Lipid-Based Mechanisms for Vesicle 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.

Shocker─A Molecular Dynamics Protocol and Tool for Accelerating and Analyzing the Effects of Osmotic Shocks

The process of osmosis, a fundamental phenomenon in life, drives water through a semipermeable membrane in response to a solute concentration gradient across this membrane. In vitro, osmotic shocks are often used to drive shape changes in lipid vesicles, for instance, to study fission events in the context of artificial cells. While experimental techniques provide a macroscopic picture of large-scale membrane remodeling processes, molecular dynamics (MD) simulations are a powerful tool to study membrane deformations at the molecular level. However, simulating an osmotic shock is a time-consuming process due to slow water diffusion across the membrane, making it practically impossible to examine its effects in classic MD simulations. In this article, we present Shocker, a Python-based MD tool for simulating the effects of an osmotic shock by selecting and relocating water particles across a membrane over the course of several pumping cycles. Although this method is primarily aimed at efficiently simulating volume changes in vesicles, it can also handle membrane tubes and double bilayer systems. Additionally, Shocker is force field-independent and compatible with both coarse-grained and all-atom systems. We demonstrate that our tool is applicable to simulate both hypertonic and hypotonic osmotic shocks for a range of vesicular and bilamellar setups, including complex multicomponent systems containing membrane proteins or crowded internal solutions.

On the role of membrane embedding, protein rigidity and transmembrane length in lipid membrane fusion

The fusion of biological membranes is ubiquitous in natural processes like exo- and endocytosis, intracellular trafficking and viral entry. Membrane fusion is also utilized in artificial biomimetic fusion systems, e.g. for drug delivery. Both the natural and the biomimetic fusion systems rely on a wide range of (artificial) proteins mediating the fusion process. Although the exact mechanisms of these proteins differ, clear analogies in their general behavior can be observed in bringing the membranes in close proximity and mediating the fusion reaction. In our study, we use molecular dynamics simulations with coarse grained models, mimicking the general behavior of fusion proteins (spikes), to systematically examine the effects of specific characteristics of these proteins on the fusion process. The protein characteristics considered are (i) the type of membrane embedding, i.e., either transmembrane or not, (ii) the rigidity, and (iii) the transmembrane domain (TMD) length. The results show essential differences in fusion pathway between monotopic and transmembrane spikes, in which transmembrane spikes seem to inhibit the formation of hemifusion diaphragms, leading to a faster fusion development. Furthermore, we observed that an increased rigidity and a decreased TMD length both proved to contribute to a faster fusion development. Finally, we show that a single spike may suffice to successfully induce a fusion reaction, provided that the spike is sufficiently rigid and attractive. Not only does this shed light on biological fusion of membranes, it also provides clear design rules for artificial membrane fusion systems.

Coarse-Grained Molecular Dynamics of pH-Sensitive Lipids

pH-sensitive lipids represent a class of lipids that can be protonated and destabilized in acidic environments, as they become positively charged in response to low-pH conditions. They can be incorporated into lipidic nanoparticles such as liposomes, which are able to change their properties and allow specific drug delivery at the acidic conditions encountered in some pathological microenvironments. In this work, we used coarse-grained molecular-dynamic simulations to study the stability of neutral and charged lipid bilayers containing POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and various kinds of ISUCA ((F)2-(imidazol-1-yl)succinic acid)-derived lipids, which can act as pH-sensitive molecules. In order to explore such systems, we used a MARTINI-derived forcefield, previously parameterized using all-atom simulation results. We calculated the average area per lipid, the second-rank order parameter and the lipid diffusion coefficient of both lipid bilayers made of pure components and mixtures of lipids in different proportions, under neutral or acidic conditions. The results show that the use of ISUCA-derived lipids disturbs the lipid bilayer structure, with the effect being particularly marked under acidic conditions. Although more-in depth studies on these systems must be carried out, these initial results are encouraging and the lipids designed in this research could be a good basis for developing new pH-sensitive liposomes.

Vesicles Balance Osmotic Stress with Bending Energy That Can Be Released to Form Daughter Vesicles

The bending energy of the lipid membrane is central to biological processes involving vesicles, such as endocytosis and exocytosis. To illustrate the role of bending energy in these processes, we study the response of single-component giant unilamellar vesicles (GUVs) subjected to external osmotic stress by glucose addition. For osmotic pressures exceeding 0.15 atm, an abrupt shape change from spherical to prolate occurs, showing that the osmotic pressure is balanced by the free energy of membrane bending. After equilibration, the external glucose solution was exchanged for pure water, yielding rapid formation of monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Our theoretical analysis shows that this process requires significant free energies stored in the deformed membrane to be kinetically allowed. The results indicate that bending energies stored in GUVs are much higher than previously implicated, with potential consequences for vesicle fusion/fission and the osmotic regulation in living cells.

Pulsed Electric Fields Promote Liposome Buddings

Background: Liposomes have been a useful tool to analyze membrane behavior. Various studies have attempted to induce biological activities, for example, buddings, divisions, and endocytosis, on liposomes, focusing on lipid rafts that move along electric fields. Materials and Methods: Liposomes consisting of soybean lecithin, phosphatidylcholine, and cholesterol were prepared, with inner and outer liquid conductivities of 0.595 and 1.564 S/m, respectively. Results: We tried to induce buddings by pulsed electric fields (PEFs) on liposomes. Results demonstrated that 1.248 kV/cm, 400 μs PEF promoted postpulse liposome buddings, which were preceded by a membrane relaxation. Although a transient thick area (a lipid raft-like area) on the membrane just after PEF application preceded buddings, it was not the sufficient factor for buddings. Conclusion: We established a brief model as follows: 1.248 kV/cm, 400 μs PEF induced the lipid membrane relaxation without electroporation to trigger buddings. The current results could be a new frontier in bioelectrics.

Light-triggered explosion of lipid vesicles

Lipid vesicles have received considerable interest because of their applications to in vitro reductionist cell membrane models as well as therapeutic delivery vehicles. In these contexts, the mechanical response of vesicles in nonequilibrium environments plays a key role in determining the corresponding dynamics. A common understanding of the response of lipid vesicles upon exposure to a hypotonic solution is a characteristic pulsatile behavior. Recent experiments, however, have shown vesicles exploding under an osmotic shock generated by photo-reactions, yet the explanatory mechanism is unknown. Here we present a generalized biophysical model incorporating a stochastic account of membrane rupture to describe both swell-burst-reseal cycling and exploding dynamics. This model agrees well with experimental observations, and it unravels that the sudden osmotic shock strains the vesicle at an extreme rate, driving the vesicle into buckling instabilities responsible for membrane fragmentation, i.e. explosion. Our work not only advances the fundamental framework for non-equilibrium vesicle dynamics under osmotic stress, but also offers design guidelines for programmable vesicle-encapsulated substance release in therapeutic carriers.

Dynamics of Growth and Form in Prebiotic Vesicles

The growth, form, and division of prebiotic vesicles, membraneous bags of fluid of varying components and shapes is hypothesized to have served as the substrate for the origin of life. The dynamics of these out-of-equilibrium structures is controlled by physicochemical processes that include the intercalation of amphiphiles into the membrane, fluid flow across the membrane, and elastic deformations of the membrane. To understand prebiotic vesicular forms and their dynamics, we construct a minimal model that couples membrane growth, deformation, and fluid permeation, ultimately couched in terms of two dimensionless parameters that characterize the relative rate of membrane growth and the membrane permeability. Numerical simulations show that our model captures the morphological diversity seen in extant precursor mimics of cellular life, and might provide simple guidelines for the synthesis of these complex shapes from simple ingredients.

Primordial sex facilitates the emergence of evolution

Compartments are ubiquitous throughout biology, and they have very likely played a crucial role at the origin of life. Here we assume that a protocell, which is a compartment enclosing functional components, requires N such components in order to be evolvable. We calculate the timescale in which a minimal evolvable protocell is produced. We show that when protocells fuse and share information, the timescales polynomially in N By contrast, in the absence of fusion, the worst-case scenario is exponential in N We discuss the implications of this result for the origin of life and other biological processes.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

Molecular mechanism of vesicle division induced by coupling between lipid geometry and membrane curvatures

We investigated the effects of lipid geometry on vesicle division using coarse grained molecular dynamics simulations. When the vesicle is composed of zero and negative spontaneous curvature lipids (ZSLs and NSLs), the difference in their molecular spontaneous curvatures destabilizes the neck of the limiting shape vesicle. In the vesicle division pathway, the neck developed into the stalk intermediates. The stalk was broken when the NSLs were expelled from the stalk. Free energy analysis shows that the coupling between the lipid geometry and the Gaussian rigidity is responsible for the observed vesicle division.

In Silico Investigations of Calcium Phosphate Mineralization in Extracellular Vesicles

Calcification in bone, cartilage, and cardiovascular tissues involves the release of specialized extracellular vesicles (EVs) that promote mineral nucleation. The small size of the EVs, however, makes molecular level studies difficult, and consequently uncertainty exists on the role and function of these structures in directing mineralization. The lack of mechanistic understanding associated with the initiators of ectopic mineral deposition has severely hindered the development of potential therapeutic options. Here, we used multiscale molecular dynamics simulations to investigate the calcification within the EVs. Results show that Ca²⁺-HPO₄^2- and phosphatidylserine complexes facilitate the early nucleation. Use of coarse-grained simulations allows investigations of Ca²⁺-PO₄^3- nucleation and crystallization in the EVs. Systematic variation in the ion-to-water ratio shows that the crystallization and growth strongly depend on the enrichment of the ions and dehydration inside the EVs. Our investigations provide insights into the role of EVs on calcium phosphate mineral nucleation and growth in both physiological and pathological mineralization.

Dynamics of a multicomponent vesicle in shear flow

We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate dynamical patterns induced by inhomogeneous bending for a two phase system. Numerical results reveal that there exist novel phase-treading and tumbling mechanisms that cannot be observed for a homogeneous vesicle. In particular, unlike the well-known steady tank-treading dynamics characterized by a fixed inclination angle, here the phase-treading mechanism leads to unsteady periodic dynamics with an oscillatory inclination angle. When the average phase concentration is around 1/2, we observe tumbling dynamics even for very low shear rate, and the excess length required for tumbling is significantly smaller than the value for the single phase case. We summarize our results in phase diagrams in terms of the excess length, shear rate, and concentration of the soft phase. These findings go beyond the well known dynamical regimes of a homogeneous vesicle and highlight the level of complexity of vesicle dynamics in a fluid due to heterogeneous material properties.

Fusion and fission inhibited by the same mechanism in electrostatically charged surfactant micelles

This paper revises the general idea about the role of intermicellar and intramiceller interactions in inhibiting fusion of self-assembled surfactant micelles. Fusion and fission of micelles are usually thought to be limited by different mechanisms. While fission is accepted to be controlled by surface instabilities (intramicellar interactions), fusion is commonly thought to be rate limited by the barrier to the close approach between two micelles due to the steric or Coulombic repulsions (intramicellar interactions). Here we describe the role of electrostatic repulsions in inhibiting fusion and fission kinetics in self-assembled micelles. We use stopped flow-fluorescence technique with hydrophobic pyrene to quantify fusion and fission in ionic/nonionic mixed micelles (Triton X-100/SDS). We show that the fusion and fission rates decrease with the same tendency with increasing the fraction of the ionic charges, while their ratio remains constant. Our results are interpreted to mean that, in slightly charged micelles, fusion shares the same limiting step with fission, which most likely involves surface instabilities and intramiceller interactions.

Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulations of Membrane Proteins and Helix-Helix Association

An extension of the recently developed PRIMO coarse-grained force field to membrane environments, PRIMO-M, is described. The membrane environment is modeled with the heterogeneous dielectric generalized Born (HDGB) methodology that simply replaces the standard generalized Born model in PRIMO without further parametrization. The resulting model was validated by comparing amino acid insertion free energy profiles and application in molecular dynamics simulations of membrane proteins and membrane-interacting peptides. Membrane proteins with 148–661 amino acids show stable root-mean-squared-deviations (RMSD) between 2 and 4 Å for most systems. Transmembrane helical peptides maintain helical shape and exhibit tilt angles in good agreement with experimental or other simulation data. The association of two glycophorin A (GpA) helices was simulated using replica exchange molecular dynamics simulations yielding the correct dimer structure with a crossing angle in agreement with previous studies. Finally, conformational sampling of the influenza fusion peptide also generates structures in agreement with previous studies. Overall, these findings suggest that PRIMO-M can be used to study membrane bound peptides and proteins and validates the transferable nature of the PRIMO coarse-grained force field.

The free energy of nanopores in tense membranes

Membrane nanopores are central players for a range of important cellular membrane remodeling processes as well as membrane rupture. Understanding pore formation in tense membranes requires comprehension of the molecular mechanism of pore formation and the associated free energy change as a function of the membrane tension. Here we propose a scheme to calculate the free energy change associated with the formation of a nanometer sized pore in molecular dynamics simulations as a function of membrane tension, which requires the calculation of only one computationally expensive potential of mean force. We show that membrane elastic theory can be used to estimate the pore formation free energy at different tension values from the free energy change in a relaxed membrane and the area expansion curves of the membranes. We have computed the pore formation free energy for a dipalmitoyl-phosphatidylcholine (DPPC) membrane at two different lateral pressure values, 1 bar and -40 bar, by calculating the potential of mean force acting on the head group of a single lipid molecule. Unrestrained simulations of the closing process confirm that the intermediate states along this reaction coordinate are reasonable and show that hydrophilic indentations spanning half the bilayer connected by a hydrophobic pore segment represent the corresponding high energy transition state. A comparison of the stability of simulated membranes to experiment at high loading rates show that, contrary to expectation, pores form too easily in small simulated membrane patches. This discrepancy originates from a combination of the absence of ions in the simulations and the small membrane size.

Membrane monolayer protrusion mediates a new nanoparticle wrapping pathway

Understanding how nanoparticles (NPs) interact with the lipid membrane is of importance for their potential applications in biomedicine and cytotoxic effects. In this paper, with the aid of computer simulation techniques, we report that NPs can be wrapped by lipid membranes in a pathway different from the conventional endocytic pathway. Our simulation results show that under the conditions of strong NP-membrane adhesion and low membrane tension, NPs can be wrapped by membranes with a pathway regulated by membrane monolayer protrusion. We also find that in the monolayer protrusion mediated wrapping pathway NPs are first trapped in the membrane and the subsequent NP internalization can be achieved by several means, including decreasing the membrane tension, breaking the membrane symmetry between upper and lower leaflets, and exerting an external force on the NPs. The findings from our simulations are well supported by the free energy analysis.

Self-healing vesicles deposit lipid-coated Janus particles into nanoscopic trenches

Using dissipative particle dynamics (DPD) simulations, we model the interaction between nanoscopic lipid vesicles and Janus nanoparticles localized on an adhesive substrate in the presence of an imposed flow. The system is immersed in a hydrophilic solution, and the hydrophilic substrate contains nanoscopic trenches, which are either step- or wedge-shaped. The fluid-driven vesicle successfully picks up Janus particles on the substrate, transports these particles as cargo along the surface, and then drops off the particles into the trenches. For Janus particles with a relatively large hydrophobic region, lipids from the bilayer membrane become detached from the vesicle and bound to the hydrophobic domain of the deposited particle. While the detachment of these lipids rips the vesicle, it provides a coating that effectively shields the hydrophobic portion of the nanoparticle from the outer solution. After the particle has been dropped off, the torn vesicle undergoes structural rearrangement, reforming into a closed structure that resembles its original shape. In effect, the vesicle displays pronounced adaptive behavior, shedding lipids to form a protective coating around the particle and undergoing a self-healing process after the particle has been deposited. This responsive, adaptive behavior is observed in cases involving both the step- and wedge-shaped trenches, but the step trench is more effective at inducing particle drop off. The results reveal that the introduction of grooves or trenches into a hydrophilic surface can facilitate the targeted delivery of amphiphilic particles by self-healing vesicles, which could be used for successive delivery events.

Vesicles and vesicle fusion: coarse-grained simulations

Biological cells are highly dynamic, and continually move material around their own volume and between their interior and exterior. Much of this transport encapsulates the material inside phospholipid vesicles that shuttle to and from, fusing with, and budding from, other membranes. A feature of vesicles that is crucial for this transport is their ability to fuse to target membranes and release their contents to the distal side. In industry, some personal care products contain vesicles to help transport reagents across the skin, and research on drug formulation shows that packaging active compounds inside vesicles delays their clearance from the blood stream. In this chapter, we survey the biological role and physicochemical properties of phospholipids, and describe progress in coarse-grained simulations of vesicles and vesicle fusion. Because coarse-grained simulations retain only those molecular details that are thought to influence the large-scale processes of interest, they act as a model embodying our current understanding. Comparing the predictions of these models with experiments reveals the importance of the retained microscopic details and also the deficiencies that can suggest missing details, thereby furthering our understanding of the complex dynamic world of vesicles.

Structural modelling and dynamics of proteins for insights into drug interactions

Proteins are the workhorses of biomolecules and their function is affected by their structure and their structural rearrangements during ligand entry, ligand binding and protein-protein interactions. Hence, the knowledge of protein structure and, importantly, the dynamic behaviour of the structure are critical for understanding how the protein performs its function. The predictions of the structure and the dynamic behaviour can be performed by combinations of structure modelling and molecular dynamics simulations. The simulations also need to be sensitive to the constraints of the environment in which the protein resides. Standard computational methods now exist in this field to support the experimental effort of solving protein structures. This review presents a comprehensive overview of the basis of the calculations and the well-established computational methods used to generate and understand protein structure and function and the study of their dynamic behaviour with the reference to lung-related targets.

Self-reproduction of fatty acid vesicles: a combined experimental and simulation study

Dilution of a fatty acid micellar solution at basic pH toward neutrality results in spontaneous formation of vesicles with a broad size distribution. However, when vesicles of a defined size are present before dilution, the size distribution of the newly formed vesicles is strongly biased toward that of the seed vesicles. This so-called matrix effect is believed to be a key feature of early life. Here we reproduced this effect for oleate micelles and seed vesicles of either oleate or dioleoylphosphatidylcholine. Fluorescence measurements showed that the vesicle contents do not leak out during the replication process. We hypothesized that the matrix effect results from vesicle fission induced by an imbalance of material across both leaflets of the vesicle upon initial insertion of fatty acids into the outer leaflet of the seed vesicle. This was supported by experiments that showed a significant increase in vesicle size when the equilibration of oleate over both leaflets was enhanced by either slowing down the rate of fatty acid addition or increasing the rate of fatty acid transbilayer movement. Coarse-grained molecular-dynamics simulations showed excellent agreement with the experimental results and provided further mechanistic details of the replication process.

Coarse grained molecular dynamics simulations of transmembrane protein-lipid systems

Many biological cellular processes occur at the micro- or millisecond time scale. With traditional all-atom molecular modeling techniques it is difficult to investigate the dynamics of long time scales or large systems, such as protein aggregation or activation. Coarse graining (CG) can be used to reduce the number of degrees of freedom in such a system, and reduce the computational complexity. In this paper the first version of a coarse grained model for transmembrane proteins is presented. This model differs from other coarse grained protein models due to the introduction of a novel angle potential as well as a hydrogen bonding potential. These new potentials are used to stabilize the backbone. The model has been validated by investigating the adaptation of the hydrophobic mismatch induced by the insertion of WALP-peptides into a lipid membrane, showing that the first step in the adaptation is an increase in the membrane thickness, followed by a tilting of the peptide.

Dynamics of multicomponent vesicles in a viscous fluid

We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibil-ity of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.

Vesicle deformation by draining: geometrical and topological shape changes

A variety of factors, including changes in temperature or osmotic pressure, can trigger morphological transitions of vesicles. Upon osmotic upshift, water diffuses across the membrane in response to the osmotic difference, resulting in a decreased vesicle volume to membrane area ratio and, consequently, a different shape. In this paper, we study the vesicle deformations on osmotic deflation using coarse grained molecular dynamics simulations. Simple deflation of a spontaneously formed spherical vesicle results in oblate ellipsoid and discous vesicles. However, when the hydration of the lipids in the outer membrane leaflet is increased, which can be the result of a changed pH or ion concentration, prolate ellipsoid, pear-shaped and budded vesicles are formed. Under certain conditions the deflation even results in vesicle fission. The simulations also show that vesicles formed by a bilayer to vesicle transition are, although spontaneously formed, not immediately stress-free. Instead, the membrane is stretched during the final stage of the transition and only reaches equilibrium once the excess interior water has diffused across the membrane. This suggests the presence of residual membrane stress immediately after vesicle closure in experimental vesicle formation and is especially important for MD simulations of vesicles where the time scale to reach equilibrium is out of reach.

Shape deformation and fission route of the lipid domain in a multicomponent vesicle

In this paper, the curvature changes and fission routes of the lipid domains in a multicomponent vesicle are studied by dissipative particle dynamics. Under different conditions of asymmetric distribution of lipids in two leaflets of lipid bilayer and area-to-volume ratio of the vesicle, we obtained different configurations of the domain in the vesicle: three typical curvature characters of the lipid domain, namely, positive, negative, and invariable curvatures compared to the vesicle are observed. Furthermore, some other morphologies of the domain and two vesicle fission routes (i.e., exocytic and endocytic fissions) are also obtained in our simulations. Particular emphasis is put on the formation of the negative curvature domain and on the behavior of endocytic fission. Based on our simulations, it is indicated that water plays an important role in the invagination and endocytic fission processes of the domain in a vesicle. For endocytic fission, domains of different sizes are evolved according to different routes under the effect of the water. Additionally, we find that both the spontaneous curvature of lipid molecules and area-to-volume ratio can promote or restrain the shape deformation of the lipid domain. Under the competition of these two factors, another possible route of endocytic fission is observed in our simulations, in that only a part of the lipid domain invaginates into the interior of the vesicle to complete the endocytic fission. Our study is helpful for understanding the possible mechanism of the shape transformation of the cellular membrane and the difference of several kinds of routes of vesicle fission.

Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission

We develop a thermodynamically consistent phase-field model to simulate the dynamics of multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature, excess (surface) energy, and a line tension between the coexisting surface phases. Our approach is similar to that recently used by Wang and Du [J. Math. Biol. 56, 347 (2008)] with a key difference. Here, we concentrate on the dynamic evolution and solve the surface mass conservation equation explicitly; this equation was not considered by Wang and Du. The resulting fourth-order strongly coupled system of nonlinear nonlocal equations are solved numerically using an adaptive finite element numerical method. Although the system is valid for three dimensions, we limit our studies here to two dimensions where the vesicle is a curve. Differences between the spontaneous curvatures and the bending rigidities of the surface phases are found numerically to lead to the formation of buds, asymmetric vesicle shapes and vesicle fission even in two dimensions. In addition, simulations of configurations far from equilibrium indicate that phase separation via spinodal decomposition and coarsening not only affect the vesicle shape but also that the vesicle shape affects the phase separation dynamics, especially the coarsening and may lead to lower energy states than might be achieved by evolving initially phase-separated configurations.

Lipids on the move: simulations of membrane pores, domains, stalks and curves

In this review we describe the state-of-the-art of computer simulation studies of lipid membranes. We focus on collective lipid-lipid and lipid-protein interactions that trigger deformations of the natural lamellar membrane state, showing that many important biological processes including self-aggregation of membrane components into domains, the formation of non-lamellar phases, and membrane poration and curving, are now amenable to detailed simulation studies.

Insight or illusion? Seeing inside the cell with mesoscopic simulations

The expulsion of material from a cell by fusion of vesicles at the plasma membrane, and the entry of a virus by membrane invagination are complex membrane-associated processes whose control is crucial to cell survival. Our ability to visualize the dynamics of such processes experimentally is limited by spatial resolution and the speed of molecular rearrangements. The increase in computing power of the last few decades enables the construction of computational tools for observing cellular processes in silico. As experiments yield increasing amounts of data on the protein and lipid constituents of the cell, computer simulations parametrized using this data are beginning to allow models of cellular processes to be interrogated in ways unavailable in the laboratory. Mesoscopic simulations retain only those molecular features that are believed to be relevant to the processes of interest. This allows the dynamics of spatially heterogeneous membranes and the crowded cytoplasmic environment to be followed at a modest computational cost. The price for such power is that the atomic detail of the constituents is much lower than in atomistic Molecular Dynamics simulations. We argue that this price is worth paying because mesoscopic simulations can generate new insight into the complex, dynamic life of a cell.