Curvature sensing as an emergent property of multiscale assembly of septins

Abstract

The ability of cells to sense and communicate their shape is central to many of their functions. Much is known about how cells generate complex shapes, yet how they sense and respond to geometric cues remains poorly understood. Septins are GTP-binding proteins that localize to sites of micrometer-scale membrane curvature. Assembly of septins is a multistep and multiscale process, but it is unknown how these discrete steps lead to curvature sensing. Here, we experimentally examine the time-dependent binding of septins at different curvatures and septin bulk concentrations. These experiments unexpectedly indicated that septins' curvature preference is not absolute but rather is sensitive to the combinations of membrane curvatures present in a reaction, suggesting that there is competition between different curvatures for septin binding. To understand the physical underpinning of this result, we developed a kinetic model that connects septins' self-assembly and curvature-sensing properties. Our experimental and modeling results are consistent with curvature-sensitive assembly being driven by cooperative associations of septin oligomers in solution with the bound septins. When combined, the work indicates that septin curvature sensing is an emergent property of the multistep, multiscale assembly of membrane-bound septins. As a result, curvature preference is not absolute and can be modulated by changing the physicochemical and geometric parameters involved in septin assembly, including bulk concentration, and the available membrane curvatures. While much geometry-sensitive assembly in biology is thought to be guided by intrinsic material properties of molecules, this is an important example of how curvature sensing can arise from multiscale assembly of polymers.

Keywords: curvature sensing; kinetic modeling; multiscale assembly; septin.

Fig. 1.

Time-lapse microscopy on spherical supported lipid bilayers shows context-dependent septin assembly kinetics. (A–C) First row: Schematic representations of the view of monodispersed (A and B) and bidispersed assays (C) containing silica microspheres coated in a lipid bilayer (purple) of 75% DOPC and 25% phosphatidylinositol; the total membrane surface area is kept fixed in all experiments. Second row: The time variations of the representative focal slices of septin adsorption (green) at various concentrations onto (A) monodispersed 1 μm and (B) 5 μm beads and (C) bidispersed mixture of beads at bulk concentration n_b = 12.5 nM. The lipid channel is in magenta, and the scale bars are 1 μm in (A), 2 μm in (B), and 1 μm in (C). Third row: Quantification of septin adsorption. Error bars correspond to the SE. (D) Diagram of the adsorption process, separated into three regimes: initiation, growth, and saturation. (E) Subprocesses involved in the septin adsorption process: ① binding of a single-septin oligomer in the bulk; ② the diffusion of bound septins on the membrane; ③ their polymerization through end-on annealing; ④ fragmentation of bound septin filaments into shorter ones; ⑤ cooperative binding of bulk septins, and ⑥ unbinding. (F) Ratio of septin adsorption at steady state on 1-μm beads to septin adsorption on 5-μm beads for monodispersed and bidispersed assays.

Fig. 2.

Single-septin complexes can detect only changes in membrane curvature through their binding rate. (A) Representative near-TIRF images showing single oligomers’ binding and unbinding events on various membrane curvatures. (Scale bar, 2 μm.) (B) Measured binding rates (J_on) for a single oligomer binding onto various membrane curvatures, κ = 1/r, at 1 nM bulk concentration. N > 200 events for each curvature. Error bars represent the SE. (C) Measured binding rates of single-septin oligomer onto membrane curvature κ = 2 μm⁻¹ at various septin concentrations. N > 200 events for each concentration. Error bars represent the SE. (D) Violin plots highlighting the distribution of measured dwell times for a single-septin oligomer on different membrane curvatures at 1 nM bulk concentration. N > 200 events per curvature. Filled circles show the experimentally measured mean values.

Fig. 3.

Single-septin complexes display subdiffusive behavior on curved membranes. (A) Top: Representative near-TIRF images of single-septin complexes on membrane-coated beads of diameter 5 μm and 3 μm, respectively. (Scale bar, 0.25 μm.) Bottom: Individual particle tracks (yellow lines) for beads of diameter 5 μm and 3 μm, respectively. (Scale bar, 0.25 μm.) (B–D) Mean squared displacements (MSDs) of single-septin oligomers vs time on a flat membrane (B) and membrane-coated beads of diameter 3 μm (C) and 5 μm (D). The filled circular symbols denote the mean values computed from analyzing the trajectory of more than 500 particles, and the solid lines represent the fit from Eq. 4 with N = 1. Shaded areas represent spread in experimental data in the interquartile range (darkest, 25% to 75%), interdecile range (next darkest, 10% to 90%), and full range (lightest, 0% to 100%).

Fig. 4.

The length distribution of septin filaments is curvature dependent. (A and B) Near-TIRF images of septin filament end-on annealing (A) and fragmentation (B) on membrane-coated rods of diameters 46 to 1,508 nm. (Scale bar, 1 μm.) (C) SEM images of septin filaments on rods of different diameters. One of the septins is labeled as a yellow solid line, and the yellow dashed line is the long axis of the rod. The angle between the septin axis and the rod axis is defined as θ. (Scale bars, 0.1 μm.) (D) Probability density of septins’ length (number of oligomers per septin) at different septin curvature intervals. The curvature is defined as ${\kappa }^{\text{s}}=R_{\text{rod}}^{-1}sin\theta$, where R_rod is the radius of the membrane-coated rod and θ is the angle of the septin filament with respect to the long axis of the rod (zero when septin filament lies along the long axis and π/2 when septin filament lies orthogonal to the long axis).

Fig. 5.

Modeling predictions are in good agreement with time-dependent adsorption experimental data. Top row: Experimental data repeated from Fig. 1 A and B) Septin adsorption over time in monodispersed assays on 1-μm (A) and 5-μm (B) beads. The filled symbols denote experimental data, and solid lines represent the predictions of our kinetic model. Error bars correspond to SE of the experimental data. (C) Septin adsorption on 1-μm (circle symbols) and 5-μm (square symbols) beads over time in bidispersed assays at 25 nM bulk septin concentration. Bottom row: Variations of the average length of septins vs. time, corresponding to the same conditions as the top row.

Fig. 6.

Reducing the degree of septin depletion from the bulk changes septins’ apparent curvature sensitivity. The ratio of steady-state septin adsorption on 1-μm to 5-μm beads in bidispersed assays, using different total membrane surface areas. The surface area is indicated as a percentage of the standard surface area we used in these assays (5 mm²). The bulk septin concentration is 6.25 nM. The blue violin plot shows the distribution of the ratio, and the black diamond indicates the average value. The orange line represents the ratio of adsorption between 1-μm and 5-μm beads at steady state in monodispersed assays; the orange belts represent spread in experimental data in the interquartile range (darkest, 25% to 75%), interdecile range (next darkest, 10% to 90%), and full range (lightest, 0% to 100%).

Fig. 7.

A schematic model of septin curvature sensitivity in competition case. Septin adsorption on 1-μm (pink) and 5-μm (blue) beads is plotted over time. Insets illustrate how septins are depleted from the bulk solution primarily by 1-μm beads, leading to faster initiation and growth phases on 1 μm and ultimately larger adsorptions. Because 5-μm beads recruit from a more depleted bulk, compared to monodispersed assays, their growth rate and final adsorption are reduced. Shades of green represent septin bulk concentration.