Shape transitions in lipid membranes and protein mediated vesicle fusion and fission

Kinetic pathway and micromechanics of fusion/fission for polyelectrolyte vesicles

Despite the wide existence of vesicles in living cells as well as their important applications like drug delivery, the underlying mechanism of vesicle fusion/fission remains under debate. Classical models cannot fully explain recent observations in experiments and simulations. Here, we develop a constrained self-consistent field theory that allows tracking the shape evolution and free energy as a function of center-of-mass separation distance. Fusion and fission are described in a unified framework. Both the kinetic pathway and the mechanical response can be simultaneously captured. By taking vesicles formed by polyelectrolytes as a model system, we predict discontinuous transitions between the three morphologies: parent vesicle with a single cavity, hemifission/hemifusion, and two separated child vesicles, as a result of breaking topological isomorphism. With the increase in inter-vesicle repulsion, we observe a great reduction in the cleavage energy, indicating that vesicle fission can be achieved without hemifission, in good agreement with simulation results. The force-extension relationship elucidates typical plasticity for separating two vesicles. The super extensibility in the mechanical response of vesicle is in stark contrast to soft particles with other morphologies, such as cylinder and sphere. Our work elucidates the fundamental physical chemistry based on intrinsic topological features of vesicle fusion/fission, which provides insights into various phenomena observed in experiments and simulations.

A Review of Continuum Mechanics for Mechanical Deformation of Lipid Membranes

Mechanical deformation of lipid membranes plays important roles in various cellular tasks. Curvature deformation and lateral stretching are two major energy contributions to the mechanical deformation of lipid membranes. In this paper, continuum theories for these two major membrane deformation events were reviewed. Theories based on curvature elasticity and lateral surface tension were introduced. Numerical methods as well as biological applications of the theories were discussed.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

Modeling Receptor Motility along Advecting Lipid Membranes

This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.

A Monte Carlo study of giant vesicle morphologies in nonequilibrium environments

It is known that giant vesicles undergo dynamic morphological changes when exposed to a detergent. The solubilization process may take multiple pathways. In this work, we identify lipid vesicle shape dynamics before the solubilization of 1,2-dioleoyl-sn-glycero-3-phosphocholine giant vesicles with Triton X-100 (TR) detergent. The violent lipid vesicle dynamics was observed with laser confocal scanning microscopy and was qualitatively explained via a numerical simulation. A three-dimensional Monte Carlo scheme was constructed that emulated the nonequilibrium conditions at the beginning stages of solubilization, accounting for a gradual addition of TR detergent molecules into the lipid bilayers. We suggest that the main driving factor for morphology change in lipid vesicles is the associative tendency of the TR molecules, which induces spontaneous curvature of the detergent inclusions, an intrinsic consequence of their molecular shape. The majority of the observed lipid vesicle shapes in the experiments were found to correspond very well to the numerically calculated shapes in the phase space of possible solutions. The results give an insight into the early stages of lipid vesicle solubilization by amphiphilic molecules, which is nonequilibrium in nature and very difficult to study.

Biomechanical characterization of TIM protein-mediated Ebola virus-host cell adhesion

Since the most recent outbreak, the Ebola virus (EBOV) epidemic remains one of the world’s public health and safety concerns. EBOV is a negative-sense RNA virus that can infect humans and non-human primates, and causes hemorrhagic fever. It has been proposed that the T-cell immunoglobulin and mucin domain (TIM) family proteins act as cell surface receptors for EBOV, and that the interaction between TIM and phosphatidylserine (PS) on the surface of EBOV mediates the EBOV–host cell attachment. Despite these initial findings, the biophysical properties of the TIM-EBOV interaction, such as the mechanical strength of the TIM-PS bond that allows the virus-cell interaction to resist external mechanical perturbations, have not yet been characterized. This study utilizes single-molecule force spectroscopy to quantify the specific interaction forces between TIM-1 or TIM-4 and the following binding partners: PS, EBOV virus-like particle, and EBOV glycoprotein/vesicular stomatitis virus pseudovirion. Depending on the loading rates, the unbinding forces between TIM and ligands ranged from 40 to 100 pN, suggesting that TIM-EBOV interactions are mechanically comparable to previously reported adhesion molecule–ligand interactions. The TIM-4–PS interaction is more resistant to mechanical force than the TIM-1–PS interaction. We have developed a simple model for virus–host cell interaction that is driven by its adhesion to cell surface receptors and resisted by membrane bending (or tension). Our model identifies critical dimensionless parameters representing the ratio of deformation and adhesion energies, showing how single-molecule adhesion measurements relate quantitatively to the mechanics of virus adhesion to the cell.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

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 Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Nanoparticle wrapping at small non-spherical vesicles: curvatures at play

Nanoparticles in biological systems encounter lipid-bilayer membranes as barriers. They interact with plasma membranes, membranous organelles, such as the endoplasmic reticulum and the Golgi apparatus, the nucleus, and intracellular and extracellular vesicles, such as autophagosomes, lysosomes, and exosomes. Extracellular vesicles have recently attracted particular attention, as they are involved in the transmission of biological signals and as regulators for biological processes. For example, exosomes, small vesicles containing proteins, mRNA, and miRNA, that are released by cells into the extracellular environment, have been suggested to participate in tumor metastasis. Furthermore, vesicles can be applied as targeted-drug-delivery systems. We systematically characterize wrapping of spherical nanoparticles that enter and exit vesicles, depending on particle size, vesicle size, vesicle reduced volume, and membrane spontaneous curvature. We predict the complex wrapping behavior, in particular for large particle-to-vesicle size ratios, where the shape changes of the free membrane contribute significantly to the deformation energy and where nanoparticle wrapping transitions and vesicle shape transitions are coupled. Partial-wrapped membrane-bound particles impose boundary conditions on the membrane that stabilise oblates and stomatocytes for particle entry, and prolates and stomatocytes for particle exit. Our results suggest that nanoparticles may stimulate autophagocytic engulfment, which would facilitate transport of the nanoparticles into lysosomes and would lead to subsequent degradation of nanoparticle-attached proteins.

Pulling force and surface tension drive membrane fusion

Despite catalyzed by fusion proteins of quite different molecular architectures, intracellular, viral, and cell-to-cell fusions are found to have the essential common features and the nearly same nature of transition states. The similarity inspires us to find a more general catalysis mechanism for membrane fusion that minimally depends on the specific structures of fusion proteins. In this work, we built a minimal model for membrane fusion, and by using dissipative particle dynamics simulations, we propose a mechanism that the pulling force generated by fusion proteins initiates the fusion process and the membrane tension regulates the subsequent fusion stages. The model shows different features compared to previous computer simulation studies: the pulling force catalyzes membrane fusion through lipid head overcrowding in the contacting region, leading to an increase in the head-head repulsion and/or the unfavorable head-tail contacts from opposing membranes, both of which destabilize the contacting leaflets and thus promote membrane fusion or vesicle rupture. Our simulations produce a variety of shapes and intermediates, closely resembling cases seen experimentally. Our work strongly supports the view that the tight pulling mechanism is a conserved feature of fusion protein-mediated fusion and that the membrane tension plays an essential role in fusion.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

Role of molecular turnover in dynamic deformation of a three-dimensional cellular membrane

In cells, the molecular constituents of membranes are dynamically turned over by transportation from one membrane to another. This molecular turnover causes the membrane to shrink or expand by sensing the stress state within the cell, changing its morphology. At present, little is known as to how this turnover regulates the dynamic deformation of cellular membranes. In this study, we propose a new physical model by which molecular turnover is coupled with three-dimensional membrane deformation to explore mechanosensing roles of turnover in cellular membrane deformations. In particular, as an example of microscopic machinery, based on a coarse-graining description, we suppose that molecular turnover depends on the local membrane strain. Using the proposed model, we demonstrate computational simulations of a single vesicle. The results show that molecular turnover adaptively facilitates vesicle deformation, owing to its stress dependence; while the vesicle drastically expands in the case with low bending rigidity, it shrinks in that with high bending rigidity. Moreover, localized active tension on the membrane causes cellular migration by driving the directional transport of molecules within the cell. These results illustrate the use of the proposed model as well as the role of turnover in the dynamic deformations of cellular membranes.

Cell mechanics: a dialogue

Under the microscope, eukaryotic animal cells can adopt a variety of different shapes and sizes. These cells also move and deform, and the physical mechanisms driving these movements and shape changes are important in fundamental cell biology, tissue mechanics, as well as disease biology. This article reviews some of the basic mechanical concepts in cells, emphasizing continuum mechanics description of cytoskeletal networks and hydrodynamic flows across the cell membrane. We discuss how cells can generate movement and shape changes by controlling mass fluxes at the cell boundary. These mass fluxes can come from polymerization/depolymerization of actin cytoskeleton, as well as osmotic and hydraulic pressure-driven flow of water across the cell membrane. By combining hydraulic pressure control with force balance conditions at the cell surface, we discuss a quantitative mechanism of cell shape and volume control. The broad consequences of this model on cell mechanosensation and tissue mechanics are outlined.

Pointlike Inclusion Interactions in Tubular Membranes

Membrane tubes and tubular networks are ubiquitous in living cells. Inclusions like proteins are vital for both the stability and the dynamics of such networks. These inclusions interact via the curvature deformations they impose on the membrane. We analytically study the resulting membrane mediated interactions in strongly curved tubular membranes. We model inclusions as constraints coupled to the curvature tensor of the membrane tube. First, as special test cases, we analyze the interaction between ring- and rod-shaped inclusions. Using Monte Carlo simulations, we further show how pointlike inclusions interact to form linear aggregates. To minimize the curvature energy of the membrane, inclusions self-assemble into either line- or ringlike patterns. Our results show that the global curvature of the membrane strongly affects the interactions between proteins embedded in it, and can lead to the spontaneous formation of biologically relevant structures.

Membrane tubule formation by banana-shaped proteins with or without transient network structure

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 no significant difference is obtained at low density. A percolated network is intermediately formed depending on the side curvature. This network suppresses tubule protrusion, leading to the slow formation of fewer tubules. Thus, the side curvature, which is generated by protein–protein and membrane–protein interactions, plays a significant role in tubulation dynamics. We also find that positive surface tensions and the vesicle membrane curvature can stabilize this network structure by suppressing the tubulation.

Pearling instability of membrane tubes driven by curved proteins and actin polymerization

Membrane deformation inside living cells is crucial for the proper shaping of various intracellular organelles and is necessary during the fission/fusion processes that allow membrane recycling and transport (e.g. endocytosis). Proteins that induce membrane curvature play a key role in such processes, mostly by adsorbing to the membrane and forming a scaffold that deforms the membrane according to the curvature of the proteins. In this paper we explore the possibility of membrane tube destabilization through a pearling mechanism enabled by the combined effects of the adsorbed curved proteins and the actin polymerization that they recruit. The pearling instability can serve as the initiation for fission of the tube into vesicles. We find that adsorbed curved proteins are more likely to stabilize the tubes, while the actin polymerization can provide the additional constrictive force needed for the robust instability. We discuss the relevance of the theoretical results to in vivo and in vitro experiments.

Physical Principles of Nanoparticle Cellular Endocytosis

This review article focuses on the physiochemical mechanisms underlying nanoparticle uptake into cells. When nanoparticles are in close vicinity to a cell, the interactions between the nanoparticles and the cell membrane generate forces from different origins. This leads to the membrane wrapping of the nanoparticles followed by cellular uptake. This article discusses how the kinetics, energetics, and forces are related to these interactions and dependent on the size, shape, and stiffness of nanoparticles, the biomechanical properties of the cell membrane, as well as the local environment of the cells. The discussed fundamental principles of the physiochemical causes for nanoparticle-cell interaction may guide new studies of nanoparticle endocytosis and lead to better strategies to design nanoparticle-based approaches for biomedical applications.

Monte Carlo simulations of fluid vesicles

Lipid vesicles are closed two dimensional fluid surfaces that are studied extensively as model systems for understanding the physical properties of biological membranes. Here we review the recent developments in the Monte Carlo techniques for simulating fluid vesicles and discuss some of their applications. The technique, which treats the membrane as an elastic sheet, is most suitable for the study of large scale conformations of membranes. The model can be used to study vesicles with fixed and varying topologies. Here we focus on the case of multi-component membranes with the local lipid and protein composition coupled to the membrane curvature leading to a variety of shapes. The phase diagram is more intriguing in the case of fluid vesicles having an in-plane orientational order that induce anisotropic directional curvatures. Methods to explore the steady state morphological structures due to active flux of materials have also been described in the context of Monte Carlo simulations.

The local forces acting on the mechanotransduction channel in hair cell stereocilia

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

Dynamics and instabilities of lipid bilayer membrane shapes

Biological membranes undergo constant shape remodeling involving the formation of highly curved structures. The lipid bilayer represents the fundamental architecture of the cellular membrane with its shapes determined by the Helfrich curvature bending energy. However, the dynamics of bilayer shape transitions, especially their modulation by membrane proteins, and the resulting shape instabilities, are still not well understood. Here, we review in a unifying manner several theories that describe the fluctuations (i.e. undulations) of bilayer shapes as well as their local coupling with lipid or protein density variation. The coupling between local membrane curvature and lipid density gives rise to a 'slipping mode' in addition to the conventional 'bending mode' for damping the membrane fluctuation. This leads to a number of interesting experimental phenomena regarding bilayer shape dynamics. More importantly, curvature-inducing proteins can couple with membrane shape and eventually render the membrane unstable. A criterion for membrane shape instability is derived from a linear stability analysis. The instability criterion reemphasizes the importance of membrane tension in regulating the stability and dynamics of membrane geometry. Recent progresses in understanding the role of membrane tension in regulating dynamical cellular processes are also reviewed. Protein density is emphasized as a key factor in regulating membrane shape transitions: a threshold density of curvature coupling proteins is required for inducing membrane morphology transitions.

Microfluidic fabrication of cell-derived nanovesicles as endogenous RNA carriers

Exosomes/microvesicles are known to shuttle biological signals between cells, possibly by transferring biological signal components such as encapsulated RNAs and proteins, plasma membrane proteins, or both. Therefore exosomes are being considered for use as RNA and protein delivery vehicles for various therapeutic applications. However, living cells in nature secrete only a small number of exosomes, and procedures to collect them are complex; these complications impede their use in mass delivery of components to targeted cells. We propose a novel and efficient method that forces cells through hydrophilic microchannels to generate artificial nanovesicles. These mimetic nanovesicles contain mRNAs, intracellular proteins and plasma membrane proteins, and are shaped like cell-secreted exosomes. When recipient cells are exposed to nanovesicles from embryonic stem cells, mRNAs of Oct 3/4 and Nanog are transferred from embryonic stem cells to the target cells. This result suggests that mimetic nanovesicles can be used as vehicles to deliver RNA. This nanovesicle formation method is expected to be used in exosome research and to have applications in drug and RNA-delivery systems.

Stereocilia membrane deformation: implications for the gating spring and mechanotransduction channel

In hair cells, although mechanotransduction channels have been localized to tips of shorter stereocilia of the mechanically sensitive hair bundle, little is known about how force is transmitted to the channel. Here, we use a biophysical model of the membrane-channel complex to analyze the nature of the gating spring compliance and channel arrangement. We use a triangulated surface model and Monte Carlo simulation to compute the deformation of the membrane under the action of tip link force. We show that depending on the gating spring stiffness, the compliant component of the gating spring arises from either the membrane alone or a combination of the membrane and a tether that connects the channel to the actin cytoskeleton. If a bundle is characterized by relatively soft gating springs, such as those of the bullfrog sacculus, the need for membrane reinforcement by channel tethering then depends on membrane parameters. With stiffer gating springs, such as those from rat outer hair cells, the channel must be tethered for all biophysically realistic parameters of the membrane. We compute the membrane forces (resultants), which depend on membrane tension, bending modulus, and curvature, and show that they can determine the fate of the channel.

Internal forces, tension and energy density in tethered cellular membranes

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.

Systems biology and physical biology of clathrin-mediated endocytosis

In this review, we describe the application of experimental data and modeling of intracellular endocytic trafficking mechanisms with a focus on the process of clathrin-mediated endocytosis. A detailed parts-list for the protein-protein interactions in clathrin-mediated endocytosis has been available for some time. However, recent experimental, theoretical, and computational tools have proved to be critical in establishing a sequence of events, cooperative dynamics, and energetics of the intracellular process. On the experimental front, total internal reflection fluorescence microscopy, photo-activated localization microscopy, and spinning-disk confocal microscopy have focused on assembly and patterning of endocytic proteins at the membrane, while on the theory front, minimal theoretical models for clathrin nucleation, biophysical models for membrane curvature and bending elasticity, as well as methods from computational structural and systems biology, have proved insightful in describing membrane topologies, curvature mechanisms, and energetics.

One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes

Biological membranes are involved in numerous intriguing biophysical and biological cellular phenomena of different length scales, ranging from nanoscale raft formation, vesiculation, to microscale shape transformations. With extended length and time scales as compared to atomistic simulations, solvent-free coarse-grained membrane models have been exploited in mesoscopic membrane simulations. In this study, we present a one-particle-thick fluid membrane model, where each particle represents a cluster of lipid molecules. The model features an anisotropic interparticle pair potential with the interaction strength weighed by the relative particle orientations. With the anisotropic pair potential, particles can robustly self-assemble into fluid membranes with experimentally relevant bending rigidity. Despite its simple mathematical form, the model is highly tunable. Three potential parameters separately and effectively control diffusivity, bending rigidity, and spontaneous curvature of the model membrane. As demonstrated by selected examples, our model can naturally simulate dynamics of phase separation in multicomponent membranes and the topological change of fluid vesicles.

Electron tomography reveals the steps in filovirus budding

The filoviruses, Marburg and Ebola, are non-segmented negative-strand RNA viruses causing severe hemorrhagic fever with high mortality rates in humans and nonhuman primates. The sequence of events that leads to release of filovirus particles from cells is poorly understood. Two contrasting mechanisms have been proposed, one proceeding via a “submarine-like” budding with the helical nucleocapsid emerging parallel to the plasma membrane, and the other via perpendicular “rocket-like” protrusion. Here we have infected cells with Marburg virus under BSL-4 containment conditions, and reconstructed the sequence of steps in the budding process in three dimensions using electron tomography of plastic-embedded cells. We find that highly infectious filamentous particles are released at early stages in infection. Budding proceeds via lateral association of intracellular nucleocapsid along its whole length with the plasma membrane, followed by rapid envelopment initiated at one end of the nucleocapsid, leading to a protruding intermediate. Scission results in local membrane instability at the rear of the virus. After prolonged infection, increased vesiculation of the plasma membrane correlates with changes in shape and infectivity of released viruses. Our observations demonstrate a cellular determinant of virus shape. They reconcile the contrasting models of filovirus budding and allow us to describe the sequence of events taking place during budding and release of Marburg virus. We propose that this represents a general sequence of events also followed by other filamentous and rod-shaped viruses.

The filoviruses, Marburg and Ebola, cause lethal hemorrhagic fever and are highest-priority bioterrorism agents. Filovirus particles contain a rod-like nucleocapsid and are normally filamentous, though other shapes are seen. It is poorly understood how such large filamentous particles are assembled and released from infected cells. Here we have studied Marburg virus production in infected cells using electron tomography. This technique allows virus particles to be visualized in three dimensions at different stages during assembly. We find that in early stages of virus production, highly infectious filamentous viruses are produced, whereas after prolonged infection poorly infectious spherical viruses are released. We also define the sequence of steps in filamentous virus release. The intracellular nucleocapsid first travels to the plasma membrane of the cell, where it binds laterally along its whole length. One end is then wrapped by the plasma membrane and wrapping proceeds rapidly until the virus protrudes vertically from the cell surface. The rear end of the virus particle then pinches off from the cell. We propose that other important filamentous and rod-shaped viruses also follow this series of steps of assembly and budding.

Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein-membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed.

Thylakoid membrane remodeling during state transitions in Arabidopsis

Adaptability of oxygenic photosynthetic organisms to fluctuations in light spectral composition and intensity is conferred by state transitions, short-term regulatory processes that enable the photosynthetic apparatus to rapidly adjust to variations in light quality. In green algae and higher plants, these processes are accompanied by reversible structural rearrangements in the thylakoid membranes. We studied these structural changes in the thylakoid membranes of Arabidopsis thaliana chloroplasts using atomic force microscopy, scanning and transmission electron microscopy, and confocal imaging. Based on our results and on the recently determined three-dimensional structure of higher-plant thylakoids trapped in one of the two major light-adapted states, we propose a model for the transitions in membrane architecture. The model suggests that reorganization of the membranes involves fission and fusion events that occur at the interface between the appressed (granal) and nonappressed (stroma lamellar) domains of the thylakoid membranes. Vertical and lateral displacements of the grana layers presumably follow these localized events, eventually leading to macroscopic rearrangements of the entire membrane network.

Chapter 23: Stochastic modeling methods in cell biology

Stochastic methods have been a staple for understanding complex systems in chemistry and physics. In the biological context, they are useful for understanding phenomena ranging from molecular-level fluctuations to cellular movement. We review the basic formalism behind stochastic methods and outline how they can be implemented for quantifying gene expression, movement of molecular motors, and the dynamics of cytoplasmic components. We show that stochastic methods are quantitative checks for proposed molecular mechanisms and can pose new questions for experiments. Structural information of cellular components can be incorporated into stochastic models to reveal new biological insights.