions, the proteins can sense a site of spontaneous curvature at distances much larger than their size; (ii) as the density of proteins increases the coupling focuses and stabilizes the curvature field to the site of the proteins; and (iii) the mapping of the protein localization and the induction of a stable curvature is a cooperative process that can be described through a Hill function.

Why Enveloped Viruses Need Cores—The Contribution of a Nucleocapsid Core to Viral Budding

“…Molecular dynamics simulations can be a useful tool to bridge the gaps between the different steps of assembly that cannot be experimentally characterized. Computational studies have already provided insightful information about virus NC assembly (20), as well as the interactions between proteins and lipid membranes (21)(22)(23). Previous simulations on budding of nanoscale particles led to important insights but did not consider the effect of GPs (24)(25)(26)(27)(28)(29)(30)(31), although budding directed by GP adsorption or capsid assembly have been the subject of continuum theoretical modeling (32)(33)(34).…”

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

“…It can also be seen from figure 2(F) that multiple curvature fields aggregate to generate a tubular protrusion in the cell membrane. The curvature field associated with a protein is parameterized either from experimental data [88] or through molecular simulations [77, 88], as described in section 2.…”

“…in the range of the undulation wave-length, in contrast to that of the curvature field itself, which may be short-ranged. In fact, as discussed in section 2, this relationship was utilized by Bradley and Radhakrishnan [77] to infer a curvature-field from the undulation spectra of the CGMD simulation data. Together, the discussion above provides a comprehensive picture of how the recruitment of CRPs can be influenced by thermal undulations, membrane excess area, and membrane tension.…”

“…Several studies have used this method to qualitatively describe how bound proteins alter the average height/deflection of a free bilayer [76, 77, 83–85]. Using bilayer deflection as a proxy for curvature introduces the first of several challenges for understanding protein-mediated membrane sculpting: are proteins sensing or creating curvature?…”

“…The broken tubule has the benefit of size and high density but lacks tension in the direction along which it is broken. Simulations of CRPs have likewise observed that membrane undulations can mediate long-ranged interactions between proteins [77]. …”