Membrane fluctuations near a plane rigid surface

Exploration of Lipid Bilayer Mechanical Properties Using Molecular Dynamics simulation

Important biological structures known for their exceptional mechanical qualities, lipid bilayers are essential to many cellular functions. Fluidity, elasticity, permeability, stiffness, tensile strength, compressibility, shear viscosity, line tension, and curvature elasticity are some of the fundamental characteristics affecting their behavior. The purpose of this review is to examine these characteristics in more detail by molecular dynamics simulation, elucidating their importance and the elements that lead to their appearance in lipid bilayers. Comprehending the mechanical characteristics of lipid bilayers is critical for creating medications, drug delivery systems, and biomaterials that interact with biological membranes because it allows one to understand how these materials respond to different stresses and deformations. The influence of mechanical characteristics on important lipid bilayer properties is examined in this review. The mechanical properties of lipid bilayers were clarified through the use of molecular dynamics simulation analysis techniques, including bilayer thickness, stress-strain analysis, lipid bilayer area compressibility, membrane bending rigidity, and time- or ensemble-averaged the area per lipid evaluation. We explain the significance of molecular dynamics simulation analysis methods, providing important new information about the stability and dynamic behavior of the bilayer. In the end, we hope to use molecular dynamics simulation to provide a comprehensive understanding of the mechanical properties and behavior of lipid bilayers, laying the groundwork for further studies and applications. Taken together, careful investigation of these mechanical aspects deepens our understanding of the adaptive capacities and functional roles of lipid bilayers in biological environments.

Statistical Mechanics of an Elastically Pinned Membrane: Static Profile and Correlations

The relation between thermal fluctuations and the mechanical response of a free membrane has been explored in great detail, both theoretically and experimentally. However, understanding this relationship for membranes locally pinned by proteins is significantly more challenging. Given that the coupling of the membrane to the cell cytoskeleton, to the extracellular matrix, and to other internal structures is crucial for the regulation of a number of cellular processes, understanding the role of the pinning is of great interest. In this manuscript, we consider a single protein (elastic spring of a finite rest length) pinning a membrane modeled in the Monge gauge. First, we determine the Green's function for the system and complement this approach by the calculation of the mode-coupling coefficients for the plane wave expansion and the orthonormal fluctuation modes, in turn building a set of tools for numerical and analytic studies of a pinned membrane. Furthermore, we explore static correlations of the free and the pinned membrane, as well as the membrane shape, showing that all three are mutually interdependent and have an identical long-range behavior characterized by the correlation length. Interestingly, the latter displays a nonmonotonic behavior as a function of membrane tension. Importantly, exploiting these relations allows for the experimental determination of the elastic parameters of the pinning. Last but not least, we calculate the interaction potential between two pinning sites and show that even in the absence of the membrane deformation, the pinnings will be subject to an attractive force because of changes in membrane fluctuations.

HIV Tat protein and amyloid-β peptide form multifibrillar structures that cause neurotoxicity

Deposition of amyloid-β plaques is increased in the brains of HIV-infected individuals, and the HIV transactivator of transcription (Tat) protein affects amyloidogenesis through several indirect mechanisms. Here, we investigated direct interactions between Tat and amyloid-β peptide. Our in vitro studies showed that in the presence of Tat, uniform amyloid fibrils become double twisted fibrils and further form populations of thick unstructured filaments and aggregates. Specifically, Tat binding to the exterior surfaces of the Aβ fibrils increases β-sheet formation and lateral aggregation into thick multifibrillar structures, thus producing fibers with increased rigidity and mechanical resistance. Furthermore, Tat and Aβ aggregates in complex synergistically induced neurotoxicity both in vitro and in animal models. Increased rigidity and mechanical resistance of the amyloid-β-Tat complexes coupled with stronger adhesion due to the presence of Tat in the fibrils may account for increased damage, potentially through pore formation in membranes.

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.

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.

Fluctuations of red blood cell membranes: The role of the cytoskeleton

We theoretically investigate the membrane fluctuations of red blood cells with focus laid on the role of the cytoskeleton, viewing the system as a membrane coupled to a sparse spring network. This model is exactly solvable and enables us to examine the coupling strength dependence of the membrane undulation. We find that the coupling modifies the fluctuation spectrum at wavelengths longer than the mesh size of the network, while leaving the fluid-like behavior of the membrane intact at shorter wavelengths. The fluctuation spectra can be markedly different, depending on not only the relative amplitude of the bilayer bending energy with respect to the cytoskeleton deformation energy but also the bilayer-cytoskelton coupling strength.

Membrane sorting via the extracellular matrix

We consider the coupling between a membrane and the extracellular matrix. Computer simulations demonstrate that the latter coupling is able to sort lipids. It is assumed that membranes are elastic manifolds, and that this manifold is disrupted by the extracellular matrix. For a solid-supported membrane with an actin network on top, regions of positive curvature are induced below the actin fibers. A similar mechanism is conceivable by assuming that the proteins which connect the cytoskeleton to the membrane induce local membrane curvature. The regions of non-zero curvature exist irrespective of any phase transition the lipids themselves may undergo. For lipids that prefer certain curvature, the extracellular matrix thus provides a spatial template for the resulting lateral domain structure of the membrane.

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

The phenomenon of thermal fluctuation of a biomembrane within a stack of like membranes was introduced in a pioneering paper [Helfrich W (1978) Z Naturforsch A 33(3):305-315]. Internal energy arises in a representative membrane through elastic resistance to bending deformation, and membrane motion is further restrained through steric interaction with adjacent membranes. Due to reflective symmetry within the stack, analysis of behavior can be reduced to study of a single membrane fluctuating between parallel rigid planes. The phenomenon is reexamined here from several viewpoints to quantify the dependence of system free energy on the size of the gap between membranes. This analysis is based on essentially the same formulation that was used in the original study, and it is found that analysis based on enforcement of the underlying principles can lead to an exact mathematical solution. On this basis, a self-consistent picture of behavior emerges showing a dependence of free energy on the width of the confining gap that is weaker than has been thought to prevail.

Nucleation of ligand-receptor domains in membrane adhesion

We present a comprehensive model for the nucleation of domains in membrane adhesion. We determine the critical number of bonds in a nucleus and calculate the probability distribution of nucleation time from a discrete master equation. The latter is characterized by only four effective rates, which account for cooperative effects between bonds. We validate our model by finding excellent agreement with extensive Langevin simulations. In the range of parameters typical for cell adhesion, we find the critical number of bonds to be small. Furthermore, we find a characteristic separation between the bonds at which nucleation is particularly fast, pointing to potential regulatory mechanisms that could be used to control the cell recognition processes.

Mechanical surface tension governs membrane thermal fluctuations

We use analytical considerations and computer simulations to show that the membrane spectrum of thermal fluctuations is governed by the mechanical and not the intrinsic tension. Our study highlights the fact that the commonly used quadratic approximation of the Helfrich effective Hamiltonian is not rotationally invariant. We demonstrate that this nonphysical feature leads to a calculated mechanical tension that differs dramatically from the correct mechanical tension. Specifically, our results suggest that the mechanical and intrinsic tensions vanish simultaneously, which contradicts recent theoretical predictions derived for the approximated Hamiltonian.

Dynamics of a driven surface

We present a Monte Carlo study of an Edwards-Wilkinson type of surface when it is driven by another random surface which drifts with a rate 0<phi<1. When it is driven by another drifting surface, it is shown to be of the Kardar-Parisi-Zhang (KPZ) type; we show that the asymptotic drift of its center of mass is preceded by a subdiffusive regime characterized by an effective exponent whose value is slightly less than that of the KPZ growth exponent (beta=1/3) because of slow crossover. Our numerical study demonstrates that the growth of fluctuations for the driven surface shows an extremely slow crossover to the KPZ regime observable only for very large system sizes. The equilibrium fluctuation of the surface exhibits a minimum at a certain driving rate phi*, which separates the regimes of entropic repulsion and entropic compliance. Since our model of interacting surfaces is a generalization of the Brownian Ratchet model for protrusions of biological cell membranes, we discuss it vis-a-vis the standard load-velocity relationship, and we compare the present model membrane to cell membranes.

Entropy-driven aggregation of adhesion sites of supported membranes

We study, by means of mean-field calculations and Monte Carlo simulations of a lattice gas model, the distribution of adhesion sites of a bilayer membrane and a supporting flat surface. Our model accounts for the many-body character of the attractive interactions between adhesion points induced by the membrane thermal fluctuations. We show that while the fluctuation-mediated interactions alone are not sufficient to allow the formation of aggregation domains, they greatly reduce the strength of the direct interactions required to facilitate cluster formation. Specifically, for adhesion molecules interacting via a short-range attractive potential, the strength of the direct interactions required for aggregation is reduced by about a factor of two to below the thermal energy k(B)T.

Fluctuation-induced attraction between adhesion sites of supported membranes

We use scaling arguments and coarse-grained Monte Carlo simulations to study the fluctuation-mediated interactions between a pair of adhesion sites of a bilayer membrane and a supporting surface. We find that the potential of mean force is an infinitely long range attractive potential that grows logarithmically with the pair distance r : ϕ(r)/k B T=c ln r, where the constant c=2 and c=1 for nonstressed and stressed membranes, respectively. When, in addition to excluded volume repulsion, the membrane also interacts with the underlying surface through a height-dependent attractive potential, the potential ϕ(r) is screened at large pair distances.