Conformational and helicoidal analysis of the molecular dynamics of proteins: "curves," dials and windows for a 50 psec dynamic trajectory of BPTI

A new procedure for the graphic analysis of molecular dynamics (MD) simulations on proteins is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the conformational and helicoidal parameters for each structure entering the analysis via the method "Curves," developed for proteins by Sklenar, Etchebest, and Lavery (Proteins: Structure, Function Genet. 6:46-60, 1989) followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels ("dials") for each torsional parameter and "windows" on the range values assumed by the linear and angular helicoidal parameters, and is present in a form isomorphous with the primary structure per se. The complete time evolution of dynamic structure can then be depicted in a set of four composite figures. Dynamic aspects of secondary and tertiary structure are also provided. The procedure is illustrated with an analysis of a 50 psec in vacuo simulation on the 58 residue protein, bovine pancreatic trypsin inhibitor (BPTI), in the vicinity of the local minimum on the energy surface corresponding to a high resolution crystal structure. The time evolution of 272 conformational and 788 helicoidal parameters for BPTI is analyzed. A number of interesting features can be discerned in the analysis, including the dynamic range of conformational and helicoidal motions, the dynamic extent of 2 degrees structure motifs, and the calculated fluctuations in the helix axis. This approach is expected to be useful for a critical analysis of the effects of various assumptions about force field parameters, truncation of potentials, solvation, and electrostatic effects, and can thus contribute to the development of more reliable simulation protocols for proteins. Extensions of the analysis to present differential changes in conformational and helicoidal parameters is expected to be valuable in MD studies of protein complexes with substrates, inhibitors, and effectors and in determining the nature of structural changes in protein-protein interactions.     

Protein conformational landscapes: Energy minimization and clustering of a long molecular dynamics trajectory

Using energy minimization and cluster analysis, we have analyzed a 1020 ps molecular dynamics trajectory of solvated bovine pancreatic trypsin inhibitor. Elucidation of conformational sub states in this way both illustrates the degree of conformational convergence in the simulation and reduces the structural data to a tractable subset. The relative movement of structures upon energy minimization was used to estimate the sizes of features on the protein potential energy surface. The structures were analyzed using their pairwise root-mean-square C_α deviations, which gave a global measure of conformational changes that would not be apparent by monitoring single degrees of freedom. At time scales of 0.1 ps, energy minimization detected sharp transitions between energy minima separated by 0.1 Å rms deviation. Larger conformational clusters containing these smaller minima and separated by 0.25 Å were seen at 1 ps time scales. Both of these small features of the conformational landscape were characterized by movements in loop regions associated with small, correlated backbone dihedral angle shifts. On a nanosecond time scale, the main features of the protein energy landscape were clusters separated by over 0.7 Å rms deviation, with only seven of these sub states visited over the 1 ns trajectory. These substates, discernible both before and after energy minimization, differ mainly in a monotonic pivot of the loop residues 11–18 over the course of the simulation. This loop contains lysine 17, which specifically binds to trypsin in the active site. The trajectory did not return to previously visited clusters, indicating that this trajectory has not been shown to have completely sampled the conformational substates available to it. Because the apparent convergence to a single region of conformation space depends on both the time scale of observation and the size of the conformational features examined, convergence must be operationally defined within the context of the simulation. © 1995 Wiley-Liss, Inc.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Crystal structures of the peanut lectin-lactose complex at acidic pH: retention of unusual quaternary structure, empty and carbohydrate bound combining sites, molecular mimicry and crystal packing directed by interactions at the combining site

The crystal structures of a monoclinic and a triclinic form of the peanut lectin-lactose complex, grown at pH 4.6, have been determined. They contain two and one crystallographically independent tetramers, respectively. The unusual "open" quaternary structure of the lectin, observed in the orthorhombic complex grown in neutral pH, is retained at the acidic pH. The sugar molecule is bound to three of the eight subunits in the monoclinic crystals, whereas the combining sites in four are empty. The lectin-sugar interactions are almost the same at neutral and acidic pH. A comparison of the sugar-bound and free subunits indicates that the geometry of the combining site is relatively unaffected by ligand binding. The combining site of the eighth subunit in the monoclinic crystals is bound to a peptide stretch in a loop from a neighboring molecule. The same interaction exists in two subunits of the triclinic crystals, whereas density corresponding to sugar exists in the combining sites of the other two subunits. Solution studies show that oligopeptides with sequences corresponding to that in the loop bind to the lectin at acidic pH, but only with reduced affinity at neutral pH. The reverse is the case with the binding of lactose to the lectin. A comparison of the neutral and acidic pH crystal structures indicates that the molecular packing in the latter is directed to a substantial extent by the increased affinity of the peptide loop to the combining site at acidic pH.     

pH-dependent conformational flexibility of the SARS-CoV main proteinase (M(pro)) dimer: molecular dynamics simulations and multiple X-ray structure analyses

The SARS coronavirus main proteinase (M(pro)) is a key enzyme in the processing of the viral polyproteins and thus an attractive target for the discovery of drugs directed against SARS. The enzyme has been shown by X-ray crystallography to undergo significant pH-dependent conformational changes. Here, we assess the conformational flexibility of the M(pro) by analysis of multiple crystal structures (including two new crystal forms) and by molecular dynamics (MD) calculations. The MD simulations take into account the different protonation states of two histidine residues in the substrate-binding site and explain the pH-activity profile of the enzyme. The low enzymatic activity of the M(pro) monomer and the need for dimerization are also discussed.     

Structure and axis curvature in two dA6 x dT6 DNA oligonucleotides: comparison of molecular dynamics simulations with results from crystallography and NMR spectroscopy

Molecular dynamics (MD) simulations have been performed on the A6 containing DNA dodecamers d(GGCAAAAAACGG) solved by NMR and d(CGCAAAAAAGCG) solved by crystallography. The experimental structures differ in the direction of axis bending and in other small but important aspects relevant to the DNA curvature problem. Five nanosecond MD simulations of each sequence have been performed, beginning with both the NMR and crystal forms as well as canonical B-form DNA. The results show that all simulations converge to a common form in close proximity to the observed NMR structure, indicating that the structure obtained in the crystal is likely a strained form due to packing effects. A-tracts in the MD model are essentially straight. The origin of axis curvature is found at pyrimidine-purine steps in the flanking sequences.     

Open interface and large quaternary structure movements in 3D domain swapped proteins: insights from molecular dynamics simulations of the C-terminal swapped dimer of ribonuclease A

Bovine pancreatic ribonuclease (RNase A) forms two three-dimensional (3D) domain swapped dimers. Crystallographic investigations have revealed that these dimers display completely different quaternary structures: one dimer (N-dimer), which presents the swapping of the N-terminal helix, is characterized by a compact structure, whereas the other (C-dimer), which is stabilized by the exchange of the C-terminal end, shows a rather loose assembly of the two subunits. The dynamic properties of monomeric RNase A and of the N-dimer have been extensively characterized. Here, we report a molecular dynamics investigation carried out on the C-dimer. This computational experiment indicates that the quaternary structure of the C-dimer undergoes large fluctuations. These motions do not perturb the proper folding of the two subunits, which retain the dynamic properties of RNase A and the N-dimer. Indeed, the individual subunits of the C-dimer display the breathing motion of the beta-sheet structure, which is important for the enzymatic activity of pancreatic-like ribonucleases. In contrast to what has been observed for the N-dimer, the breathing motion of the two subunits of the C-dimer is not coupled. This finding suggests that the intersubunit communications in a 3D domain swapped dimer strongly rely on the extent of the interchain interface. Furthermore, the observation that the C-dimer is endowed with a high intrinsic flexibility holds interesting implications for the specific properties of 3D domain swapped dimers. Indeed, a survey of the quaternary structures of the other 3D domain swapped dimers shows that large variations are often observed when the structural determinations are conducted in different experimental conditions. The 3D domain swapping phenomenon coupled with the high flexibility of the quaternary structure may be relevant for protein-protein recognition, and in particular for the pathological aggregations.