(747d) Protein-Sorting, Curvature-Induction and Curvature Sensing in Lipid Membranes: Quantification of Free Energies in a Mesoscale Cell Membrane Model

Background:Curvature inducing cell membrane proteins are an essential component of many cell membrane remodeling processes including cell motility and internalization of proteins/cargo through endocytosis. Membrane proteins such as Epsin and Ampiphysins have been shown to tubulate liposomes in vitro, and migrate along mean curvature gradients in vitro [1, 2]. This curvature-mediated recruitment may play a role in vivo during Epsin recruitment to a nascent endocytic budding. Membrane proteins are thought to induce curvature through either the insertion of a amphipathic helix, or electrostatic scaffolding [3,4,5].  Some proteins induce curvature through a combination of these mechanisms [6]. It is not clear how these proteins sense mean curvature gradients with different affinities, and what major determinants impact their segregation. Some of the physical properties and experimental conditions that are relevant to the curvature-induction and sensing process are the magnitude and extent of the induced curvature by a single protein on the membrane, the membrane bending stiffness and background curvature, interfacial tension etc.

Methods: In this work, the lipid/cell membrane is modeled with a continuum Monte Carlo model evolved with the Helfrich Hamiltonian [7, 8].  In the model the membrane is described by a triangulated sheet that can access length scales on the order of 100 nm. Membrane proteins interact with the membrane through the intrinsic curvature field, and can move along the triangulated mesh according to Metropolis.  The curvature field is approximated as a Gaussian, with Gaussian parameters derived from relating the curvature energy to isothermal titration experiments measuring Epsins association energy with the bilayer.  Membrane proteins thought to induce an anisotropic curvature field are modeled by an anisotropic two-dimensional Gaussian function.

The Widom particle insertion method is a free energy calculation developed to compute a system’s chemical potential [10]. Widom insertion probes chemical potential by randomly inserting a ghost particle, and determining the energy difference due to the extra particle. This method is only efficient for systems at low-moderate density. We employ the Widom insertion method to inhomogeneous systems where the excess chemical potential is computed along an intrinsically inhomogeneous axis of the system.

Results: Using our mesoscale membrane model, the chemical potential of curvature inducing proteins is quantified for two in vitro systems: (1) cylindrical lipid tethers (20-50 nm diameter) pulled from giant unilamellar vesicles (GUVs), and supported bilayers placed atop fabricated wavy substrates [2,9].  

In order to compare our results to these in vitro experiments three model geometries were simulated, namely, a plane, a tube, and a sinusoid.  The tube geometry approximates a membrane tether, while the sinusoidal surface is analogous to curvature sensing experiments on wavy substrates.  All geometries are subject to periodic boundary conditions. The effect of random pinning to maintain the overall membrane topology is also investigated.  A pinning study shows that as pinning density increases and membrane fluctuations are suppressed, the chemical potential of a curvature inducing protein increases nonlinearly.  

In the planar geometry, the chemical potential required to bend the membrane to a certain curvature field is shown to depend on both the extent as well as the amplitude of the curvature field. A larger curvature field senses mean curvature gradients to a greater degree.   The chemical potential also scales linearly with bending rigidity.  In the tube geometry, there is a constant background mean curvature, as the radius of the tube increases, the mean curvature decreases, and the chemical potential increases.  This finding is consistent with experiments performed on lipid tethers, which show a linear increase in fluorescence intensity with decreasing radius.

In the sinusoid geometry there is a gradient of mean curvature, this allows calculation of the density scaling of membrane proteins with mean curvature through inhomogeneous Widom insertion method.  Experiments on wavy substrates show changes in density scaling for several different curvature inducing proteins.  Simulations capture different scaling behavior according to a range of different Gaussian curvature field parameters.  Anisotropic curvature fields are found to prefer parallel alignment with mean curvature gradients.  This result is found by generalizing inhomogeneous Widom insertion along both the axis of the sine wave, and the angle of the curvature inducing protein.  Simulations calculate lower chemical potential when the curvature field best matches the background mean curvature field.

In summary, the chemical potential of a curvature inducing protein in the dilute limit is shown to be dependent on the form and strength of the curvature field, the bending rigidity, and thermal fluctuations.  For an anisotropic curvature inducing protein, the chemical potential shows preferential alignment/orientational favorability over spatial gradients in mean curvature. Our results are also shown to be consistent with in vitro experiments of protein segregation on curvature fields.

References:
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