Membrane tension controls the assembly of curvature-generating proteins

Abstract

Proteins containing a Bin/Amphiphysin/Rvs (BAR) domain regulate membrane curvature in the cell. Recent simulations have revealed that BAR proteins assemble into linear aggregates, strongly affecting membrane curvature and its in-plane stress profile. Here, we explore the opposite question: do mechanical properties of the membrane impact protein association? By using coarse-grained molecular dynamics simulations, we show that increased surface tension significantly impacts the dynamics of protein assembly. While tensionless membranes promote a rapid formation of long-living linear aggregates of N-BAR proteins, increase in tension alters the geometry of protein association. At high tension, protein interactions are strongly inhibited. Increasing surface density of proteins leads to a wider range of protein association geometries, promoting the formation of meshes, which can be broken apart with membrane tension. Our work indicates that surface tension may play a key role in recruiting proteins to membrane-remodelling sites in the cell.

Figure 1. Dynamics of dimerization of N-BARs at 4% surface coverage.

The kymogram is generated by observing a protein and recording, at each time step, the dimer (D) or the monomer (M) state. Increasing tension significantly reduces the lifetime of dimers. Each plot is a representative of three individual measurements.

Figure 2. Membrane tension inhibits protein aggregation.

(a) Polymerization free energy (F_p) as a function of end-to-end distance (d) between the incoming N-BAR molecule and a linear chain with: 3 N-BARs, 1 N-BAR or 5 N-BARs, as depicted at the bottom of each plot. For all plots, measurement done from two independent umbrella-sampling calculations, each using 34 different sampling windows (except at zero tension, where 46 windows were used), each window run for 100,000 time steps. (b) Magnitude of F_p and the interaction length scale (λ) as a function of membrane tension (σ) for the three chain lengths, where N is the total number of proteins in the chain. Dots represent free-energy minima taken from measurements in a. Cross marks denote values obtained using , where κ=15 k_BT.

Figure 3. Membrane tension alters N-BAR orientation.

(a) Self-assembly of N-BAR proteins at different membrane tensions (in mN m⁻¹). Scale bar, 10 nm. Each simulation shows a representative snapshot from three simulations, totalling 30 million time steps per configuration. (b) Orientation free energy (F_o) as a function of dimer angle (φ) at 4% protein coverage, for different membrane tensions (in mN m⁻¹). Measured by inverting the Boltzmann distribution of dimerization angles, each plot averaged from simulations in a. (c) Self-assembly of spherical nanoparticles at different membrane tensions (in mN m⁻¹). Panel shows a representative snapshot from two simulations, each run for 10 million time steps.

Figure 4. Aggregation dynamics of spherical particles at different tensions.

Kymograms show the lifetime of observed dimers, trimers and tetramers of spherical particles, in some cases leading to the formation of a linear aggregate. The y axis in all plots represents the number of distinct aggregates. Shown are simulations of particles with 10% membrane coverage, at different membrane tensions, each run for 5 (zero tension) or 10 (non-zero tension) million time steps. Bottom: snapshots from a simulation at 0.05 mN m⁻¹ taken at time steps (a–d) as denoted in the plot above.

Figure 5. The influence of protein density on self-assembly.

Self-assembly at different tensions (in mN m⁻¹) at 10% (a) and 20% (b) N-BAR surface coverage. The scale in all panels is the same. Scale bar, 10 nm (a,b). Shown are representative snapshots from three simulations, totalling 30 million time steps per configuration. (c) The orientation free energy (F_o) at 2% (left) and 10% (right) surface coverage at different membrane tensions (in mN m⁻¹). Measured by inverting the Boltzmann distribution of dimerization angles, each plot representing data from three simulations, totalling 30 million time steps per configuration.

Figure 6. Predicting the dimerization geometry from numerical expressions.

(a) Free energy of end-to-end (F_e) dimers versus side-by-side (F_s) dimers as a function of membrane–protein interaction strength (w) at σ=0 (left) and membrane tension at w=5 kJ mol⁻¹ nm⁻² (right). End-to-end dimerization is favoured when F_e−F_s<0. (b) Configurational diagram relating protein aspect ratio (L/R) to w, on tensionless and tensed membranes. Red squares: side-by-side dimers, blue squares: end-to-end dimers. In all calculations, we used α=0.5, R=2.0 nm and κ=15 k_BT except when these values were varied.