Multiscale coupling of mesoscopic- and atomistic-level lipid bilayer simulations

A multiscale method is presented to bridge between the atomistic and mesoscopic membrane systems. The atomistic model in this case is the united atom dimyristoylphosphatidylcholine membrane system, although the method is completely general. Atomistic molecular dynamics provides the expansion modulus which is used to parametrize a mesoscopic elastic membrane model. The resulting elastic membrane model, including explicit mesoscopic solvent, shows appropriate static and dynamic undulation behaviors. Large membranes of approximately 100 nm in length can then be easily simulated using the mesoscopic membrane system. The critical feedback from the mesoscopic system back down to the atomistic-scale system is accomplished by bridging the stress (or surface tension) of a small region in the mesoscopic membrane to the corresponding atomistic membrane system. Because of long length-scale modes of membranes such as undulation and buckling, the local tension responds differently from the frame tension, when subjected to external perturbations. The effect of these membrane modes is shown for the stress response of a local membrane region and therefore the atomistic membrane system. In addition, certain equilibrium static and dynamic properties of stand-alone and multiscale coupled systems are presented for several different membrane sizes. Although static properties such as two-dimensional pair-correlation function and order parameters show no noticeable discrepancy for the different systems, lipid self-diffusion and the rotational relaxation of lipid dipoles have a strong dependence on the membrane size (or long-wavelength membrane motions), which is properly modeled by the present multiscale method.     

耗散粒子动力学模拟Nafion膜和PVA/Nafion共混膜的介观结构

采用耗散粒子动力学模拟方法研究了水化Nafion膜和水化聚乙烯醇(PVA)/Nafion共混膜的微结构.模拟结果表明水化Nafion膜和水化PVA/Nafion共混膜均能形成相分离的微结构.在水化Nafion膜中,水与磺酸根混合形成管状的水团簇.随着膜内水含量增多,管状水团簇的尺寸逐渐变大并在膜内形成连续的水通道.在水化PVA/Nafion共混膜中,PVA、水、磺酸根混合形成亲水性区域.共混膜中PVA的质量分数和水含量共同影响膜的微结构.当膜中PVA质量分数较低时,PVA主要分布在Nafion的磺酸根基团周围;PVA质量分数升高后,PVA会在膜内单独成一相.当膜中的水含量相对较低时,水分子会溶解于PVA中,此时膜内不存在单独的水团簇;膜中的水含量增多后,膜内会形成接近于球形的水团簇.本文工作可为直接甲醇燃料电池用的PVA改性Nafion膜的开发提供参考.     

Hydrodynamic effects on spinodal decomposition kinetics in planar lipid bilayer membranes

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, domain growth in the presence of hydrodynamic interactions both within the (effectively) two-dimensional membrane and in the three-dimensional solvent in which the membrane is immersed has received little attention. In this work, we explore the role of hydrodynamic effects on spinodal decomposition kinetics via continuum simulations of a convective Cahn-Hilliard equation for membrane composition coupled to the Stokes equation. Our approach explicitly includes hydrodynamics both within the planar membrane and in the three-dimensional solvent in the viscously dominated flow regime. Numerical simulations reveal that dynamical scaling breaks down for critical lipid mixtures due to distinct coarsening mechanisms for elongated versus more isotropic compositional lipid domains. The breakdown in scaling should be readily observable in experiments on model membrane systems.     

Coarse-grain model for lipid bilayer self-assembly and dynamics: Multiparticle collision description of the solvent

A mesoscopic coarse-grain model for computationally efficient simulations of biomembranes is presented. It combines molecular dynamics simulations for the lipids, modeled as elastic chains of beads, with multiparticle collision dynamics for the solvent. Self-assembly of a membrane from a uniform mixture of lipids is observed. Simulations at different temperatures demonstrate that it reproduces the gel and liquid phases of lipid bilayers. Investigations of lipid diffusion in different phases reveals a crossover from subdiffusion to normal diffusion at long times. Macroscopic membrane properties, such as stretching and bending elastic moduli, are determined directly from the mesoscopic simulations. Velocity correlation functions for membrane flows are determined and analyzed.     

Mesoscopic description of solvent effects on polymer dynamics

Solvent effects on polymer dynamics and structure are investigated using a mesoscopic solvent model that accounts for hydrodynamic interactions among the polymer beads. The simulation method combines molecular dynamics of the polymer chain, interacting with the solvent molecules through intermolecular forces, with mesoscopic multiparticle collision dynamics for the solvent molecules. Changes in the intermolecular forces between the polymer beads and mesoscopic solvent molecules are used to vary the solvent conditions from those for good to poor solvents. Polymer collapse and expansion dynamics following changes in solvent conditions are studied for homopolymer and block copolymer solutions. The frictional properties of polymers are also investigated.     

Viscosity scaling for the glassy phase of protein folding

Although commendable progress has been made in the understanding of the physics of protein folding, a key unresolved issue is whether Kramers' diffusion model of chemical reactions is generally applicable to activated barrier crossing events during folding. To examine the solvent viscosity effect on the folding transition of native-like trapped intermediates, laser flash photolysis has been used to measure the microsecond folding kinetics of a natively folded state of CO-liganded ferrocytochrome c (M-state) in the 1-250 cP range of glycerol viscosity at pH 7.0, 20 degrees C. The single rate coefficient for the folding of the M-state to the native state of the protein (i.e., the M --> N folding process) decreases initially when the solvent viscosity is low (<10 cP), but saturates at higher viscosity, indicating that Kramers model is not general enough for scaling the viscosity dependence of post-transition folding involving glassy dynamics. Analysis based on the Grote-Hynes idea of time dependent friction in conjunction with defect diffusion dynamics can account for the observed non-Kramers scaling.     

Pores in bilayer membranes of amphiphilic molecules: coarse-grained molecular dynamics simulations compared with simple mesoscopic models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tensionless membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard disks. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two-dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential.     

Mesoscopic simulation of an ionomeric membrane based on sulfonated aromatic poly(ether ether ketone)

Mesoscopic simulation in the framework of the mesoscopic dynamics method (a version of the dynamic density functional method) was performed for a proton conducting membrane based on sulfonated aromatic poly(ether ether ketone) in a wide range of water content in the system. For the selected parametric field, the model demonstrates microphase separation of hydrophilic and hydrophobic segments of the polymer. In the bulk of the membrane, a spatial network of water channels forms, whose walls consist of polar (sulfonated) units of the macromolecule. Independent molecular dynamics simulation for one set of parameters gives close values of the structural characteristics of the membrane, which confirms the correctness of the mesoscopic model.     

Unforced translocation of a polymer chain through a nanopore: the solvent effect

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.     

制膜液黏度对单皮层PVDF中空纤维膜纺制的影响

以二甲基乙酰胺(DMAc)为溶剂,制备聚偏氟乙烯(PVDF)浓度为15%的制膜液,考察了DMAc同时作为内凝胶浴时膜结构的变化.为保持纺膜过程中的稳定性,分别考察了添加剂LiCl、水以及表面活性剂对制膜液黏度的影响.实验发现添加LiCl可以大大提高制膜液的黏度,而水作为添加剂时对黏度的影响与制膜液本身的浓度有关.在不提高制膜液浓度的基础上,通过提高制膜液黏度克服了膜在纺制过程中的不稳定问题,得到阻力较小的,指状孔贯穿的单外皮层中空纤维膜.     

Is hairpin formation in single-stranded polynucleotide diffusion-controlled?

An intriguing puzzle in biopolymer science is the observation that single-stranded DNA and RNA oligomers form hairpin structures on time scales of tens of microseconds, considerably slower than the estimated time for loop formation for a semiflexible polymer of similar length. To address the origin of the slow kinetics and to determine whether hairpin dynamics are diffusion-controlled, the effect of solvent viscosity (eta) on hairpin kinetics was investigated using laser temperature-jump techniques. The viscosity was varied by addition of glycerol, which significantly destabilizes hairpins. A previous study on the viscosity dependence of hairpin dynamics, in which all the changes in the measured rates were attributed to a change in solvent viscosity, reported an apparent scaling of relaxation times (tau(r)) on eta as tau(r) approximately eta(0.8). In this study, we demonstrate that if the effect of viscosity on the measured rates is not deconvoluted from the inevitable effect of change in stability, then separation of tau(r) into opening (tau(o)) and closing (tau(c)) times yields erroneous behavior, with different values (and opposite signs) of the apparent scaling exponents, tau(o) approximately eta(-0.4) and tau(c) approximately eta(1.5). Under isostability conditions, obtained by varying the temperature to compensate for the destabilizing effect of glycerol, both tau(o) and tau(c) scale as approximately eta(1.1+/-0.1). Thus, hairpin dynamics are strongly coupled to solvent viscosity, indicating that diffusion of the polynucleotide chain through the solvent is involved in the rate-determining step.     

A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes

Reliable computer simulations of complex biological environments such as integral membrane proteins with explicit water and lipid molecules remain a challenging task. We propose a modification of the standard generalized Born theory of homogeneous solvent for modeling the heterogeneous dielectric environments such as lipid/water interfaces. Our model allows the representation of biological membranes in the form of multiple layered dielectric regions with dielectric constants that are different from the solute cavity. The proposed new formalism is shown to predict the electrostatic component of solvation free energy with a relative error of 0.17% compared to exact finite-difference solutions of the Poisson equation for a transmembrane helix test system. Molecular dynamics simulations of melittin and bacteriorhodopsin are carried out and performed over 10 ns and 7 ns of simulation time, respectively. The center of melittin along the membrane normal in these stable simulations is in excellent agreement with the relevant experimental data. Simulations of bacteriorhodopsin started from the experimental structure remained stable and in close agreement with experiment. We also examined the free energy profiles of water and amino acid side chain analogs upon membrane insertion. The results with our implicit membrane model agree well with the experimental transfer free energy data from cyclohexane to water as well as explicit solvent simulations of water and selected side chain analogs.     

The mesoscopic modeling of the structure of a hydrated ionomeric membrane based on a sulfonated aromatic poly(ether-ether-ketone)

A proton conducting hydrated membrane on the basis of sulfonated aromatic poly(ether-ether-ketone) was modeled for the first time using dynamic density functional theory (the “mesoscopic dynamics” method). The model constructed was used to demonstrate the microphase separation of hydrophilic and hydrophobic polymer chain units in the selected region of parameters. A spatial network of water domains formed in the membrane volume. The domain walls consisted of polar (sulfonated) macromolecule units. A comparison with the well-studied Nafion-1100 membrane showed that the cross sections of water channels in the two systems had similar values. This must ensure approximately equal ionic conductivity characteristics.     

Performance of solvent-resistant membranes for non-aqueous systems: solvent permeation results and modeling

Membrane processes like reverse osmosis (RO) and nanofiltration (NF) can be low energy consuming operations as compared to the traditional chemical engineering unit operations and have been widely used for aqueous systems. Since such membrane processes are low energy consuming operations, their use in non-aqueous systems would offer considerable energy savings. Thus, the study is directed towards development and experimental verification of membrane materials and transport models to explain permeation properties of non-aqueous solvent systems. The understanding of polymer–solvent interactions is critical towards the development of suitable materials and also the prediction of the transport mechanisms.Pure solvent permeation studies were conducted to understand the mechanism of solvent transport through polymeric membranes. Different membrane materials (hydrophilic and hydrophobic) as well as different solvents (polar and non-polar) were used for the study. Pure solvent fluxes for hydrophilic membranes used showed that polar solvents (methanol, ethanol, iso-propanol) had a significantly higher flux (8–10 times) than that of the non-polar solvents (pentane, hexane, octane). On the contrary, the non-polar solvent flux was two to four times that of the polar solvents for hydrophobic membranes. For example, hexane flux at ∼13 bar through a hydrophobic silicone based NF membrane was ∼0.6×10⁻⁴ cm³/cm² s. And that through a hydrophilic aromatic polyamide based NF membrane was ∼6×10⁻⁴ cm³/cm² s. A simple model based on a solution-diffusion approach is proposed for predicting the pure solvent permeation through hydrophobic polymeric membranes. The model uses molar volume and viscosity of the solvent as parameters for predicting the pure solvent permeability. The model reasonably predicts the pure solvent permeation (R²=0.89, S.E.∼4%) for hydrophobic membranes. The model has also been experimentally verified using high solution temperatures and also literature experimental data. To extend the predictions to different membranes (hydrophilic and hydrophobic), surface energy and sorption values have been used as a parameter along with the solvent physical properties.     

Shear-induced parallel-to-perpendicular orientation transition in the amphiphilic lamellar phase: a nonequilibrium molecular-dynamics simulation study

The present work is devoted to a study of the shear-induced parallel-to-perpendicular orientation transition in the lamellar system by the large-scale nonequilibrium molecular-dynamics (NEMD) simulation. An effective generic model-A2B2 tetramer for amphiphilies is used. The NEMD simulation produces unambiguous evidence that undulation instability along the vorticity direction sets in well above a critical shear rate and grows in magnitude as the shear rate is further increased. At a certain high shear rate, the coherent undulation instability grows so large that defects are nucleated and the global lamellar monodomain breaks into several aligned lamellar domains. Subsequently layers in these domains rotate into the perpendicular orientation with the rotation of chains towards the y direction, merge into a global perpendicular-aligned lamellar monodomain, and organize into a perfect well-aligned perpendicular lamellar phase by the migration and annihilation of edge dislocations and disclinations. The macroscopic observable viscosity as a function of time or shear rate is correlated with the structural response such as the mesoscopic domain morphology and the microscopic chain conformation. The onset of undulation instability concurs with the start-up of shear-thinning behavior. During the orientation transformation at the high shear rate, the complex time-dependent thixotropic behavior is observed. The smaller viscosity in the perpendicular lamellar phase gives an energetic reason for the shear-induced orientation transition.     

Relationship between ionic conductivity of perfluorinated ionomeric membranes and nonaqueous solvent properties

Ionic conductivity and swelling data are measured for Nafion^® perfluorinated ionomeric membranes in nonaqueous solvents and solvent mixtures and correlated with solvent physical properties. The dependence of ionic conductivity on solvent uptake and cation type is examined for Nafion^® 117 membranes with a nominal equivalent weight of 1100 g/eq. The most important factors determining ionic conductivity in membranes swollen with polar nonaqueous solvents are the solvent viscosity, molar volume, donor properties, and the solvent uptake by the membrane. Ionic conductivity is generally limited by dissociation of the cation from the fixed anion site indicating that the ionomer fixed anion site basicity is the critical membrane property. Means for increasing membrane ionic conductivity are discussed.     

聚乙二醇对聚醚砜微孔膜致孔作用的研究

以聚醚砜聚乙二醇溶剂为铸膜液体系、采用干湿相转化法制备微孔滤膜,研究了各种制膜条件对膜孔径结构的影响.实验发现聚乙二醇在体系中起到分散稳定的作用,只有到浓度大于70%时,才会对铸膜液的粘度产生明显影响,聚合物在铸膜液中的溶解状态也随之改变,进而影响膜的结构.不同溶剂NMP、DMF、DMAc、DMSO等极性溶剂或固体溶剂己内酰胺均可制得开孔率较高的微孔膜,但对膜的结构和性能影响差别不大.在本研究体系中,膜的结构取决于聚乙二醇、溶剂的浓度比例关系.