Model-free methods of analyzing domain motions in proteins from simulation: A comparison of normal mode analysis and molecular dynamics simulation of lysozyme

Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations. For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by modes of motion external to the domains. To analyze the molecular dynamics trajectory, a principal component analysis tailored specifically to analyze interdomain motions is applied. A method based on the curl of the atomic displacements is described, which yields a sharp discrimination of domains, and which defines a unique interdomain screw-axis. Hinge axes are defined and classified as twist or closure axes depending on their direction. The methods have been tested on lysozyme. A remarkable correspondence was found between the first normal mode axis and the first principal mode axis, with both axes passing within 3 Å of the alpha-carbon atoms of residues 2, 39, and 56 of human lysozyme, and near the interdomain helix. The axes of the first modes are overwhelmingly closure axes. A lesser degree of correspondence is found for the second modes, but in both cases they are more twist axes than closure axes. Both analyses reveal that the interdomain connections allow only these two degrees of freedom, one more than provided by a pure mechanical hinge. Proteins 27:425–437, 1997. © 1997 Wiley-Liss, Inc.     

Systematic analysis of domain motions in proteins from conformational change: New results on citrate synthase and T4 lysozyme

Methods developed originally to analyze domain motions from simulation [Proteins 27:425–437, 1997] are adapted and extended for the analysis of X-ray conformers and for proteins with more than two domains. The method can be applied as an automatic procedure to any case where more than one conformation is available. The basis of the methodology is that domains can be recognized from the difference in the parameters governing their quasi-rigid body motion, and in particular their rotation vectors. A clustering algorithm is used to determine clusters of rotation vectors corresponding to main-chain segments that form possible dynamic domains. Domains are accepted for further analysis on the basis of a ratio of interdomain to intradomain fluctuation, and Chasles' theorem is used to determine interdomain screw axes. Finally residues involved in the interdomain motion are identified. The methodology is tested on citrate synthase and the M6I mutant of T4 lysozyme. In both cases new aspects to their conformational change are revealed, as are individual residues intimately involved in their dynamics. For citrate synthase the beta sheet is identified to be part of the hinging mechanism. In the case of T4 lysozyme, one of the four transitions in the pathway from the closed to the open conformation, furnished four dynamic domains rather than the expected two. This result indicates that the number of dynamic domains a protein possesses may not be a constant of the motion. Proteins 30:144–154, 1998. © 1998 Wiley-Liss, Inc.     

Global and local motions in ribonuclease A: a molecular dynamics study

The understanding of protein dynamics is one of the major goals of structural biology. A direct link between protein dynamics and function has been provided by x-ray studies performed on ribonuclease A (RNase A) (B. F. Rasmussen et al., Nature, 1992, Vol. 357, pp. 423-424; L. Vitagliano et al., Proteins: Structure, Function, and Genetics, 2002, Vol. 46, pp. 97-104). Here we report a 3 ns molecular dynamics simulation of RNase A in water aimed at characterizing the dynamical behavior of the enzyme. The analysis of local and global motions provides interesting insight on the dynamics/function relationship of RNase A. In agreement with previous crystallographic reports, the present study confirms that the RNase A active site is constituted by rigid (His12, Asn44, Thr45) and flexible (Lys41, Asp83, His119, Asp121) residues. The analysis of the global motions, performed using essential dynamics, shows that the two beta-sheet regions of RNase A move coherently in opposite directions, thus modifying solvent accessibility of the active site, and that the mixed alpha/3(10)-helix (residues 50-60) behaves as a mechanical hinge during the breathing motion of the protein. These data demonstrate that this motion, essential for RNase A substrate binding and release, is an intrinsic dynamical property of the ligand-free enzyme.     

On the similarity of properties in solution or in the crystalline state: A molecular dynamics study of hen lysozyme

As protein crystals generally possess a high water content, it is assumed that the behaviour of a protein in solution and in crystal environment is very similar. This assumption can be investigated by molecular dynamics (MD) simulation of proteins in the different environments. Two 2ns simulations of hen egg white lysozyme (HEWL) in crystal and solution environment are compared to one another and to experimental data derived from both X-ray and NMR experiments, such as crystallographic B-factors, NOE atom–atom distance bounds, ³J_{H N}-coupling constants, and ¹H-¹⁵N bond vector order parameters. Both MD simulations give very similar results. The crystal simulation reproduces X-ray and NMR data slightly better than the solution simulation.     

Essential dynamics sampling study of adenylate kinase: comparison to citrate synthase and implication for the hinge and shear mechanisms of domain motions

Essential dynamics sampling simulations of the domain conformations of unliganded Escherichia coli adenylate kinase have been performed to determine whether the ligand-induced closed-domain conformation is accessible to the open unliganded enzyme. Adenylate kinase is a three- domain protein with a central CORE domain and twoflanking domains, the LID and the NMPbind domains. The sampling simulations were applied to the CORE and NMPbind domain pair and the CORE and LID domain pair separately. One aim is to compare the results to those of a similar study on the enzyme citrate synthase to determine whether a similar domain-locking mechanism operates in adenylate kinase. Although for adenylate kinase the simulations suggest that the closed-domain conformation of the unliganded enzyme is at a slightly higher free energy than the open for both domain pairs, the results are radically different to those found for citrate synthase. In adenylate kinase the targeted domain conformations could always be achieved, whereas this was not the case in citrate synthase due to an apparent free-energy barrier between the open and closed conformations. Adenylate kinase has been classified as a protein that undergoes closure through a hinge mechanism, whereas citrate synthase has been assigned to the shear mechanism. This was quantified here in terms of the change in the number of interdomain contacting atoms upon closure which showed a considerable increase in adenylate kinase. For citrate synthase this number remained largely the same, suggesting that the domain faces slide over each other during closure. This suggests that shear and hinge mechanisms of domain closure may relate to the existence or absence of an appreciable barrier to closure for the unliganded protein, as the latter can hinge comparatively freely, whereas the former must follow a more constrained path. In general though it appears a bias toward keeping the unliganded enzyme in the open-domain conformation may be a common feature of domain enzymes.     

A molecular dynamics simulation of bacteriophage T4 lysozyme.

An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. The simulation was carried out with all hydrogen atoms modeled explicitly, the inclusion of all 152 crystallographic waters and at a temperature of 300 K. Temporal analysis of the trajectory versus energy, hydrogen bond stability, r.m.s. deviation from the starting crystal structure and radius of gyration, demonstrates that the simulation was both stable and representative of the average experimental structure. Average structural properties were calculated from the enzyme trajectory and compared with the crystal structure. The mean value of the C alpha displacements of the average simulated structure from the X-ray structure was 1.1 +/- 0.1 A; differences of the backbone phi and psi angles between the average simulated structure and the crystal structure were also examined. Thermal-B factors were calculated from the simulation for heavy and backbone atoms and both were in good agreement with experimental values. Relationships between protein secondary structure elements and internal motions were studied by examining the positional fluctuations of individual helix, sheet and turn structures. The structural integrity in the secondary structure units was preserved throughout the simulation; however, the A helix did show some unusually high atomic fluctuations. The largest backbone atom r.m.s. fluctuations were found in non-secondary structure regions; similar results were observed for r.m.s. fluctuations of non-secondary structure phi and psi angles. In general, the calculated values of r.m.s. fluctuations were quite small for the secondary structure elements. In contrast, surface loops and turns exhibited much larger values, being able to sample larger regions of conformational space. The C alpha difference distance matrix and super-positioning analyses comparing the X-ray structure with the average dynamics structure suggest that a 'hinge-bending' motion occurs between the N- and C-terminal domains.     

Torsion angle dynamics: Reduced variable conformational sampling enhances crystallographic structure refinement

A reduced variable conformational sampling strategy for macromolecules based on molecular dynamics in torsion angle space is evaluated using crystallographic refinement as a prototypical search problem. Bae and Haug's algorithm for constrained dynamics [Bae, D. S., Haug, E. J. A recursive formulation for constrained mechanical system dynamics. Mech. Struct. Mach. 15:359–382, 1987], originally developed for robotics, was used. Their formulation solves the equations of motion exactly for arbitrary holonomic constraints, and hence differs from commonly used approximation algorithms. It uses gradients calculated in Cartesian coordinates, and thus also differs from internal coordinate formulations. Molecular dynamics can be carried out at significantly higher temperatures due to the elimination of the high frequency bond and angle vibrations. The sampling strategy presented here combines high temperature torsion angle dynamics with repeated trajectories using different initial velocities. The best solutions can be identified by the free R value, or the R value if experimental phase information is appropriately included in the refinement. Applications to crystallographic refinement show a significantly increased radius of convergence over conventional techniques. For a test system with diffraction data to 2 Å resolution, slow-cooling protocols fail to converge if the backbone atom root mean square (rms) coordinate deviation from the crystal structure is greater than 1.25 Å, but torsion angle refinement can correct backbone atom rms coordinate deviations up to approximately 1.7 Å. © 1994 Wiley-Liss, Inc.     

Catalytic mechanism of cyclophilin as observed in molecular dynamics simulations: pathway prediction and reconciliation of X-ray crystallographic and NMR solution data

Cyclophilins are proteins that catalyze X-proline cis-trans interconversion, where X represents any amino acid. Its mechanism of action has been investigated over the past years but still generates discussion, especially because until recently structures of the ligand in the cis and trans conformations for the same system were lacking. X-ray crystallographic structures for the complex cyclophilin A and HIV-1 capsid mutants with ligands in the cis and trans conformations suggest a mechanism where the N-terminal portion of the ligand rotates during the cis-trans isomerization. However, a few years before, a C-terminal rotating ligand was proposed to explain NMR solution data. In the present study we use molecular dynamics (MD) simulations to generate a trans structure starting from the cis structure. From simulations starting from the cis and trans structures obtained through the rotational pathways, the seeming contradiction between the two sets of experimental data could be resolved. The simulated N-terminal rotated trans structure shows good agreement with the equivalent crystal structure and, moreover, is consistent with the NMR data. These results illustrate the use of MD simulation at atomic resolution to model structural transitions and to interpret experimental data.     

Exploring subdomain cooperativity in T4 lysozyme I: structural and energetic studies of a circular permutant and protein fragment

Small proteins are generally observed to fold in an apparent two-state manner. Recently, however, more sensitive techniques have demonstrated that even seemingly single-domain proteins are actually made up of smaller subdomains. T4 lysozyme is one such protein. We explored the relative autonomy of its two individual subdomains and their contribution to the overall stability of T4 lysozyme by examining a circular permutation (CP13*) that relocates the N-terminal A-helix, creating subdomains that are contiguous in sequence. By determining the high-resolution structure of CP13* and characterizing its energy landscape using native state hydrogen exchange (NSHX), we show that connectivity between the subdomains is an important determinant of the energetic cooperativity but not structural integrity of the protein. The circular permutation results in a protein more easily able to populate a partially unfolded form in which the C-terminal subdomain is folded and the N-terminal subdomain is unfolded. We also created a fragment model of this intermediate and demonstrate using X-ray crystallography that its structure is identical to the corresponding residues in the full-length protein with the exception of a small network of hydrophobic interactions. In sum, we conclude that the C-terminal subdomain dominates the energetics of T4 lysozyme folding, and the A-helix serves an important role in coupling the two subdomains.     

Essential domain motions in barnase revealed by MD simulations

The wealth of data accumulated on the bacterial ribonuclease barnase is complemented by molecular dynamics trajectories starting from four different experimental structures and covering a total of >10 ns. Using principal component analysis, the simulations are interpreted in view of dynamic domains and hinges promoting relative motions of these domains. Two domains with residues 7-22 and 52-108 for the first domain and residues 25-51 for the second domain were consistently observed. Hinge regions consist primarily of Tyr24, Ser50, Ile51, and Gly52. Earlier mutation studies have demonstrated that the residues of the hinge regions play essential roles for the stability and activity of barnase. The domain motions are correlated to inter-domain interactions involving functionally important active site residues, such as Lys27 and Glu73. A model is presented that combines the observation of dynamic domains and their motions with the extensive mutation data from the literature. Enthalpic energy contributions originating from specific inter-domain interactions as well as entropic energy contributions due to the domain motions are discussed in the frame of this model and compared with destabilization energies measured for corresponding mutants.     

Substrate binding modifies the hinge bending characteristics of human 3‐phosphoglycerate kinase: A molecular dynamics study

3‐Phosphogycerate kinase (PGK) is a two domain enzyme, with a binding site of the 1,3‐bisphosphoglycerate on the N‐domain and of the ADP on the C‐domain. To transfer a phosphate group the enzyme has to undergo a hinge bending motion from open to closed conformation to bring the substrates to close proximity. Molecular dynamics simulation was used to elucidate the effect of ligand binding onto the domain motions of this enzyme. The simulation results of the apo form indicate a hinge bending motion in the ns timescale while the time period of the hinge bending motion of the complex form is clearly over the 20 ns simulation time. The apo form exhibits several hinge points that contribute to the hinge bending motion while upon binding the ligands, the hinge bending becomes strictly restrained with one dominant hinge point in the vicinity of the substrates. At the same time, ligand binding results in an enhanced correlation of internal domain motions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

A model binding site for testing scoring functions in molecular docking

Prediction of interaction energies between ligands and their receptors remains a major challenge for structure-based inhibitor discovery. Much effort has been devoted to developing scoring schemes that can successfully rank the affinities of a diverse set of possible ligands to a binding site for which the structure is known. To test these scoring functions, well-characterized experimental systems can be very useful. Here, mutation-created binding sites in T4 lysozyme were used to investigate how the quality of atomic charges and solvation energies affects molecular docking. Atomic charges and solvation energies were calculated for 172,118 molecules in the Available Chemicals Directory using a semi-empirical quantum mechanical approach by the program AMSOL. The database was first screened against the apolar cavity site created by the mutation Leu99Ala (L99A). Compared to the electronegativity-based charges that are widely used, the new charges and desolvation energies improved ranking of known apolar ligands, and better distinguished them from more polar isosteres that are not observed to bind. To investigate whether the new charges had predictive value, the non-polar residue Met102, which forms part of the binding site, was changed to the polar residue glutamine. The structure of the resulting Leu99Ala and Met102Gln double mutant of T4 lysozyme (L99A/M102Q) was determined and the docking calculation was repeated for the new site. Seven representative polar molecules that preferentially docked to the polar versus the apolar binding site were tested experimentally. All seven bind to the polar cavity (L99A/M102Q) but do not detectably bind to the apolar cavity (L99A). Five ligand-bound structures of L99A/M102Q were determined by X-ray crystallography. Docking predictions corresponded to the crystallographic results to within 0.4A RMSD. Improved treatment of partial atomic charges and desolvation energies in database docking appears feasible and leads to better distinction of true ligands. Simple model binding sites, such as L99A and its more polar variants, may find broad use in the development and testing of docking algorithms.     

An evaluation of implicit and explicit solvent model systems for the molecular dynamics simulation of bacteriophage T4 lysozyme

In this report we examine several solvent models for use in molecular dynamics simulations of protein molecules with the Discover program from Biosym Technologies. Our goal was to find a solvent system which strikes a reasonable balance among theoretical rigor, computational efficiency, and experimental reality. We chose phage T4 lysozyme as our model protein and analyzed 14 simulations using different solvent models. We tested both implicit and explicit solvent models using either a linear distance-dependent dielectric or a constant dielectric. Use of a linear distance-dependent dielectric with implicit solvent significantly diminished atomic fluctuations in the protein and kept the protein close to the starting crystal structure. In systems using a constant dielectric and explicit solvent, atomic fluctuations were much greater and the protein was able to sample a larger portion of conformational space. A series of nonbonded cutoff distances (9.0, 11.5, 15.0, 20.0 Å) using both abrupt and smooth truncation of the nonbonded cutoff distances were tested. The method of dual cutoffs was also tested. We found that a minimum nonbonded cutoff distance of 15.0 Å was needed in order to properly couple solvent and solute. Distances shorter than 15.0 Å resulted in a significant temperature gradient between the solvent and solute. In all trajectories using the proprietary Discover switching function, we found significant denaturation in the protein backbone; we were able to run successful trajectories only in those simulations that used no switching function. We were able to significantly reduce the computational burden by using dual cutoffs and still calculate a quality trajectory. In this method, we found that an outer cutoff distance of 15.0 Å and an inner cutoff distance of 11.5 worked well. While a 10 Å shell of explicit water yielded the best results, a 6 A shell of water yielded satisfactory results with nearly a 40% reduction in computational cost. © 1994 John Wiley & Sons, Inc.     

Structure and dynamics of the active site gorge of acetylcholinesterase: synergistic use of molecular dynamics simulation and X-ray crystallography.

The active site of acetylcholinesterase (AChE) from Torpedo californica is located 20 A from the enzyme surface at the bottom of a narrow gorge. To understand the role of this gorge in the function of AChE, we have studied simulations of its molecular dynamics. When simulations were conducted with pure water filling the gorge, residues in the vicinity of the active site deviated quickly and markedly from the crystal structure. Further study of the original crystallographic data suggests that a bis-quaternary decamethonium (DECA) ion, acquired during enzyme purification, residues in the gorge. There is additional electron density within the gorge that may represent small bound cations. When DECA and 2 cations are placed within the gorge, the simulation and the crystal structure are dramatically reconciled. The small cations, more so than DECA, appear to stabilize part of the gorge wall through electrostatic interactions. This part of the gorge wall is relatively thin and may regulate substrate, product, and water movement through the active site.     

Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme

A method is presented to describe the internal motions of proteins obtained from molecular dynamics or Monte Carlo simulations as motions of normal mode variables. This method calculates normal mode variables by projecting trajectories of these simulations onto the axes of normal modes and expresses the trajectories as a linear combination of normal mode variables. This method is applied to the result of the molecular dynamics and the Monte Carlo simulations of human lysozyme. The motion of the lowest frequency mode extracted from the simulations represents the hinge bending motion very faithfully. Analysis of the obtained motions of the normal mode variables provides an explanation of the anharmonic aspects of protein dynamics as due first to the anharmonicity of the actual potential energy surface near a minimum and second to trans-minimum conformational changes.     

Structural and dynamical properties of KTS‐disintegrins: A comparison between Obtustatin and Lebestatin

Obtustatin and Lebestatin are lysine‐threonine‐serine (KTS)‐disintegrins, which are a family of low molecular weight polypeptides present in many viperidae venoms and are potent and specific inhibitors of collagen‐binding integrins. The integrin binding loop, harboring the ²¹KTS²³ motif, and the C‐terminal tail are known to be responsible for the selective binding to the α1β1 integrin. Despite a very high sequence homology (only two mutations are present in Lebestatin relative to Obtustatin, namely R24L and S38L), Lebestatin exhibits a higher inhibitory effect than Obtustatin on cell adhesion and cell migration to collagens I and IV. Here we show, by means of molecular dynamics simulations of the two polypeptides in aqueous solution, that Lebestatin possesses a higher flexibility of the C‐terminal tail and a greater solvent accessibility of the integrin binding loop than Obtustatin. It may be hypothesized that these properties may contribute to the higher binding‐affinity of Lebestatin to its biological partner. © 2012 Wiley Periodicals, Inc.     

Relation between hen egg white lysozyme and bacteriophage T4 lysozyme: Evolutionary implications

Hen egg white lysozyme and T4 bacteriophage lysozyme have the same catalytic function, but have non-homologous amino acid sequences. Notwithstanding the differences in their primary structures, the two lysozymes have similarities in their overall backbone conformations, in their modes of binding substrates and probably in their mechanisms of action.By different criteria, the similarity between the folding of the two enzymes can be shown to be statistically significant. Also the transformation which optimizes the agreement between the backbones of the two molecules is shown to accurately align their active site clefts, so that saccharide units bound in the A, B, C and D subsites of hen egg white lysozyme coincide within 1 to 2 Å with analogous saccharides bound to phage lysozyme. Furthermore, a number of the specific interactions between enzyme and substrate which were observed for hen egg white lysozyme, and thought to be important for catalysis, are found to occur in a structurally analogous way in the phage enzyme. Fifty-four atoms from the respective active sites which appear to be equivalent, including saccharides bound in the B and C sites, superimpose with a root-mean-square discrepancy of 1.35 Å.These structural and functional similarities suggest that the two lysozymes have arisen by divergent evolution from a common precursor. This is the first case in which two proteins of completely different amino acid sequence have been shown, with high probability, to have evolved by divergent rather than convergent evolution.     

Hydration pattern of A4T4 and T4A4 DNA: a molecular dynamics study

Hydration pattern and energetics of 'A-tract' containing duplexes have been studied using molecular dynamics on 12-mer self-complementary sequences 5'-d(GCA4T4GC)-3' and 5'-d(CGT4A4CG)-3'. The structural features for the simulated duplexes showed correlation with the corresponding experimental structures. Analysis of the hydration pattern confirmed that water network around the simulated duplexes is more conformation specific rather than sequence specific. The calculated heat capacity change upon duplex formation showed that the process is entropically driven for both the sequences. Furthermore, the theoretical free energy estimates calculated using MMPBSA approach showed a higher net electrostatic contribution for A4T4 duplex formation than for T4A4, however, energetically both the duplexes are observed to be equally stable.     

Automatic identification of discrete substates in proteins: Singular value decomposition analysis of time-averaged crystallographic refinements

The singular value decomposition (SVD) provides a method for decomposing a molecular dynamics trajectory into fundamental modes of atomic motion. The right singular vectors are projections of the protein conformations onto these modes showing the protein motion in a generalized low-dimensional basis. Statistical analysis of the right singular vectors can be used to classify discrete configurational substates in the protein. The configuration space portraits formed from the right singular vectors can also be used to visualize complex high-dimensional motion and to examine the extent of configuration space sampling by the simulation. © 1995 Wiley-Liss, Inc.