Monolayerwise application of linear elasticity theory well describes strongly deformed lipid membranes and the effect of solvent

Mechanical Responses of a Single Myelin Layer: A Molecular Simulation Study

The myelin sheath provides insulation to the brain's neuron cells, which aids in signal transmission and communication with the body. Degenerated myelin hampers the connection between the glial cells, which are the front row responders during traumatic brain injury mitigation. Thus, the structural integrity of the myelin layer is critical for protecting the brain tissue from traumatic injury. At the molecular level, myelin consists of a lipid bilayer, myelin basic proteins (MBP), proteolipid proteins (PLP), water and ions. Structurally, the myelin sheath is formed by repeatedly wrapping forty or more myelin layers around an axon. Here, we have used molecular dynamic simulations to model and capture the tensile response of a single myelin layer. An openly available molecular dynamic solver, LAMMPS, was used to conduct the simulations. The interatomic potentials for the interacting atoms and molecules were defined using CHARMM force fields. Following a standard equilibration process, the molecular model was stretched uniaxially at a deformation rate of 5 Å/ps. We observed that, at around 10% applied strain, the myelin started to cohesively fail via flaw formation inside the bilayers. Further stretching led to a continued expansion of the defect inside the bilayer, both radially and transversely. This study provides the cellular-level mechanisms of myelin damage due to mechanical load.

Three membrane fusion pore families determine the pathway to pore dilation

During exocytosis secretory vesicles fuse with a target membrane and release neurotransmitters, hormones, or other bioactive molecules through a membrane fusion pore. The initially small pore may subsequently dilate for full contents release, as commonly observed in amperometric traces. The size, shape, and evolution of the pore is critical to the course of contents release, but exact fusion pore solutions accounting for membrane tension and bending energy constraints have not been available. Here, we obtained exact solutions for fusion pores between two membranes. We find three families: a narrow pore, a wide pore, and an intermediate tether-like pore. For high tensions these are close to the catenoidal and tether solutions recently reported for freely hinged membrane boundaries. We suggest membrane fusion initially generates a stable narrow pore, and the dilation pathway is a transition to the stable wide pore family. The unstable intermediate pore is the transition state that sets the energy barrier for this dilation pathway. Pore dilation is mechanosensitive, as the energy barrier is lowered by increased membrane tension. Finally, we study fusion pores in nanodiscs, powerful systems for the study of individual pores. We show that nanodiscs stabilize fusion pores by locking them into the narrow pore family.

Determination of elastic parameters of lipid membranes from simulation under varied external pressure

Many cellular processes such as endocytosis, exocytosis, and vesicle trafficking involve membrane deformations, which can be analyzed in the framework of the elastic theories of lipid membranes. These models operate with phenomenological elastic parameters. A connection between these parameters and the internal structure of lipid membranes can be provided by three-dimensional (3D) elastic theories. Considering a membrane as a 3D layer, Campelo et al. [F. Campelo et al., Adv. Colloid Interface Sci. 208, 25 (2014)10.1016/j.cis.2014.01.018] developed a theoretical basis for the calculation of elastic parameters. In this work we generalize and improve this approach by considering a more general condition of global incompressibility instead of local incompressibility. Crucially, we find an important correction to the theory of Campelo et al., which if not taken into account leads to a significant miscalculation of elastic parameters. With the total volume conservation taken into account, we derive an expression for the local Poisson's ratio, which determines how the local volume changes upon stretching and permits a more precise determination of elastic parameters. Also, we substantially simplify the procedure by calculating the derivatives of the moments of the local tension with respect to stretching instead of calculating the local stretching modulus. We obtain a relation between the Gaussian curvature modulus as a function of stretching and the bending modulus, showing that these two elastic parameters are not independent, as was previously assumed. The proposed algorithm is applied to membranes composed of pure dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and their mixture. The following elastic parameters of these systems are obtained: the monolayer bending and stretching moduli, spontaneous curvature, neutral surface position, and local Poisson's ratio. It is shown that the bending modulus of the DPPC/DOPC mixture follows a more complex trend than predicted by the classical Reuss averaging, which is often employed in theoretical frameworks.

Membrane Lipid Reshaping Underlies Oxidative Stress Sensing by the Mitochondrial Proteins UCP1 and ANT1

Oxidative stress and ROS are important players in the pathogenesis of numerous diseases. In addition to directly altering proteins, ROS also affects lipids with negative intrinsic curvature such as phosphatidylethanolamine (PE), producing PE adducts and lysolipids. The formation of PE adducts potentiates the protonophoric activity of mitochondrial uncoupling proteins, but the molecular mechanism remains unclear. Here, we linked the ROS-mediated change in lipid shape to the mechanical properties of the membrane and the function of uncoupling protein 1 (UCP1) and adenine nucleotide translocase 1 (ANT1). We show that the increase in the protonophoric activity of both proteins occurs due to the decrease in bending modulus in lipid bilayers in the presence of lysophosphatidylcholines (OPC and MPC) and PE adducts. Moreover, MD simulations showed that modified PEs and lysolipids change the lateral pressure profile of the membrane in the same direction and by the similar amplitude, indicating that modified PEs act as lipids with positive intrinsic curvature. Both results indicate that oxidative stress decreases stored curvature elastic stress (SCES) in the lipid bilayer membrane. We demonstrated that UCP1 and ANT1 sense SCES and proposed a novel regulatory mechanism for the function of these proteins. The new findings should draw the attention of the scientific community to this important and unexplored area of redox biochemistry.

Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects

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 development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the determination of intrinsic elastic parameters of lipid mixtures, which is complicated due to the composition-curvature coupling effect.

Molecular Shape Solution for Mesoscopic Remodeling of Cellular Membranes

Cellular membranes self-assemble from and interact with various molecular species. Each molecule locally shapes the lipid bilayer, the soft elastic core of cellular membranes. The dynamic architecture of intracellular membrane systems is based on elastic transformations and lateral redistribution of these elementary shapes, driven by chemical and curvature stress gradients. The minimization of the total elastic stress by such redistribution composes the most basic, primordial mechanism of membrane curvature-composition coupling (CCC). Although CCC is generally considered in the context of dynamic compositional heterogeneity of cellular membrane systems, in this article we discuss a broader involvement of CCC in controlling membrane deformations. We focus specifically on the mesoscale membrane transformations in open, reservoir-governed systems, such as membrane budding, tubulation, and the emergence of highly curved sites of membrane fusion and fission. We reveal that the reshuffling of molecular shapes constitutes an independent deformation mode with complex rheological properties.This mode controls effective elasticity of local deformations as well as stationary elastic stress, thus emerging as a major regulator of intracellular membrane remodeling.

Peptide-induced membrane elastic deformations decelerate gramicidin dimer-monomer equilibration

Gramicidin A (gA) is a hydrophobic pentadecapeptide readily incorporating into a planar bilayer lipid membrane (BLM), thereby inducing a large macroscopic current across the BLM. This current results from ion-channel formation due to head-to-head transbilayer dimerization of gA monomers with rapidly established monomer-dimer equilibrium. Any disturbance of the equilibrium, e.g., by sensitized photoinactivation of a portion of gA monomers, causes relaxation toward a new equilibrium state. According to previous studies, the characteristic relaxation time of the gA-mediated electric current decreases as the current increases upon elevating the gA concentration in the membrane. Here, we report data on the current relaxation kinetics for gA analogs with N-terminal valine replaced by glycine or tyrosine. Surprisingly, the relaxation time increased rather than decreased upon elevation of the total membrane conductance induced by these gA analogs, thus contradicting the classical kinetic scheme. We developed a general theoretical model that accounts for lateral interaction of monomers and dimers mediated by membrane elastic deformations. The modified kinetic scheme of the gramicidin dimerization predicts the reverse dependence of the relaxation time on membrane conductance for gA analogs, with a decreased dimerization constant that is in a good agreement with our experimental data. The equilibration process may be also modulated by incorporation of other peptides ("impurities") into the lipid membrane.

Ectodomain Pulling Combines with Fusion Peptide Inserting to Provide Cooperative Fusion for Influenza Virus and HIV

Enveloped viruses include the most dangerous human and animal pathogens, in particular coronavirus, influenza virus, and human immunodeficiency virus (HIV). For these viruses, receptor binding and entry are accomplished by a single viral envelope protein (termed the fusion protein), the structural changes of which trigger the remodeling and merger of the viral and target cellular membranes. The number of fusion proteins required for fusion activity is still under debate, and several studies report this value to range from 1 to 9 for type I fusion proteins. Here, we consider the earliest stage of viral fusion based on the continuum theory of membrane elasticity. We demonstrate that membrane deformations induced by the oblique insertion of amphipathic fusion peptides mediate the lateral interaction of these peptides and drive them to form into a symmetric fusion rosette. The pulling force produced by the structural rearrangements of the fusion protein ectodomains gives additional torque, which deforms the membrane and additionally stabilizes the symmetric fusion rosette, thus allowing a reduction in the number of fusion peptides needed for fusion. These findings can resolve the large range of published cooperativity indices for HIV, influenza, and other type I fusion proteins.

Continuum Models of Membrane Fusion: Evolution of the Theory

Starting from fertilization, through tissue growth, hormone secretion, synaptic transmission, and sometimes morbid events of carcinogenesis and viral infections, membrane fusion regulates the whole life of high organisms. Despite that, a lot of fusion processes still lack well-established models and even a list of main actors. A merger of membranes requires their topological rearrangements controlled by elastic properties of a lipid bilayer. That is why continuum models based on theories of membrane elasticity are actively applied for the construction of physical models of membrane fusion. Started from the view on the membrane as a structureless film with postulated geometry of fusion intermediates, they developed along with experimental and computational techniques to a powerful tool for prediction of the whole process with molecular accuracy. In the present review, focusing on fusion processes occurring in eukaryotic cells, we scrutinize the history of these models, their evolution and complication, as well as open questions and remaining theoretical problems. We show that modern approaches in this field allow continuum models of membrane fusion to stand shoulder to shoulder with molecular dynamics simulations, and provide the deepest understanding of this process in multiple biological systems.

Elastic deformations mediate interaction of the raft boundary with membrane inclusions leading to their effective lateral sorting

Liquid-ordered lipid domains represent a lateral inhomogeneity in cellular membranes. These domains have elastic and physicochemical properties different from those of the surrounding membrane. In particular, their thickness exceeds that of the disordered membrane. Thus, elastic deformations arise at the domain boundary in order to compensate for the thickness mismatch. In equilibrium, the deformations lead to an incomplete register of monolayer ordered domains: the elastic energy is minimal if domains in opposing monolayers lie on the top of each other, and their boundaries are laterally shifted by about 3 nm. This configuration introduces a region, composed of one ordered and one disordered monolayers, with an intermediate bilayer thickness. Besides, a jump in a local monolayer curvature takes place in this intermediate region, concentrating here most of the elastic stress. This region can participate in a lateral sorting of membrane inclusions by offering them an optimal bilayer thickness and local curvature conditions. In the present study, we consider the sorting of deformable lipid inclusions, undeformable peripheral and deeply incorporated peptide inclusions, and undeformable transmembrane inclusions of different molecular geometry. With rare exceptions, all types of inclusions have an affinity to the ordered domain boundary as compared to the bulk phases. The optimal lateral distribution of inclusions allows relaxing the elastic stress at the boundary of domains.