Dynamical membrane curvature instability controlled by intermonolayer friction

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

Dynamic correlations in lipid bilayer membranes over finite time intervals

Recent single-molecule measurements [Schoch et al., Proc. Natl. Acad. Sci. U. S. A. 118, e2113202118 (2021)] have observed dynamic lipid-lipid correlations in membranes with submicrometer spatial resolution and submillisecond temporal resolution. While short from an instrumentation standpoint, these length and time scales remain long compared to microscopic molecular motions. Theoretical expressions are derived to infer experimentally measurable correlations from the two-body diffusion matrix appropriate for membrane-bound bodies coupled by hydrodynamic interactions. The temporal (and associated spatial) averaging resulting from finite acquisition times has the effect of washing out correlations as compared to naive predictions (i.e., the bare elements of the diffusion matrix), which would be expected to hold for instantaneous measurements. The theoretical predictions are shown to be in excellent agreement with Brownian dynamics simulations of experimental measurements. Numerical results suggest that the experimental measurement of membrane protein diffusion, in complement to lipid diffusion measurements, might help to resolve the experimental ambiguities encountered for certain black lipid membranes.

Systematic measurements of interleaflet friction in supported bilayers

When lipid membranes curve or are subjected to strong shear forces, the two apposed leaflets of the bilayer slide past each other. The drag that one leaflet creates on the other is quantified by the coefficient of interleaflet friction, b. Existing measurements of this coefficient range over several orders of magnitude, so we used a recently developed microfluidic technique to measure it systematically in supported lipid membranes. Fluid shear stress was used to force the top leaflet of a supported membrane to slide over the stationary lower leaflet. Here, we show that this technique yields a reproducible measurement of the friction coefficient and is sensitive enough to detect differences in friction between membranes made from saturated and unsaturated lipids. Adding cholesterol to saturated and unsaturated membranes increased interleaflet friction significantly. We also discovered that fluid shear stress can reversibly induce gel phase in supported lipid bilayers that are close to the gel-transition temperature.

Mitochondrial Cristae Architecture and Functions: Lessons from Minimal Model Systems

Mitochondria are known as the powerhouse of eukaryotic cells. Energy production occurs in specific dynamic membrane invaginations in the inner mitochondrial membrane called cristae. Although the integrity of these structures is recognized as a key point for proper mitochondrial function, less is known about the mechanisms at the origin of their plasticity and organization, and how they can influence mitochondria function. Here, we review the studies which question the role of lipid membrane composition based mainly on minimal model systems.

Surface Shear Viscosity and Interleaflet Friction from Nonequilibrium Simulations of Lipid Bilayers

Nonequilibrium simulation protocols based on shear deformations are applied to determine the surface viscosity and interleaflet friction of lipid bilayers. At high shear rates, a non-Newtonian shear thinning regime is observed, but lower shear rates yield a Newtonian plateau and results that are consistent with equilibrium measurements based on fluctuation-dissipation theorems. Application to all-atom bilayers modeled with the CHARMM36 parameter set yields values for the surface viscosity that are consistent with microscopic measurements based on membrane protein diffusion but are approximately 10 times lower than more macroscopic experimental measurements. The interleaflet friction is about 10 times lower than experimental measurements. Trends across different lipids, temperatures, and ternary liquid-disordered phase mixtures produce results that are consistent with experimental diffusion constants. Application of the protocol to the liquid-ordered phase fails to yield a Newtonian plateau, suggesting more complex rheology.

Transbilayer Colocalization of Lipid Domains Explained via Measurement of Strong Coupling Parameters

When micron-scale compositional heterogeneity develops in membranes, the distribution of lipids on one face of the membrane strongly affects the distribution on the other. Specifically, when lipid membranes phase separate into coexisting liquid phases, domains in each monolayer leaflet of the membrane are colocalized with domains in the opposite leaflet. Colocalized domains have never been observed to spontaneously move out of registry. This result indicates that the lipid compositions in one leaflet are strongly coupled to compositions in the opposing leaflet. Predictions of the interleaflet coupling parameter, Λ, vary by a factor of 50. We measure the value of Λ by applying high shear forces to supported lipid bilayers. This causes the upper leaflet to slide over the lower leaflet, moving domains out of registry. We find that the threshold shear stress required to deregister domains in the upper and lower leaflets increases with the inverse length of domains. We derive a simple, closed-form expression relating the threshold shear to Λ, and find Λ = 0.016 ± 0.004 kBT/nm2.

Mixed Mechanism of Lubrication by Lipid Bilayer Stacks

Although the key role of lipid bilayer stacks in biological lubrication is generally accepted, the mechanisms underlying their extreme efficiency remain elusive. In this article, we report molecular dynamics simulations of lipid bilayer stacks undergoing load and shear. When the hydration level is reduced, the velocity accommodation mechanism changes from viscous shear in hydration water to interlayer sliding in the bilayers. This enables stacks of hydrated lipid bilayers to act as efficient boundary lubricants for various hydration conditions, structures, and mechanical loads. We also propose an estimation for the friction coefficient; thanks to the strong hydration forces between lipid bilayers, the high local viscosity is not in contradiction with low friction coefficients.

Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant

In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is attributable to direct phospholipid packing modification in the outer leaflet, that is promoted by protonation of cardiolipin headgroups. In this study, we compare the case of cardiolipin-containing giant unilamellar vesicles with that of giant unilamellar vesicles that contain phosphatidylglycerol (PG). Local acidification also promotes formation of tubules in the latter. However, compared with cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling, and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH gradient. Simulations using a fully nonlinear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.

Dynamics and instabilities of lipid bilayer membrane shapes

Biological membranes undergo constant shape remodeling involving the formation of highly curved structures. The lipid bilayer represents the fundamental architecture of the cellular membrane with its shapes determined by the Helfrich curvature bending energy. However, the dynamics of bilayer shape transitions, especially their modulation by membrane proteins, and the resulting shape instabilities, are still not well understood. Here, we review in a unifying manner several theories that describe the fluctuations (i.e. undulations) of bilayer shapes as well as their local coupling with lipid or protein density variation. The coupling between local membrane curvature and lipid density gives rise to a 'slipping mode' in addition to the conventional 'bending mode' for damping the membrane fluctuation. This leads to a number of interesting experimental phenomena regarding bilayer shape dynamics. More importantly, curvature-inducing proteins can couple with membrane shape and eventually render the membrane unstable. A criterion for membrane shape instability is derived from a linear stability analysis. The instability criterion reemphasizes the importance of membrane tension in regulating the stability and dynamics of membrane geometry. Recent progresses in understanding the role of membrane tension in regulating dynamical cellular processes are also reviewed. Protein density is emphasized as a key factor in regulating membrane shape transitions: a threshold density of curvature coupling proteins is required for inducing membrane morphology transitions.

Diffusion coefficients in leaflets of bilayer membranes

We study diffusion coefficients of liquid domains by explicitly taking into account the two-layered structure called leaflets of the bilayer membrane. In general, the velocity fields associated with each leaflet are different and the layers sliding past each other cause frictional coupling. We obtain analytical results of diffusion coefficients for a circular liquid domain in a leaflet, and quantitatively study their dependence on the interleaflet friction. We also show that the diffusion coefficients diverge in the absence of coupling between the bilayer and solvents, even when the interleaflet friction is taken into account. In order to corroborate our theory, the effect of the interleaflet friction on the correlated diffusion is examined.

Membrane properties revealed by spatiotemporal response to a local inhomogeneity

We study theoretically the spatiotemporal response of a lipid membrane submitted to a local chemical change of its environment, taking into account the time-dependent profile of the reagent concentration due to diffusion in the solution above the membrane. We show that the effect of the evolution of the reagent concentration profile becomes negligible after some time. It then becomes possible to extract interesting properties of the membrane response to the chemical modification. We find that a local density asymmetry between the two monolayers relaxes by spreading diffusively in the whole membrane. This behavior is driven by intermonolayer friction. Moreover, we show how the ratio of the spontaneous curvature change to the equilibrium density change induced by the chemical modification can be extracted from the dynamics of the local membrane deformation. Such information cannot be obtained by analyzing the equilibrium vesicle shapes that exist in different membrane environments in light of the area-difference elasticity model.

The mechanics behind cell polarity

The generation of cell polarity is one of the most intriguing symmetry-breaking events in biology. It is involved in almost all physiological and developmental processes and, despite the differences between plant and animal cell structures, cell polarity is generated by a similar core mechanism that comprises the extracellular matrix (ECM), Rho GTPase, the cytoskeleton, and the membranes. Several recent articles show that mechanical factors also contribute to the establishment and robustness of cell polarity, and the different molecular actors of cell polarity are now viewed as integrators of both biochemical and mechanical signals. Although cell polarity remains a complex process, some level of functional convergence between plants and animals is revealed. Following comparative presentation of cell polarity in plants and animals, we will discuss the theoretical background behind the role of mechanics in polarity and the relevant experimental tests, focusing on ECM anchorage, cytoskeleton behavior, and membrane tension.