Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes

Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the ill-understood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substrate-bound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tip-membrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of force-displacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membrane-protein interactions, including membrane remodeling in nanotube scission and vesicle formation.

Popular Summary

Lipid bilayers make membranes that delineate the boundaries of living cells or intracellular compartments, and they are continuously remodeled by various types of proteins. In particular, membranes can form cylinders called nanotubes with diameters of 20 to 200 nm. In the cell, nanotubes are cut by specialized proteins to form vesicles, which are then used to transport molecules to a different location of the same cell. The physical mechanisms by which nanotubes assemble and disassemble are unclear because of a lack of experimental techniques to map their morphology and mechanics at the nanoscale. We remedy this problem by developing a new platform to study nanotubes and biological membranes using atomic force microscopy.

We locally probe the mechanics and topography of these soft biological nano-objects by touching their surface with a nanometric indenter: We poke the nanotube surface with the atomic force microscope tip and record force-indentation curves. From these curves, we derive the tube morphology as well as the local tension and bending rigidity of the lipid membrane. Moreover, we test our approach on nanotubes covered by proteins—a network of the cytoskeletal protein actin—and show how actin networks enlarge and stiffen nanotubes.

Our new atomic force microscopy platform may be useful for deciphering the details of nanotube remodeling by proteins and thereby help researchers understand the physics underlying some fundamental cellular processes.

Figure 1

Nanomechanical mapping of membrane nanotubes. (a) Schematic illustrating the specific attachment of the nanotube lipids to the functionalized glass surface (not to scale). (b) AFM topography image (yellow and brown) of two nanotubes superimposed on the fluorescence image (gray) displaying the same nanotubes. AFM height scale (0–140 nm) displays high and low regions as bright and dark, respectively. (c) AFM mapping of the rigidity (colors) superimposed on the 3D topographic representation of the nanotube heights. Colors show stiff and soft materials as bright and dark, respectively. Both nanotubes have a rigidity of $38\pm 14\mathrm{kPa}$.

Figure 2

Multiple force-distance curves collected at a single point of contact on a nanotube. (a) AFM image of a SMC nanotube. The arrow points to where all the force curves analyzed in (b)–(e) are recorded. (b) Example of a force curve recorded at a speed of $2\mu \mathrm{m}/\mathrm{s}$. The blue line is the result of fitting the equation $f=K{\delta }^2$ to the data and returns the rigidity (here $K=24\mathrm{kPa}$). (c) Distribution of $K$ derived from force curves collected at different indentation speeds. Blue lines are Gaussian fits to the data. (d) Time versus vertical tip position (VTP), which indicates the height at which the AFM tip contacts the nanotube during its downward vertical movement. (e) $K$ plotted as a function of the VTP. In this graph $K$ is derived from force curves collected at a speed of $20\mu \mathrm{m}/s$ and it corresponds to the data displayed in (d) and in the bottom graph in (c).

Figure 3

High resilience of SMC nanotubes. (a) Force-distance curves collected at a speed of $20\mu \mathrm{m}/\mathrm{s}$ and (b) at a speed of $0.4\mu \mathrm{m}/\mathrm{s}$ on the same nanotube. Note that in both graphs $K$ are similar, although the amount of thermal noise is clearly higher at higher speed. (c) Force-distance curves collected on another nanotube (height $130\pm 10\mathrm{nm}$) with a high setpoint force of 400 pN. At such high force, the nanotube is fully compressed (i.e., maximum indentation depth similar to nanotube height) and the indenter pushes on a double bilayer, as indicated by the sudden increase in force when indentation depth reaches $\sim 130\mathrm{nm}$ (circle). N.B., in all graphs, the approach and retract curves overlap, at least for forces under 100 pN (i.e., maximum setpoint force typically used for imaging), indicating no hysteresis and thence purely elastic behavior. Furthermore, as the tip retracts from the nanotube, the nanotube does not maintain contact with the tip, indicating the absence of (detectable) nonspecific adhesion between the tip and the nanotube.

Figure 4

High-throughput probing of nanotube morphologies by AFM. (a) Examples of QI mode AFM images collected for nanotubes with two different lipid compositions, resulting in different rigidities. The bending rigidities $\kappa$ listed here were independently determined for lipid bilayers in vesicles at room temperature [32, 33]. Force curves were collected, and the heights measured at forces of 0, 2, and 50 pN are reported in separate images. (b) From top to bottom: heights, widths, aspect ratios, cross-sectional areas of all nanotubes ($N=62$ for SMC and $N=28$ for DOPC). Aspect ratios and cross-sectional areas are calculated using the height at 0 pN and the width at 2 pN (see Sec. 6 for details). Black horizontal lines and gray boxes represent the mean plus or minus 1 standard deviation.

Figure 5

Nanomechanical properties of membrane nanotubes. (a) Rigidity $K$ plotted against the AFM height $h$. Each data point represents one nanotube. Lines display the model with no adjustable parameter $K=22{\kappa }^{3/2}{(k_{B}T)}^{-1/2}{h}^{-3}$, with $\kappa$ the bending rigidity of the membrane (see text for details). (b) Schematics of the flattened nanotube and indentation geometry considered in our model. $f$ is the force exerted on the membrane by the AFM tip, $\delta$ the indentation depth, $h$ and $w$ the nanotube height and width, respectively. (c) Normalized rigidity $\tilde{K}=K/[22{\kappa }^{3/2}{(k_{B}T)}^{-1/2}]$ versus height for all nanotubes. Data points from the two sets of nanotubes (SMC and DOPC) collapse on the same master curve (black line), as predicted by the model.

Figure 6

Fluorescence imaging of actin filament networks on membrane nanotubes. Nanotubes are attached to a streptavidin-coated glass surface prior to incubation with actin and/or the activators of actin polymerization (essentially, SpVCA and $\mathrm{Arp}2/3$; see Sec. 6 for details). (a) DOPC nanotubes incubated with actin and with the activators of actin polymerization. (b) DOPC nanotubes incubated only with the activators of actin polymerization.

Figure 7

Morphology and mechanics of nanotubes modified by actin. (a) AFM images of SMC nanotubes before (left) and after modification by actin and the activators of actin polymerization (right). Black rectangles delimit regions of the images scanned with a higher resolution. (b) From left to right: Heights, widths, and rigidities of the same SMC nanotubes before and after modification by actin (median and interquartile range; Wilcoxon match-paired test, $*p<0.0005$). Heights and widths were obtained from 0 and 2 pN height maps, respectively. (c) Rigidity versus height for the same SMC nanotubes, before and after modification by actin. The solid lines represent fits to the data of the relationship $K=\chi h^{-3}$ with $\chi$ an adjustable parameter. The dashed lines are given by Eq. (4) without any adjustable parameter. (d) Rigidity versus height for all the SMC nanotubes that we analyzed over multiple experiments, including a control dataset (control act.) in which only the activators of actin polymerization were incubated with the nanotubes (but not actin). (e) Rigidity versus height for all the DOPC nanotubes that we analyzed.

Figure 8

Force-extension curves indicating the pulling of actin filaments from a SMC nanotube. This graph displays five distinct approach-retract cycles of the AFM tip. The retract curves clearly show some force peaks, indicating that the AFM tip pulls actin filaments or actin filament networks out of the nanotube surface when moving upward. The sudden drops in force in the retract curves indicate when the actin filaments or actin filament networks either unfold or detach from the AFM tip.

Figure 9

AFM rigidity maps of actin-coated SMC nanotubes. In all images the white lines delimit the contours (determined from 2 pN AFM height maps; see Sec. 6) of the same nanotubes imaged prior to actin polymerization. In the four examples provided here, the actin coating clearly increases nanotube apparent width, and the actin networks siding nanotubes look softer than the nanotubes themselves.

Figure 10

Measuring the rigidity of a nanotube. (a) AFM rigidity map of two nanotubes. Red square: region enlarged in (b). (b) Enlarged region of the AFM map in (a). (c)–(e) Distributions of the rigidity $K$ in the AFM images. (c) Distribution of $K$ in the entire image in (a). Blue rectangle: central region of the nanotube. (d) Distribution of $K$ in the red square in (a), i.e., in the entire image in (b). (e) Distribution of $K$ in the region delimited by a blue rectangle in (b). A Gaussian is fitted to the data to determine the $K$ (mean plus or minus 1 s.d.) of the nanotube. Here the Gaussian fit results in $K=38\pm 14\mathrm{kPa}$. (f) Rigidity versus height for all bare nanotubes. The data points are the same as in Fig. 5; in addition, here we display the error bars on the height and rigidity. The data point in blue corresponds to the nanotube analyzed in (b) and (e).

Figure 11

Determination of the height and width of a membrane nanotube. (a) Contact point (i.e., height at zero force) maps. (b) Maps of the height at 2 pN. (c) Rigidity maps. (d) Maps of fit residuals. (e) Force-distance curves collected at locations marked by dots in the maps of (a)–(d). The red lines are the results of smoothing the force curves and are used to build the 2 pN height maps, which provide the best description of the nanotube width. The blue lines come from least-squares fitting of the data using $f=K{\delta }^2$ for $\delta >0$, where $f$ is the force, $K$ the rigidity, and $\delta$ the indentation depth. Vertical dashed lines show the position where $\delta =0$ that we use to determine the local nanotube height. Note that, at points 2 and 5 (edges of the nanotube), the force starts increasing but quickly drops, which indicates that the nanotube has been pushed laterally by the AFM tip. As a result, the contact point and 2 pN height maps show clear differences.

Figure 12

Nanotube morphologies considered here. (a) When the adhesion between the (white) lipids and the (gray) adherent surface is very weak, the membrane shape is determined by the balance between its bending rigidity and its tension, resulting in a cylindrical morphology. (b) In the opposite limit of strong adhesion, the nanotube undergoes significant flattening ($w\gg h$).

Figure 13

Wide nanotube deformation. (a) Parametrization of the membrane deformation induced by the (gray) indenter. (b) Nonlinear relation between the indentation depth $\delta$ and the contact radius $x$ depending on the dimensionless membrane width $w$. Solid lines represent the full relation of Eq. (a14), and dashed lines picture the $\delta \to 0$ asymptotic relation of Eq. (a15).

Figure 14

Correspondence between the heuristic force dependence of Eq. (a19) and the theoretical expression of Eq. (a21). Here we use dimensionless units such that $k=1$ and $k_{B}T=1$. (a) Best fit of $f_{\mathrm{quad}}(\delta +{\delta }_0)$ to $f_{\mathrm{thermal}}(\delta )$ over the interval $\delta \in [-2,2]$ using as fitting parameters ${\delta }_0$ and the coefficient $a$ from Eq. (a22). (b) Best-fit value obtained for $a$ when performing the fit over an interval $\delta \in [-\mathrm{\Delta }\delta /2,\mathrm{\Delta }\delta /2]$ as a function of $\mathrm{\Delta }\delta$. For our experimental data, $\mathrm{\Delta }\delta$ is typically comprised between 3 and 5.