Mobility Measurements Probe Conformational Changes in Membrane Proteins due to Tension

Active flows and deformable surfaces in development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

Curvature-Regulated Lipid Membrane Softening of Nano-Vesicles

The physico-mechanical properties of nanoscale lipid vesicles (e.g., natural nano-vesicles and artificial nano-liposomes) dictate their interaction with biological systems. Understanding the interplay between vesicle size and stiffness is critical to both the understanding of the biological functions of natural nano-vesicles and the optimization of nano-vesicle-based diagnostics and therapeutics. It has been predicted that, when vesicle size is comparable to its membrane thickness, the effective bending stiffness of the vesicle increases dramatically due to both the entropic effect as a result of reduced thermal undulation and the nonlinear curvature elasticity effect. Through systematic molecular dynamics simulations, we show that the vesicle membrane thins and softens with the decrease in vesicle size, which effectively counteracts the stiffening effects as already mentioned. Our simulations indicate that the softening of nano-vesicles results from a change in the bilayer's interior structure - a decrease in lipid packing order - as the membrane curvature increases. Our work thus leads to a more complete physical framework to understand the physico-mechanical properties of nanoscale lipid vesicles, paving the way to further advances in the biophysics of nano-vesicles and their biomedical applications.

Shear-Driven Instabilities of Membrane Tubes and Dynamin-Induced Scission

Motivated by the mechanics of dynamin-mediated membrane tube fission, we analyze the stability of fluid membrane tubes subjected to shear flow in azimuthal direction. We find a novel helical instability driven by the membrane shear flow which results in a nonequilibrium steady state for the tube fluctuations. This instability has its onset at shear rates that may be physiologically accessible under the action of dynamin and could also be probed using in vitro experiments on membrane nanotubes, e.g., using magnetic tweezers. We discuss how such an instability may play a role in the mechanism for dynamin-mediated membrane tube fission.

Saffman-Delbrück and beyond: A pointlike approach

We show that a very good analytical approximation of Saffman-Delbrück's (SD) law (mobility of a bio-membrane inclusion) can be obtained easily from the velocity field produced by a pointlike force in a 2D fluid embedded in a solvent, by using a small wavelength cutoff of the order of the particle's radius a . With this method, we obtain analytical generalizations of the SD law that take into account the bilayer nature of the membrane and the intermonolayer friction b . We also derive, in a calculation that consistently couples the quasi-planar two-dimensional (2D) membrane flow with the 3D solvent flow, the correction to the SD law arising when the inclusion creates a local spontaneous curvature. For an inclusion spanning a flat bilayer, the SD law is found to hold simply upon replacing the 2D viscosity [Formula: see text] of the membrane by the sum of the monolayer viscosities, without influence of b as long as b is above a threshold in practice well below known experimental values. For an inclusion located in only one of the two monolayers (or adhering to one monolayer), the SD law is influenced by b when b < [Formula: see text]/(4a²) . In this case, the mobility can be increased by up to a factor of two, as the opposite monolayer is not fully dragged by the inclusion. For an inclusion creating a local spontaneous curvature, we show that the total friction is the sum of the SD friction and that due to the pull-back created by the membrane deformation, a point that was assumed without demonstration in the literature.

Signatures of Mechanosensitive Gating

The question of how mechanically gated membrane channels open and close is notoriously difficult to address, especially if the protein structure is not available. This perspective highlights the relevance of micropipette-aspirated single-particle tracking-used to obtain a channel's diffusion coefficient, D, as a function of applied membrane tension, σ-as an indirect assay for determining functional behavior in mechanosensitive channels. While ensuring that the protein remains integral to the membrane, such methods can be used to identify not only the gating mechanism of a protein, but also associated physical moduli, such as torsional and dilational rigidity, which correspond to the protein's effective shape change. As an example, three distinct D-versus-σ "signatures" are calculated, corresponding to gating by dilation, gating by tilt, and gating by a combination of both dilation and tilt. Both advantages and disadvantages of the approach are discussed.

Optical measurement of receptor tyrosine kinase oligomerization on live cells

Receptor tyrosine kinases (RTK) are important cell surface receptors that transduce extracellular signals across the plasma membrane. The traditional view of how these receptors function is that ligand binding to the extracellular domains acts as a master-switch that enables receptor monomers to dimerize and subsequently trans-phosphorylate each other on their intracellular domains. However, a growing body of evidence suggests that receptor oligomerization is not merely a consequence of ligand binding, but is instead part of a complex process responsible for regulation of receptor activation. Importantly, the oligomerization dynamics and subsequent activation of these receptors are affected by other cellular components, such as cytoskeletal machineries and cell membrane lipid characteristics. Thus receptor activation is not an isolated molecular event mediated by the ligand-receptor interaction, but instead involves orchestrated interactions between the receptors and other cellular components. Measuring receptor oligomerization dynamics on live cells can yield important insights into the characteristics of these interactions. Therefore, it is imperative to develop techniques that can probe receptor movements on the plasma membrane with optimal temporal and spatial resolutions. Various microscopic techniques have been used for this purpose. Optical techniques including single molecule tracking (SMT) and fluorescence correlation spectroscopy (FCS) measure receptor diffusion on live cells. Receptor-receptor interactions can also be assessed by detecting Förster resonance energy transfer (FRET) between fluorescently-labeled receptors situated in close proximity or by counting the number of receptors within a diffraction limited fluorescence spot (stepwise bleaching). This review will describe recent developments of optical techniques that have been used to study receptor oligomerization on living cells. This article is part of a Special Issue entitled: Interactions between membrane receptors in cellular membranes edited by Kalina Hristova.

Lateral Diffusion of a Submicrometer Particle on a Lipid Bilayer Membrane

In past decades, nanoparticles and nanomaterials have been actively used for applications such as visualizing nano/submicrometer cell structure, killing cancer cells, and using drug delivery systems. It is important to understand the physicochemical mechanisms that govern the motion of nanoparticles on a plasma membrane surface. However, the motion of small particles of <1000 nm on lipid membranes is poorly understood. In this study, we investigated the diffusion of particles with a diameter of 200-800 nm on a lipid membrane using cell-sized liposomes. Particle-associated liposomes were obtained by applying centrifugal force to a mixture of liposomes and particle solutions. We measured the thermal motion of the particles by phase-contrast microscopy. We found that (i) the particle-size dependence of the diffusion of particles adhering to membranes was better described by the DADL model rather than the Einstein-Stokes model, (ii) the diffusion coefficient of a particle strongly depends on the adsorption state of the particle, such as fully or partially wrapped by the membrane, and (iii) anomalous diffusion was induced by the localization of particles on the neck of budded vesicles.

Curvature correction to the mobility of fluid membrane inclusions

Using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces, we provide, via a Stokeslet-type approach, a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions.