Molecular dynamics simulations of a mixed DOPC/DOPG bilayer

We have constructed a mixed dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylglycerol bilayer (DOPG) bilayer utilizing MD simulations. The aim was to develop an explicit molecular model of biological membranes as a complementary technique to neutron diffraction studies that are well established within the group. A monolayer was constructed by taking a previously customized PDB file of each molecule and arranging them in a seven rows of ten molecules and duplicated and rotated to form a bilayer. The 140-molecule bilayer contained 98 DOPC molecules and 42 DOPG molecules, in a 7:3 ratio in favour of DOPC. Sodium counter ions were placed near the phosphate moiety of DOPG to counteract the negative charge of DOPG. This was representative of the lipid ratio in a sample used for neutron diffraction. The MD package GROMACS was used for confining the bilayer in a triclinic box, adding Simple Polar Charge water molecules, energy minimization (EM). The bilayer/solvent system was subjected to EM using the steepest descent method to nullify bad contacts and reduce the potential energy of the system. Subsequent MD simulation using an initial NVT (constant number of particles, volume and temperature) for a 20 ps MD run followed by a NPT (constant number of particles, pressure and temperature) was performed. Structural parameters including volume of lipid, area of lipid, order parameter of the fatty acyl carbons and electron density profiles generated by the MD simulation were verified with values obtained from experimental data of DOPC, as there are no comparable experimental data available for the mixed bilayer.     

Molecular dynamics simulations of a mixed DOPC/DOPG bilayer

The European Physical Journal E - We have constructed a mixed dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylglycerol bilayer (DOPG) bilayer utilizing MD simulations. The aim was to...     

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications.     

Lipid Bilayer Interactions of Amyloidogenic N-Terminal Fragment of Apolipoprotein A-I Probed by Förster Resonance Energy Transfer and Molecular Dynamics Simulations

The effects of one of the amyloidogenic mutations of apolipoprotein A-I (apoA-I), G26R, on the thermal stability, structural dynamics and lipid-associating properties of the 1–83 N-terminal fragment of apoA-I (A83) have been investigated using the Förster resonance energy transfer (FRET) and molecular dynamics (MD) simulation. The measurements of FRET between the tryptophan residues of the single Trp variants of A83 as donors and the membrane-incorporated fluorescent probe 4-dimethylaminochalcone as an acceptor provided evidence for a less depth of A83/G26R penetration into phosphatidylcholine (PC) bilayer compared to WT counterpart. The unfolding MD simulations showed that G26R mutation destabilizes the overall structure of A83, with individual alpha-helices differing in their thermal stability. The MD simulations performed at physiological temperature revealed that A83 and A83/G26R differ in their conformational behavior in an aqueous solution, PC and PC/Cholesterol bilayers. These findings may prove of importance for deeper understanding of the key determinants of apoA-I amyloidogenesis.     

Structure of symmetric and asymmetric "ripple" phases in lipid bilayers

We reproduce the symmetric and asymmetric "rippled" P(beta') states of lipid membranes by Monte Carlo simulations of a coarse-grained molecular model for lipid-solvent mixtures. The structure and properties compare favorably with experiments. The asymmetric ripple state is characterized by a periodic array of fully interdigitated "defect" lines. The symmetric ripple state maintains a bilayer structure, but is otherwise structurally similar. The main force driving the formation of both ripple states is the propensity of lipid molecules with large head groups to exhibit splay.     

Subterahertz Longitudinal Phonon Modes Propagating in a Lipid Bilayer Immersed in an Aqueous Medium

The properties of subterahertz longitudinal acoustic phonon modes in the hydrophobic region of a lipid bilayer immersed in a compressible viscous aqueous medium are investigated theoretically. An approximate expression is obtained for the Mandelstam–Brillouin components of the dynamic structure factor of a bilayer. The analysis is based on a generalized hydrodynamic model of the “two-dimensional lipid bilayer + three-dimensional fluid medium” system, as well as on known sharp estimates for the frequencies and lifetimes of long-wavelength longitudinal acoustic phonons in a free hydrated lipid bilayer and in water, obtained from inelastic X-ray scattering experiments and molecular dynamics simulations. It is shown that, for characteristic values of the parameters of the membrane system, subterahertz longitudinal phonon-like excitations in the hydrophobic part of the bilayer are underdamped. In this case, the contribution of the viscous flow of the aqueous medium to the damping of a longitudinal membrane mode is small compared with the contribution of the lipid bilayer. Quantitative estimates of the damping ratio agree well with the experimental results for the vibration mode of the enzyme lysozyme in aqueous solution [1]. It is also shown that a coupling between longitudinal phonon modes of the bilayer and relaxation processes in its fluid environment gives rise to an additional peak in the scattering spectrum, which corresponds to a non-propagating mode.     

Influences of the Structure of Lipids on Thermal Stability of Lipid Membranes

The binding free energy (BFE) of lipid to lipid bilayer is a critical factor to determine the thermal or mechanical stability of the bilayer. Although the molecular structure of lipids has significant impacts on BFE of the lipid, there lacks a systematic study on this issue. In this paper we use coarse-grained molecular dynamics simulation to investigate this problem for several typical phospholipids. We find that both the tail length and tail unsaturation can significantly affect the BFE of lipids but in opposite way, namely, BFE decreases linearly with increasing length, but increases linearly with addition of unsaturated bonds. Inspired by the specific structure of cholesterol which is a crucial component of biomembrane, we also find that introduction of carbo-ring-like structures to the lipid tail or to the bilayer may greatly enhance the stability of the bilayer. Our simulation also shows that temperature can influence the bilayer stability and this effect can be significant when the bilayer undergoes phase transition. These results may be helpful to the design of liposome or other self-assembled lipid systems.     

Diffusion of gases across lipid membranes with OmpA channel: a molecular dynamics study

Molecular transport across biological membranes occurs in a range of important chemical and biological processes. The biological membrane can usually be modelled as a phospholipid bilayer, but to correctly represent biological transport, the embedded transmembrane proteins must also be included. In previous molecular simulation studies on transport of small gas molecules in dipalmitoylphosphatidylcholine (DPPC) bilayer membrane, a coarse-grained model was used to provide direct insight into collective phenomena in biological membranes. Coarse graining allowed investigation of longer time and length scales by reducing the degrees of freedom and employing suitable potentials. In this work, membranes that include transmembrane proteins are modelled. This allows one to compare the molecular transport across a lipid membrane with and without the assistance of transmembrane channels. Outer membrane protein A (OmpA) – a porin from Escherichia coli with a small pore size – was chosen in this study because its detailed structure is known, it has high stability and is known to form a nonspecific diffusion channel that permits the penetration of various solutes. In this work the pore characteristics and interaction between lipid and protein were investigated and transport of water and other small gas molecules within the channel were studied. The MD simulation results obtained are compared with previous simulation results and available experimental data. The results obtained from this study will lead to better understanding of protein functionality and advance the development of biochips and drug delivery systems.     

Permeation of nanocrystals across lipid membranes

Biological membranes are one of the major structural elements of cells, and play a key role as a selective barrier and substrate for many proteins that facilitate transport and signaling processes. Understanding the structural and mechanical properties of lipid membranes during permeation of nanomaterials is of prime importance in determining the toxicity of nanomaterials to living cells. It has been shown that the interaction between lipid membranes and nanomaterials and the disruption of lipid membranes are often determined by physicochemical properties of nanomaterials, such as size, shape and surface composition. In this work, molecular dynamic simulations were carried out using various sizes of nanocrystals as a probe to explore the transport of nanomaterials across dipalmitoylphosphatidylcholine (DPPC) bilayers and the changes in the structural and mechanical properties of DPPC bilayers during the permeation. A coarse-grained model was used to provide insight at large time and length scales. In this work, an external driving force helps the nanocrystals across the lipid bilayer. The minimum forces needed to penetrate the model membrane and the interaction of nanocrystals and lipid bilayers were investigated in simulations. The elastic and dynamic properties of lipid bilayers, including the local and bulk properties during the permeation of the nanocrystals, which are of considerable fundamental interest, were also studied. The findings described will lead to better understanding of nanomaterial–lipid membrane interactions and the mechanical and dynamic properties of lipid membranes under permeation.     

Fluorescence Study of Lipid Bilayer Interactions of Eu(III) Coordination Complexes

The interaction between Eu(III) tris-β-diketonato coordination complexes (EC), displaying antitumor activity, and lipid vesicles composed of zwitterionic lipid phosphatidylcholine has been studied using fluorescence spectroscopy techniques. To characterize EC-membrane binding, several fluorescent probes, including pyrene, Prodan and 1,6-diphenyl-1,3,5-hexatriene, have been employed. It has been found that EC display effective partitioning into lipid phase, giving rise to structural modifications of both polar and nonpolar lipid bilayer regions, viz. enhancement of membrane hydration and increase in tightness of lipid chain packing. The fact that EC accumulating in lipid bilayer are incapable of inducing significant disruption of membrane structural integrity creates strong prerequisites for development of liposomal nanocarriers of these potential antitumor drugs. Such a possibility is also corroborated by the observation that EC membrane incorporation does not prevent lipid bilayer partitioning of long-wavelength squaraine dyes which represent promising candidates for visualization of liposome biodistribution.     

Molecular dynamics simulations of the effects of sodium dodecyl sulfate on lipid bilayer

Molecular dynamics simulations have been performed on the fully hydrated lipid bilayer with different concentrations of sodium dodecyl sulfate(SDS). SDS can readily penetrate into the membrane. The insertion of SDS causes a decrease in the bilayer area and increases in the bilayer thickness and lipid tail order, when the fraction of SDS is less than 28%.Through calculating the binding energy, we confirm that the presence of SDS strengthens the interactions among the DPPC lipids, while SDS molecules act as intermedia. Both the strong hydrophilic interactions between sulfate and phosphocholine groups and the hydrophobic interactions between SDS and DPPC hydrocarbon chains contribute to the tight packing and ordered alignment of the lipids. These results are in good agreement with the experimental observations and provide atomic level information that complements the experiments.     

Lateral pressure profile in lipid membranes with curvature: Analytical calculation

An analytical expression is obtained for the lateral pressure profile in the hydrophobic part of a lipid bilayer of finite curvature. Calculations are carried out within a microscopic model of a lipid bilayer, according to which the energy of a lipid chain represents the energy of a flexible string of finite thickness and the interaction between lipid chains is considered as a steric (entropic) repulsion. This microscopic model allows one to obtain an expression for the distribution of lateral pressure in membranes with given curvature if one considers the bending of a membrane as a small deviation from a flat conformation and applies perturbation theory in the small parameter L ₀ J, where L ₀ is the hydrophobic thickness of a monolayer and J is the mean curvature of the lipid bilayer. The resulting pressure profile depends on the microscopic parameters of the lipid chain: the bending modulus of the lipid chain, incompressible area per lipid chain, and the thickness of a flat monolayer. The coefficient of entropic repulsion between lipids is calculated self-consistently. The analytical results obtained for the lateral pressure distribution are in qualitative agreement with molecular dynamic simulations.     

Examining Protein-Lipid Interactions in Model Systems with a New Squarylium Fluorescent Dye

The applicability of newly synthesized squarylium dye Sq to probing the changes in physical characteristics of lipid bilayer on the formation of protein-lipid complexes has been evaluated. Lipid vesicles composed of zwitterionic phospholipid phosphatidylcholine (PC) and its mixtures with positively charged detergent cetyltrimethylammonium bromide (CTAB), anionic phospholipid cardiolipin (CL), and cholesterol (Chol) were employed as lipid component of model membrane systems while protein constituent was represented by lysozyme (Lz). Fluorescence intensity of Sq was found to decrease on Lz association with lipid bilayer. This effect was observed in all kinds of model systems suggesting that Sq is sensitive to modification of lipid bilayer physical properties on hydrophobic protein-lipid interactions. It was found that Sq spectral response to variations in Chol content depends on relative contributions of electrostatic and hydrophobic components of Lz-membrane binding.     

The New Fluorescent Membrane Probe Ahba: A Comparative Study with the Largely Used Laurdan

Lipid bilayers have been largely used as model systems for biological membranes. Hence, their structures, and alterations caused on them by biological active molecules, have been the subject of many studies. Accordingly, fluorescent probes incorporated into lipid bilayers have been extensively used for characterizing lipid bilayer fluidity and/or polarity. However, for the proper analysis of the alterations undergone by a membrane, a comprehensive knowledge of the fluorescent properties of the probe is fundamental. Therefore, the present work compares fluorescent properties of a relative new fluorescent membrane probe, 2-amino-N-hexadecyl-benzamide (Ahba), with the largely used probe 6-dodecanoyl-N,N-dimethyl-2-naphthylamine (Laurdan), using both static and time resolved fluorescence. Both Ahba and Laurdan have the fluorescent moiety close to the bilayer surface; Ahba has a rather small fluorescent moiety, which was shown to be very sensitive to the bilayer surface pH. The main goal was to point out the fluorescent properties of each probe that are most sensitive to structural alterations on a lipid bilayer. The two probes were incorporated into bilayers of the well-studied zwitterionic lipid dimyristoyl phosphatidylcholine (DMPC), which exhibits a gel-fluid transition around 23 °C. The system was monitored between 5 and 50 °C, hence allowing the study of the two different lipid structures, the gel and fluid bilayer phases, and the transition between them. As it is known, the fluorescent emission spectrum of Laurdan is highly sensitive to the bilayer gel-fluid transition, whereas the Ahba fluorescence spectrum was found to be insensitive to changes in bilayer structure and polarity, which are known to happen at the gel-fluid transition. However, both probes monitor the bilayer gel-fluid transition through fluorescence anisotropy measurements. With time-resolved fluorescence, it was possible to show that bilayer structural variations can be monitored by Laurdan excited state lifetimes changes, whereas Ahba lifetimes were found to be insensitive to bilayer structural modifications. Through anisotropy time decay measurements, both probes could monitor structural bilayer changes, but the limiting anisotropy was found to be a better parameter than the rotational correlation time. It is interesting to have in mind that the relatively small fluorophore of Ahba (o-Abz) could possibly be bound to a phospholipid hydrocarbon chain, not disturbing much the bilayer packing and being a sensitive probe for the bilayer core.     

Refined dynamic structure factor of a lipid bilayer on scales comparable to its thickness

The structural inhomogeneity of a lipid bilayer is an obstacle to applying the classical Canham–Helfrich model to describe its dynamics on nanometer length scales. In this paper, a refined expression for the free energy of a single-component lipid bilayer is used to describe the dynamics of lipid density fluctuations. In particular, the expression with a term involving the gradient of the area per lipid [8] is used for the free energy per lipid. A refined expression has been derived for the dynamic structure factor of a free lipid bilayer in the hydrodynamic region. It leads to differences in the interpretation and values of the bilayer parameters in comparison with the standard model.     

Improved beam theory for multilayer graphene nanoribbons with interlayer shear effect

The bending of multilayer graphene nanoribbons incorporating the effect of interlayer shear is analyzed in this Letter. An improved beam theory is adopted and extended in which the in-plane extension of each layer is also taken into account. The governing equations for bilayer and trilayer graphene nanoribbons subjected to bending are presented as illustrative examples. Exact solutions for cantilever multilayer graphene nanoribbons are derived. Compared with the molecular dynamics (MD) simulations, the present beam model predicts much better results than the previous beam model in which the in-plane extension is ignored. The current study provides a strong evidence to include the in-plane extension effect in the continuum modeling of multilayer graphene structures.     

A network of conformational transitions in an unfolding process of HP-35 revealed by high-temperature MD simulation and a Markov state model

An understanding of protein folding/unfolding processes has important implications for all biological processes, including protein degradation, protein translocation, aging, and diseases. All-atom molecular dynamics(MD) simulations are uniquely suitable for it because of their atomic level resolution and accuracy. However, limited by computational capabilities, nowadays even for small and fast-folding proteins, all-atom MD simulations of protein folding still presents a great challenge. An alternative way is to study unfolding process using MD simulations at high temperature. High temperature provides more energy to overcome energetic barriers to unfolding, and information obtained from studying unfolding can shed light on the mechanism of folding. In the present study, a 1000-ns MD simulation at high temperature(500 K)was performed to investigate the unfolding process of a small protein, chicken villin headpiece(HP-35). To infer the folding mechanism, a Markov state model was also built from our simulation, which maps out six macrostates during the folding/unfolding process as well as critical transitions between them, revealing the folding mechanism unambiguously.     

Thermal undulations of lipid bilayers relax by intermonolayer friction at submicrometer length scales

The time correlation functions of the thermal undulations of a lipid membrane have been studied by molecular dynamics simulations of a coarse-grained bilayer model. We observe a double-exponential decay, with relaxation rates in good agreement with the theory by Seifert and Langer, [Europhys. Lett. 23, 71 (1993)]. Intermonolayer friction resulting from local velocity differences between the two monolayers is shown to be the dominant dissipative mechanism for fluctuations with wave lengths below approximately -0.1 microm.     

Interactions of Fullerene (C60) and its Hydroxyl Derivatives with Lipid Bilayer: A Coarse-Grained Molecular Dynamics Simulation

Coarse-grained molecular dynamic simulations were employed to study the interactions of fullerene (C₆₀) and its hydroxyl derivatives (C₆₀(OH)_n, n?=?4, 5, 6, 8, 12, and 16) with a lipid bilayer composed of dipalmitoylphosphatidylcholine molecules. It was found that the C₆₀ moves towards the center of the bilayer and laid between central and peripheral regions of the bilayer. The potential mean force was calculated to estimate free energy profile when pulling the fullerene from its initial position to the center of the bilayer using an umbrella sampling method. Results showed that the hydrophobic region of the membrane acts as a barrier to transport a nonpolar C₆₀ molecule through the bilayer. This makes a deep minimum in the free energy profile between the center and head regions of membrane. Various numbers of polar functional groups (–OH) were then used to make derivatives of fullerene and change the hydrophilic of the molecule. It was found that optimal number of hydroxyl groups to facilitate the transportation of C₆₀(OH)_n through the bilayer is 4.     

Multiscale simulation from atomistic to continuum – coupling molecular dynamics (MD) with the material point method (MPM)

A new multiscale simulation approach is introduced that couples atomistic-scale simulations using molecular dynamics (MD) with continuum-scale simulations using the recently developed material point method (MPM). In MPM, material continuum is represented by a finite collection of material points carrying all relevant physical characteristics, such as mass, acceleration, velocity, strain and stress. The use of material points at the continuum level provides a natural connection with the atoms in the lattice at the atomistic scale. A hierarchical mesh refinement technique in MPM is presented to scale down the continuum level to the atomistic level, so that material points at the fine level in MPM are allowed to directly couple with the atoms in MD. A one-to-one correspondence of MD atoms and MPM points is used in the transition region and non-local elastic theory is used to assure compatibility between MD and MPM regions, so that seamless coupling between MD and MPM can be accomplished. A silicon single crystal under uniaxial tension is used in demonstrating the viability of the technique. A Tersoff-type, three-body potential was used in the MD simulations. The coupled MD/MPM simulations show that silicon under nanometric tension experiences, with increasing elongation in elasticity, dislocation generation and plasticity by slip, void formation and propagation, formation of amorphous structure, necking, and final rupture. Results are presented in terms of stress–strain relationships at several strain rates, as well as the rate dependence of uniaxial material properties. This new multiscale computational method has potential for use in cases where a detailed atomistic-level analysis is necessary in localized spatially separated regions whereas continuum mechanics is adequate in the rest of the material.