Rigid proteins and softening of biological membranes-with application to HIV-induced cell membrane softening

Abstract

A key step in the HIV-infection process is the fusion of the virion membrane with the target cell membrane and the concomitant transfer of the viral RNA. Experimental evidence suggests that the fusion is preceded by considerable elastic softening of the cell membranes due to the insertion of fusion peptide in the membrane. What are the mechanisms underpinning the elastic softening of the membrane upon peptide insertion? A broader question may be posed: insertion of rigid proteins in soft membranes ought to stiffen the membranes not soften them. However, experimental observations perplexingly appear to show that rigid proteins may either soften or harden membranes even though conventional wisdom only suggests stiffening. In this work, we argue that regarding proteins as merely non-specific rigid inclusions is flawed, and each protein has a unique mechanical signature dictated by its specific interfacial coupling to the surrounding membrane. Predicated on this hypothesis, we have carried out atomistic simulations to investigate peptide-membrane interactions. Together with a continuum model, we reconcile contrasting experimental data in the literature including the case of HIV-fusion peptide induced softening. We conclude that the structural rearrangements of the lipids around the inclusions cause the softening or stiffening of the biological membranes.

Figure 1. A schematic of the HIV Fusion Peptide softening a lipid bilayer membrane.

The picture shows an HIV entering the host cell via membrane softening and thinning. Subsequently, through the creation of pore, the genetic material of HIV (shown in yellow) is injected into the host cell.

Figure 2. Large Scale all-atom MD simulations were performed on a system of 1600 lipids with 16 HIV FP23.

The lipids are represented as yellow dots while the proteins are represented as red “blobs”. The size of the simulation box is 22.35 nm × 22.35 nm surrounded by water molecules—which are shown in blue.

Figure 3. Thickness and bending modulus of the membrane as a function of the MD simulation time-steps.

Only converged values are used for comparison. We note that the converged values clearly show decrease in thickness and bending modulus upon addition of HIV FP23 to the virgin lipid membrane.

Figure 4

(a) The two red bars represent two FP23 separated by a distance of 4.6 nm from their centers. The plot shows decrease in the mean area per lipid as we move away from the center of protein, which again increases as we approach the other protein, (b) The mean splay angle reduces while moving away from protein, which indicates lessening of the impact of proteins on the surrounding lipids. Due to the decrease of splay, they occupy less area.

Figure 5. The left figure shows a peptide or protein of radius a and bending modulus embedded in a membrane of radius b and bending modulus .

The outer boundary of the membrane is represented by and the inner boundary between peptide and membrane by ∂Ω. We use an homogenization approach to obtain the effective bending modulus of this protein-membrane system, represented by .

Figure 6. The central concept behind the theoretical model is the introduction of special interfacial boundary conditions represented by the parameters k₁ and k₂.

The thin interface between protein and membrane is represented by solid bars and springs in the top figure. The bottom figure shows a peptide of radius a embedded in a membrane of radius b. The thin interface between peptide and lipid is also taken into account in this case. The outer surface of the membrane is represented by . The inner surface of the protein is represented by ∂Ω⁻ and outer surface (which is towards the membrane) by ∂Ω⁺. The effective bending modulus of this protein membrane system is found by modifying the Helfrich Hamiltonian and taking into account the interface by introducing jump energies parametrized by k₁ and k₂.

Figure 7. The plot shows effective bending modulus as a function of area fraction of peptide in a membrane for HIV FP23, Alamethicin and Magnanin.

The solid lines represent the theoretical values of effective bending modulus corresponding to the area fraction f. The dotted points in corresponding colors are the experimentally observed values of the bending modulus corresponding to that f for that protein. Our theoretical predictions match well with that of experimental observations and explain the mechanics behind the softening process.

Figure 8

(a,b) The figure shows the spatial arrangement of FP23 with respect to the membrane. The red line is the hydrophobic-hydrophilic interface. The fusion peptide is almost parallel to the interface. Also, being mostly hydrophobic it lies with the hydrophobic tails of the bilayer, shown as black lines. (c) It shows the cross section of protein and lipids shown in (b). The lipids adjacent to the protein show positive splay.

Figure 9

(a) A convergence study was performed to evaluate how far lipids can actually “feel” each other. Quantitatively, we compute a parameter called ‘splay modulus’ which is the energy penalty due to the splay distortion of the lipid molecules. This splay distortion costs more energy when the lipids are closer than when they are far away. Hence we need to chose an optimum cut-off distance beyond which the lipid pairs contribute minimally to the energy. It is the point at which the splay modulus saturates, and we find it to be 8 nm, (b) The figure shows 8 periodic images of the membrane-protein system, which is the middle box, surrounded by the 8 images. We accounted for influence of these images on the computation of splay modulus of the system. The quantity ‘r’ in the figure is the nearest neighbor cut-off distance (8 nm).

Figure 10

(a,b) Normalized probability densities P(α) of finding a pair of DMPC at an angle α with respect to each other. (c,d) The figure shows PMF (Potential of Mean Force) defined as where α are the angles between lipid-lipid pairs. A quadratic fit is performed to the PMF at small angles of α to evaluate Splay Modulus of the lipid monolayer.