On achieving better than 1-A accuracy in a simulation of a large protein: Streptomyces griseus protease A

Mechanism of androgen receptor antagonism by bicalutamide in the treatment of prostate cancer

The androgen receptor (AR) plays a key role in regulating gene expression in a variety of tissues, including the prostate. In that role, it is one of the primary targets in the development of new chemotherapeutics for treatment of prostate cancer and the target of the most widely prescribed current drug, bicalutamide (Bcu), for this disease. In view of its importance, and the absence of a crystal structure for any antagonist--AR complex, we have conducted a series of molecular dynamics-based simulations of the AR--Bcu complex and quantum mechanical (QM) calculations of Bcu, to elucidate the structural basis for antagonism of this key target. The structures that emerge show that bicalutamide antagonizes AR by accessing an additional binding pocket (B-site) adjacent to the hormone binding site (HBS), induced by displacing helix 12. This distorts the coactivator binding site and results in the inactivation of transcription. An alternative equienergetic conformational state of bicalutamide was found to bind in an expanded hormone pocket without materially perturbing either helix 12 or the coactivator binding site. Thus, both the structural basis of antagonism and the mechanism underlying agonist properties displayed by bicalutamide in different environments may be rationalized in terms of these structures. In addition, the antagonist structure and especially the induced second site (B-site) provide a structural framework for the design of novel antiandrogens.

Atomistic modeling of collagen proteins in their fibrillar environment

Molecular dynamics simulations can aid studies of the structural and physicochemical properties of proteins, by predicting their dynamics, energetics, and interactions with their local environment at the atomistic level. We argue that nonstandard protocols are needed to realistically model collagen proteins, which in their biological state aggregate to form collagen fibrils, and so should not be treated as fully solvated molecules. A new modeling approach is presented that can account for the local environment of collagen molecules within a fibril and which therefore simulates aspects of their behavior that would not otherwise be distinguished. This modeling approach exploits periodic boundaries to replicate the supermolecular arrangement of collagen proteins within the fibril, in an approach that is more commonly associated with modeling crystalline solids rather than mesoscopic protein aggregates. Initial simulations show agreement with experimental observations and corroborate theories of the fibril's structure.

Molecular dynamics simulations of a reversibly folding beta-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions

Eight 100-ns molecular dynamics simulations of a beta-heptapeptide in methanol at 340 K (within cubic periodic computational boxes of about 6-nm edge) are reported and compared. These simulations were performed with three different charge-state combinations at the peptide termini, one of them with or without a neutralizing chloride counterion, and using either the lattice-sum (LS) or reaction-field (RF) scheme to handle electrostatic interactions. The choice of the electrostatic scheme has essentially no influence on the folding-unfolding equilibrium when the peptide termini are uncharged and only a small influence when the peptide is positively charged at its N-terminus (with or without inclusion of a neutralizing chloride counterion). However, when the peptide is zwitterionic, the LS scheme leads to preferential sampling of the high-dipole folded helical state, whereas the RF scheme leads to preferential sampling of a low-dipole unfolded salt-bridged state. A continuum electrostatics analysis based on the sampled configurations (zwitterionic case) suggests that the LS scheme stabilizes the helical state through artificial periodicity, but that the magnitude of this perturbation is essentially negligible (compared to the thermal energy) for the large box size and relatively polar solvent considered. The results thus provide clear evidence (continuum electrostatics analysis) for the absence of LS artifacts and some indications (still not definitive because of the limited sampling of the folding-unfolding transition) for the presence of RF artifacts in this specific system.

Molecular dynamics simulations of a double unit cell in a protein crystal: volume relaxation at constant pressure and correlation of motions between the two unit cells

Eight molecular dynamics simulations of a double crystal unit cell of ubiquitin were performed to investigate the effects of simulating at constant pressure and of simulating two unit cells compared to a single unit cell. To examine the influence of different simulation conditions, the constant-pressure and constant-volume simulations were each performed with and without counterions and using two different treatments of the long-range electrostatic interactions (lattice-sum and reaction-field methods). The constant-pressure simulations were analyzed in terms of unit cell deformation and accompanying protein deformations. Energetic and structural properties of the proteins in the simulations of the double unit cell were compared to the results of previously reported one-unit-cell simulations. Correlation between the two unit cells was also investigated based on relative translational and rotational movements of the proteins and on dipole fluctuations. The box in the constant-pressure simulations is found to deform slowly to reach convergence only after 5-10 ns. This deformation does not result from a distortion in the structure of the proteins but rather from changes in protein packing within the unit cell. The results of the double-unit-cell simulations are closely similar to the results of the single-unit-cell simulations, and little motional correlation is found between the two unit cells.

On the truncation of long-range electrostatic interactions in DNA

Long-range interactions are known to play an important role in highly polar biomolecules like DNA. In molecular dynamics simulations of nucleic acids and proteins, an accurate treatment of the long-range interactions are crucial for achieving stable nanosecond trajectories. In this report, we evaluate the structural and dynamic effects on a highly charged oligonucleotide in aqueous solution from different long-range truncation methods. Two group-based truncation methods, one with a switching function and one with a force-switching function were found to fail to give accurate stable trajectories close to the crystal structure. For these group-based truncation methods, large root mean square (rms) deviations from the initial structure were obtained and severe distortions of the oligonucleotide were observed. Another group-based truncation scheme, which used an abrupt truncation at 8. 0 A or at 12.0 A was also investigated. For the short cutoff distance, the conformations deviated far away from the initial structure and were significantly distorted. However, for the longer cutoff, where all necessary electrostatic interactions were included, the trajectory was quite stable. For the particle mesh Ewald (PME) truncation method, a stable DNA simulation with a heavy atom rms deviation of 1.5 A was obtained. The atom-based truncation methods also resulted in stable trajectories, according to the rms deviation from the initial B-DNA structure, of between 1.5 and 1.7 A for the heavy atoms. In these stable simulations, the heavy atom rms deviations were approximately 0.6-1.0 A lower for the bases than for the backbone. An increase of the cutoff radius from 8 to 12 A decreased the rms deviation by approximately 0.2 A for the atom-based truncation method with a force-shifting function, but increased the computational time by a factor of 2. Increasing the cutoff from 12 to 18 A for the atom-based truncation method with a force-shifting function requires 2-3 times more computational time, but did not significantly change the rms deviation. Similar rms deviations from the initial structure were found for the atom-based method with a force-shifting function and for the PME method. The computational cost was longer for the PME method with a cutoff of 12. 0 A for the direct space nonbonded calculations than for the atom-based truncation method with a force-shifting function and a cutoff of 12.0 A. If a nonperiodic boundary, e.g., a spherical boundary, was used, a considerable speedup could be achieved. From the rms fluctuations, the terminal nucleotides and especially the cytidines were found to be more flexible than the nonterminal nucleotides. The B-DNA form of the oligonucleotide was maintained throughout the simulations and is judged to depend on the parameters of the energy function and not on the truncation method used to handle the long-range electrostatic interactions. To perform accurate and stable simulations of highly charged biological macromolecules, we recommend that the atom-based force-shift method or the PME method should be used for the long-range electrostatics interactions.

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.

Study of the electrostatics treatment in molecular dynamics simulations

This article considers the treatment of long-range interactions in molecular dynamics simulations. We investigate the effects of using different cutoff distances, constant versus distance-dependent dielectric, and different smoothing methods. In contrast to findings of earlier studies, we find that increasing the cutoff over 8 A does not significantly improve the accuracy (Arnold and Ornstein, Proteins 1994;18:19-33), and using a distance-dependent dielectric instead of a constant dielectric also does not improve accuracy (Guenot and Kollman, Protein Sci 1992;1:1185-1205). This might depend on differences in simulation protocols or force fields, or both, because we use the CHARMM22 force field with stochastic boundary conditions, whereas earlier studies used other protocols and energy functions. We also note that the stability of the simulations is highly dependent on the starting structure, showing that accurate molecular simulations not only depend on a realistic simulation protocol but also on correct initial conditions.

Corticotropin-releasing hormone receptor antagonists: framework design and synthesis guided by ligand conformational studies

As described in the preceding paper (Arvanitis et al. J. Med. Chem. 1999, 42), anilinopyrimidines I were identified as potent antagonists of corticotropin-releasing hormone-1 receptor (CRH1-R, also referred to as corticotropin-releasing factor, CRF1-R). Our next goal was to understand the receptor-bound conformation of the antagonists and to use this information to help guide preclinical optimization of the series and to develop new leads. Since receptor structural information was not available, we assumed that these small, high-affinity antagonists would tend to bind in conformations at or energetically close to their global minima and that rigid analogues that maintained the important stereoelectronic features of the bound anilinopyrimidine would also bind tightly. Conformational preferences and barriers to rotation of the anilinopyrimidines were determined by semiempirical methods, and X-ray and variable-temperature NMR spectroscopy provided experimental results that correlated well with calculated structures. Using these data, a key dihedral angle was constrained to design fused-ring analogues, substituted N-arylpyrrolopyridines II, synthesis of which provided CRH1 receptor antagonists with potency equal to that of the initial congeneric leads (Ki = 1 nM) and which closely matched the conformation held by the original compound, as determined by crystallography. In addition to providing a useful template for further analogue synthesis, the study unequivocally determined the active conformation of the anilinopyrimidines. Theoretical and spectroscopic studies, synthesis, and receptor binding data are presented.

Hydrogen bonding in helical polypeptides from molecular dynamics simulations and amide hydrogen exchange analysis: alamethicin and melittin in methanol

Molecular dynamics simulations of ion channel peptides alamethicin and melittin, solvated in methanol at 27 degrees C, were run with either regular alpha-helical starting structures (alamethicin, 1 ns; melittin 500 ps either with or without chloride counterions), or with the x-ray crystal coordinates of alamethicin as a starting structure (1 ns). The hydrogen bond patterns and stabilities were characterized by analysis of the dynamics trajectories with specified hydrogen bond angle and distance criteria, and were compared with hydrogen bond patterns and stabilities previously determined from high-resolution NMR structural analysis and amide hydrogen exchange measurements in methanol. The two alamethicin simulations rapidly converged to a persistent hydrogen bond pattern with a high level of 3(10) hydrogen bonding involving the amide NH's of residues 3, 4, 9, 15, and 18. The 3(10) hydrogen bonds stabilizing amide NH's of residues C-terminal to P2 and P14 were previously proposed to explain their high amide exchange stabilities. The absence, or low levels of 3(10) hydrogen bonds at the N-terminus or for A15 NH, respectively, in the melittin simulations, is also consistent with interpretations from amide exchange analysis. Perturbation of helical hydrogen bonding in the residues before P14 (Aib10-P14, alamethicin; T11-P14, melittin) was characterized in both peptides by variable hydrogen bond patterns that included pi and gamma hydrogen bonds. The general agreement in hydrogen bond patterns determined in the simulations and from spectroscopic analysis indicates that with suitable conditions (including solvent composition and counterions where required), local hydrogen-bonded secondary structure in helical peptides may be predicted from dynamics simulations from alpha-helical starting structures. Each peptide, particularly alamethicin, underwent some large amplitude structural fluctuations in which several hydrogen bonds were cooperatively broken. The recovery of the persistent hydrogen bonding patterns after these fluctuations demonstrates the stability of intramolecular hydrogen-bonded secondary structure in methanol (consistent with spectroscopic observations), and is promising for simulations on extended timescales to characterize the nature of the backbone fluctuations that underlie amide exchange from isolated helical polypeptides.

A further implementation of the rotational symmetry boundary conditions for calculations of P4(3)2(1)2 symmetry crystals

One of the most accurate styles of protein simulation is to calculate proteins in crystalline environment without neglect of long-range interactions. The long-range interactions can be accelerated by various methods. However, as a unit cell of a protein crystal is a large molecular assembly, its simulation is still unpractical without high-speed computers. Thus this article is addressed to the reduction of calculational volumes for protein crystal simulation by a further implementation of the rotational symmetry boundary condition method. For protein crystals in P4(3)2(1)2 symmetry, a computational cell and related tables were developed. A 120-ps molecular dynamics simulation was performed for a P4(3)2(1)2 symmetry crystal of glycogen phosphorylase b under rotational symmetry boundary conditions. The computational cell was one-eighth of the unit cell in volume, and less than about one-fourth of the conventional periodic boundary box. Generation of neighbor atom pair lists was greatly accelerated, and thus the simulation was practical even with a personal computer.

Transmembrane helix structure, dynamics, and interactions: multi-nanosecond molecular dynamics simulations

To probe the fundamentals of membrane/protein interactions, all-atom multi-nanosecond molecular dynamics simulations were conducted on a single transmembrane poly(32)alanine helix in a fully solvated dimyristoyphosphatidylcholine (DMPC) bilayer. The central 12 residues, which interact only with the lipid hydrocarbon chains, maintained a very stable helical structure. Helical regions extended beyond these central 12 residues, but interactions with the lipid fatty-acyl ester linkages, the lipid headgroups, and water molecules made the helix less stable in this region. The C and N termini, exposed largely to water, existed as random coils. As a whole, the helix tilted substantially, from perpendicular to the bilayer plane (0 degree) to a 30 degrees tilt. The helix experienced a bend at its middle, and the two halves of the helix at times assumed substantially different tilts. Frequent hydrogen bonding, of up to 0.7 ns in duration, occurred between peptide and lipid molecules. This resulted in correlated translational diffusion between the helix and a few lipid molecules. Because of the large variation in lipid conformation, the lipid environment of the peptide was not well defined in terms of "annular" lipids and on average consisted of 18 lipid molecules. When compared with a "neat" bilayer without peptide, no significant difference was seen in the bilayer thickness, lipid conformations or diffusion, or headgroup orientation. However, the lipid hydrocarbon chain order parameters showed a significant decrease in order, especially in those methylene groups closest to the headgroup.

RNA hydration: three nanoseconds of multiple molecular dynamics simulations of the solvated tRNA(Asp) anticodon hairpin

The hydration of the tRNA(Asp) anticodon hairpin was investigated through the analysis of six 500 ps multiple molecular dynamics (MMD) trajectories generated by using the particle mesh Ewald method for the treatment of the long-range electrostatic interactions. Although similar in their dynamical characteristics, these six trajectories display different local hydration patterns reflecting the landscape of the "theoretical" conformational space being explored. The statistical view gained through the MMD strategy allowed us to characterize the hydration patterns around important RNA structural motifs such as a G-U base-pair, the anticodon U-turn, and two modified bases: pseudouridine and 1-methylguanine. The binding of ammonium counterions to the hairpin has also been investigated. No long-lived hydrogen bond between water and a 2'-hydroxyl has been observed. Water molecules with long-residence times are found bridging adjacent pro-Rp phosphate atoms. The conformation of the pseudouridine is stiffened by a water-mediated base-backbone interaction and the 1-methylguanine is additionally stabilized by long-lived hydration patterns. Such long-lived hydration patterns are essential to ensure the structural integrity of this hairpin motif. Consequently, our simulations confirm the conclusion reached from an analysis of X-ray crystal structures according to which water molecules form an integral part of nucleic acid structure. The fact that the same conclusion is reached from a static and a dynamic point of view suggests that RNA and water together constitute the biologically relevant functional entity.

Protein folding simulations with genetic algorithms and a detailed molecular description

We have explored the application of genetic algorithms (GA) to the determination of protein structure from sequence, using a full atom representation. A free energy function with point charge electrostatics and an area based solvation model is used. The method is found to be superior to previously investigated Monte Carlo algorithms. For selected fragments, up to 14 residues long, the lowest free energy structures produced by the GA are similar in conformation to the corresponding experimental structures in most cases. There are three main conclusions from these results. First, the genetic algorithm is an effective method for searching amongst the compact conformations of a polypeptide chain. Second, the free energy function is generally able to select native-like conformations. However, some deficiencies are identified, and further development is proposed. Third, the selection of native-like conformations for some protein fragments establishes that in these cases the conformation observed in the full protein structure is largely context independent. The implications for the nature of protein folding pathways are discussed.

Comparison of database potentials and molecular mechanics force fields

The advantages and disadvantages of database and molecular mechanics force fields for the study of macromolecules are compared, with emphasis on the ability to distinguish between correct and incorrect structures. Molecular mechanics force fields have the advantage of resting on a clear theoretical basis, permitting an in-depth analysis of different contributions. On the other hand, large simplifications are necessary for tractable computing, and there has so far been little effective testing at the macromolecular level. Database potentials allow greater freedom of functional form and have been shown to be effective at discriminating between correct and incorrect complete structures. The principal negative is a controversial relationship to free energy. More testing and comparison of both sorts of potential are needed.

H-bond stability in the tRNA(Asp) anticodon hairpin: 3 ns of multiple molecular dynamics simulations

Multiple molecular dynamics trajectories of the solvated and neutralized 17-residue tRNA(Asp) anticodon hairpin were generated for a total of 3 ns. Explicit treatment of all long-ranged electrostatic interactions by the particle mesh Ewald algorithm, as implemented in the AMBER MD software package, effected a degree of structural stabilization not previously achieved by use of a long 16-A solvent interaction truncation scheme. The increased stability of this multiple molecular dynamics set was appropriate for an in-depth analysis of the six 500-ps-long trajectories and allowed the characterization of a number of key structural interactions. The dynamical behavior of the standard Watson-Crick base pairs, the noncanonical G30-U40 "wobble" base pair, and the psi 32-C38 pseudo-base pair is presented as well as that of two C--H... O hydrogen bonds found to contribute to the array of tertiary interactions that stabilize the seven-nucleotide native loop conformation. The least mobile residue in the loop is U33, which forms the U-turn motif and which participates in several hydrogen-bonding interactions, whereas the most mobile residue is the apical residue G34 at the wobble position, a factor undoubtedly important in its biological function. The set of multiple molecular dynamics trajectories obtained does not converge on a 500-ps time scale to a unique dynamical model but instead describes an ensemble of structural microstates accessible to the system under the present simulation protocol, which is the result of local structural heterogeneity rather than of global conformational changes.

Destabilizing effect of proline substitutions in two helical regions of T4 lysozyme: leucine 66 to proline and leucine 91 to proline

A class of temperature-sensitive (ts) mutants of T4 lysozyme with reduced activity at 30 degrees C and no activity at 43 degrees C has been selected. These mutants, designated "tight" ts mutants, differ from most other T4 lysozyme mutants that are active at 43 degrees C, but only manifest their ts lesion by a reduced halo size around phage plaques after exposure of the growth plates to chloroform vapors. For example, in the series of T4 lysozyme mutants at position 157, the original randomly selected mutant, T1571, is the least stable of the series, yet, apart from the halo assay and subsequent in vitro protein stability measurements, this mutant is indistinguishable from wild type (WT) even at 43 degrees C. Two mutants were identified: L91P and L66P. Both insert proline residues into alpha-helical regions of the WT protein structure. The stabilities (delta delta G) as determined by urea denaturation are 8.2 kcal/mol for L91P and 7.1 kcal/mol for L66P. CD spectra indicate that no major conformational changes have occurred in the mutant structures. The structures of the mutants were modeled with a 40-ps molecular dynamics simulation using explicit solvent. For L91P, the reduction of stability appears to be due to an unsatisfied hydrogen bond in the alpha-helix and to a new buried cavity. For L66P, the reduction of stability appears to be due to a disruption of the interdomain alpha-helix, at least two unsatisfied hydrogen bonds, and a newly formed solvent-filled pocket that protrudes into the hydrophobic core, possibly reducing the stabilizing contribution of a partially buried intrachain salt bridge.

As MAD as can be

With the recent demonstration that multiwavelength anomalous dispersion (MAD) can provide accurate experimental phases at high resolution, crystallographers have gained a tool with which to study solvation and flexibility in proteins, and a test-bed for the development of crystallographic methods.

Hydration of C-H groups in tRNA

Molecular dynamic (MD) simulations of the anticodon hairpin of tRNA(Asp) and of the full tRNA, both in a solvent bath with neutralizing NH4+ counter-ions, have been produced with the particle mesh ewald (PME) method and the multiple molecular dynamics (MMD) strategy. The latter consists of generating uncorrelated trajectories starting from the same initial configuration but with a slightly perturbed initial velocity distribution. The 3 ns (six uncorrelated 500 ps MD trajectories) MMD set of the 17 nucleotide anticodon fragment and the single 500 ps trajectory of the 75 nucleotide tRNA were analyzed with the aim of characterizing long lived C-H...Ow interactions for the two main nucleic acid base and ribose C-H bond types. Some C-H sites present very long residence lifetimes for water molecules, especially those around the ribose H(3') and the pyrimidine H(5) atoms. The C(3')-H(3')...Ow contacts occur concurrently with the strong hydration of the anionic phosphate oxygen atoms and especially with the water bridges linking successive phosphate groups along the polynucleotide chain. Therefore, these contacts are of opportunistic character and result from the geometries of the covalent structure and adjacent interactions. On the other hand, the pyrimidine H(5) atoms display a hydrophilic character with interaction geometries indicating that water contacts in which they are involved should be considered as bona fide hydrogen bonds.

Methodological advances in molecular dynamics simulations of biological systems

New advances in the techniques used to simulate specific statistical ensembles provide molecular dynamics algorithms that permit rigorous connections to be made between thermodynamic observables and calculated quantities in simulations of biological molecules. The complete inclusion of electrostatic forces in simulations also improves the comparison between calculations of simple structural measures in crystals and X-ray crystallographic results. These advances coupled with the ongoing development of more accurate inter/intramolecular forcefields with enhanced accuracy provide guidelines and benchmarks for comparison as we move to study more complicated biological problems.

Atomic-level accuracy in simulations of large protein crystals

Proper treatment of long-range Coulombic forces presents a major obstacle to providing realistic molecular dynamics simulations of macromolecules. Traditional approximations made to lessen computational cost ultimately lead to unrealistic behavior. The particle mesh Ewald method accommodates long-range Coulombic forces accurately and efficiently by use of fast Fourier transform techniques. We report a 1-ns simulation of bovine pancreatic trypsin inhibitor in a crystal unit cell using the particle mesh Ewald methodology. We find an rms backbone deviation from the x-ray structure (0.33 A) that is lower than that observed between bovine pancreatic trypsin inhibitor in different crystal forms and much lower than those of previous simulations. These results bridge the gap between structures obtained from molecular simulation and those from experiment.