Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations.

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.

Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations.

Molecular dynamics simulations of fully hydrated Dipalmitoylphosphatidylcholine bilayers, extending temporal and spatial scales by almost one order of magnitude, are presented. The present work reaches system sizes of 1024 lipids and times 10-60 ns. The simulations uncover significant dynamics and fluctuations on scales of several nanoseconds, and enable direct observation and spectral decomposition of both undulatory and thickness fluctuation modes. Although the former modes are strongly damped, the latter exhibit signs of oscillatory behavior. From this, it has been possible to calculate mesoscopic continuum properties in good agreement with experimental values. A bending modulus of 4 x 10(-20) J, bilayer area compressibility of 250-300 mN/m, and mode relaxation times in the nanosecond range are obtained. The theory of undulatory motions is revised and further extended to cover thickness fluctuations. Finally, it is proposed that thickness fluctuations is the explanation to the observed system-size dependence of equilibrium-projected area per lipid.

The effect of water on the Fe(3+)/Fe(2+) reduction potential of heme.

Hemeproteins can act as catalysts, oxygen carriers or electron conductors. The ferric/ferrous reduction potential E(m7) of iron in the center of the prosthetic group ranges from negative values for peroxidases to an extreme positive value for cytochrome a(3) with Hb and Mb in the middle [1]. Proteins exercise their influence on E(m7) in several ways: via substituents at the periphery of the chelate structure, via the proximal ligand, and via interaction with the surrounding medium, amino acid side chains, or polar solvents. Work on recombined proteins and 2,4-substituted free hemes documented that the first two effects are additive [2]. For the third effect, models of the dielectric media on a molecular level have been successfully applied [3-5]. E(m7) has also been empirically correlated to the degree of heme exposure to water [6-8]. The apoprotein/porphyrin and water/porphyrin interfaces are complementary since water molecules fill any empty space in the crevice and surround any pertinent part of heme outside the protein boundary. The present work links to this idea by a combination of statistical mechanics simulations and quantum mechanical calculations comparing heme in water with heme in an apolar environment. Our results show that polarization of the porphyrin pi-electron cloud by the field from water dipoles influences E(m7). The dominant effect of this and other determinates of iron electron availability is perturbations of delocalized electron density in the porphyrin chelate, reproduced by a model where the prosthetic group is treated as a disc of uniform electron density. The present work is also of interest since the interfacial energy constitutes the main barrier for heme-protein separation [9-11].

A fast and simple method to calculate protonation states in proteins.

A simple model for electrostatic interactions in proteins, based on a distance and position dependent screening of the electrostatic potential, is presented. It is applied in conjunction with a Monte Carlo algorithm to calculate pK(alpha) values of ionizable groups in proteins. The purpose is to furnish a simple, fast, and sufficiently accurate model to be incorporated into molecular dynamic simulations. This will allow for dynamic protonation calculations and for coupling between changes in structure and protonation state during the simulation. The best method of calculating protonation states available today is based on solving the linearized Poisson-Boltzmann equation on a finite difference grid. However, this model consumes far too much computer time to be a practical alternative. Tests are reported for fixed structures on bacteriorhodopsin, lysozyme, myoglobin, and calbindin. The studies include comparisons with Poisson-Boltzmann calculations with dielectric constants 4 and 20 inside the protein, a model with uniform dielectric constant 80 and distance-dependent dielectric models. The accuracy is comparable to that of Poisson-Boltzmann calculations with dielectric constant 20, and it is considerably better than that with epsilon = 4. The time to calculate the protonation at one pH value is at least 100 times less than that of a Poisson-Boltzmann calculation. Proteins 1999;36:474-483.

Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature.

Molecular dynamics simulations of 500 ps were performed on a system consisting of a bilayer of 64 molecules of the lipid dipalmitoylphosphatidylcholine and 23 water molecules per lipid at an isotropic pressure of 1 atm and 50 degrees C. Special attention was devoted to reproduce the correct density of the lipid, because this quantity is known experimentally with a precision better than 1%. For this purpose, the Lennard-Jones parameters of the hydrocarbon chains were adjusted by simulating a system consisting of 128 pentadecane molecules and varying the Lennard-Jones parameters until the experimental density and heat of vaporization were obtained. With these parameters the lipid density resulted in perfect agreement with the experimental density. The orientational order parameter of the hydrocarbon chains agreed perfectly well with the experimental values, which, because of its correlation with the area per lipid, makes it possible to give a proper estimate of the area per lipid of 0.61 +/- 0.01 nm2.

pK(a) calculations along a bacteriorhodopsin molecular dynamics trajectory.

Electrostatic calculations of pK(a-values) are reported along a 400 ps molecular dynamics trajectory of bacteriorhodopsin. The sensitivity of calculated pK(a) values to a number of structural factors and factors related to the modelling of the electrostatics are also studied. The results are very sensitive to the choice of internal dielectric constant of the protein (in the interval 2-4). Moreover it is important to include internal water molecules and to average over a long enough portion ( approximately 100 ps) of an equilibrium molecular dynamics trajectory. The internal waters are necessary to get an ion-counter ion complex with the Schiff base and Arg 82 protonated and the aspartic groups (85 and 212) deprotonated. The fluctuations along the MD-trajectory do not change the protonation state of internal residues at neutral pH. However, at other pH values the averaging along a trajectory maybe crucial to get correct protonation states. A relationship is found between the arginine group 82, the aspartic group 85 and the glutamate group 204. Glu 204 is protonated in the ground state but the pK(a) value decreases towards deprotonation when the chromophore isomerizes into the cis state.

Investigation of the proton release channel of bacteriorhodopsin in different intermediates of the photo cycle. A molecular dynamics study.

Molecular dynamics simulations on bacteriorhodopsin were performed starting from a conformation based on electron cryomicroscopy studies [Henderson, R., et al. (1990) J. Mol. Biol. 213, 899-929]. We examined the proton release channel in different intermediates of the bacteriorhodopsin photocycle. In the simulations of the ground state, two stable sets of conformations were observed differing in the distance of the guanidinium group of Arg82 to the Schiff base. The set of conformations in which Arg82 is located closer to the Schiff base has a lower potential energy and agrees better with experimental data than the other set. With both sets, we performed a series of simulations in which the chromophore was isomerized to different states using purposive and nonpurposive methods. The energetic consideration of the different states argues for the location of the guanidinium group of Arg82 close to the Schiff base. The results also show that no C13-C14, C14-C15 dicis conformation of the retinal occurs in the K/L-intermediate of the photocycle instead supporting the occurrence of C13-C14 cis in these intermediates. In a last series of simulations, we modeled the M-intermediate of the bacteriorhodopsin photocycle. Again, comparison to different experimental data indicates that Arg82 points toward the Schiff base. We conclude that the guanidinium group of Arg82 is located close to the Schiff base at a distance of approximately 4.5 A and stays there at least up to the M-intermediate of the photocycle.

Dynamics of proteins in different solvent systems: analysis of essential motion in lipases.

We have investigated the effect of different solvents on the dynamics of Rhizomucor miehei lipase. Molecular dynamics simulations were performed in water, methyl hexanoate, and cyclohexane. Analysis of the 400-ps trajectories showed that the solvent has a pronounced effect on the geometrical properties of the protein. The radius of gyration and total accessibility surface decrease in organic solvents, whereas the number of hydrogen bonds increases. The essential motions of the protein in different solvents can be described in a low-dimensional "essential subspace," and the dynamic behavior in this subspace correlates with the polarity of the solvent. Methyl hexanoate, which is a substrate for R. miehei lipase, significantly increases the fluctuations in the active-site loop. During the simulation, a methyl hexanoate entered the active-site groove. This observation provides insight into the possible docking mechanism of the substrate.

Structure and fluctuations of bacteriorhodopsin in the purple membrane: a molecular dynamics study.

Molecular dynamics simulations on bacteriorhodopsin were performed starting from the model structure described by Henderson et al. The simulations were gradually improved by first treating a monomer in vacuum and then adding further monomers, lipids, and water to finally simulate a unit cell of the hexagonal lattice of the purple membrane containing a trimer and lipids and water on both sides. During all simulations, the protein structure moved away from the model structure to reach a root-mean-square (r.m.s.) deviation of 2 to 3 A. In the simulations with the trimer, the structures of the three monomers differed by about the same amount and averaging over them led to an average structure with a considerably smaller r.m.s. deviation. The best average structure obtained had an r.m.s. deviation from the model structure of 1.3 A. Fluctuations of the protein, the lipids, and water were analyzed in detail. As expected, the membrane-spanning helices of the protein fluctuate less than the peripheral loops. Unexpected, however, was the finding that the fluctuations of the protein are asymmetric with respect to the midplane of the membrane. The fluctuations of the loops and the ends of the helices on the inner side of the membrane are much stronger than on the outer side. This asymmetry is also reflected by the fluctuations for the lipids, the lipids of the inner leaflet fluctuating more strongly than those of the outer leaflet. The asymmetry was observed only in the presence of water on both sides of the membrane. On the average, nine water molecules were found inside the protein, most of them undergoing exchange with external water.

Molecular dynamics simulations of an enzyme surrounded by vacuum, water, or a hydrophobic solvent.

We report on molecular dynamics simulations of a medium-sized protein, a lipase from Rhizomucor miehei, in vacuum, in water, and in a nonpolar solvent, methyl hexanoate. Depending on force field and solvent, the molecular dynamics structures obtained as averages over 150 ps had root-mean-square deviations in the range of 1.9 to 3.6 A from the crystal structure. The largest differences between the structures were in hydrogen bonding and exposed surface areas of the protein. The surface area increased in both solvents and became smaller in vacuum. The change of surface exposure varied greatly between different residues and occurred in accordance with the hydrophobicity of the residue and the nature of the solvent. The fluctuations of the atoms were largest in the external loops and agreed well with crystallographic temperature factors. Root-mean-square fluctuations were significantly smaller in the nonpolar solvents than they were in water, which is in accordance with the notion that proteins become more rigid in nonpolar solvents. In methyl hexanoate a partial opening of the lid covering the active site occurred, letting a methyl hexanoate molecule approach the active site.

Molecular dynamics study of the binding of phenylalanine stereoisomers to thermolysin.

The stereospecificity in binding of phenylalanine as inhibitor in the active site of the thermolysin, has been investigated by means of molecular dynamics simulations using free energy integration techniques. The difference in the free energy of binding was found to be 2.0 +/- 1.8 kJ/mol in favour of the D-form. This agrees with the experimental value, 2.8 kJ/mol. The result was obtained using a standard empirical force field (that of GROMOS). A different force field with 30% bigger charges (more like ab initio charges) was also tried. This resulted in less fluctuations and a more precise binding, but in a free energy difference that was clearly larger than the experimental one. The phenylalanine backbone is located close to the zinc atom and the ring stays in the hydrophobic pocket in both the cases. The two stereoisomers differ mainly in the orientation of the backbone plane with respect to the active site and the rotational state of the dihedral around the C alpha-C beta bond.

Theoretical studies of Rhizomucor miehei lipase activation.

Computational methods have been used to study the extensive conformational change of Rhizomucor miehei lipase upon activation. The present study considers the possible activation route, the energies involved and molecular interactions during the conformational change of the lipase in a hydrophobic environment. The conformational change was studied by conventional molecular dynamics methods and with a combined molecular dynamics and mechanics protocol, in which the conformational change was simulated by restraining C alpha pseudotorsional angles in small steps between the two crystallographically observed positions of the lid. In the closed conformer of the enzyme the active site is completely buried under a short helical loop, 'the lid'. The activation of the lipase consists of a movement of the lid, which results in an open conformer with an exposed active site. From the results of the simulations in the present work we suggest that the lipase in a hydrophobic environment is stabilized in the open form by electrostatic interactions.

Cholesterol in model membranes. A molecular dynamics simulation.

Molecular dynamics simulations of a model membrane with inserted cholesterol molecules have been performed to study the perturbing influence of cholesterol. In the fluid phase of a lipid bilayer at 13 mol% concentration of cholesterol, local ordering of the hydrocarbon chains is induced. This perturbation decays with the distance from the cholesterol, and the effect extends 1.25 nm. It can be monitored in several ways, e.g., by an order parameter corresponding to deuterium nuclear magnetic resonance quadrupolar splittings, by the fraction of gauche bonds, or by the local bilayer thickness. At constant surface density, the local ordering is accompanied by disordering of the bulk phase, and, consequently, the net ordering effect is small. After compressing the system laterally in accordance with experimentally known surface areas, the bulk order parameters agree with those of a pure system, and the average order parameters are in accordance with experimental data. The necessity for this lateral compression is supported by calculated lateral pressures. At lower cholesterol concentration (3%), no direct perturbing effect is observed. A smaller lateral pressure than in a pure system indicates that the system with cholesterol is expected to have a smaller surface area, which would result in an increase of the order parameters, thus accounting for the experimental observations. The lack of spatial variation is, however, puzzling and may indicate a cooperative ordering effect.

Modeling of the structure of bacteriorhodopsin. A molecular dynamics study.

Secondary structure predictions for membrane proteins are relatively reliable and permit the construction of model structures that may serve as initial conformations for molecular dynamics simulations. This might provide a scheme to predict the three-dimensional structures of membrane proteins. The feasibility of such an approach is tested for bacteriorhodopsin. We were not able to fully predict the kidney-shaped structure of bacteriorhodopsin. However, features compatible with this structure developed in a simulation starting from a circular arrangement of the seven predicted helices. When instead we started from the kidney shape, assigning the seven predicted helices in different ways to those on the structure, we could distinguish between the different assignments on the basis of energy and tilt of the helices. In this way we could select the correct assignment from a few others. For the correct assignment, the helices spontaneously adopted a tilt that agrees remarkably well with the experimental model structure derived by others. The root-mean-square deviation between our best molecular dynamics structure and the experimental model structure is 3.8 A, caused mainly by deviations in the internal degrees of freedom of the helices.

Conformation and aggregation of M13 coat protein studied by molecular dynamics.

Molecular dynamics (MD) simulations are performed on M13 coat protein, a small membrane protein for which both alpha- and beta-structures have been suggested. The simulations are started from initial conformations that are either monomers or dimers of alpha-helices or U-shaped beta-sheets. The lipid bilayer is represented by a hydrophobic potential. The results are analyzed in terms of stability, energy and secondary structure. The U-shaped beta-structure changes from a planar to a twisted form with larger twist for the monomer than the dimer. The beta-sheet is much more flexible than the alpha-helix as monitored by the root mean square (rms) fluctuations of the C alpha atoms. A comparison of the energies after 100 ps MD simulation shows that of the monomers, the alpha-helix has the lowest energy. The energy difference between alpha- and beta-structures decreases from 266 kJ/mol to 148 kJ/mol, when going from monomers to dimers. It is expected that this difference will decrease with higher aggregation numbers.

The structure of a membrane-spanning polypeptide studied by molecular dynamics.

We have performed a molecular dynamics simulation of a 46-residue segment of glycophorin which includes the hydrophobic membrane-spanning region of this protein. The presence of a membrane and of water is taken into account in a continuum approximation which makes use of phenomenological hydrophobic energies. The initial alpha-helical conformation and the membrane incorporation of the hydrophobic segment remain stable for the length of the simulation which is 100 ps. Moreover, when the hydrophobic segment is partially shifted out of the membrane, it moves back into the membrane. Superimposed on these deterministic effects one also observes thermal fluctuations in the form of bending and tilting of the membrane-spanning helix.

Lipid bilayer polypeptide interactions studied by molecular dynamics simulation.

A model membrane with a polypeptide alpha-helix inserted has been simulated by molecular dynamics at a temperature well above the gel/liquid crystalline phase transition temperature. Order parameters of the lipids and other equilibrium and dynamic quantities have been calculated. Three systems, polyglycine constrained into an alpha-helical configuration, glycophorin with similarly conformationally constrained backbone and finally glycophorin free to change its backbone conformation, have been studied. In all cases there was an ordering of the chains close to the helix. This effect was, however, much smaller for glycophorin with its rather bulky side chains than for polyglycine. The dynamics of the lipids were affected by the neighbouring helix, not drastically however. Lateral diffusion and reorientational time correlations of lipids close to the helix were slower than for the bulk ones, but not more than two or three times. Thus, we did not find any evidence of bound or frozen boundary lipids.