Molecular dynamics simulations of membrane proteins

Membrane proteins control the traffic across cell membranes and thereby play an essential role in cell function from transport of various solutes to immune response via molecular recognition. Because it is very difficult to determine the structures of membrane proteins experimentally, computational methods have been increasingly used to study their structure and function. Here we focus on two classes of membrane proteins—ion channels and transporters—which are responsible for the generation of action potentials in nerves, muscles, and other excitable cells. We describe how computational methods have been used to construct models for these proteins and to study the transport mechanism. The main computational tool is the molecular dynamics (MD) simulation, which can be used for everything from refinement of protein structures to free energy calculations of transport processes. We illustrate with specific examples from gramicidin and potassium channels and aspartate transporters how the function of these membrane proteins can be investigated using MD simulations.     

Coarse-grained molecular dynamics simulations of membrane proteins and peptides

Molecular dynamics (MD) simulations provide a valuable approach to the dynamics, structure, and stability of membrane-protein systems. Coarse-grained (CG) models, in which small groups of atoms are treated as single particles, enable extended (>100 ns) timescales to be addressed. In this study, we explore how CG-MD methods that have been developed for detergents and lipids may be extended to membrane proteins. In particular, CG-MD simulations of a number of membrane peptides and proteins are used to characterize their interactions with lipid bilayers. CG-MD is used to simulate the insertion of synthetic model membrane peptides (WALPs and LS3) into a lipid (PC) bilayer. WALP peptides insert in a transmembrane orientation, whilst the LS3 peptide adopts an interfacial location, both in agreement with experimental biophysical data. This approach is extended to a transmembrane fragment of the Vpu protein from HIV-1, and to the coat protein from fd phage. Again, simulated protein/membrane interactions are in good agreement with solid state NMR data for these proteins. CG-MD has also been applied to an M3-M4 fragment from the CFTR protein. Simulations of CFTR M3-M4 in a detergent micelle reveal formation of an alpha-helical hairpin, consistent with a variety of biophysical data. In an I231D mutant, the M3-M4 hairpin is additionally stabilized via an inter-helix Q207/D231 interaction. Finally, CG-MD simulations are extended to a more complex membrane protein, the bacterial sugar transporter LacY. Comparison of a 200 ns CG-MD simulation of LacY in a DPPC bilayer with a 50 ns atomistic simulation of the same protein in a DMPC bilayer shows that the two methods yield comparable predictions of lipid-protein interactions. Taken together, these results demonstrate the utility of CG-MD simulations for studies of membrane/protein interactions.     

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.     

Molecular dynamics simulations of heme reorientational motions in myoglobin.

Molecular dynamics simulations of 2-ns duration were performed on carbonmonoxymyoglobin and deoxymyoglobin in vacuo to study the reorientational dynamics of the heme group. The heme in both simulations undergoes reorientations of approximately 5 degrees amplitude on a subpicosecond time scale, which produce a rapid initial decay in the reorientational correlation function to about 0.99. The heme also experiences infrequent changes in average orientation of approximately 10 degrees amplitude, which lead to a larger slow decay of the reorientational correlation function over a period of hundreds of picoseconds. The simulations have not converged with respect to these infrequent transitions. However, an estimate of the order parameter for rapid internal motions of the heme from those orientations which are sampled by the simulations suggests that the subnanosecond orientational dynamics of the heme accounts for at least 30% of the unresolved initial anisotropy decay observed in the nanosecond time-resolved optical absorption experiments on myoglobin reported by Ansari et al. in a companion paper (Ansari, A., C.M. Jones, E.R. Henry, J. Hofrichter, and W.A. Eaton. 1992. Biophys. J. 64:852-868.). A more complete sampling of the accessible heme orientations would most likely increase this fraction further. The simulation of the liganded molecule also suggests that the conformational dynamics of the CO ligand may contribute significantly to discrepancies between the ligand conformation as probed by x-ray diffraction and by infrared-optical photoselection experiments. The protein back-bone explores multiple conformations during the simulations, with the largest structural changes appearing in the E and F helices, which are in contact with the heme. The variations in the heme orientation correlate with the conformational dynamics of the protein on a time scale of hundreds of picoseconds, suggesting that the heme orientation may provide a useful probe of dynamical processes in the protein.     

Molecular dynamics simulations of evolved collective motions of atoms in the myosin motor domain upon perturbation of the ATPase pocket

A crucial point for mechanical force generation in actomyosin systems is how the energy released by ATP hydrolysis in the myosin motor domain gives rise to the movement of the myosin head along the actin filament. We assumed the signal of the ATP hydrolysis to be transmitted as modulated atomic vibrations from the nucleotide-binding site throughout the myosin head, and carried out 1-ns all-atom molecular dynamics simulations for that signal transmission. We distributed the released energy to atoms located around the ATPase pocket as kinetic energies and examined how the effect of disturbance extended throughout the motor domain. The result showed that the disturbance signal extended over the motor domain in 150 ps and induced slowly varying collective motions of atoms at the actin-binding site and the junction with the neck, both of which are relevant to the movement of the myosin head along the actin filament. We also performed a principal component analysis of thermal atomic motions for the motor domain, and the first principal component was consistent with the response to the disturbance given to the ATPase pocket.     

Molecular dynamics simulations of proteins in lipid bilayers

With recent advances in X-ray crystallography of membrane proteins promising many new high-resolution structures, molecular dynamics simulations will become increasingly valuable for understanding membrane protein function, as they can reveal the dynamic behavior concealed in the static structures. Dramatic increases in computational power, in synergy with more efficient computational methodologies, now allow us to carry out molecular dynamics simulations of any structurally known membrane protein in its native environment, covering timescales of up to 0.1 micros. At the frontiers of membrane protein simulations are ion channels, aquaporins, passive and active transporters, and bioenergetic proteins.     

The consistency of large concerted motions in proteins in molecular dynamics simulations.

A detailed investigation is presented into the effect of limited sampling time and small changes in the force field on molecular dynamics simulations of a protein. Thirteen independent simulations of the B1 IgG-binding domain of streptococcal protein G were performed, with small changes in the simulation parameters in each simulation. Parameters studied included temperature, bond constraints, cut-off radius for electrostatic interactions, and initial placement of hydrogen atoms. The essential dynamics technique was used to reveal dynamic differences between the simulations. Similar essential dynamics properties were found for all simulations, indicating that the large concerted motions found in the simulations are not particularly sensitive to small changes in the force field. A thorough investigation into the stability of the essential dynamics properties as derived from a molecular dynamics simulation of a few hundred picoseconds is provided. Although the definition of the essential modes of motion has not fully converged in these short simulations, the subspace in which these modes are confined is found to be reproducible.     

Molecular dynamics simulations of N-terminal peptides from a nucleotide binding protein

Molecular dynamics (MD) simulations of N-terminal peptides from lactate dehydrogenase (LDH) with increasing length and individual secondary structure elements were used to study their stability in relation to folding. Ten simulations of 1–2 ns of different peptides in water starting from the coordinates of the crystal structure were performed. The stability of the peptides was compared qualitatively by analyzing the root mean square deviation (RMSD) from the crystal structure, radius of gyration, secondary and tertiary structure, and solvent accessible surface area. In agreement with earlier MD studies, relatively short (< 15 amino acids) peptides containing individual secondary structure elements were generally found to be unstable; the hydrophobic α₁-helix of the nucleotide binding fold displayed a significantly higher stability, however. Our simulations further showed that the first βαβ supersecondary unit of the characteristic dinucleotide binding fold (Rossmann fold) of LDH is somewhat more stable than other units of similar length and that the α₂-helix, which unfolds by itself, is stabilized by binding to this unit. This finding suggests that the first βαβ unit could function as an N-terminal folding nucleus, upon which the remainder of the polypeptide chain can be assembled. Indeed, simulations with longer units (βαβα and βαβαββ) showed that all structural elements of these units are rather stable. The outcome of our studies is in line with suggestions that folding of the N-terminal portion of LDH in vivo can be a cotranslational process that takes place during the ribosomal peptide synthesis.     

Molecular dynamics simulations

Molecular dynamics simulations have become a standard tool for the investigation of biomolecules. Simulations are performed of ever bigger systems using more realistic boundary conditions and better sampling due to longer sampling times. Recently, realistic simulations of systems as complex as transmembrane channels have become feasible. Simulations aid our understanding of biochemical processes and give a dynamic dimension to structural data; for example, the transformation of harmless prion protein into the disease-causing agent has been modeled.     

Molecular dynamics simulations of membrane proteins under asymmetric ionic concentrations

A computational method is developed to allow molecular dynamics simulations of biomembrane systems under realistic ionic gradients and asymmetric salt concentrations while maintaining the conventional periodic boundary conditions required to minimize finite-size effects in an all-atom explicit solvent representation. The method, which consists of introducing a nonperiodic energy step acting on the ionic species at the edge of the simulation cell, is first tested with illustrative applications to a simple membrane slab model and a phospholipid membrane bilayer. The nonperiodic energy-step method is then used to calculate the reversal potential of the bacterial porin OmpF, a large cation-specific β-barrel channel, by simulating the I-V curve under an asymmetric 10:1 KCl concentration gradient. The calculated reversal potential of 28.6 mV is found to be in excellent agreement with the values of 26–27 mV measured from lipid bilayer experiments, thereby demonstrating that the method allows realistic simulations of nonequilibrium membrane transport with quantitative accuracy. As a final example, the pore domain of Kv1.2, a highly selective voltage-activated K⁺ channel, is simulated in a lipid bilayer under conditions that recreate, for the first time, the physiological K⁺ and Na⁺ concentration gradients and the electrostatic potential difference of living cells.     

Molecular dynamics simulations of small peptides: dependence on dielectric model and pH

There has been much interest recently in the structure of small peptides in solution. A recent study by Bradley and co-workers [(1989) in Techniques of Protein Chemistry, Hugli, T.E., Ed., Academic Press, Orlando, FL, pp. 531-546; (1990) Journal of Molecular Biology, 215, pp. 607-622] describes a 17-residue peptide that is stable as a monomeric helix in aqueous solution at low pH, as determined by two-dimensional nmr and CD spectroscopy. They also have determined the helix content of the peptide as a function of pH using CD. We performed molecular dynamics simulations, with an empirical force field, of this peptide at low pH, with three different dielectric models: a linear distance-dependent dielectric function (epsilon = R); a modified form [J. Ramstein and R. Lavery (1988) Proceedings of the National Academy of Science, USA, Vol. 85, pp. 7231-7235] of the sigmoidal distance-dependent dielectric function of Hingerty and co-workers [(1985) Biopolymers, Vol. 24, pp. 427-439]; and epsilon = 1 with the peptide immersed in a bath of water molecules. We found that simulations with the sigmoidal dielectric function and the model with explicit water molecules resulted in average distances for particular interactions that were consistent with the experimental nmr results, with the sigmoidal function best representing the data. However, these models exhibited very different helix-stabilizing interactions. We also performed simulations using the sigmoidal function at moderate and high pH to compare to experimental determinations of the pH dependence of helix content. Helix content did not decrease with increases in pH, as shown experimentally. We did, however, observe changes in a specific side chain-helix dipole interaction that was implicated in determining the pH-dependent behavior of this peptide. Overall, the sigmoidal dielectric function was a reasonable alternative to adding explicit water molecules. In comparing 100 ps molecular dynamics simulations, the sigmoidal function was much less computer intensive and sampled more of conformational space than the treatment using explicit water molecules. Sampling is especially important for this system since the peptide has been shown experimentally to populate both helical and nonhelical conformations.     

Molecular dynamics simulations of the folding of poly(alanine) peptides

The secondary structures and the shapes of long-chain polyalanine (PA) molecules were investigated by all-atom molecular dynamics simulations using a modified Amber force field. Homopolymers of polyaminoacids such as PA are convenient models to study the mechanism of protein folding. It was found that the conformational structures of PA peptides are highly sensitive to the chain length. In the absence of solvent, straight α-helices dominate in short (n ∼ 20) peptides at room temperature. A shape transition occurs at a chain length n of 40–45; the compact helix-turn-helix structure (the double-leg hairpin) becomes favored over a straight α-helix. For n = 60, double-leg and the triple-leg hairpins are the only structures present in PA molecules. An exploration of a chain organization in a cubic cavity revealed a clear predisposition of PA molecules for additional breaks in α-helices and the formation of multifolded hairpins. Furthermore, under confinement the hairpin structure becomes much looser, the antiparallel positions of helical stems are disturbed, and a sizeable proportion of the helical stems are transformed from α-helices into 3₁₀-helices.     

The third leg: Molecular dynamics simulations of lipid binding proteins

Molecular dynamics computer simulations can provide a third leg which balances the contributions of both structural biology and binding studies performed on the lipid binding protein family. In this context, these calculations help to establish a dialogue between all three communities, by relating experimental observables with details of structure. Working towards this connection is important, since experience has shown the difficulty of inferring thermodynamic properties from a single static conformation. The challenge is exemplified by ongoing attempts to interpret the impact of mutagenesis on structure and function (i.e. binding). A detailed atomic-level understanding of this system could be achieved with the support of all three legs, paving the way towards rational design of proteins with novel specificities. This paper provides an outline of the connections possible between experiment and theory concerning lipid binding proteins.     

Molecular dynamics simulations of small DNA plasmids: Effects of sequence and supercoiling on intramolecular motions

Small (600 base pair) DNA plasmids were modeled with a simplified representation (3DNA) and the intramolecular motions were studied using molecular mechanics and molecular dynamics techniques. The model is detailed enough to incorporate sequence effects. At the same time, it is simple enough to allow long molecular dynamics simulations. The simulations revealed that large-scale slithering occurs in a homogeneous sequence. In a heterogeneous sequence, containing numerous small intrinsic curves, the centers of the curves are preferentially positioned at the tips of loops. With more curves than loop tips (two in unbranched supercoiled DNA), the heterogeneous sequence plasmid slithers short distances to reposition other curves into the loop tips. However, the DNA is immobilized most of the time, with the loop tips positioned over a few favored curve centers. Branching or looping also appears in the heterogeneous sequence as a new method of repositioning the loop tips. Instead of a smooth progression of increasing writhing with increasing linking difference, theoretical studies have predicted that there is a threshold between unwrithed and writhed DNA at a linking difference between one and two. This has previously been observed in simulations of static structures and is demonstrated here for dynamic homogeneous closed DNA. Such an abrupt transition is not found in the heterogeneous sequence in both the static and dynamic cases. © 1996 John Wiley & Sons, Inc.     

Molecular dynamics simulations of peptides from the central domain of smooth muscle caldesmon

The central domain of smooth muscle caldesmon contains a highly charged region consisting of ten 13-residue repeats. Experimental evidence obtained from the intact protein and fragments thereof suggests that this entire region forms a single stretch of stable alpha-helix. We have carried out molecular dynamics simulations on peptides consisting of one, two and three repeats to examine the mechanism of alpha-helical stability of the central domain at the atomic level. All three peptides show high helical stability on the timescale of the MD simulations. Deviations from alpha-helical structure in all the simulations arise mainly from the formation of long stretches of pi-helix. Interconversion between alpha-helical and pi-helical conformations occurs through insertion of water molecules into alpha-helical hydrogen bonds and subsequent formation of reverse turns. The alpha-helical structure is stabilized by electrostatic interactions (salt bridges) between oppositely charged sidechains with i,i+4 spacings, while the pi-helix is stabilized by i,i+5 salt bridge interactions. Possible i,i+3 salt bridges are of minor importance. There is a strong preference for salt bridges with a Glu residue N-terminal to a basic sidechain as compared to the opposite orientation. In the double and triple repeat peptides, strong i,i+4 salt bridges exist between the last Glu residue of one repeat and the first Lys residue of the next. This demonstrates a relationship between the repetitive nature of the central domain sequence and its ability to form very long stretches of alpha-helical structure.     

Molecular recognition with designed peptides and proteins

The design of proteins and peptides as molecular receptors is a rapidly growing area of research. Two primary approaches have been utilized, involving the minimization of known protein binding motifs or the de novo design of binding pockets within well-folded protein structures. These approaches are complementary and help define the minimum requirements necessary for biomolecular recognition. Recent advances in this area include the design of cavities within helix bundles for the binding of anesthetics, the design of beta-hairpins for the recognition of nucleotides and oligonucleotides, the redesign of protein binding sites for unique ligands, and the design of mini-proteins via protein grafting for the recognition of proteins and DNA. These advances provide exciting new opportunities to develop novel biosensors, de novo designed catalysts, exogenously triggered synthetic signal transduction cascades, and novel approaches to therapeutic treatments.     

Molecular dynamics study of secondary structure motions in proteins: application to myohemerythrin

The concept of secondary structure motions is examined in a molecular dynamics simulation of the protein myohemerythrin. We extracted from the simulation a corresponding trajectory of helices and demonstrated that the fluctuations of the protein are dominated by a rigid shift of these secondary structure elements. The relative motions of the helices are irregular, with no clear periodicity. They are bounded by approximately 2 A for the center of mass motions and by 20 degrees for the relative orientations. The potential of mean force for the interactions of the helices was calculated, and the correlations between the different extended motions were investigated. It is shown that the one-dimensional mean force potentials are close to quadratic for most of the helices coordinates. The anharmonicity is reflected by changes in the direction of the normal modes as a function of the energy and by the existence of multiple free energy minima for the helices packing. The multiple conformations are associated with a single type of secondary structure coordinate: the angle that describes the relative orientation of the helices in a plane perpendicular to the line connecting their center of mass.     

Molecular dynamics simulations of metalloproteins

Molecular dynamics simulations are now commonly applied to metalloproteins, despite the challenges introduced by the presence of metal ions. Force field parameters are nowadays available also for these 'exotic' atoms and several biological systems have been successfully studied. Some of the most relevant results and methodological advancements are reviewed.     

Molecular dynamics simulations of xDNA

xDNA is a modified DNA, which contains natural as well as expanded bases. Expanded bases are generated by the addition of a benzene spacer to the natural bases. A set of AMBER force‐field parameters were derived for the expanded bases and the structural dynamics of the xDNA decamer ( xT5 ′ G xT A xC xG C xA xG T3′ ) · ( xA5′ C T xG C G xT A xC A3′) was explored using a 22 ns molecular dynamics simulation in explicit solvent. During the simulation, the duplex retained its Watson‐Crick base‐pairing and double helical structure, with deviations from the starting B‐form geometry towards A‐form; the deviations are mainly in the backbone torsion angles and in the helical parameters. The sugar pucker of the residues were distributed among a variety of modes; C2′ endo, C1′ exo, O4′ endo, C4′ exo, C2′ exo, and C3′ endo. The enhanced stacking interactions on account of the modification in the bases could help to retain the duplex nature of the helix with minor deviations from the ideal geometry. In our simulation, the xDNA showed a reduced minor groove width and an enlarged major groove width in comparison with the NMR structure. Both the grooves are larger than that of standard B‐DNA, but major groove width is larger than that of A‐DNA with almost equal minor groove width. The enlarged groove widths and the possibility of additional hydration in the grooves makes xDNA a potential molecule for various applications. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 351–360, 2009. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com