Simulation of protein conformational freedom as a function of pH: constant-pH molecular dynamics using implicit titration

Solution pH is a determinant parameter on protein function and stability, and its inclusion in molecular dynamics simulations is attractive for studies at the molecular level. Current molecular dynamics simulations can consider pH only in a very limited way, through a somewhat arbitrary choice of a set of fixed charges on the titrable sites. Conversely, continuum electrostatic methods that explicitly treat pH effects assume a single protein conformation whose choice is not clearly defined. In this paper we describe a general method that combines both titration and conformational freedom. The method is based on a potential of mean force for implicit titration and combines both usual molecular dynamics and pH-dependent calculations based on continuum methods. A simple implementation of the method, using a mean field approximation, is presented and applied to the bovine pancreatic trypsin inhibitor. We believe that this constant-pH molecular dynamics method, by correctly sampling both charges and conformation, can become a valuable help in the understanding of the dependence of protein function and stability on pH. © 1997 Wiley-Liss Inc.     

Formation of collective conformational degrees of freedom during macromolecular chain folding dynamics in a viscous medium

Computational methods were used to study the dynamics of the formation of the collective conformational degrees of freedom in the relaxation folding of a model biopolymer chain of 50 nodes in a viscous medium; the model has been described previously. Collective conformational motions of the nodes were shown to arise due to friction forces in a viscous medium. The collective motions have several typical forms, including a wave of differently directed motions of chain nodes that propagates from one end of the chain to another (like a soliton) in response to a pertubation in terminal group position. Individual nodes located at the middle of the chain make approximately equal contributions to the total energy dissipation rate. The end nodes contribute approximately 2–4 times more than internal nodes to the total energy dissipation. The results of numerical experiments are consistent with the theoretical concept developed earlier to describe the dynamics of linear macromolecular chains in a viscous medium in the limit of a very large number of nodes.     

Synthesis, conformational studies, and molecular dynamics calculations of two cyclic tetrapeptides with 17- and 18-membered rings

Two cyclic tetrapeptides [Boc-cyclo(-Xxx-Pro-Asn-Lys-)OMe (Xxx = Asp or Glu)] were synthesized and investigated by NMR spectroscopy. They were designed in order to mimic the salt bridge found in physalaemin. Isomers of the urethane bond were observed in DMSO solution. The ROESY spectrum allowed the assignment of many signals of the minor isomer of both compounds. Conformational studies based on the temperature gradients of the NH chemical shifts, coupling constants, and ROEs revealed a similar conformation for the Asp analogue as proposed for physalaemin. A beta I turn with Pro and Asn in the corner positions was found for the major isomer. No hydrogen bonds were detected for the major isomer of the cyclic Glu analogue. Molecular dynamics calculations, using the NMR based initial structures, yielded sets of conformations in agreement with the experimental data. It is concluded that the salt bridge in physalaemin is best approximated by a lactam formed from the original amino acids.     

Entropy versus aromaticity in the conformational dynamics of aromatic rings

Comparison of the results of Car-Parrinello molecular dynamics simulations of isolated benzene, pyrimidine and 1,2,4-triazine molecules reveals that the unusually low population of planar geometry of the benzene ring is caused by entropy effects despite its high aromaticity. The decrease in symmetry of the molecule results in smaller changes in entropy and Gibbs free energy due to out-of-plane deformations of the ring, leading to an increase in the population of planar geometry of the ring. This leads to differences in the topology of potential energy and Gibbs free energy surfaces.

In silico studies of conformational dynamics of Mu opioid receptor performed using gaussian accelerated molecular dynamics

G-protein-coupled receptors play a crucial role in various signaling pathways and function as targets for treating a wide spectrum of diseases. Since the twentieth century, extensive research has been conducted on the Mu opioid receptor (MOR) as a drug target. We examined the MOR inactivation and activation processes using an enhanced sampling method (Gaussian accelerated molecular dynamics), the binding pocket site area method, the root mean square deviation method, and the free energy (potential of mean force) method. This study revealed two important intermediate MOR structures (intermediate and intermediate inactive), and the results suggest that the intermediate MOR structure is responsible for the selectivity of opioids.     

Exploration of conformational transition in the aryl-binding site of human FXa using molecular dynamics simulations

Human coagulation Factor X (FX), a member of the vitamin K-dependent serine protease family, is a crucial component of the human coagulation cascade. Activated FX (FXa) participates in forming the prothrombinase complex on activated platelets to convert prothrombin to thrombin in coagulation reactions. In the current study, 30-ns MD simulations were performed on both the open and closed states of human FXa. Root mean squares (RMS) fluctuations showed that structural fluctuations concentrated on the loop regions of FXa, and the presence of a ligand in the closed system resulted in larger fluctuations of the gating residues. The open system had a gating distance from 9.23 to 11.33 ?, i.e., significantly larger than that of the closed system (4.69-6.35 ?), which allows diversified substrates of variable size to enter. Although the solvent accessible surface areas (SASA) of FXa remained the same in both systems, the open system generally had a larger total SASA or hydrophobic SASA (or both) for residues surrounding the S4 pocket. Additionally, more hydrogen bonds were formed in the closed state than in the open state of FXa, which is believed to play a significant role in maintaining the closed confirmation of the aryl-binding site. Based on the results of MD simulations, we propose that an induced-fit mechanism governs the functioning of human coagulation FX, which helps provide a better understanding of the interactions between FXa and its substrate, and the mechanism of the conformational changes involved in human coagulation.     

Studies on the conformational behaviour of GlcNAc-Man3-GlcNAc2 oligosaccharides using molecular dynamics simulations

Three-dimensional structures of the natural substrate unit for the enzyme N-acetylglucosamine-transferase II, GlcNAc-Man3-GlcNAc2, were investigated by molecular modelling methods. Molecular dynamics (MD) and molecular mechanics calculations on two hexasaccharides, namely GlcNAc-Man3-GlcNAc2-Asn and GlcNAc-Man3-GlcNAc2-OMe were performed by the Biosym/MSI software using the CVFF and CFF95 force fields in vacuum. The MD simulations were calculated for 3 ns at different simulation temperatures and for two values of dielectric constant, = 1 and = 4. From each 3 ns trajectory, 3050 structures have been optimized. The local minima obtained have been clustered into families exhibiting similar values of glycosidic torsional angles phi, psi, and omega. The influence of the simulation conditions and force fields used on the conformational behaviour and structure of the title oligosaccharides is discussed.     

Crystal structure,conformational analysis,and molecular dynamics of tetra-O-methyl-(+) -catechin

The structure of tetra-O-methyl- (+) -catechin has been determined in the crystalline state. Two independent molecules, denoted structure A and structure B, exist in the unit cell. Crystals are triclinic, space group P1, a = 4.8125(2) Å, b = 12.9148(8) Å, c = 13.8862(11) Å, α = 86.962(6) °, β = 89.120(5)°, γ = 88.044(5)°, Z = 2, D_c = 1.336 g cm^?3, R = 0.033 for 6830 observations. The heterocyclic rings of the crystal structures are compared to previous results for 8-bromotetra-O-methyl-(+)-catechin, penta-O-acetyl-(+)-catechin, and (?) -epicatechin. One of the two molecules has a heterocyclic ring conformation similar to that observed previously for (?)-epicatechin, and the other has a heterocyclic ring conformation similar to one predicted earlier in a theoretical analysis of dimers of (+)-catechin and (?) -epicatechin. Both structure A and structure B in the crystal have heterocyclic ring conformations that place the dimethoxyphenyl substituent at C(2) in the equatorial position. However, this heterocyclic ring conformation does not explain the proton nmr coupling constant measured in solution. Molecular dynamics simulations show an equatorial ? axial interconversion of the heterocyclic ring, which can explain the nmr results. © 1993 John Wiley & Sons, Inc.     

Quantitative conformational analysis of the core region of N-glycans using residual dipolar couplings, aqueous molecular dynamics, and steric alignment

A method is described for quantitatively investigating the dynamic conformation of small oligosaccharides containing an (16) linkage. It was applied to the oligosaccharide Man-(13) {Man- (16)}Man--O-Me, which is a core region frequently observed in N-linked glycans. The approach tests an aqueous molecular dynamics simulation, capable of predicting microscopic dynamics, against experimental residual dipolar couplings, by assuming that alignment is caused purely by steric hindrance. The experimental constraints were heteronuclear and homonuclear residual dipolar couplings, and in particular those within the (16) linkage itself. Powerful spin-state-selective pulse sequences and editing schemes were used to obtain the most relevant couplings for testing the model. Molecular dynamics simulations in water over a period of 50 ns were not able to predict the correct rotamer population at the (16) linkage to agree with the experimental data. However, this sampling problem could be corrected using a simple maximum likelihood optimisation, indicating that the simulation was modelling local dynamics correctly. The maximum likelihood prediction of the residual dipolar couplings was found to be an almost equal population of the gg and gt rotamer conformations at the (16) linkage, and the tg conformation was predicted to be unstable and unpopulated in aqueous solution. In this case all twelve measured residual dipolar couplings could be satisfied. This conformer population could also be used to make predictions of scalar couplings with the use of a previously derived empirical equation, and is qualitatively in agreement with previous predictions based on NMR, X-ray crystallography and optical data.     

Exploration of the conformational space of myosin recovery stroke via molecular dynamics

Muscle contractions are driven by cyclic conformational changes of myosin, whose molecular mechanisms of operation are being elucidated by recent advances in crystallographic studies and single molecule experiments. To complement such structural studies and consider the energetics of the conformational changes of myosin head, umbrella sampling molecular dynamics (MD) simulations were performed with the all-atom model of the scallop myosin sub-fragment 1 (S1) with a bound ATP in solution in explicit water using the crystallographic near-rigor and transition state conformations as two references. The constraints on RMSD reaction coordinates used for the umbrella sampling were found to steer the conformational changes efficiently, and relatively close correlations have been observed between the set of characteristic structural changes including the lever arm rotation and the closing of the nucleotide binding pocket. The lever arm angle and key residue interaction distances in the nucleotide binding pocket and the relay helix show gradual changes along the recovery stroke reaction coordinate, consistent with previous crystallographic and computational minimum energy studies. Thermal fluctuations, however, appear to make the switch-2 coordination of ATP more flexible than suggested by crystal structures. The local solvation environment of the fluorescence probe, Trp 507 (scallop numbering), also appears highly mobile in the presence of thermal fluctuations.     

Assessment of the accuracy of a human arm model with seven degrees of freedom

We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was defined as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5-0.6cm for sensor positions and 5-7 degrees for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.     

Conformation, dynamics, solvation and relative stabilities of selected beta-hexopyranoses in water: a molecular dynamics study with the GROMOS 45A4 force field

The present article reports long timescale (200 ns) simulations of four beta-D-hexopyranoses (beta-D-glucose, beta-D-mannose, beta-D-galactose and beta-D-talose) using explicit-solvent (water) molecular dynamics and vacuum stochastic dynamics simulations together with the GROMOS 45A4 force field. Free-energy and solvation free-energy differences between the four compounds are also calculated using thermodynamic integration. Along with previous experimental findings, the present results suggest that the formation of intramolecular hydrogen-bonds in water is an 'opportunistic' consequence of the close proximity of hydrogen-bonding groups, rather than a major conformational driving force promoting this proximity. In particular, the conformational preferences of the hydroxymethyl group in aqueous environment appear to be dominated by 1,3-syn-diaxial repulsion, with gauche and solvation effects being secondary, and intramolecular hydrogen-bonding essentially negligible. The rotational dynamics of the exocyclic hydroxyl groups, which cannot be probed experimentally, is found to be rapid (10-100 ps timescale) and correlated (flip-flop hydrogen-bonds interconverting preferentially through an asynchronous disrotatory pathway). Structured solvent environments are observed between the ring and lactol oxygen atoms, as well as between the 4-OH and hydroxymethyl groups. The calculated stability differences between the four compounds are dominated by intramolecular effects, while the corresponding differences in solvation free energies are small. An inversion of the stereochemistry at either C(2) or C(4) from equatorial to axial is associated with a raise in free energy. Finally, the particularly low hydrophilicity of beta-D-talose appears to be caused by the formation of a high-occurrence hydrogen-bonded bridge between the 1,3-syn-diaxial 2-OH and 4-OH groups. Overall, good agreement is found with available experimental and theoretical data on the structural, dynamical, solvation and energetic properties of these compounds. However, this detailed comparison also reveals some discrepancies, suggesting the need (and providing a solid basis) for further refinement.     

Analysis of ligand binding to proteins using molecular dynamics simulations

This work aims to explore theoretically the molecular mechanisms of ligand binding to proteins through the use of molecular dynamics simulations. The binding of sodium dodecyl sulfate (SDS) to cobra cardio toxin A3 (CTX A3) and thiourea (TOU) to lysozyme have been chosen as the two model systems. Data acquisitions were made by Gromacs software. To begin with, the collisions of ligand molecules with every residue of CTX A3 and lysozyme were evaluated. With this information in hand, the average numbers of collisions with each residue was defined and then assessed. Next, a measure of the affinity of a residue, P_i, referred to as conformational factor, toward a ligand molecule was established. Based on the results provided, all site-making residues for CTX A3 and lysozyme were identified. The results are in good agreement with the experimental data. Finally, based on this method, all site-making residues of bovine carbonic anhydrase (BCA) toward the SDS ligand were predicted.     

Structural analysis of prolyl oligopeptidases using molecular docking and dynamics: insights into conformational changes and ligand binding

Prolyl oligopeptidase (POP) is considered as an important pharmaceutical target for the treatment of numerous diseases. Despite enormous studies on various aspects of POPs structure and function still some of the questions are intriguing like conformational dynamics of the protein and interplay between ligand entry/egress. Here, we have used molecular modeling and docking based approaches to unravel questions like differences in ligand binding affinities in three POP species (porcine, human and A. thaliana). Despite high sequence and structural similarity, they possess different affinities for the ligands. Interestingly, human POP was found to be more specific, selective and incapable of binding to a few planar ligands which showed extrapolation of porcine POP in human context is more complicated. Possible routes for substrate entry and product egress were also investigated by detailed analyses of molecular dynamics (MD) simulations for the three proteins. Trajectory analysis of bound and unbound forms of three species showed differences in conformational dynamics, especially variations in β-propeller pore size, which was found to be hidden by five lysine residues present on blades one and seven. During simulation, β-propeller pore size was increased by ∼2 Å in porcine ligand-bound form which might act as a passage for smaller product movement as free energy barrier was reduced, while there were no significant changes in human and A. thaliana POPs. We also suggest that these differences in pore size could lead to fundamental differences in mode of product egress among three species. This analysis also showed some functionally important residues which can be used further for in vitro mutagenesis and inhibitor design. This study can help us in better understanding of the etiology of POPs in several neurodegenerative diseases.     

Structure and thermodynamics of RNA-protein binding: using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change

An adaptive binding mechanism, requiring large conformational rearrangements, occurs commonly with many RNA-protein associations. To explore this process of reorganization, we have investigated the conformational change upon spliceosomal U1A-RNA binding with molecular dynamics (MD) simulations and free energy analyses. We computed the energetic cost of conformational change in U1A-hairpin and U1A-internal loop binding using a hybrid of molecular mechanics and continuum solvent methods. Encouragingly, in all four free energy comparisons (two slightly different proteins, two different RNAs), the free macromolecule was more stable than the bound form by the physically reasonable value of approximately 10 kcal/mol. We calculated the absolute binding free energies for both complexes to be in the same range as that found experimentally.