Entropic pressure between biomembranes in a periodic stack due to thermal fluctuations

Intercellular Receptor-ligand Binding: Effect of Protein-membrane Interaction

Gaining insights into the intercellular receptor-ligand binding is of great importance for understanding numerous physiological and pathological processes, and stimulating new strategies in drug design and discovery. In contrast to the in vitro protein interaction in solution, the anchored receptor and ligand molecules interact with membrane in situ, which affects the intercellular receptor-ligand binding. Here, we review theoretical, simulation and experimental works regarding the regulatory effects of protein-membrane interactions on intercellular receptor-ligand binding mainly from the following aspects: membrane fluctuations, membrane curvature, glycocalyx, and lipid raft. In addition, we discuss biomedical significances and possible research directions to advance the field and highlight the importance of understanding of coupling effects of these factors in pharmaceutical development.

Colloidal Flatlands Confronted with Urge for the Third Dimension

Two-dimensional sheets are a relatively neglected form of soft matter, interesting because of their capability to deform into the third dimension with little energy cost. Here, we confront colloidal sheets with an abruptly imposed potential tending to produce strings normal to the plane. Experimentally, this is implemented first by using ultrasound-induced acoustic levitation to produce planar sheets and then by abruptly imposing AC electric fields that introduce dipolar interactions. Seeking to identify the microscopic mechanisms underlying the observed collective behavior, we find that the patterns quantified from our fast confocal experimental imaging are reproduced by our Brownian dynamics simulations. We follow the evolution of these patterns, including their structure factor, from start to final steady state, and from successful parametrization we predict simulation phases not yet observed in experiment. The transient-state evolution toward final outcome includes monocrystalline hexagonal lattice, polycrystalline body-centered tetragonal lattice with grain boundaries, interconnected rings, serpentine zigzag chains, and columns vertical to the plane, and a "fat worm" serpentine pattern. To explain the counterintuitive findings presented here, we map dependence on softness of the confining potential.

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length

In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or "lubrication limit", of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds- and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate a parameter regime in which the time it takes for an active force to drive local contact actually increases if the cells are being held closer together (e.g., by nonspecific adhesion), a phenomenon we attribute to the thin-layer effect. This leads to an optimal initial cell-cell separation for fastest receptor-ligand binding, which could have relevance for the role of cellular protrusions like microvilli. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect.

Nanometric thermal fluctuations of weakly confined biomembranes measured with microsecond time-resolution

We probe the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles (GUVs) bound to a substrate by a weak potential arising from generic interactions. The substrate is either homogeneous, with GUVs bound only by the weak potential, or is chemically functionalized with a micro-pattern of very strong specific binders. In both cases, the weakly adhered membrane is seen to be confined at a well-defined distance above the surface while it continues to fluctuate strongly. We quantify the fluctuations of the weakly confined membrane at the substrate proximal surface as well as of the free membrane at the distal surface of the same GUV. This strategy enables us to probe in detail the damping of fluctuations in the presence of the substrate, and to independently measure the membrane tension and the strength of the generic interaction potential. Measurements were done using two complementary techniques - dynamic optical displacement spectroscopy (DODS, resolution: 20 nm, 10 μs), and dual wavelength reflection interference contrast microscopy (DW-RICM, resolution: 4 nm, 50 ms). After accounting for the spatio-temporal resolution of the techniques, an excellent agreement between the two measurements was obtained. For both weakly confined systems we explore in detail the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.

Thermal fluctuations of vesicles and nonlinear curvature elasticity--implications for size-dependent renormalized bending rigidity and vesicle size distribution

Both closed and open biological membranes noticeably undulate at physiological temperatures. These thermal fluctuations influence a broad range of biophysical phenomena, ranging from self-assembly to adhesion. In particular, the experimentally measured thermal fluctuation spectra also provide a facile route to the assessment of mechanical and certain other physical properties of biological membranes. The theoretical assessment of thermal fluctuations, be it for closed vesicles or the simpler case of flat open lipid bilayers, is predicated upon assuming that the elastic curvature energy is a quadratic functional of the curvature tensor. However, a qualitatively correct description of several phenomena such as binding-unbinding transition, vesicle-to-bicelle transition, appearance of hats and saddles among others, appears to require consideration of constitutively nonlinear elasticity that includes fourth order curvature contributions rather than just quadratic. In particular, such nonlinear considerations are relevant in the context of large-curvature or small-sized vesicles. In this work we discuss the statistical mechanics of closed membranes (vesicles) incorporating both constitutive and geometrical nonlinearities. We derive results for the renormalized bending rigidity of small vesicles and show that significant stiffening may occur for sub-20 nm vesicle sizes. Our closed-form results may also be used to determine nonlinear curvature elasticity properties from either experimentally measured fluctuation spectra or microscopic calculations such as molecular dynamics. Finally, in the context of our results on thermal fluctuations of vesicles and nonlinear curvature elasticity, we reexamine the problem of determining the size distribution of vesicles and obtain results that reconcile well with experimental observations. However, our results are somewhat paradoxical. Specifically, the molecular dynamics predictions for the thermo-mechanical behavior of small vesicles of prior studies appear to be inconsistent with the nonlinear elastic properties that we estimate by fitting to the experimentally determined vesicle size-distribution trends and data.

An unresolved LINC in the nuclear envelope

The nuclear envelope segregates the nucleoplasm from the cytoplasm and is a key feature of eukaryotic cells. Nuclear envelope architecture is comprised of two concentric membrane shells which fuse at multiple sites and yet maintain a uniform separation of 30-50 nm over the rest of the membrane. Studies have revealed the roles for numerous nuclear proteins in forming and maintaining the architecture of the nuclear envelope. However, there is a lack of consensus on the fundamental forces and physical mechanisms that establish the geometry. The objective of this review is to discuss recent findings in the context of membrane mechanics in an effort to define open questions and possible answers.

Flexoelectricity in two-dimensional crystalline and biological membranes

The ability of a material to convert electrical stimuli into mechanical deformation, i.e. piezoelectricity, is a remarkable property of a rather small subset of insulating materials. The phenomenon of flexoelectricity, on the other hand, is universal. All dielectrics exhibit the flexoelectric effect whereby non-uniform strain (or strain gradients) can polarize the material and conversely non-uniform electric fields may cause mechanical deformation. The flexoelectric effect is strongly enhanced at the nanoscale and accordingly, all two-dimensional membranes of atomistic scale thickness exhibit a strong two-way coupling between the curvature and electric field. In this review, we highlight the recent advances made in our understanding of flexoelectricity in two-dimensional (2D) membranes-whether the crystalline ones such as dielectric graphene nanoribbons or the soft lipid bilayer membranes that are ubiquitous in biology. Aside from the fundamental mechanisms, phenomenology, and recent findings, we focus on rapidly emerging directions in this field and discuss applications such as energy harvesting, understanding of the mammalian hearing mechanism and ion transport among others.

Effective interactions between fluid membranes

A self-consistent theory is proposed for the general problem of interacting undulating fluid membranes subject to the constraint that they do not interpenetrate. We implement the steric constraint via an exact functional integral representation and, through the use of a saddle-point approximation, transform it into a novel effective steric potential. The steric potential is found to consist of two contributions: one generated by zero-mode fluctuations of the membranes and the other by thermal bending fluctuations. For membranes of cross-sectional area S, we find that the bending fluctuation part scales with the intermembrane separation d as d-2 for d≪√S but crosses over to d-4 scaling for d≫√S, whereas the zero-mode part of the steric potential always scales as d-2. For membranes interacting exclusively via the steric potential, we obtain closed-form expressions for the effective interaction potential and for the rms undulation amplitude σ, which becomes small at low temperatures T and/or large bending stiffnesses κ. Moreover, σ scales as d for d≪√S but saturates at √kBTS/κ for d≫√S. In addition, using variational Gaussian theory, we apply our self-consistent treatment to study intermembrane interactions subject to different types of potentials: (i) the Moreira-Netz potential for a pair of strongly charged membranes with an intervening solution of multivalent counterions, (ii) an attractive square well, (iii) the Morse potential, and (iv) a combination of hydration and van der Waals interactions.

Hydration Forces Between Lipid Bilayers: A Theoretical Overview and a Look on Methods Exploring Dehydration

Although, many biological systems fulfil their functions under the condition of excess hydration, the behaviour of bound water as well as the processes accompanying dehydration are nevertheless important to investigate. Dehydration can be a result of applied mechanical pressure, lowered humidity or cryogenic conditions. The effort required to dehydrate a lipid membrane at relatively low degree of hydration can be described by a disjoining pressure which is called hydration pressure or hydration force. This force is short-ranging (a few nm) and is usually considered to be independent of other surface forces, such as ionic or undulation forces. Different theories were developed to explain hydration forces that are usually not consistent with each other and which are also partially in conflict with experimental or numerical data.Over the last decades it has been more and more realised that one experimental method alone is not capable of providing much new insight into the world of such hydration forces. Therefore, research requires the comparison of results obtained from the different methods. This chapter thus deals with an overview on the theory of hydration forces, ranging from polarisation theory to protrusion forces, and presents a selection of experimental techniques appropriate for their characterisation, such as X-ray diffraction, atomic force microscopy and even calorimetry.

Frozen states and order-disorder transition in the dynamics of confined membranes

The adhesion dynamics of a membrane confined between two permeable walls is studied using a two-dimensional hydrodynamic model. The membrane morphology decomposes into adhesion patches on the upper and the lower walls and obeys a nonlinear evolution equation that resembles that of phase-separation dynamics, which is known to lead to coarsening, i.e., to the endless growth of the adhesion patches. However, due to the membrane bending rigidity, the system evolves toward a frozen state without coarsening. This frozen state exhibits an order-disorder transition when increasing the permeability of the walls.

The undulation force; theoretical results versus experimental demonstrations

In 1978 Wolfgang Helfrich published a paper (Helfrich W. Z Naturforsch 1978; 33a:305) where he introduced the notion of an undulation force between bilayers. This is caused by thermal excitations of the bending modes being restricted by the presence of neighboring layers. Although there is now a consensus on the qualitative picture put forward by Helfrich there is still a debate concerning the quantitative aspects. We discuss in particular the distance dependence of the interaction and also the value of the numerical coefficient of the force law derived by Helfrich.

Fluctuation pressure of biomembranes in planar confinement

The fluctuation pressure of a lipid-bilayer membrane is important for the stability of lamellar phases and the adhesion of membranes to surfaces. In contrast to many theoretical studies, which predict a decrease of the pressure with the cubed inverse distance between the membranes, Freund suggested very recently a linear inverse distance dependence [Proc. Natl. Acad. Sci. USA 110, 2047 (2013)]. We address this discrepancy by performing Monte Carlo simulations for a membrane model discretized on a square lattice and employ the wall theorem to evaluate the pressure for a single membrane between parallel walls. For distances that are small compared with the lattice constant, the pressure indeed depends on the inverse distance as predicted by Freund. For intermediate distances, the pressure depends on the cubed inverse distance as predicted by Helfrich [Z. Naturforsch. A 33, 305 (1978)]. Here, the crossover length between the two regimes is a molecular length scale. Finally, for distances large compared with the mean squared fluctuations of the membrane, the entire membrane acts as a soft particle and the pressure on the walls again depends linearly on the inverse distance.