Molecular Dynamic Simulation of Transmembrane Pore Growth

A molecular dynamic approach was applied for simulation of dynamics of pore formation and growth in a phospholipid bilayer in the presence of an external electric field. Processing the simulation results permitted recovery of the kinetic coefficients used in the Einstein–Smoluchowski equation describing the dynamics of pore evolution. Two different models of the bilayer membrane were considered: membrane consisting of POPC and POPE lipids. The simulations permitted us to find nonempirical values of the pore energy parameters, which are compared with empirical values. It was found that the parameters are sensitive to membrane type.     

Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects

Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.     

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation

Tubular protrusions are a common feature of living cells, arising from polymerization of stiff protein filaments against a comparably soft membrane. Although this process involves many accessory proteins in cells, in vitro experiments indicate that similar tube-like structures can emerge without them, through spontaneous bundling of filaments mediated by the membrane. Using theory and simulation of physical models, we have elaborated how nonequilibrium fluctuations in growth kinetics and membrane shape can yield such protrusions. Enabled by a new grand canonical Monte Carlo method for membrane simulation, our work reveals a cascade of dynamical transitions from individually polymerizing filaments to highly cooperatively growing bundles as a dynamical bottleneck to tube formation. Filament network organization as well as adhesion points to the membrane, which bias filament bending and constrain membrane height fluctuations, screen the effective attractive interactions between filaments, significantly delaying bundling and tube formation.     

Experimental determination of folding factor of benign breast cancer cell (MCF10A) and its effect on contact models and 3D manipulation of biological particles

Plasma membrane of most cells is not smooth. The surfaces of both small and large micropermeable cells are folded and corrugated which makes mammalian cells to have a larger membrane surface than the supposed ideal mode, that is, the smooth sphere of the same volume. Since cancer is an anthropic disease, cancer cells tend to have a larger membrane area than normal cells. Therefore, cancer cells have higher folding factor and larger radius than normal and healthy cells. On the other hand, the prevalence of breast cancer has prompted researchers to improve the treatment options raised for the disease in the past. In this paper, the impact of folding factor of the cell surface has been investigated. Considering that AFM is one of the most effective tools in performing the tests at micro- and nanoscales, it was used to determine the topography of MCF10 cells and then the resulting images and results were used to experimentally extract the folding factor of cells. By applying this factor in the Hertz, DMT and JKR contact models in the elastic and viscoelastic states, these models have been modified and the simulation of the three models shows that the simulation results are closer to the experimental results by considering the folding in the calculations. Additionally, the simulation of 3D manipulation has been done in both elastic and viscoelastic states with and without consideration of folding. Finally, the results were compared to investigate the effects of folding of the cell surface to the critical force and critical time of sliding and rolling in contact with the substrate and AFM tip in the 3D manipulation model.     

Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles

Domain formation is modeled on the surface of giant unilamellar vesicles using a Landau field theory model for phase coexistence coupled to elastic deformation mechanics (e.g., membrane curvature). Smooth particle applied mechanics, a form of smoothed particle continuum mechanics, is used to solve either the time-dependent Landau-Ginzburg or Cahn-Hilliard free-energy models for the composition dynamics. At the same time, the underlying elastic membrane is modeled using smooth particle applied mechanics, resulting in a unified computational scheme capable of treating the response of the composition fields to arbitrary deformations of the vesicle and vice versa. The results indicate that curvature coupling, along with the field theory model for composition free energy, gives domain formations that are correlated with surface defects on the vesicle. In the case that external deformations are included, the domain structures are seen to respond to such deformations. The present simulation capability provides a significant step forward toward the simulation of realistic cellular membrane processes.     

Molecular dynamics simulations and membrane protein structure quality

Despite a growing repertoire of membrane protein structures (currently ∼120 unique structures), considerations of low resolution and crystallization in the absence of a lipid bilayer require the development of techniques to assess the global quality of membrane protein folds. This is also the case for assessment of, e.g. homology models of human membrane proteins based on structures of (distant) bacterial homologues. Molecular dynamics (MD) simulations may be used to help evaluate the quality of a membrane protein structure or model. We have used a structure of the bacterial ABC transporter MsbA which has the correct transmembrane helices but an incorrect handedness and topology of their packing to test simulation methods of quality assessment. An MD simulation of the MsbA model in a lipid bilayer is compared to a simulation of another bacterial ABC transporter, BtuCD. The latter structure has demonstrated good conformational stability in the same bilayer environment and over the same timescale (20 ns) as for the MsbA model simulation. A number of comparative analyses of the two simulations were performed to assess changes in the structural integrity of each protein. The results show a significant difference between the two simulations, chiefly due to the dramatic structural deformations of MsbA. We therefore propose that MD could become a useful quality control tool for membrane protein structural biology. In particular, it provides a way in which to explore the global conformational stability of a model membrane protein fold.     

Coarse-grained Brownian ratchet model of membrane protrusion on cellular scale

Membrane protrusion is a mechanochemical process of active membrane deformation driven by actin polymerization. Previously, Brownian ratchet (BR) was modeled on the basis of the underlying molecular mechanism. However, because the BR requires a priori load that cannot be determined without information of the cell shape, it cannot be effective in studies in which resultant shapes are to be solved. Other cellular-scale models describing the protrusion have also been suggested for modeling a whole cell; however, these models were not developed on the basis of coarse-grained physics representing the underlying molecular mechanism. Therefore, to express the membrane protrusion on the cellular scale, we propose a novel mathematical model, the coarse-grained BR (CBR), which is derived on the basis of nonequilibrium thermodynamics theory. The CBR can reproduce the BR within the limit of the quasistatic process of membrane protrusion and can estimate the protrusion velocity consistently with an effective elastic constant that represents the state of the energy of the membrane. Finally, to demonstrate the applicability of the CBR, we attempt to perform a cellular-scale simulation of migrating keratocyte in which the proposed CBR is used for the membrane protrusion model on the cellular scale. The results show that the experimentally observed shapes of the leading edge are well reproduced by the simulation. In addition, The trend of dependences of the protrusion velocity on the curvature of the leading edge, the temperature, and the substrate stiffness also agreed with the other experimental results. Thus, the CBR can be considered an appropriate cellular-scale model to express the membrane protrusion on the basis of its underlying molecular mechanism.     

Interaction of the Antimicrobial Peptide Polymyxin B1 with Both Membranes of E. coli: A Molecular Dynamics Study

Antimicrobial peptides are small, cationic proteins that can induce lysis of bacterial cells through interaction with their membranes. Different mechanisms for cell lysis have been proposed, but these models tend to neglect the role of the chemical composition of the membrane, which differs between bacterial species and can be heterogeneous even within a single cell. Moreover, the cell envelope of Gram-negative bacteria such as E. coli contains two membranes with differing compositions. To this end, we report the first molecular dynamics simulation study of the interaction of the antimicrobial peptide, polymyxin B1 with complex models of both the inner and outer membranes of E. coli. The results of >16 microseconds of simulation predict that polymyxin B1 is likely to interact with the membranes via distinct mechanisms. The lipopeptides aggregate in the lipopolysaccharide headgroup region of the outer membrane with limited tendency for insertion within the lipid A tails. In contrast, the lipopeptides readily insert into the inner membrane core, and the concomitant increased hydration may be responsible for bilayer destabilization and antimicrobial function. Given the urgent need to develop novel, potent antibiotics, the results presented here reveal key mechanistic details that may be exploited for future rational drug development.     

The effects of calcium++ on bursting neurons. A modeling study.

Many observed effects of ionized calcium on bursting pacemaker neurons may be accounted for by assuming that calcium has multiple effects on the membrane conductance mechanisms. Two models are proposed that represent extreme cases of a set of possible models for these multiple effects. Both models are a priori designed to account for directly observed phenomena, and both are found to be able to simulate a posteriori certain observed phenomena, including persistent inactivation, increasing spike width, and decreasing after-polarization. Experimental tests are proposed for the decision of validity between the set of models discussed and the null hypothesis, and for the decision of validity between the two models themselves. Extensions of the models are discussed. One of these extensions leads to a simulation of the behavior of the cell when placed in a calcium-free bathing medium.     

A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayers

We present an elastic Hamiltonian for membrane energetics that captures bilayer undulation and peristaltic deformations over all wavelengths, including the short wavelength protrusion regime. The model implies continuous functional forms for thermal undulation and peristaltic amplitudes as a function of wavelength and predicts previously overlooked relationships between these curves. Undulation and peristaltic spectra display excellent agreement with data from both atomistic and coarse-grained models over all simulated length scales. Additionally, the model accurately predicts the bilayer's response to a cylindrical protein inclusion as observed in coarse-grained simulation. This elastic response provides an explanation for gramicidin ion channel lifetime versus membrane thickness data that requires no fit constants. The physical parameters inherent to this picture may be expressed in terms of familiar material properties associated with lipid monolayers. Inclusion of a finite monolayer spontaneous curvature is essential to obtain fully consistent agreement between theory and the full range of available simulation/experimental data.     

A novel two-layer, coupled finite element approach for modeling the nonlinear elastic and viscoelastic behavior of human erythrocytes

A novel finite element approach is presented to simulate the mechanical behavior of human red blood cells (RBC, erythrocytes). As the RBC membrane comprises a phospholipid bilayer with an intervening protein network, we propose to model the membrane with two distinct layers. The fairly complex characteristics of the very thin lipid bilayer are represented by special incompressible solid shell elements and an anisotropic viscoelastic constitutive model. Properties of the protein network are modeled with an isotropic hyperelastic third-order material. The elastic behavior of the model is validated with existing optical tweezers studies with quasi-static deformations. Employing material parameters consistent with literature, simulation results are in excellent agreement with experimental data. Available models in literature neglect either the surface area conservation of the RBC membrane or realistic loading conditions of the optical tweezers experiments. The importance of these modeling assumptions, that are both included in this study, are discussed and their influence quantified. For the simulation of the dynamic motion of RBC, the model is extended to incorporate the cytoplasm. This is realized with a monolithic fully coupled fluid-structure interaction simulation, where the fluid is described by the incompressible Navier–Stokes equations in an arbitrary Lagrangian Eulerian framework. It is shown that both membrane viscosity and cytoplasm viscosity have significant influence on simulation results. Characteristic recovery times and energy dissipation for varying strain rates in dynamic laser trap experiments are calculated for the first time and are found to be comparable with experimental data.     

跨膜蛋白CD3ε与磷脂酰肌醇二磷酸在脂筏域体系中蛋白质-脂质相互作用的粗粒化模拟研究

细胞膜局部区域可形成富含饱和脂质、胆固醇、鞘脂的脂筏域作为其信号转导调控平台。传统实验手段在研究脂筏及其功能时受到系统复杂度高及区域结构瞬时性强等制约。近年来,分子动力学模拟技术为细胞膜的组织原则提供了重要的理论支撑,从简单的单一组分模型到多组分系统转变,最终形成了越来越多的细胞膜仿真模型。其中,粗粒化模拟由于其简化模型,可大副拓展模拟体系的复杂程度与模拟时间,在细胞膜以及蛋白质-脂质相互作用相关研究中得到了广泛应用。本文采用MARTINI粗粒化力场模拟,构建了一种含有阴离子脂质磷脂酰肌醇二磷酸(phosphatidylinositol diphosphate, PIP2)的混合膜体系。模拟结果表明,该体系在适当温度及饱和度条件下,能自发分层形成脂筏域;膜厚度、膜组分分布、膜组分流动性等多种参数均表明,脂筏结构形成且符合其结构特征;少量PIP2添加不影响分层特性且PIP2对脂筏具有显著亲和性。此外,利用该模型以跨膜信号蛋白CD3ε为例研究了脂筏域体系中蛋白质-脂质相互作用。结果表明,PIP2-CD3ε胞内区相互作用可能是脂筏招募CD3ε的驱动力,且该过程可受钙离子调控。本工作体现了粗粒化模拟在仿真膜相关研究中的巨大优势及良好应用前景。     

A Comparative Study on the Ability of Two Implicit Solvent Lipid Models to Predict Transmembrane Helix Tilt Angles

Free-energy profiles describing the relative orientation of membrane proteins along predefined coordinates can be efficiently calculated by means of umbrella simulations. Such simulations generate reliable orientational distributions but are difficult to converge because of the very long equilibration times of the solvent and the lipid bilayer in explicit representation. Two implicit lipid membrane models are here applied in combination with the umbrella sampling strategy to the simulation of the transmembrane (TM) helical segment from virus protein U (Vpu). The models are used to study both orientation and energetics of this α-helical peptide as a function of hydrophobic mismatch. We observe that increasing the degree of positive hydrophobic mismatch increased the tilt angle of Vpu. These findings agree well with experimental data and as such validate the solvation models used in this study.     

New direct dynamic models of protein interactions coupled to photosynthetic electron transport reactions

This review covers the methods of computer simulation of protein interactions taking part in photosynthetic electron transport reactions. A direct multiparticle simulation method that simulates reactions describing interactions of ensembles of molecules in the heterogeneous interior of a cell is developed. In the models, protein molecules move according to the laws of Brownian dynamics, mutually orient themselves in the electrical field, and form complexes in the 3D scene. The method allows us to visualize the processes of molecule interactions and to calculate the rate constants for protein complex formation reactions in the solution and in the photosynthetic membrane. Three-dimensional multiparticle computer models for simulating the complex formation kinetics for plastocyanin with photosystem I and cytochrome bf complex, and ferredoxin with photosystem I and ferredoxin:NADP⁺-reductase are considered. Effects of ionic strength are featured for wild type and mutant proteins. The computer multiparticle models describe nonmonotonic dependences of complex formation rates on the ionic strength as the result of long-range electrostatic interactions.     

Shedding light on the puzzle of drug-membrane interactions: Experimental techniques and molecular dynamics simulations

Lipid membranes work as barriers, which leads to inevitable drug-membrane interactions in vivo. These interactions affect the pharmacokinetic properties of drugs, such as their diffusion, transport, distribution, and accumulation inside the membrane. Furthermore, these interactions also affect their pharmacodynamic properties with respect to both therapeutic and toxic effects. Experimental membrane models have been used to perform in vitro assessment of the effects of drugs on the biophysical properties of membranes by employing different experimental techniques. In in silico studies, molecular dynamics simulations have been used to provide new insights at an atomistic level, which enables the study of properties that are difficult or even impossible to measure experimentally. Each model and technique has its advantages and disadvantages. Hence, combining different models and techniques is necessary for a more reliable study. In this review, the theoretical backgrounds of these (in vitro and in silico) approaches are presented, followed by a discussion of the pharmacokinetic and pharmacodynamic properties of drugs that are related to their interactions with membranes. All approaches are discussed in parallel to present for a better connection between experimental and simulation studies. Finally, an overview of the molecular dynamics simulation studies used for drug-membrane interactions is provided.     

Membrane simulations: bigger and better?

Molecular dynamics simulations of biological membranes have come of age. Simulations of pure lipid bilayers are extending our understanding of both optimal simulation procedures and the detailed structural dynamics of lipids in these systems. Simulation methods established using simple bilayer-embedded peptides are being extended to a wide range of membrane proteins and membrane protein models, and are beginning to reveal some of the complexities of membrane protein structural dynamics and their relationship to biological function.     

Coupling field theory with mesoscopic dynamical simulations of multicomponent lipid bilayers

A method for simulating a two-component lipid bilayer membrane in the mesoscopic regime is presented. The membrane is modeled as an elastic network of bonded points; the spring constants of these bonds are parameterized by the microscopic bulk modulus estimated from earlier atomistic nonequilibrium molecular dynamics simulations for several bilayer mixtures of DMPC and cholesterol. The modulus depends on the composition of a point in the elastic membrane model. The dynamics of the composition field is governed by the Cahn-Hilliard equation where a free energy functional models the coupling between the composition and curvature fields. The strength of the bonds in the elastic network are then modulated noting local changes in the composition and using a fit to the nonequilibrium molecular dynamics simulation data. Estimates for the magnitude and sign of the coupling parameter in the free energy model are made treating the bending modulus as a function of composition. A procedure for assigning the remaining parameters in the free energy model is also outlined. It is found that the square of the mean curvature averaged over the entire simulation box is enhanced if the strength of the bonds in the elastic network are modulated in response to local changes in the composition field. We suggest that this simulation method could also be used to determine if phase coexistence affects the stress response of the membrane to uniform dilations in area. This response, measured in the mesoscopic regime, is already known to be conditioned or renormalized by thermal undulations.     

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to compute the biophysical stimuli generated within a cell under mechanical loading. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of atomic force microscopy indentation was performed and results showed a force/indentation simulation with the range of experimental results. A parametric analysis of both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age) was performed. Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain as compared with young cells, but the difference, surprisingly, is very small and may not be measurable experimentally. Ageing is predicted to have a more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models; correspondence between computed and measured force/displacement behaviours provides a high-level validation of the model. Regarding the effect of ageing, the models suggest only small, although possibly physiologically significant, differences in internal biophysical stimuli between normal and aged cells.     

Markov state modeling of membrane transport proteins

The flux of ions and molecules in and out of the cell is vital for maintaining the basis of various biological processes. The permeation of substrates across the cellular membrane is mediated through the function of specialized integral membrane proteins commonly known as membrane transporters. These proteins undergo a series of structural rearrangements that allow a primary substrate binding site to be accessed from either side of the membrane at a given time. Structural insights provided by experimentally resolved structures of membrane transporters have aided in the biophysical characterization of these important molecular drug targets. However, characterizing the transitions between conformational states remains challenging to achieve both experimentally and computationally. Though molecular dynamics simulations are a powerful approach to provide atomistic resolution of protein dynamics, a recurring challenge is its ability to efficiently obtain relevant timescales of large conformational transitions as exhibited in transporters. One approach to overcome this difficulty is to adaptively guide the simulation to favor exploration of the conformational landscape, otherwise known as adaptive sampling. Furthermore, such sampling is greatly benefited by the statistical analysis of Markov state models. Historically, the use of Markov state models has been effective in quantifying slow dynamics or long timescale behaviors such as protein folding. Here, we review recent implementations of adaptive sampling and Markov state models to not only address current limitations of molecular dynamics simulations, but to also highlight how Markov state modeling can be applied to investigate the structure–function mechanisms of large, complex membrane transporters.     

Accelerating membrane insertion of peripheral proteins with a novel membrane mimetic model

Characterizing atomic details of membrane binding of peripheral membrane proteins by molecular dynamics (MD) has been significantly hindered by the slow dynamics of membrane reorganization associated with the phenomena. To expedite lateral diffusion of lipid molecules without sacrificing the atomic details of such interactions, we have developed a novel membrane representation, to our knowledge, termed the highly mobile membrane-mimetic (HMMM) model to study binding and insertion of various molecular species into the membrane. The HMMM model takes advantage of an organic solvent layer to represent the hydrophobic core of the membrane and short-tailed phospholipids for the headgroup region. We demonstrate that using these components, bilayer structures are formed spontaneously and rapidly, regardless of the initial position and orientation of the lipids. In the HMMM membrane, lipid molecules exhibit one to two orders of magnitude enhancement in lateral diffusion. At the same time, the membrane atomic density profile of the headgroup region produced by the HMMM model is essentially identical to those obtained for full-membrane models, indicating the faithful representation of the membrane surface by the model. We demonstrate the efficiency of the model in capturing spontaneous binding and insertion of peripheral proteins by using the membrane anchor (γ-carboxyglutamic-acid-rich domain; GLA domain) of human coagulation factor VII as a test model. Achieving full insertion of the GLA domain consistently in 10 independent unbiased simulations within short simulation times clearly indicates the robustness of the HMMM model in capturing membrane association of peripheral proteins very efficiently and reproducibly. The HMMM model will provide significant improvements to the current all-atom models by accelerating lipid dynamics to examine protein-membrane interactions more efficiently.