Molecular Dynamics Simulations of Homo-oligomeric Bundles Embedded Within a Lipid Bilayer

Using molecular dynamics simulations, we studied the structure, interhelix interactions, and dynamics of transmembrane proteins. Specifically, we investigated homooligomeric helical bundle systems consisting of synthetic α-helices with either the sequence Ac-(LSLLLSL)₃-NH₂ (LS2) or Ac-(LSSLLSL)₃-NH₂ (LS3). The LS2 and LS3 helical peptides are designed to have amphipathic characteristics that form ion channels in membrane. We simulated bundles containing one to six peptides that were embedded in palmitoyl-oleoyl-phosphatidylcholine (POPC) lipid bilayer and placed between two lamellae of water. We aim to provide a fundamental understanding of how amphipathic helical peptides interact with each other and their dynamical behaviors in different homooligomeric states. To understand structural properties, we examined the helix lengths, tilt angles of individual helices and the entire bundle, interhelix distances, interhelix cross-angles, helix hydrophobic-to-hydrophilic vector projections, and the average number of interhelix hydrophilic (serine–serine) contacts lining the pore of the transmembrane channel. To analyze dynamical properties, we calculated the rotational autocorrelation function of each helix and the cross-correlation of the rotational velocity between adjacent helices. The observed structural and dynamical characteristics show that higher order bundles containing four to six peptides are composed of multiple lower order bundles of one to three peptides. For example, the LS2 channel was found to be stable in a tetrameric bundle composed of a “dimer of dimers.” In addition, we observed that there is a minimum of two strong hydrophilic contacts between a pair of adjacent helices in the dimer to tetramer systems and only one strong hydrophilic interhelix contact in helix pairs of the pentamer and hexamer systems. We believe these results are general and can be applied to more complex ion channels, providing insight into ion channel stability and assembly.     

Lipid Configurations from Molecular Dynamics Simulations

The extent to which current force fields faithfully reproduce conformational properties of lipids in bilayer membranes, and whether these reflect the structural principles established for phospholipids in bilayer crystals, are central to biomembrane simulations. We determine the distribution of dihedral angles in palmitoyl-oleoyl phosphatidylcholine from molecular dynamics simulations of hydrated fluid bilayer membranes. We compare results from the widely used lipid force field of Berger et al. with those from the most recent C36 release of the CHARMM force field for lipids. Only the CHARMM force field produces the chain inequivalence with sn-1 as leading chain that is characteristic of glycerolipid packing in fluid bilayers. The exposure and high partial charge of the backbone carbonyls in Berger lipids leads to artifactual binding of Na⁺ ions reported in the literature. Both force fields predict coupled, near-symmetrical distributions of headgroup dihedral angles, which is compatible with models of interconverting mirror-image conformations used originally to interpret NMR order parameters. The Berger force field produces rotamer populations that correspond to the headgroup conformation found in a phosphatidylcholine lipid bilayer crystal, whereas CHARMM36 rotamer populations are closer to the more relaxed crystal conformations of phosphatidylethanolamine and glycerophosphocholine. CHARMM36 alone predicts the correct relative signs of the time-average headgroup order parameters, and reasonably reproduces the full range of NMR data from the phosphate diester to the choline methyls. There is strong motivation to seek further experimental criteria for verifying predicted conformational distributions in the choline headgroup, including the ³¹P chemical shift anisotropy and ¹⁴N and CD₃ NMR quadrupole splittings.     

Molecular Dynamics Simulations of a DMPC Bilayer Using Nonadditive Interaction Models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.     

Molecular Dynamics Simulations of Lipid Membrane Electroporation

The permeability of cell membranes can be transiently increased following the application of external electric fields. Theoretical approaches such as molecular modeling provide a significant insight into the processes affecting, at the molecular level, the integrity of lipid cell membranes when these are subject to voltage gradients under similar conditions as those used in experiments. This article reports on the progress made so far using such simulations to model membrane—lipid bilayer—electroporation. We first describe the methods devised to perform in silico experiments of membranes subject to nanosecond, megavolt-per-meter pulsed electric fields and of membranes subject to charge imbalance, mimicking therefore the application of low-voltage, long-duration pulses. We show then that, at the molecular level, the two types of pulses produce similar effects: provided the TM voltage these pulses create are higher than a certain threshold, hydrophilic pores stabilized by the membrane lipid headgroups form within the nanosecond time scale across the lipid core. Similarly, when the pulses are switched off, the pores collapse (close) within similar time scales. It is shown that for similar TM voltages applied, both methods induce similar electric field distributions within the membrane core. The cascade of events following the application of the pulses, and taking place at the membrane, is a direct consequence of such an electric field distribution.     

Dynamic Structure Factors from Lipid Membrane Molecular Dynamics Simulations

Dynamic structure factors for a lipid bilayer have been calculated from molecular dynamics simulations. From trajectories of a system containing 1024 lipids we obtain wave vectors down to 0.34 nm⁻¹, which enables us to directly resolve the Rayleigh and Brillouin lines of the spectrum. The results confirm the validity of a model based on generalized hydrodynamics, but also improves the line widths and the position of the Brillouin lines. The improved resolution shows that the Rayleigh line is narrower than in earlier studies, which corresponds to a smaller thermal diffusivity. From a detailed analysis of the power spectrum, we can, in fact, distinguish two dispersive contributions to the elastic scattering. These translate to two exponential relaxation processes in separate time domains. Further, by including a first correction to the wave-vector-dependent position of the Brillouin lines, the results agree favorably to generalized hydrodynamics even up to intermediate wave vectors, and also yields a 20% higher adiabatic sound velocity. The width of the Brillouin lines shows a linear, not quadratic, dependence to low wave vectors.     

Lipid Converter,A Framework for Lipid Manipulations in Molecular Dynamics Simulations

Construction of lipid membrane and membrane protein systems for molecular dynamics simulations can be a challenging process. In addition, there are few available tools to extend existing studies by repeating simulations using other force fields and lipid compositions. To facilitate this, we introduce Lipid Converter, a modular Python framework for exchanging force fields and lipid composition in coordinate files obtained from simulations. Force fields and lipids are specified by simple text files, making it easy to introduce support for additional force fields and lipids. The converter produces simulation input files that can be used for structural relaxation of the new membranes.     

A Molecular Dynamics Simulation Study of Nanomechanical Properties of Asymmetric Lipid Bilayer

A very important part of the living cells of biological systems is the lipid membrane. The mechanical properties of this membrane play an important role in biophysical studies. Investigation as to how the insertion of additional phospholipids in one leaflet of a bilayer affects the physical properties of the obtained asymmetric lipid membrane is of recent practical interest. In this work a coarse-grained molecular dynamics simulation was carried out in order to compute the pressure tensor, the lateral pressure, the surface tension and the first moment of lateral pressure in each leaflet of such a bilayer. Our simulations indicate that adding more phospholipids into one monolayer results in asymmetrical changes in the lateral pressure of the individual bilayer leaflets. Interestingly, it has been observed that a change in phospholipid density in one leaflet affects the physical properties of unperturbed leaflet as well. The asymmetric behavior of the physical properties of the two leaflets as a result of a change in the contribution of the various intermolecular forces in the presence of additional phospholipids may be expressed formally.     

Capsaicin Interaction with TRPV1 Channels in a Lipid Bilayer: Molecular Dynamics Simulation

Transient receptor potential vanilloid subtype 1 (TRPV1) is a heat-sensitive ion channel also involved in pain sensation, and is the receptor for capsaicin, the active ingredient of hot chili peppers. The recent structures of TRPV1 revealed putative ligand density within the S1 to S4 voltage-sensor-like domain of the protein. However, questions remain regarding the dynamic role of the lipid bilayer in ligand binding to TRPV1. Molecular dynamics simulations were used to explore behavior of capsaicin in a 1-palmitoyl-2-oleoyl phosphatidylcholine bilayer and with the target S1–S4 transmembrane helices of TRPV1. Equilibrium simulations reveal a preferred interfacial localization for capsaicin. We also observed a capsaicin molecule flipping from the extracellular to the intracellular leaflet, and subsequently able to access the intracellular TRPV1 binding site. Calculation of the potential of mean force (i.e., free energy profile) of capsaicin along the bilayer normal confirms that it prefers an interfacial localization. The free energy profile indicates that there is a nontrivial but surmountable barrier to the flipping of capsaicin between opposing leaflets of the bilayer. Molecular dynamics of the S1–S4 transmembrane helices of the TRPV1 in a lipid bilayer confirm that Y511, known to be crucial to capsaicin binding, has a distribution along the bilayer normal similar to that of the aromatic group of capsaicin. Simulations were conducted of the TRPV1 S1–S4 transmembrane helices in the presence of capsaicin placed in the aqueous phase, in the lipid, or docked to the protein. No stable interaction between ligand and protein was seen for simulations initiated with capsaicin in the bilayer. However, interactions were seen between TRPV1 and capsaicin starting from the cytosolic aqueous phase, and capsaicin remained stable in the majority of simulations from the docked pose. We discuss the significance of capsaicin flipping from the extracellular to the intracellular leaflet and mechanisms of binding site access by capsaicin.     

A Molecular Dynamics Investigation of Lipid Bilayer Perturbation by PIP2

Phosphoinositides like phosphatidylinositol 4,5-bisphosphate (PIP₂) are negatively charged lipids that play a pivotal role in membrane trafficking, signal transduction, and protein anchoring. We have designed a force field for the PIP₂ headgroup using quantum mechanical methods and characterized its properties inside a lipid bilayer using molecular dynamics simulations. Macroscopic properties such as area/headgroup, density profiles, and lipid order parameters calculated from these simulations agree well with the experimental values. However, microscopically, the PIP₂ introduces a local perturbation of the lipid bilayer. The average PIP₂ headgroup orientation of 45° relative to the bilayer normal induces a unique, distance-dependent organization of the lipids that surround PIP₂. The headgroups of these lipids preferentially orient closer to the bilayer normal. This perturbation creates a PIP₂ lipid microdomain with the neighboring lipids. We propose that the PIP₂ lipid microdomain enables the PIP₂ to function as a membrane-bound anchoring molecule.     

Lipid Membrane Structure and Dynamics Studied by All-Atom Molecular Dynamics Simulations of Hydrated Phospholipid Bilayers

Abstract

The structure and dynamics of phosphatidylcholine bilayers are examined by reviewing the results of several nanoseconds of molecular dynamics simulations on a number of bilayer and monolayer models. The lengths of these simulations, the longest single one of which was 2 nanoseconds, were sufficiently long to effectively sample many of the longer-scale motions governing the behaviour of biomembranes. These simulations reproduce many experimental observables well and provide a degree of resolution currently unavailable experimentally.     

Phase Transitions in Coarse-Grained Lipid Bilayers Containing Cholesterol by Molecular Dynamics Simulations

Coarse-grained simulations of model membranes containing mixtures of phospholipid and cholesterol molecules at different concentrations and temperatures have been performed. A random mixing without tendencies for segregation or formation of domains was observed on spatial scales corresponding to a few thousand lipids and timescales up to several microseconds. The gel-to-liquid crystalline phase transition is successively weakened with increasing amounts of cholesterol without disappearing completely even at a concentration of cholesterol as high as 60%. The phase transition temperature increases slightly depending on the cholesterol concentration. The gel phase system undergoes a transition with increasing amounts of cholesterol from a solid-ordered phase into a liquid-ordered one. In the solid phase, the amplitude of the oscillations in the radial distribution function decays algebraically with a prefactor that goes to zero at the solid-liquid transition.     

Undulation Contributions to the Area Compressibility in Lipid Bilayer Simulations

It is here shown that there is a considerable system size-dependence in the area compressibility calculated from area fluctuations in lipid bilayers. This is caused by the contributions to the area fluctuations from undulations. This is also the case in experiments. At present, such a contribution, in most cases, is subtracted from the experimental values to obtain a true area compressibility. This should also be done with the simulation values. Here, this is done by extrapolating area compressibility versus system size, down to very small (zero) system size, where undulations no longer exist. The area compressibility moduli obtained from such simulations do not agree with experimental true area compressibility moduli as well as the uncorrected ones from contemporary or earlier simulations, but tend, instead, to be ∼50% too large. As a byproduct, the bending modulus can be calculated from the slope of the compressibility modulus versus system-size. The values obtained in this way for the bending modulus are then in good agreement with experiment.     

Molecular Dynamics Simulations of Phospholipid Bilayers

Abstract

Molecular dynamics (MD) simulations at 37°C have been performed on three phospholipid bilayer systems composed of the lipids DLPE, DOPE, and DOPC. The model used included 24 explicit lipid molecules and explicit waters of solvation in the polar head group regions, together with constant-pressure periodic boundary conditions in three dimensions. Using this model, a MD simulation samples part of an infinite planar lipid bilayer. The lipid dynamics and packing behavior were characterized. Furthermore, using the results of the simulations, a number of diverse properties including bilayer structural parameters, hydrocarbon chain order parameters, dihedral conformations, electron density profile, hydration per lipid, and water distribution along the bilayer normal were calculated. Many of these properties are available for the three lipid systems chosen, making them well suited for evaluating the model and protocols used in these simulations by direct comparisons with experimental data. The calculated MD behavior, chain disorder, and lipid packing parameter, i.e. the ratio of the effective areas of hydrocarbon tails and head group per lipid (a_t/a_h), correctly predict the aggregation preferences of the three lipids observed experimentally at 37°C, namely: a gel bilayer for DLPE, a hexagonal tube for DOPE, and a liquid crystalline bilayer for DOPC. In addition, the model and conditions used in the MD simulations led to good agreement of the calculated properties of the bilayers with available experimental results, demonstrating the reliability of the simulations. The effects of the cis unsaturation in the hydrocarbon chains of DOPE and DOPC, compared to the fully saturated one in DLPE, as well as the effects of the different polar head groups of PC and PE with the same unsaturated chains on the lipid packing and bilayer structure have been investigated. The results of these studies indicate the ability of MD methods to provide molecular-level insights into the structure and dynamics of lipid assemblies.     

Molecular Dynamics Simulations of a Calmodulin-peptide Complex in Solution

Abstract

We have performed an 4-ns MD simulation of calmodulin complexed with a target peptide in explicit water, under realistic conditions of constant temperature and pressure, in the presence of a physiological concentration of counterions and using Ewald summation to avoid truncation of long-range electrostatic forces. During the simulation the system tended to perform small fluctuations around a structure similar to, but somewhat looser than the starting crystal structure. The calmodulin-peptide complex was quite rigid and did not exhibit any large amplitude domain motions such as previously seen in apo- and calcium-bound calmodulin. We analyzed the calmodulin-peptide interactions by calculating buried surface areas, CHARMM interaction energies and continuum model interaction free energies. In the trajectory, the protein surface area buried by contact with the peptide is 1373 Ų, approximately evenly divided between the calmodulin N-terminal, C-terminal and central linker regions. A majority of this buried surface, 803 ·A², comes from nonpolar residues, in contrast to the protein as a whole, for which the surface is made up of mostly polar and charged groups. Our continuum calculations indicate that the largest favorable contribution to pep- tide binding comes from burial of molecular surface upon complex formation. Electrostatic contributions are favorable but smaller in the trajectory structures, and actually unfavorable for binding in the crystal structure. Since nonpolar groups make up most of buried surface of the protein, our calculations suggest that the hydrophobic effect is the main driving force for binding the helical peptide to calmodulin, consistent with thermodynamic analysis of experimental data. Besides the burial of nonpolar surface area, secondary contributions to peptide binding come from burial of polar surface and electrostatic interactions. In the nonpolar interactions a crucial role is played by the nine methionines of calmodulin. In the electrostatic interactions the negatively charged protein residues and positively charged peptide residues play a dominant role.     

Peptide Aggregation and Pore Formation in a Lipid Bilayer: A Combined Coarse-Grained and All Atom Molecular Dynamics Study

We present a simulation study where different resolutions, namely coarse-grained (CG) and all-atom (AA) molecular dynamics simulations, are used sequentially to combine the long timescale reachable by CG simulations with the high resolution of AA simulations, to describe the complete processes of peptide aggregation and pore formation by alamethicin peptides in a hydrated lipid bilayer. In the 1-μs CG simulations the peptides spontaneously aggregate in the lipid bilayer and exhibit occasional transitions between the membrane-spanning and the surface-bound configurations. One of the CG systems at t = 1 μs is reverted to an AA representation and subjected to AA simulation for 50 ns, during which water molecules penetrate the lipid bilayer through interactions with the peptide aggregates, and the membrane starts leaking water. During the AA simulation significant deviations from the α-helical structure of the peptides are observed, however, the size and arrangement of the clusters are not affected within the studied time frame. Solid-state NMR experiments designed to match closely the setup used in the molecular dynamics simulations provide strong support for our finding that alamethicin peptides adopt a diverse set of configurations in a lipid bilayer, which is in sharp contrast to the prevailing view of alamethicin oligomers formed by perfectly aligned helical alamethicin peptides in a lipid bilayer.     

Molecular Dynamics Simulations of a Nucleosome and Free DNA

Abstract

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.     

Molecular Dynamics Simulations for Metallic Nanosystems

Nanotechnology is a crucial field for future scientific development where many different disciplines meet. Computational modelization of nanometer-sized structures is a key issue in this development because (i) it allows a considerable saving of resources and costly experimental setups intended to fabricate nanometric test devices and (ii) nowadays the study of nanometric sized systems is feasible with thoroughly designed computational codes and relatively low cost computational resources. This article describes how molecular dynamics simulations, in combination with potentials obtained in the framework of the embedded atom method, are able to describe the properties of two systems of interest for the development of future nanoelectronic devices: metallic nanowires and metallic nanofilms. Our results show that nanowire stretching results in a series of well-defined geometric structures (shells) and that thin films experiment a crystallographic phase transition for a decreasing number of layers. In both cases, good agreement with experiments is found.