We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear modes of coupling a near continuum system to a discrete system using a nonlinear coupling are examined. This numerical model is a first step towards investigating the dynamical behavior of a flexible sheet coupled nonlinearly to a semi-rigid support, a system which could conceivably represent a biological cell membrane with a supporting protein network. General implications for the dynamical behavior of continuum systems coupled nonlinearly to discrete systems are introduced.
In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with prescribed volume and surface area constraints. By comparing our numerical simulations with recent experiments, it is demonstrated that the phase field models can capture the rich phenomena associated with the membrane transformation, thus it offers great functionality in the simulation and modeling of multicomponen…
In this work, we study the adhesion of multi-component vesicle membrane to both flat and curved substrates, based on the conventional Helfrich bending energy for multi-component vesicles and adhesion potentials of different forms. A phase field formulation is used to describe the different components of the vesicle. For the axisymmetric case, a number of representative equilibrium vesicle shapes are computed and some energy diagrams are presented which reveal the dependence of the calculated shapes and solution branches on various parameters including both bending moduli and spontaneous curvat…
The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the t…
BAR superfamily proteins have a banana-shaped domain that causes the local bending of lipid membranes. We study as to how such a local anisotropic curvature induces effective interaction between proteins and changes the global shape of vesicles and membrane tubes using meshless membrane simulations. The proteins are modeled as banana-shaped rods strongly adhered to the membrane. Our study reveals that the rods assemble via two continuous directional phase separations unlike a conventional two-dimensional phase separation. As the rod curvature increases, in the membrane tube the rods assemble a…
The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in de…
We present a general dynamical theory of a membrane coupled to an actin cortex containing polymerizing filaments with active stresses and currents, and demonstrate that active membrane dynamics [Phys. Rev. Lett \textbf{84}, 3494 (2000)] and spontaneous shape oscillations emerge from this description. We also consider membrane instabilities and patterns induced by the presence of filaments with polar orientational correlations in the tangent plane of the membrane. The dynamical features we predict should be seen in a variety of cellular contexts involving the dynamics of the membrane-cytoskelet…
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…
Active force generation by actin-myosin cortex coupled to the cell membrane allows the cell to deform, respond to the environment, and mediate cell motility and division. Several membrane-bound activator proteins move along it and couple to the membrane curvature. Besides, they can act as nucleating sites for the growth of filamentous actin. Actin polymerization can generate a local outward push on the membrane. Inward pull from the contractile actomyosin cortex can propagate along the membrane via actin filaments. We use coupled evolution of fields to perform linear stability analysis and num…
Chungnam National University（忠南大学）；Institute for Basic Science（基础科学研究所）；University of Chicago（芝加哥大学）
In the human ear, the basilar membrane plays a central role in sound recognition. When excited by sound, this membrane responds with a frequency-dependent displacement pattern that is detected and identified by the auditory hair cells combined with the human neural system. Inspired by this structure, we designed and fabricated an artificial membrane that produces a spatial displacement pattern in response to an audible signal, which we used to train a convolutional neural network (CNN). When trained with single frequency tones, this system can unambiguously distinguish tones closely spaced in …
By constructing a Landau-like energy functional, we investigate the molecular organization of a three-component mixture in cell membranes. In the strongly interacting limit, we model the interaction between molecules using pseudospin variables and convert them into non-interacting variables using a mean-field theory. Next, we construct the two-order parameter Landau-type energy functional through the Helmholtz free energy. By analyzing the Landau free energy, we map out the phase diagram focusing on homogeneous and various phase separated states on the cell membrane.
The membrane components of cellular organelles have been shown to segregate into domains as the result of biochemical maturation. We propose that the dynamical competition between maturation and lateral segregation of membrane components regulates domain formation. We study a two- component fluid membrane in which enzymatic reaction irreversibly converts one component into another, and phase separation triggers the formation of transient membrane domains. The maximum domains size is shown to depend on the maturation rate as a power-law similar to the one observed for domain growth with time in…
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…
Membrane fluidity, well-known to be essential for cell functions, is obviously affected by copper. However, the underlying mechanism is still far from being understood, especially on the atomic level. Here, we unexpectedly observed that a decrease in phospholipid (PL) bilayer fluidity caused by Cu2+ was much more significant than those induced by Zn2+ and Ca2+, while a comparable reduction occurred in the last two ions. This finding clearly disagrees with the placement in the periodic table of Cu just next to Zn and far from Ca. The physical nature was revealed to be a special attraction betwe…
Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle…
Ever since the raft model for biomembranes has been proposed, the traditional view of biomembranes based on the fluid-mosaic model has been altered. In the raft model, dynamical heterogeneities in multi-component lipid bilayers play an essential role. Focusing on the lateral phase separation of biomembranes and vesicles, we review some of the most relevant research conducted over the last decade. We mainly refer to those experimental works that are based on physical chemistry approach, and to theoretical explanations given in terms of soft matter physics. In the first part, we describe the pha…
By means of lattice-based Monte Carlo simulations, we address properties of two-component lipid membranes on the experimentally relevant spatial scales of order of a micrometer and time intervals of order of a second, using DMPC/DSPC lipid mixtures as a model system. Our large-scale simulations allowed us to obtain important results previously not reported in simulation studies of lipid membranes. We find that, within a certain range of lipid compositions, the phase transition from the fluid phase to the fluid-gel phase coexistence proceeds via near-critical fluctuations, while for other lipid…
提出了一个多组分流体膜的非束缚转变的唯象模型，其中的非束缚转变用类似于聚合物的Flory-Huggins理论的理论来描述。包合物分子的横向相分离和膜-基底距离之间的耦合解释了两个未结合相之间的相共存，如Marx等人在最近的实验中观察到的[Phys. Rev. Lett. 88，138102（2002）]。在临界终点温度下，我们发现对于多组分膜，解束缚转变为一级反应。
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a two-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the cell interface dynamics. The equation includes the normal velocity of the membrane, curvature, volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This…
We discuss different mechanisms for curvature-induced domain formation in multicomponent lipid membranes and present a theoretical model that allows us to study the interplay between the domains. The model represents the membrane by two coupled monolayers, which each carry an additional order parameter field describing the local lipid composition. The spontaneous curvature of each monolayer is coupled to the local composition, moreover, the lipid compositions on opposing monolayers are coupled to each other. Using this model, we calculate the phase behavior of the bilayer in mean-field approxi…
The collective dynamics of $N$ weakly coupled processive molecular motors are considered theoretically. We show, using a discrete lattice model, that the velocity-force curves strongly depend on the effective dynamic interactions between motors and differ significantly from a simple mean field prediction. They become essentially independent of $N$ if it is large enough. For strongly biased motors such as kinesin this occurs if $N\gtrsim 5$. The study of a two-state model shows that the existence of internal states can induce effective interactions.
We present a minimal model of plasma membrane heterogeneity that combines criticality with connectivity to cortical cytoskeleton. Our model is motivated by recent observations of micron-sized critical fluctuations in plasma membrane vesicles that are detached from their cortical cytoskeleton. We incorporate criticality using a conserved order parameter Ising model coupled to a simple actin cytoskeleton interacting through point-like pinning sites. Using this minimal model, we recapitulate several experimental observations of plasma membrane raft heterogeneity. Small (r~20nm) and dynamic fluctu…
Quenched Dipole Pairs in Viscous Fluid Membranes across the Saffman Crossover: Integrable Hamiltonian Dynamics
Birla Institute of Technology and Science, Pilani（比拉理工学院）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Indian Institute of Technology Bombay（印度孟买理工学院）；Stanford University（斯坦福大学）；Massachusetts Institute of Technology（麻省理工学院）；Indian Statistical Institute（印度统计研究所）；Indian Institute of Technology Kharagpur（印度卡拉格普尔理工学院）
Giant unilamellar vesicles (GUVs), are a convenient tool to study membrane-bound processes using optical microscopy. An increasing number of studies highlights the potential of these model membranes when addressing questions in membrane biophysics and cell biology. Among them, phase transitions and domain formation, dynamics and stability in raft-like mixtures are probably some of the most intensively investigated. In doing so, many research teams rely on standard protocols for GUV preparation and handling involving the use of sugar solutions. Here, we demonstrate that following such a standar…
We propose a model describing the phase behavior of two-component membranes consisting of binary mixtures of electrically charged and neutral lipids. We take into account the structural phase transition (main-transition) of the hydrocarbon chains, and investigate the interplay between this phase transition and the lateral phase separation. The presence of charged lipids significantly affects the phase behavior of the multi-component membrane. Due to the conservation of lipid molecular volume, the main-transition temperature of charged lipids is lower than that of neutral ones. Furthermore, as …
