Parallel helix bundles and ion channels: molecular modeling via simulated annealing and restrained molecular dynamics.

A parallel bundle of transmembrane (TM) alpha-helices surrounding a central pore is present in several classes of ion channel, including the nicotinic acetylcholine receptor (nAChR). We have modeled bundles of hydrophobic and of amphipathic helices using simulated annealing via restrained molecular dynamics. Bundles of Ala20 helices, with N = 4, 5, or 6 helices/bundle were generated. For all three N values the helices formed left-handed coiled coils, with pitches ranging from 160 A (N = 4) to 240 A (N = 6). Pore radius profiles revealed constrictions at residues 3, 6, 10, 13, and 17. A left-handed coiled coil and a similar pattern of pore constrictions were observed for N = 5 bundles of Leu20. In contrast, N = 5 bundles of Ile20 formed right-handed coiled coils, reflecting loosened packing of helices containing beta-branched side chains. Bundles formed by each of two classes of amphipathic helices were examined: (a) M2a, M2b, and M2c derived from sequences of M2 helices of nAChR; and (b) (LSSLLSL)3, a synthetic channel-forming peptide. Both classes of amphipathic helix formed left-handed coiled coils. For (LSSLLSL)3 the pitch of the coil increased as N increased from 4 to 6. The M2c N = 5 helix bundle is discussed in the context of possible models of the pore domain of nAChR.     

OmpA: Gating and dynamics via molecular dynamics simulations

Outer membrane proteins (OMPs) of Gram-negative bacteria have a variety of functions including passive transport, active transport, catalysis, pathogenesis and signal transduction. Whilst the structures of ∼ 25 OMPs are currently known, there is relatively little known about their dynamics in different environments. The outer membrane protein, OmpA from Escherichia coli has been studied extensively in different environments both experimentally and computationally, and thus provides an ideal test case for the study of the dynamics and environmental interactions of outer membrane proteins. We review molecular dynamics simulations of OmpA and its homologues in a variety of different environments and discuss possible mechanisms of pore gating. The transmembrane domain of E. coli OmpA shows subtle differences in dynamics and interactions between a detergent micelle and a lipid bilayer environment. Simulations of the crystallographic unit cell reveal a micelle-like network of detergent molecules interacting with the protein monomers. Simulation and modelling studies emphasise the role of an electrostatic-switch mechanism in the pore-gating mechanism. Simulation studies have been extended to comparative models of OmpA homologues from Pseudomonas aeruginosa (OprF) and Pasteurella multocida (PmOmpA), the latter model including the periplasmic C-terminal domain.     

Conformational properties of oxytocin in dimethyl sulfoxide solution: NMR and restrained molecular dynamics studies.

The conformation of oxytocin, the neurohypophyseal nonapeptide hormone, in solution in deuterated dimethyl sulfoxide has been determined by 1H-nmr. The structural determination is based on the experimental data set of nuclear Overhauser effect restraints. Obtained after the restrained molecular dynamics simulation on an initial structure of extended conformation, five resultant structures satisfy the experimental restraints well. These structures resemble that of the crystal structure of deamino-oxytocin, an analogue of oxytocin, in terms of a close correlation observed both at two beta-turn regions of the 20-membered tocin ring and at the tripeptide tail end. Based on this comparison and analysis of restrained molecular dynamics trajectories, we found that, although the turns are stabilized by the formation of hydrogen bonds, the oxytocin molecule possesses a slight twist in DMSO solution relative to the orientation of deamino-oxytocin in the crystalline state. Analyses of oxytocin conformation indicate that the tripeptide tail is more flexible than the tocin ring.     

Conformation of secretin in dimethyl sulfoxide solution. NMR studies and restrained molecular dynamics

The solution conformation of the 27-residue polypeptide hormone secretin in dimethyl sulfoxide has been determined on the basis of 1H-NMR measurements. The experimental data set used in the structure determination consisted of 98 nuclear-Overhauser-enhancement-derived interproton and dihedral angle restraints from coupling constants. The NH-NH and H alpha-NH NOEs were determined from build-up rates, while the remaining distances were classified in a qualitative manner. The structure calculations consisted of two phases. First, dynamical simulated annealing calculations were carried out to find conformations of the peptide which satisfy NOE and phi dihedral restraints. The convergence of ten calculated structures was good except for those regions of the molecule where NOE data were not unambiguous. From the calculated set another initial structure was built which was again minimized in several 5-ps calculations now employing the full empirical energy function. The resulting structures of secretin reveal conformationally well-defined regions, but not a single uniform secondary structure. The structure is different from the calculated structure from trifluoroethanol/water measurements.     

Exploration of disorder in protein structures by X-ray restrained molecular dynamics

Conformational disorder in crystal structures of ribonuclease-A and crambin is studied by including two independent structures in least-squares optimizations against X-ray data. The optimizations are carried out by X-ray restrained molecular dynamics (simulated annealing refinement) and by conventional least-squares optimization. Starting from two identical structures, the optimizations against X-ray data lead to significant deviations between the two, with rms backbone displacements of 0.45 A for refinement of ribonuclease at 1.53 A resolution, and 0.31 A for crambin at 0.945 A. More than 15 independent X-ray restrained molecular dynamics runs have been carried out for ribonuclease, and the displacements between the resulting structures are highly reproducible for most atoms. These include residues with two or more conformations with significant dihedral angle differences and alternative hydrogen bonding, as well as groups of residues that undergo displacements that are suggestive of rigid-body librations. The crystallographic R-values obtained are approximately 13%, as compared to 15.3% for a comparable refinement with a single structure. Least-squares optimization without an intervening restrained molecular dynamics stage is sufficient to reproduce most of the observed displacements. Similar results are obtained for crambin, where the higher resolution of the X-ray data allows for refinement of unconstrained individual anisotropic temperature factors. These are shown to be correlated with the displacements in the two-structure refinements.     

Characterization of de novo four-helix bundles by molecular dynamics simulations

We have investigated the structure and dynamics of three cavitand-based four-helix bundles (caviteins) by computer simulation. In these systems, designed de novo, each of the four helices contain the identical basis sequence EELLKKLEELLKKG (N1). Each cavitein consists of a rigid macrocycle (cavitand) with four aryl linkages, to each of which is connected an N1 peptide by means of a linker peptide. The three caviteins studied here differ only in the linker peptide, which consist of one, two, or three glycine residues. Previous experimental work has shown that these systems exhibit very different behavior in terms of stability and oligomerization states despite the small differences in the linker peptide. Given that to date no three-dimensional structure is available for these caviteins, we have undertaken a series of molecular dynamics (MD) simulations in explicit water to try to rationalize the large differences in the experimentally observed behavior of these systems. Our results provide insight, for the first time, into why and how the cavitein with a single glycine linker forms dimers. In addition, our results indicate why although the two- and three-glycine-linked caviteins have similar stabilities, they have different native-like characteristics: the cavitein with three glycines can form a supercoiled helix, whereas the one with two glycines cannot. These findings may provide a useful guide in the rational de novo design of novel proteins with finely tunable structures and functions in the future.     

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for ¹⁵N relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.     

Conformation of a neurokinin antagonist in solution. 2D NMR and restrained molecular dynamics study.

The hexapeptide [cyclo(Leu1 psi(CH2NH2)Leu2-Gln3-Trp4-Phe5-Gly6)]+1 is a potent antagonist of neurokinin A activity in tissues of hamster urinary bladder. The solution conformation of this cyclic hexapeptide has been characterized by the combined use of two dimensional nuclear magnetic resonance spectroscopy and restrained molecular dynamics. The proton spectrum of the peptide was fully assigned by the sequential assignment procedure. Interproton distances were derived from crosspeak volumes in two dimensional Nuclear Overhauser Effect spectra, and dihedral angles were calculated from appropriate coupling constants. Temperature coefficients of the amide protons were determined. Restrained molecular dynamics simulations were carried out using the backbone interproton distances as constraints. During 210 ps of restrained molecular dynamics the peptide interconverted among three closely related families of conformations. These interconversions occurred at picosecond timescales under the simulation conditions.     

Temperature-dependent molecular dynamics and restrained X-ray refinement simulations of a Z-DNA hexamer

Molecular dynamics simulations of the Z-DNA hexamer 5BrdC-dG-5BrdC-dG-5BrdC-dG were performed at several temperatures between 100 K and 300 K. Above 250 K, a strong sequence-dependent flexibility in the nucleic acid is observed, with the guanine sugar and the phosphate of GpC sequences much more mobile than the cytosine sugar and phosphate of CpG sequences. At 300 K, the hexamer is in dynamic equilibrium between several Z forms, including the crystallographically determined ZI and ZII forms. The local base-pair geometry, however, is not very variable, except for the roll of the base-pairs. The hexamer molecular dynamics trajectories have been used to test the restrained parameter crystallographic refinement model for nucleic acids. X-ray diffraction intensities corresponding to observed diffraction data were computed. The average structures obtained from the simulations were then refined against the calculated intensities, using a restrained least-squares program developed for nucleic acids in order to analyse the effects of the refinement model on the derived quantities. In general, the temperature dependence of the atomic fluctuations determined directly from the refined Debye-Waller factors is in reasonably good agreement with the results obtained by calculating the atomic fluctuations directly from the Z-DNA molecular dynamics trajectories. The agreement is best for refinement of temperature factors without restraints. At the highest temperature studied (300 K), the effect of the refinement on the most mobile atoms (phosphates) is to significantly reduce the mean-square atomic fluctuations estimated from the refined Debye-Waller factors below the actual values (less than (delta r)2 greater than congruent to 0.5 A2). Analysis of the temperature-dependence of the mean-square atomic fluctuations provides information concerning the conformational potential within which the atoms move. The calculated temperature-dependence and anharmonicity of the Z-DNA helix are compared with the results observed for proteins. The average structures from the simulations were refined against the experimental X-ray intensities. It is found that low-temperature molecular dynamics simulations provide a useful tool for optimizing the refinement of X-ray structures.     

Solution structure of regioselectively addressable functionalized templates: An NMR and restrained molecular dynamics investigation

Three cyclic peptides that are Regioselectively Addressable Functionalized Templates (RAFT) for use in protein de novo design have been investigated using a combination of nmr, restrained molecular dynamics, and CD spectroscopy. These peptides contain up to four selectively addressable sites (orthogonally protected lysine side chains) or have selectively addressable faces. The results show a common stable conformation for templates of this kind based on two type II β-turns and an associated β-sheet structure. A preferential orientation for the side chains is also demonstrated. The significance of these findings is discussed in the context of applications of RAFT that rely on their conformational rigidity and ability to present functionalities in a defined spatial arrangement. © 1996 John Wiley & Sons, Inc.     

Structural refinement of membrane proteins by restrained molecular dynamics and solvent accessibility data

We present an approach for incorporating solvent accessibility data from electron paramagnetic resonance experiments in the structural refinement of membrane proteins through restrained molecular dynamics simulations. The restraints have been parameterized from oxygen (ΠO₂) and nickel-ethylenediaminediacetic acid (ΠNiEdda) collision frequencies, as indicators of lipid or aqueous exposed spin-label sites. These are enforced through interactions between a pseudoatom representation of the covalently attached Nitroxide spin-label and virtual “solvent” particles corresponding to O₂ and NiEdda in the surrounding environment. Interactions were computed using an empirical potential function, where the parameters have been optimized to account for the different accessibilities of the spin-label pseudoatoms to the surrounding environment. This approach, “pseudoatom-driven solvent accessibility refinement”, was validated by refolding distorted conformations of the Streptomyces lividans potassium channel (KcsA), corresponding to a range of 2-30 Å root mean-square deviations away from the native structure. Molecular dynamics simulations based on up to 58 electron paramagnetic resonance restraints derived from spin-label mutants were able to converge toward the native structure within 1-3 Å root mean-square deviations with minimal computational cost. The use of energy-based ranking and structure similarity clustering as selection criteria helped in the convergence and identification of correctly folded structures from a large number of simulations. This approach can be applied to a variety of integral membrane protein systems, regardless of oligomeric state, and should be particularly useful in calculating conformational changes from a known reference crystal structure.     

Symmetry‐restrained molecular dynamics simulations improve homology models of potassium channels

Most crystallized homo‐oligomeric ion channels are highly symmetric, which dramatically decreases conformational space and facilitates building homology models (HMs). However, in molecular dynamics (MD) simulations channels deviate from ideal symmetry and accumulate thermal defects, which complicate the refinement of HMs using MD. In this work we evaluate the ability of symmetry constrained MD simulations to improve HMs accuracy, using an approach conceptually similar to Critical Assessment of techniques for protein Structure Prediction (CASP) competition: build HMs of channels with known structure and evaluate the efficiency of proposed methods in improving HMs accuracy (measured as deviation from experimental structure). Results indicate that unrestrained MD does not improve the accuracy of HMs, instantaneous symmetrization improves accuracy but not stability of HMs during subsequent unrestrained MD, while gradually imposing symmetry constraints improves both accuracy (by 5–50%) and stability of HMs. Moreover, accuracy and stability are strongly correlated, making stability a reliable criterion in predicting the accuracy of new HMs. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Coarse-grained molecular dynamics of tetrameric transmembrane peptide bundles within a lipid bilayer

The conformations of model transmembrane peptides are studied to understand the structural and dynamical aspects of tetrameric bundles using a series of coarse grain (CG) molecular dynamics (MD) simulations since membrane proteins play a crucial role in cell function. In this work, two different amphipathic models have been constructed using similar hydrophobic/hydrophilic characteristics with two structurally distinct morphologies to evaluate the effect of roughness and hydrophilic topology on the structure of tetrameric bundles, one class that forms an ion-channel and one class that does not. Free energy calculations of typical amphipathic peptide topologies show that using a relatively smooth surface morphology allows for a stable conformation of the tetramer bundle in a diamond formation. However, the model with side chains attached to the core in order to roughen the surface has a stable square tetramer bundle which is consistent with experimental data and all-atom (AA) MD simulations. Comparisons of the CG simulations with AA MD simulations are in reasonable agreement with the formation of tetrameric homo-oligomers, partitioning within the lipid bilayer and tilt angle with respect to the bilayer normal. We concluded that a square or diamond shape tetrameric homo-oligomers could be stabilized by rational design of the peptide morphology and topology of the surface, thus allowing us to tune the permeability of the bundle or channel.     

Solution conformation of human neuropeptide Y by 1H nuclear magnetic resonance and restrained molecular dynamics.

The solution structure of human neuropeptide Y has been solved by conventional two-dimensional NMR techniques followed by distance-geometry and molecular-dynamics methods. The conformation obtained is composed of two short contiguous alpha-helices comprising residues 15-26 and 28-35, linked by a hinge inducing a 100 degree angle. The first helix (15-26) is connected to a polyproline stretch (residues 1-10) by a tight hairpin (residues 11-14). The helices and the polyproline stretch are packed together by hydrophobic interactions. This structure is related to that of the homologous avian pancreatic polypeptide and bovine pancreatic polypeptide. The C- and N-terminii, known to be involved in the biological activity for respectively the receptor binding and activation, are close together in space. The side chains of residues Arg33, Arg35 and Tyr36 on the one hand, and Tyr1 and Pro2 on the other, form a continuous solvent-exposed surface of 4.9 mm2 which is supposed to interact with the receptor for neuropeptide Y.     

Simulated annealing with restrained molecular dynamics using a flexible restraint potential: theory and evaluation with simulated NMR constraints.

A new functional representation of NMR-derived distance constraints, the flexible restraint potential, has been implemented in the program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168) for molecular structure generation. In addition, flat-bottomed restraint potentials for representing dihedral angle and vicinal scalar coupling constraints have been introduced into CONGEN. An effective simulated annealing (SA) protocol that combines both weight annealing and temperature annealing is described. Calculations have been performed using ideal simulated NMR constraints, in order to evaluate the use of restrained molecular dynamics (MD) with these target functions as implemented in CONGEN. In this benchmark study, internuclear distance, dihedral angle, and vicinal coupling constant constraints were calculated from the energy-minimized X-ray crystal structure of the 46-amino acid polypeptide crambin (ICRN). Three-dimensional structures of crambin that satisfy these simulated NMR constraints were generated using restrained MD and SA. Polypeptide structures with extended backbone and side-chain conformations were used as starting conformations. Dynamical annealing calculations using extended starting conformations and assignments of initial velocities taken randomly from a Maxwellian distribution were found to adequately sample the conformational space consistent with the constraints. These calculations also show that loosened internuclear constraints can allow molecules to overcome local minima in the search for a global minimum with respect to both the NMR-derived constraints and conformational energy. This protocol and the modified version of the CONGEN program described here are shown to be reliable and robust, and are applicable generally for protein structure determination by dynamical simulated annealing using NMR data.     

Prevalent mutations of human prion protein: a molecular modeling and molecular dynamics study

Point mutations in the human prion protein gene, leading to amino acid substitutions in the human prion protein contribute to conversion of PrPC to PrPSc and amyloid formation, resulting in prion diseases such as familial Creutzfeldt-Jakob disease (CJD), Gerstmann-Straussler-Scheinker disease (GSS), and fatal familial insomnia. We have investigated impressions of prevalent mutations including Q217R, D202N, F198S, on the human prion protein and compared the mutant models with wild types. Structural analyses of models were performed with molecular modeling and molecular dynamics simulation methods. According to our results, frequently occurred mutations are observed in conserved and fully conserved sequences of human prion protein and the most fluctuation values occur in the Helix 1 around residues 144-152 and C-terminal end of the Helix 2. Our analysis of results obtained from MD simulation clearly shows that this long-range effect plays an important role in the conformational fluctuations in mutant structures of human prion protein. Results obtained from molecular modeling such as creation or elimination of some hydrogen bonds, increase or decrease of the accessible surface area and molecular surface, loss or accumulation of negative or positive charges on specific positions, and altering the polarity and pKa values, show that amino acid point mutations, though not urgently change the stability of PrP, might have some local impacts on the protein interactions which are required for oligomerization into fibrillar species.     

Homology modeling and molecular dynamics simulations of lymphotactin

We have modeled the structure of human lymphotactin (hLpnt), by homology modeling and molecular dynamics simulations. This chemokine is unique in having a single disulfide bond and a long C-terminal tail. Because other structural classes of chemokines have two pairs of Cys residues, compared to one in Lpnt, and because it has been shown that both disulfide bonds are required for stability and function, the question arises how the Lpnt maintains its structural integrity. The initial structure of hLpnt was constructed by homology modeling. The first 63 residues in the monomer of hLpnt were modeled using the structure of the human CC chemokine, RANTES, whose sequence appeared most similar. The structure of the long C-terminal tail, missing in RANTES, was taken from the human muscle fatty-acid binding protein. In a Protein Data Bank search, this protein was found to contain a sequence that was most homologous to the long tail. Consequently, the modeled hLpnt C-terminal tail consisted of both alpha-helical and beta-motifs. The complete model of the hLpnt monomer consisted of two alpha-helices located above the five-stranded beta-sheet. Molecular dynamics simulations of the solvated initial model have indicated that the stability of the predicted fold is related to the geometry of Pro78. The five-stranded beta-sheet appeared to be preserved only when Pro78 was modeled in the cis conformation. Simulations were also performed both for the C-terminal truncated forms of the hLpnt that contained one or two (CC chemokine-like) disulfide bonds, and for the chicken Lpnt (cLpnt). Our MD simulations indicated that the turn region (T30-G34) in hLpnt is important for the interactions with the receptor, and that the long C-terminal region stabilizes both the turn (T30-G34) and the five-stranded beta-sheet. The major conclusion from our theoretical studies is that the lack of one disulfide bond and the extension of the C-terminus in hLptn are mutually complementary. It is very likely that removal of two Cys residues sufficiently destabilizes the structure of a chemokine molecule, particularly the core beta-sheet, to abolish its biological function. However, this situation is rectified by the long C-terminal segment. The role of this long region is most likely to stabilize the first beta-turn region and alpha-helix H1, explaining how this chemokine can function with a single disulfide bond.     

Homology modeling and molecular dynamics simulation of human prothrombin fragment 1.

The crystallographic structure of bovine prothrombin fragment 1 bound with calcium ions was used to construct the corresponding human prothrombin structure (hf1/Ca). The model structure was refined by molecular dynamics to estimate the average solution structure. Accommodation of long-range ionic forces was essential to reach a stable solution structure. The gamma-carboxyglutamic acid (Gla) domain and the kringle domain of hf1/Ca independently equilibrated. Likewise, the hydrogen bond network and the calcium ion coordinations were well preserved. A discussion of the phospholipid binding of the vitamin K-dependent coagulation proteins in the context of the structure and mutational data of the Gla domain is presented.     

Solution structure of the EcoRI DNA octamer containing 5-fluorouracil via restrained molecular dynamics using distance and torsion angle constraints extracted from NMR spectral simulations.

The self-complementary DNA octamer [d(GGAATUFCC)]2, containing the EcoRI recognition sequence with one of the thymines replaced by 5-fluorouracil (UF), was synthesized. Proton homonuclear two-dimensional nuclear Overhauser effect (2D NOE) and double-quantum-filtered correlation (2QF-COSY) spectra, as well as one-dimensional spectra at different temperatures, were recorded for the octamer. Consequently, all proton resonances were assigned. The thermally induced transition from the duplex to single strands has been followed, demonstrating the stability of the duplex containing 5-fluorouracil. Simulations of the 2QF-COSY cross-peaks by means of the programs SPHINX and LINSHA were compared with experimental data, establishing scalar coupling constants for the sugar ring protons and hence sugar pucker parameters. The deoxyribose rings exhibit a dynamic equilibrium of N- and S-type conformers with 75-95% populations of the latter. Two programs used for complete relaxation matrix analysis 2D NOE spectra, CORMA and MARDIGRAS, were modified to account for the influence of the fluorines on dipolar interactions in the proton system. Quantitative assessment of the 2D NOE cross-peak intensities for different mixing times, in conjunction with the program MARDIGRAS, gave a set of interproton distances for each mixing time. The largest and smallest values of each of the interproton distances were chosen as the upper and lower bounds for each distance constraint. The distance bounds define the size of a flat-well potential function term, incorporated into the AMBER force field, which was employed for restrained molecular dynamics calculations. Torsion angle constraints in the form of a flat-well potential were also constructed from the analysis of the sugar pucker data. Several restrained molecular dynamics runs of 35 ps were performed, utilizing 284 experimental distance and torsion angle constraints and two different starting structures, energy-minimized A- and B-DNA. Convergence to similar structures with a root-mean-square deviation of 1.2 A was achieved for the central hexamer of the octamer, starting from A- and B-DNA. The average structure from six different molecular dynamics runs was subjected to final restrained energy minimization. The resulting final structure was in good agreement with the structures derived from different molecular dynamics runs and showed a substantial improvement of the 2D NOE sixth-root residual index in comparison with classical and energy-minimized B-DNA. A detailed analysis of the conformation of the final structure and comparison with structures of similar sequences, obtained by different methods, were performed.