Membrane shape as a reporter for applied forces

Single-cell topographical profiling of the immune synapse reveals a biomechanical signature of cytotoxicity

Immune cells have intensely physical lifestyles characterized by structural plasticity and force exertion. To investigate whether specific immune functions require stereotyped mechanical outputs, we used super-resolution traction force microscopy to compare the immune synapses formed by cytotoxic T cells with contacts formed by other T cell subsets and by macrophages. T cell synapses were globally compressive, which was fundamentally different from the pulling and pinching associated with macrophage phagocytosis. Spectral decomposition of force exertion patterns from each cell type linked cytotoxicity to compressive strength, local protrusiveness, and the induction of complex, asymmetric topography. These features were validated as cytotoxic drivers by genetic disruption of cytoskeletal regulators, live imaging of synaptic secretion, and in silico analysis of interfacial distortion. Synapse architecture and force exertion were sensitive to target stiffness and size, suggesting that the mechanical potentiation of killing is biophysically adaptive. We conclude that cellular cytotoxicity and, by implication, other effector responses are supported by specialized patterns of efferent force.

Modelling membrane curvature generation using mechanics and machine learning

The deformation of cellular membranes regulates trafficking processes, such as exocytosis and endocytosis. Classically, the Helfrich continuum model is used to characterize the forces and mechanical parameters that cells tune to accomplish membrane shape changes. While this classical model effectively captures curvature generation, one of the core challenges in using it to approximate a biological process is selecting a set of mechanical parameters (including bending modulus and membrane tension) from a large set of reasonable values. We used the Helfrich model to generate a large synthetic dataset from a random sampling of realistic mechanical parameters and used this dataset to train machine-learning models. These models produced promising results, accurately classifying model behaviour and predicting membrane shape from mechanical parameters. We also note emerging methods in machine learning that can leverage the physical insight of the Helfrich model to improve performance and draw greater insight into how cells control membrane shape change.

Value of models for membrane budding

The budding of membranes and curvature generation is common to many forms of trafficking in cells. Clathrin-mediated endocytosis, as a prototypical example of trafficking, has been studied in great detail using a variety of experimental systems and methods. Recently, advances in experimental methods have led to great strides in insights on the molecular mechanisms and the spatiotemporal dynamics of the protein machinery associated with membrane curvature generation. These advances have been ably supported by computational models, which have given us insights into the underlying mechanical principles of clathrin-mediated endocytosis. On the other hand, targeted experimental perturbation of membranes has lagged behind that of proteins in cells. In this area, modeling is especially critical to interpret experimental measurements in a mechanistic context. Here, we discuss the contributions made by these models to our understanding of endocytosis and identify opportunities to strengthen the connections between models and experiments.

The role of traction in membrane curvature generation

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape.

Catch Bonds at T Cell Interfaces: Impact of Surface Reorganization and Membrane Fluctuations

Catch bonds are characterized by average lifetimes that initially increase with increasing tensile force. Recently, they have been implicated in T cell activation, where small numbers of antigenic receptor-ligand bonds at a cell-cell interface can stimulate a T cell. Here, we use computational methods to investigate small numbers of bonds at the interface between two membranes. We characterize the time-dependent forces on the bonds in response to changes in the membrane shape and the organization of other surface molecules. We then determine the distributions of bond lifetimes using recent force-dependent lifetime data for T cell receptors bound to various ligands. Strong agonists, which exhibit catch bond behavior, are markedly more likely to remain intact than an antagonist whose average lifetime decreases with increasing force. Thermal fluctuations of the membrane shape enhance the decay of the average force on a bond, but also lead to fluctuations of the force. These fluctuations promote bond rupture, but the effect is buffered by catch bonds. When more than one bond is present, the bonds experience reduced average forces that depend on their relative positions, leading to changes in bond lifetimes. Our results highlight the importance of force-dependent binding kinetics when bonds experience time-dependent and fluctuating forces, as well as potential consequences of collective bond behavior relevant to T cell activation.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Nanomechanical mechanism for lipid bilayer damage induced by carbon nanotubes confined in intracellular vesicles

Understanding the behavior of low-dimensional nanomaterials confined in intracellular vesicles has been limited by the resolution of bioimaging techniques and the complex nature of the problem. Recent studies report that long, stiff carbon nanotubes are more cytotoxic than flexible varieties, but the mechanistic link between stiffness and cytotoxicity is not understood. Here we combine analytical modeling, molecular dynamics simulations, and in vitro intracellular imaging methods to reveal 1D carbon nanotube behavior within intracellular vesicles. We show that stiff nanotubes beyond a critical length are compressed by lysosomal membranes causing persistent tip contact with the inner membrane leaflet, leading to lipid extraction, lysosomal permeabilization, release of cathepsin B (a lysosomal protease) into the cytoplasm, and cell death. The precise material parameters needed to activate this unique mechanical pathway of nanomaterials interaction with intracellular vesicles were identified through coupled modeling, simulation, and experimental studies on carbon nanomaterials with wide variation in size, shape, and stiffness, leading to a generalized classification diagram for 1D nanocarbons that distinguishes pathogenic from biocompatible varieties based on a nanomechanical buckling criterion. For a wide variety of other 1D material classes (metal, oxide, polymer), this generalized classification diagram shows a critical threshold in length/width space that represents a transition from biologically soft to stiff, and thus identifies the important subset of all 1D materials with the potential to induce lysosomal permeability by the nanomechanical mechanism under investigation.

Trans-membrane area asymmetry controls the shape of cellular organelles

Membrane organelles often have complicated shapes and differ in their volume, surface area and membrane curvature. The ratio between the surface area of the cytosolic and luminal leaflets (trans-membrane area asymmetry (TAA)) determines the membrane curvature within different sites of the organelle. Thus, the shape of the organelle could be critically dependent on TAA. Here, using mathematical modeling and stereological measurements of TAA during fast transformation of organelle shapes, we present evidence that suggests that when organelle volume and surface area are constant, TAA can regulate transformation of the shape of the Golgi apparatus, endosomal multivesicular bodies, and microvilli of brush borders of kidney epithelial cells. Extraction of membrane curvature by small spheres, such as COPI-dependent vesicles within the Golgi (extraction of positive curvature), or by intraluminal vesicles within endosomes (extraction of negative curvature) controls the shape of these organelles. For instance, Golgi tubulation is critically dependent on the fusion of COPI vesicles with Golgi cisternae, and vice versa, for the extraction of membrane curvature into 50–60 nm vesicles, to induce transformation of Golgi tubules into cisternae. Also, formation of intraluminal ultra-small vesicles after fusion of endosomes allows equilibration of their TAA, volume and surface area. Finally, when microvilli of the brush border are broken into vesicles and microvilli fragments, TAA of these membranes remains the same as TAA of the microvilli. Thus, TAA has a significant role in transformation of organelle shape when other factors remain constant.

Elucidating driving forces for liposome rupture: external perturbations and chemical affinity

Atomic force microscopy (AFM) studies under aqueous buffer probed the role of chemical affinity between liposomes, consisting of large unilamellar vesicles, and substrate surfaces in driving vesicle rupture and tethered lipid bilayer membrane (tLBM) formation on Au surfaces. 1,2-Distearoyl-sn-glycero-3-phosphoethanolamine-N-poly(ethylene glycol)-2000-N-[3-(2-pyridyldithio) propionate] (DSPE-PEG-PDP) was added to 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) vesicles to promote interactions via Au-thiolate bond formation. Forces induced by an AFM tip leading to vesicle rupture on Au were quantified as a function of DSPE-PEG-PDP composition with and without osmotic pressure. The critical forces needed to initiate rupture of vesicles with 2.5, 5, and 10 mol % DSPE-PEG-PDP are approximately 1.1, 0.8, and 0.5 nN, respectively. The critical force needed for tLBM formation decreases from 1.1 nN (without osmotic pressure) to 0.6 nN (with an osmotic pressure due to 5 mM of CaCl(2)) for vesicles having 2.5 mol % DSPE-PEG-PDP. Forces as high as 5 nN did not lead to LBM formation from pure POPC vesicles on Au. DSPE-PEG-PDP appears to be important to anchor and deform vesicles on Au surfaces. This study demonstrates how functional lipids can be used to tune vesicle-surface interactions and elucidates the role of vesicle-substrate interactions in vesicle rupture.

AFM-based force-clamp monitors lipid bilayer failure kinetics

The lipid bilayer rupture phenomenon is here explored by means of atomic force microscopy (AFM)-based force clamp, for the first time to our knowledge, to evaluate how lipid membranes respond when compressed under an external constant force, in the range of nanonewtons. Using this method, we were able to directly quantify the kinetics of the membrane rupture event and the associated energy barriers, for both single supported bilayers and multibilayers, in contradistinction to the classic studies performed at constant velocity. Moreover, the affected area of the membrane during the rupture process was calculated using an elastic deformation model. The elucidated information not only contributes to a better understanding of such relevant process, but also proves the suitability of AFM-based force clamp to study model structures as lipid bilayers. These findings on the kinetics of lipid bilayers rupture could be extended and applied to the study of other molecular thin films. Furthermore, systems of higher complexity such as models mimicking cell membranes could be studied by means of AFM-based force-clamp technique.

Internal forces, tension and energy density in tethered cellular membranes

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.

Interplay between hydration water and headgroup dynamics in lipid bilayers

In this study, the interplay between water and lipid dynamics has been investigated by broadband dielectric spectroscopy and modulated differential scanning calorimetry (MDSC). The multilamellar lipid bilayer system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) has been studied over a broad temperature range at three different water contents: about 3, 6, and 9 water molecules per lipid molecule. The results from the dielectric relaxation measurements show that at temperatures <250 K the lipid headgroup rotation is described by a super-Arrhenius temperature dependence at the lowest hydration level and by the Arrhenius law at the highest hydration level. This difference in the temperature dependence of the lipid headgroup rotation can be explained by the increasing interaction between the headgroups with decreasing water content, which causes their rotational motion to be more cooperative in character. The main water relaxation shows an anomalous dependence on the water content in the supercooled and glassy regime. In contrast to the general behavior of interfacial water, the water dynamics is fastest in the driest sample and its temperature dependence is best described by a super-Arrhenius temperature dependence. The best explanation for this anomalous behavior is that the water relaxation becomes more determined by fast local lipid motions than by the intrinsic water dynamics at low water contents. In support for this interpretation is the finding that the relaxation time of the main water process is faster than that in most other host systems at temperatures below 180 K. Thus, the dielectric relaxation data show clearly the strong interplay between water and lipid dynamics; the water influences the lipid dynamics and vice versa. In the MDSC data, we observe a weak enthalpy relaxation at 203 K for the driest sample and at 179 K for the most hydrated sample, attributed to the freezing-in of the lipid headgroup rotation observed in the dielectric data, since this motion reaches a time scale of about 100 s at about the same temperatures.