We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to nontrivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect.
We study the force generation by a set of parallel actin filaments growing against an elastic membrane. The elastic membrane tries to stay flat and any deformation from this flat state, either caused by thermal fluctuations or due to protrusive polymerization force exerted by the filaments, costs energy. We study two lattice models to describe the membrane dynamics. In one case, the energy cost is assumed to be proportional to the absolute magnitude of the height gradient (gradient model) and in the other case it is proportional to the square of the height gradient (Gaussian model). For the gr…
Eukaryotic cells intrinsically change their shape, by changing the composition of their membrane and by restructuring their underlying cytoskeleton. We present here further studies and extensions of a minimal physical model, describing a closed vesicle with mobile curved membrane protein complexes. The cytoskeletal forces describe the protrusive force due to actin polymerization which is recruited to the membrane by the curved protein complexes. We characterize the phase diagrams of this model, as function of the magnitude of the active forces, nearest-neighbor protein interactions and the pro…
The actin cortex is a thin layer of actin filaments and myosin motors beneath the outer membrane of animal cells. It determines the cells' mechanical properties and forms important morphological structures. Physical descriptions of the cortex as a contractile active gel suggest that these structures can result from dynamic instabilities. However, in these analyses the cortex is described as a two-dimensional layer. Here, we show that the dynamics of the cortex is qualitatively different when gel fluxes in the direction perpendicular to the membrane are taken into account. In particular, an iso…
A method to calculate the bending rigidity $κ$, saddle-splay modulus $\barκ$, and spontaneous curvature $C_0$ of a fluid membrane is proposed. Virtual work for the bending deformations into cylindrical and spherical shapes is calculated for a flat membrane. This method does not require a force decomposition, unlike the existing stress-profile method. The first derivative of the deformation gives $κC_0$ and is a discrete form of the first moment of the stress profile. The second derivatives give $κ$ and $\barκ$, and include the variance terms of the first derivatives, which are not accounted fo…
Gaining access to the cell interior is fundamental for many applications, such as electrical recording, drug and biomolecular delivery. A very promising technique consists of culturing cells on nano/micro pillars. The tight adhesion and high local deformation of cells in contact with nanostructures can promote the permeabilization of lipids at the plasma membrane, providing access to the internal compartment. However, there is still much experimental controversy regarding when and how the intracellular environment is targeted and the role of the geometry and interactions with surfaces. Consequ…
For endocytosis and exocytosis, membranes transition between planar, budding, and vesicular topographies through nanoscale reorganization of lipids, proteins, and carbohydrates. However, prior attempts to understand the initial stages of nanoscale bending have been limited by experimental resolution. Through the implementation of polarized localization microscopy (PLM), this manuscript reports the inherent membrane bending capability of cholera toxin subunit B (CTxB) in quasi-one component supported lipid bilayers. Membrane buds were first detected with <50 nm radius, grew to >200 nm radius, a…
我们使用计算机模拟和一个简单的自由能模型来研究双层膜的负（压缩）机械张力的应用程序的响应。这种张力使巨囊泡的长波长波动模式不稳定，但当考虑小膜和囊泡时，它可以持续。我们的负张力模拟结果揭示了两个制度-（i）一个弱的负张力制度，其特征在于拉伸为主的弹性，和（ii）一个强的负张力制度，其特征在于弯曲为主的弹性行为。这类似于在巨大单层囊泡（GUV）中的经典Evans和Rawicz微量移液管抽吸实验的发现[Phys，Rev. Lett. { \bf 64}，2094（1990）]。然而，在GUV中，两种弹性状态之间的交叉发生在小的正表面张力下，而在较小的膜中，它发生在中等的负张力下。关于小膜对负表面张力的响应的另一个有趣的观察与机械张力和波动张力之间的关系有关，对于非负值，机械张力和波动张力彼此相等。当张力减小到负值时，波动张力$γ$在小的负张力区域中比$τ$下降得稍微快一些，然后在大的负张力下饱和（并且变得大于$τ$）。弯曲模量呈现“相反”的趋势。它几乎保持不变，在拉伸为主的弹性制度，并减少在弯曲为主的制度。热高度波动和投影面积变化的振幅在机械不稳定性开始时发散。
The curvature of biological membranes at the nanometer scale is critically important for vesicle trafficking, organelle morphology, and disease propagation. This manuscript reports the development of Polarized Localization Microscopy (PLM), a pointillist optical imaging technique for the detection of nanoscale membrane curvature in correlation with single-molecule dynamics and molecular sorting. PLM combines polarized total internal reflection fluorescence microscopy (TIRFM) and single-molecule localization microscopy to reveal membrane orientation with sub-diffraction-limited resolution witho…
In living cells, membrane morphology is regulated by various proteins. Many membrane reshaping proteins contain a Bin/Amphiphysin/Rvs (BAR) domain, which consists of a banana-shaped rod. The BAR domain bends the biomembrane along the rod axis and the features of this anisotropic bending have recently been studied. Here, we report on the role of the BAR protein rods in inducing membrane tubulation, using large-scale coarse-grained simulations. We reveal that a small spontaneous side curvature perpendicular to the rod can drastically alter the tubulation dynamics at high protein density, whereas…
Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins, and el…
A widely used method to measure the bending rigidity of bilayer membranes is fluctuation spectroscopy, which analyses the thermally-driven membrane undulations of giant unilamellar vesicles recorded with either phase-contrast or confocal microscopy. Here, we analyze the fluctuations of the same vesicle using both techniques and obtain consistent values for the bending modulus. We discuss the factors that may lead to discrepancies.
Elastic confinements play an important role in many soft matter systems and affect the transport properties of suspended particles in viscous flow. On the basis of low-Reynolds-number hydrodynamics, we present an analytical theory of the axisymmetric flow induced by a point-force singularity (Stokeslet) directed along the symmetry axis of a finite-sized circular elastic membrane endowed with resistance toward shear and bending. The solution for the viscous incompressible flow surrounding the membrane is formulated as a mixed boundary value problem, which is then reduced into a system of dual i…
It has been known that the uptake mechanisms of cell-penetrating peptides(CPPs) depend on the experimental conditions such as concentration of peptides, lipid composition, temperature, etc. In this study we investigate the temperature dependence of the penetration of Arg9s into a DOPC/DOPG(4:1) membrane using molecular dynamics(MD) simulations at two different temperatures, T = 310 K and T = 288 K. Although it is difficult to identify the temperature dependence because of having only one single simulation at each temperature and no evidence of translocation of Arg9s across the membrane at both…
We study theoretically and numerically the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance towards shear and bending. Using a combination of the multipole expansion and Faxen's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities, and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency…
When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry induced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady state lift force exerted on a rigid…
Salt is a very common molecule in aqueous environments but the question of whether the interactions of monovalent ions Na^+ and Cl^- ,with the neutral heads of phospholipids are impactful enough to change the membrane rigidity is still a mystery. To provide a resolution to this long simmering debate, we investigated the dynamics of DOPC vesicles in the fluid phase with increasing external salt concentration. At higher salt concentrations, we observe an increase in bending rigidity from neutron spin echo spectroscopy (NSE) and an increase in bilayer thickness from small-angle X-ray scattering (…
Titanium surface treated with titanium oxide nanotubes was used in many studies to quantify the effect of surface topography on cell fate. However, the predicted optimal diameter of nanotubes considerably differs among studies. We propose a model that explain cell adhesion to nanostructured surface by considering deformation energy of cell protrusions into titanium nanotubes and adhesion to surface. The optimal surface topology is defined as a geometry that gives membrane a minimum energy shape. A dimensionless parameter, the cell interaction index, was proposed to describe interplay between t…
We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending, and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte…
Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves--crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highlysimplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes. Such gradients can lead to…
In this paper, we present an analytical calculation of the rotational mobility functions of a particle rotating on the centerline of an elastic cylindrical tube whose membrane exhibits resistance towards shearing and bending. We find that the correction to the particle rotational mobility about the cylinder axis depends solely on membrane shearing properties while both shearing and bending manifest themselves for the rotational mobility about an axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing frequency, the particle rotational mobility nearby a no-slip rigid cyl…
