We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modelling approach and taking into account the thermodynamics laws, we derive the equations governing the ternary fluid flow and dynamics of the membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method, employed for resolving the evolution equations of the ternary fluid in an Eulerian description, coupled to the immersed boundary method, allowing for the membrane equations of motion to be solved in a Lagrangian system. The configuration of an elastic capsule placed at a fluid-fluid interface is considered for validation purposes. Systematic simulations are performed for a detailed comparison with reference numerical results obtained by Surface Evolver, and the Galilean invariance of the proposed model is also proven. The proposed approach is versatile, and a wide range of geometries can be simulated. To demonstrate this, the problem of a capillary bridge formed between two deformable capsules is investigated here.
We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel, but not in the perpendicular direction. We also compute analytically the membrane d…
The dynamics of drop impact on solid surfaces can be changed significantly by tuning the elasticity of the solid. Most prominently, the substrate deformation causes an increase in the splashing threshold as compared to impact onto perfectly rigid surfaces, and can thus lead to splash suppression. Here, we experimentally determine the splashing threshold for impact on thin membranes as a function of the tension in the membrane and its elastic properties. The drop dynamics is correlated to the membrane deformation, which is simultaneously measured using a laser profilometry technique. The experi…
The physical approach of a small particle (virus, medical drug) to the cell membrane represents the crucial first step before active internalization and is governed by thermal diffusion. Using a fully analytical theory we show that the stretching and bending of the elastic membrane by the approaching particle induces a memory in the system which leads to anomalous diffusion, even though the particle is immersed in a purely Newtonian liquid. For typical cell membranes the transient subdiffusive regime extends beyond 10 ms and can enhance residence times and possibly binding rates up to 50\%. Ou…
We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements …
Tension in lipid membranes is often controlled externally, by pulling on the boundary of the membrane or changing osmotic pressure across a curved membrane. But modifications of the tension can also be induced in an internal fashion, for instance as a byproduct of changing a membranes electric potential or, as observed experimentally, by activity of membrane proteins. Here we develop a theory which demonstrate how such internal contributions to the tension are moderated through elastic stretching of the membrane when the membrane is initially in a low tension floppy state.
We show using theory and experiments that a small particle moving along an elastic membrane through a viscous fluid is repelled from the membrane due to hydro-elastic forces. The viscous stress field produces an elastic disturbance leading to particle-wave coupling. We derive an analytic expression for the particle trajectory in the lubrication limit, bypassing the construction of the detailed velocity and pressure fields. The normal force is quadratic in the parallel speed, and is a function of the tension and bending resistance of the membrane. Experimentally, we measure the normal displacem…
Up-down asymmetric inclusions impose a local, spontaneous curvature to an elastic membrane. When several of them are inserted in a same membrane, they feel effective forces mediated by the membrane, both of elastic and entropic nature. Following an approach initiated by Dommersnes and Fournier in the vanishing tension case [Eur. Phys. J. B 12, 9 (1999)], and also using a pseudo-analytical micellization theory, we derive the statistical mechanics of asymmetric inclusion assemblies when they are also subject to an additional short-range, attractive interaction. Our main conclusion is that generi…
A deep understanding of the physical interactions between nanoparticles and target cell membranes is important in designing efficient nanocarrier systems for drug delivery applications. Here, we present a theoretical framework to describe the hydrodynamic flow field induced by a point-force singularity (Stokeslet) directed parallel to a finite-sized elastic membrane endowed with shear and bending rigidities. We formulate the elastohydrodynamic problem as a mixed-boundary-value problem, which we then reduce into a well-behaved system of integro-differential equations. It follows that shear and …
Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multi-folded states, whereas stiff membranes oscillates between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mecha…
Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.
With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoparticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by particle-based computer simulations, the penetration process of an active particle through a planar two-dimensional elastic membrane is studied. The membrane is …
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…
Chiral rodlike colloids exposed to strong depletion attraction may self-assemble into chiral membranes whose twisted director field differs from that of a 3D bulk chiral nematic. We formulate a simple microscopic variational theory to determine the elastic moduli of rods assembled into a bi-dimensional smectic membrane. The approach is based on a simple Onsager-Straley theory for a non-uniform director field that we apply to describe rod twist within the membrane. A microscopic approach enables a detailed estimate of the individual Frank elastic moduli (splay, twist and bend) as well as the tw…
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…
For a wide range of applications, we need DEM simulations of granular matter in contact with flexible elastic boundaries. We present a novel method to describe the interaction between granular particles and a flexible elastic membrane. Here, the standard mass-spring model approach is supplemented by surface patches given by triangulation of the membrane. In contrast to standard mass-spring models, our simulation method allows for an efficient simulation even for large particle size dispersion. The novel method allows coarsening of the mass-spring system leading to a substantial increase in com…
Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the develop…
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…
We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_ξ]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_ξ$, which corresponds to the area of the membrane coarse-grained at the mesh size $ξ$. We show that the meshwork modifies the membrane tension $σ$ both below and above the scale $ξ$, inducing a tension-jump $Δσ=dF_\mathrm{el}/dA_ξ$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes cou…
We analyse the effect of thermal fluctuations on the elastic constants of the decoupled lamellar phase of tethered, crystalline membranes. Using a momentum-shell renormalization group technique, we show that the smectic-A -like compressional elastic constant, the in-plane Lamé coefficients, and the cross-coupling elastic constant vanish as (\ln q)^{- a} whereas the bend elastic constant diverges as (\ln q)^{b}, with a, b > 0, as the wavenumber q tends to zero. The exponents a and b satisfy the relation a + 3b = 2.
Fluid membranes endowed with tangent-plane order (TPO) such as tilt- and hexatic order afford unique soft matter systems for investigating the interplay between elasticity, shape, topology, and thermal fluctuations. Using the spin-connection formulation of membrane energy we obtain equa- tions of equilibrium together with free boundary conditions for ground states of such membranes. We extend the spin-connection formulation to smectic liquid crystals with TPO and show that for chiral smectics-C* this generalization leads to experimentally verifiable consequences for dispirations having topolog…
Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are presented. Several analytic solutions to these equations and their corresponding configurations are demonstrated.
The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for compressible and incompressible layers) are constructed based on the simplifying assumptions that the generalized plane stress conditions apply to the coating layer, and the flexural stiffness of the coating layer is negligible compared to its tensile stiffness.
Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without an initial pre-stretch, and may be initially curved prior to indentation. General indenter shapes are considered, and the load-indentation curves that result for a range of spheroidal tips are obtained for both flat and curved membranes. Wrinkling may occur when the membrane is initially curved, and a relaxed strain-energy function is used to calculate the de…
A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived from a free energy functional with a value which is dependent upon the geometric properties of the membrane. The method is validated in two dimensions with a free energy functional which imposes the constraint of constant membrane length, constant enclosed area, a bending rigidity and a preferred curvature. The method is shown to recover the expected equili…
The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussia…
Using a covariant geometric approach we obtain the effective bending couplings for a 2-dimensional rigid membrane embedded into a $(2+D)$-dimensional Euclidean space. The Hamiltonian for the membrane has three terms: The first one is quadratic in its mean extrinsic curvature. The second one is proportional to its Gaussian curvature, and the last one is proportional to its area. The results we obtain are in agreement with those finding that thermal fluctuations soften the 2-dimensional membrane embedded into a 3-dimensional Euclidean space.
When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension …
A flexible membrane deforming its shape in time can self-propel in a viscous fluid. Alternatively, if the membrane is anchored, its deformation will lead to fluid transport. Past work in this area focused on situations where the deformation kinematics of the membrane were prescribed. Here we consider models where the deformation of the membrane is not prescribed, but instead the membrane is internally forced. Both the time-varying membrane shape, and the resulting fluid motion, result then from a balance between prescribed internal active stresses, internal passive resistance, and external vis…
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically stu…
We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its fluctuations, recently derived for spherical shapes, is recovered for cylindrical curvature. Employing curvilinear coordinates, we then discuss stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian curvature is not renormalized in the presence of fluctuations, and show for the first time that any spontaneous curvature also remains unchange…
Cellular wrapping of elastic particles by a supported lipid membrane
Université Paris Cité, CNRS, Institut Jacques Monod（巴黎西岱大学，法国国家科学研究中心，雅克·莫诺研究所）；Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168（居里研究所，巴黎文理研究大学，索邦大学，法国国家科学研究中心联合研究实验室）；Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学研究高级学院物理系）；Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学物理与天文学系）
Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of …
We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral membrane proteins that impart a curvature on the bilayer surrounding them. Such proteins exhibit a substantial reduction in diffusion coefficient relative to "flat" proteins; this effect is explained by elementary hydrodynamic considerations.
The elastic properties of two-component bilayer membranes are studied using a coarse grain model for amphiphilic molecules. The two species of amphiphiles considered here differ only in their length. Molecular Dynamics simulations are performed in order to analyze the shape fluctuations of the two-component bilayer membranes and to determine their bending rigidity. Both the bending rigidity and its inverse are found to be nonmonotonic functions of the mole fraction $x_{\rm B}$ of the shorter B-amphiphiles and, thus, do not satisfy a simple lever rule. The intrinsic area of the bilayer also exh…
Stochastic thermodynamics provides a useful set of tools to analyze and constrain the behavior of far from equilibrium systems. In this paper, we report an application of ideas from stochastic thermodynamics to the problem of membrane growth. Non-equilibrium forcing of the membrane can cause it to buckle and undergo a morphological transformation. We show how ideas from stochastic thermodynamics, in particular the recently derived thermodynamic uncertainty relations, can be used to phenomenologically describe and constrain the parameters required to excite morphological changes during a non-eq…
Active assembly and non-reciprocal dynamics of elastic membranes
The Martin Fisher School of Physics, Brandeis University（布兰迪斯大学马丁·费舍尔物理学院）；Department of Physics, University of California at Santa Barbara（加州大学圣塔芭芭拉分校物理系）；School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院）；Kavli Institute of Theoretical Physics（卡弗里理论物理研究所）；Leinweber Institute for Theoretical Physics, University of Chicago（芝加哥大学莱因韦伯理论物理研究所）；James Frank Institute, University of Chicago（芝加哥大学詹姆斯·弗兰克研究所）
The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane strain energy plus Helfrich's curvature energy [Z. Naturforsch. C \textbf{28}, 693 (1973)]. The elastic constants in the free energy are obtained by discussing two simplified models: one is the polymer membrane without in-plane strains and asymmetry between its two sides, which is the counterpart of quantum mechanics in curved surface [Jensen and Koppe, Ann. …
Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this paper, we show that the classical elastic model of lipid membranes cannot account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, and a viscous-elastic formulation is necessary to fully describe the system. Ther…
The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as conductivities of the internal and external fluid media as well as capacitance and conductance of the membrane lead to a net interfacial Maxwell stress which can cause the deformation of such an elastic capsule. We investigate this problem considering well established membrane laws for a thin elastic membrane, with fully resolved hydrodynamics in the Stokes…
The adhesive behaviour of biological attachment structures such as spider web anchorages is usually studied using single or multiple peeling models involving "tapes", i.e. one-dimensional contacts elements. This is an oversimplification for many practical problems, since the actual delamination process requires the modelling of complex two-dimensional adhesive elements. To achieve this, we develop a numerical approach to simulate the detachment of an elastic membrane of finite size from a substrate, using a 3D cohesive law. The model is validated using existing analytical results for simple ge…
By using the grand canonical Monte Carlo simulations on spherical surfaces with two fixed vertices separated by the distance L, we find that the second-order phase transition changes to the first-order one when L is sufficiently large. We find that string tension σ\not= 0 in the smooth phase while σ\to 0 in the wrinkled phase.
We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, …
On elastic spherical membranes, there is no stress induced by the bending energy and the corresponding Laplace-Young law does not involve the elastic bending stiffness. However, when considering an axially symmetrical perturbation that pinches the sphere, it induces nontrivial stresses on the entire membrane. In this paper we introduce a theoretical framework to examine the stress induced by perturbations of geometry around the sphere. We find the local balance force equations along the normal direction to the vesicle, and along the unit binormal, tangent to the membrane; likewise, the global …
We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the s…
Motivated by a freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky 1992). The experimental realization of atom-thin graphene sheets has driven a resurgence in this fasci…
A very common strategy to penetrate the cell membrane and access the internal compartment, consists of using sharp tips or nano needles. However recent experiments of cell penetration by atomic force microscopy tips show, contrary to expectations, a weak dependence of penetration force on the curvature of the tip. Using molecular dynamics simulations and analytical arguments, here we show that membrane disruption can be driven either by elastic or entropic forces depending on the membrane size. Our findings have potentially relevant implications in tissue engineering and drug delivery, as they…
Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line tension and the bending moduli, are crucially involved in the kinetics and the asymptotic behavior of phase separation. In this Letter we present a combined analytical and experimental approach to determine the properties of phase-separated vesicle systems. First we develop an analytical model for the vesicle shape of weakly budded biphasic vesicles. Subsequen…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The k…
While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions. For the experimental model system of mechanosensitive ion channels we find that the sign and strength of elastic interactions depend on the protein shape, yielding distinct cooperative gating curves fo…
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in various regimes of a 2-dimensional parameter space $(ε,ν)$ that defines the relevant mechanical and geometrical conditions. Theses parameters are, respectively, the ratio between compression and tension, and the wavelength contrast along the tension direction. In particular, our theory associates the repetitive increase of pattern periodicity, recently observed on…
We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At harmonic level, in-plane orientational (nematic) order is stable to thermal fluctuations, that lead to short-range in-plane translational (phonon) correlations. To treat thermal fluctuations and relevant elastic nonlinearities, we introduce two generalizations of two-dimensional membranes in a three dimensional space to arbitrary D-dimensional membranes embedded…
We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion of the sphere and the membrane during contact. The free-boundary problem of finding the contact surface, over which forces caused by the collision act, is solved by an iterative method. This results in a model that produces detailed predictions of the trajectory of the sphere, the deflection of the membrane, and the pressure distribution during contact. Our …
The plasma membrane of human red blood cells consists of a lipid bilayer attached to a regular network of underlying cytoskeletal polymers. We model this system at a dynamic coarse-grained level, treating the bilayer as an elastic sheet and the cytoskeletal network as a series of phantom entropic springs. In contrast to prior simulation efforts, we explicitly account for dynamics of the cytoskeletal network, both via motion of the protein anchors that attach the cytoskeleton to the bilayer and through breaking and reconnection of individual cytoskeletal filaments. Simulation results are explai…
Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the in…
We study the stress distribution profiles and the height and thickness fluctuations of lipid membranes in the tilted gel state by Monte Carlo simulations of a generic coarse-grained model for lipid membranes, which reproduces many known properties of DPPC bilayers. The results are related to the corresponding properties of fluid membranes, and to theoretical predictions for crystalline and hexatic membranes. One striking observation is that the spontaneous curvature of the monolayers changes sign from the fluid to the gel phase. In the gel phase, the long-wavelength height fluctuations are sup…
