Refinement of the solution structure of the DNA decamer 5'd(CTGGATCCAG)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary DNA decamer 5'd(CTGGATCCAG)2 comprising the specific target site for the restriction endonuclease BamH1 is investigated by using nuclear magnetic resonance sectroscopy and restrained molecular dynamics. With the exception of the H5'/H5" sugar proton resonances, all the nonexchangeable proton resonances are assigned sequentially by using pure-phase absorption two-dimensional nuclear Overhauser enhancement spectroscopy. From the time dependence of the nuclear Overhauser effects a set of 160 approximate interproton distances is determined and used as the basis of a structure refinement employing restrained molecular dynamics in which the interproton distances are incorporated into the total energy function of the system in the form of an effective potential term. Two restrained dynamics simulations are carried out, starting from classical B- and A-DNA [atomic root mean square (rms) difference 5.7 A]. In both cases convergence is achieved to very similar B-type structures with an atomic rms difference of 0.9 A which is comparable to the rms fluctuations of the atoms about their average positions. In addition, the rms difference between the experimental and calculated values of the interproton distances for both average restrained dynamics structures is approximately 0.3 A. These results suggest that the converged restrained molecular dynamics structures represent reasonable approximations of the solution structure. The average restrained dynamics structures exhibit clear sequence-dependent variations of torsion angles and helical parameters. In addition, the structures exhibit a small bend of around 10-20 degrees at the second (TpG) and eighth (CpA) base pair steps. This can be attributed to the positive base roll angles and large base pair slide values at the two Pyr-Pur steps. The central core of the decamer comprising the six-base recognition site for BamH1 (GGATCC), however, is straight.     

Structure determination of [d(ATATATAUAT)]2 via two-dimensional NOE spectroscopy and molecular dynamics calculations

Proton homonuclear two-dimensional (2D) NOE spectra were obtained for the decamer [d(ATATATAUAT)]2 as a function of mixing time, and proton resonance assignments were made. Quantitative assessment of the 2D NOE cross-peak intensities was used in conjunction with the program MARDIGRAS, which entails a complete relaxation matrix analysis of the 2D NOE peak intensities, to obtain a set of upper and lower bound interproton distance constraints. The analysis with MARDIGRAS was carried out using three initial models: A-DNA, B-DNA and Z-DNA. The distance constraints determined were essentially the same regardless of initial structure. These experimental structural constraints were used with restrained molecular dynamics calculations to determine the solution structure of the decamer. The molecular dynamics program AMBER was run using A-DNA or B-DNA as starting model. The root-mean-square (rms) difference between these two starting models is 0.504 nm. The two starting models were subjected to 22.5 ps of restrained molecular dynamics calculations. The coordinates of the last 10.5 ps of the molecular dynamics runs were averaged to give two final structures. MDA and MDB. The rms difference between these two structures is 0.09 nm, implying convergence of the two molecular dynamics runs. The 2D NOE spectral intensities calculated for the derived structures are in good agreement with experimental spectra, based on sixth-root residual index analysis of intensities. A detailed examination of the structural features suggests that while the decamer is in the B-family of DNA structures, many torsion angle and helical parameters alternate from purine to pyrimidine, with kinks occurring at the U-A steps.     

Refinement of the solution structure of the ribonucleotide 5'r(GCAUGC)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary hexamer 5'r(GCAUGC)2 is investigated by means of nuclear magnetic resonance spectroscopy and restrained molecular dynamics. The proton resonances are assigned in a sequential manner, and a set of 110 approximate interproton distance restraints are derived from the two-dimensional nuclear Overhauser enhancement spectra. These distances are used as the basis of a structure refinement by restrained molecular dynamics in which the experimental restraints are incorporated into the total energy function of the system in the form of effective potentials. Eight restrained molecular dynamics simulations are carried out, four starting from a structure with regular A-type geometry and four from one with regular B-type geometry. The atomic root mean square (rms) difference between the initial structures is 3.2 A. In the case of all eight simulations, convergence is achieved both globally and locally to a set of very similar A-type structures with an average atomic rms difference between them of 0.8 +/- 0.2 A. Further, the atomic rms differences between the restrained dynamics structures obtained by starting out from the same initial structures but with different random number seeds for the assignment of the initial velocities are the same as those between the restrained dynamics structures starting out from the two different initial structures. These results suggest that the restrained dynamics structures represent good approximations of the solution structure. The converged structures exhibit clear sequence-dependent variation in some of the helical parameters, in particular helix twist, roll, slide, and propellor twist.(ABSTRACT TRUNCATED AT 250 WORDS)     

Three-dimensional structure of the apo form of the N-terminal EGF-like module of blood coagulation factor X as determined by NMR spectroscopy and simulated folding.

The three-dimensional structure of a 42-residue fragment containing the N-terminal EGF-like module of blood coagulation factor X was determined by means of 2D NMR spectroscopy and computer simulation. The spectroscopic data consisted of 370 NOE distances and 27 dihedral angle constraints. These were used to generate peptide conformations by molecular dynamics simulation. The simulations used a novel functional form for the constraint potentials and were performed with two time steps to ensure rapid execution. Apart from preliminary runs to aid assignment of NOEs, 60 runs resulted in 13 accepted structures, which have two antiparallel beta sheets, no alpha helices, and five tight turns. There is no hydrophobic cluster. The root mean square deviation for the backbone of the 13 conformations is 0.65 +/- 0.11 A against their mean conformation. About half of the side chains have well-defined structure. The overall conformation is similar to that of murine EGF.     

Refinement of the solution structure of the DNA hexamer 5'd(GCATGC)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary DNA hexamer 5'd(GCATGC)2 comprising the specific target site for the restriction endonuclease Sph 1 is investigated by using nuclear magnetic resonance spectroscopy and restrained molecular dynamics. All the nonexchangeable proton resonances are assigned sequentially, and from time-dependent nuclear Overhauser enhancement measurements a set of 158 approximate interproton distances are determined. These distances are used as the basis of a structure refinement using restrained molecular dynamics in which the interproton distances are incorporated into the total energy function of the system in the form of an effective potential term. Two restrained molecular dynamics simulations are carried out, starting from classical B- and A-DNA [atomic root mean square (rms) difference 3.3 A]. In both cases convergence is achieved to essentially identical structures satisfying the experimental restraints and having a root mean square difference of only 0.3 A between them, which is within the rms fluctuations of the atoms about their average positions. These results suggest that the restrained molecular dynamics structures represent reasonable approximations of the solution structure. The converged structures are of the B type and exhibit clear sequence-dependent variations of helical parameters, some of which follow Calladine's rules and can be attributed to the relief of interstrand purine-purine clash at adjacent base pairs. In addition, the converged restrained dynamics structures appear bent with a radius of curvature of approximately 20 A. This bending appears to be due almost entirely to the large positive base roll angles, particularly at the Pyr-Pur steps. Further, the global and local helix axes are not coincident, and the global helix axis represents a superhelical axis which the bent DNA, when extended into an "infinite" helix by repeated translation and rotation, wraps around.     

Standard conformations of a polypeptide chain in irregular protein regions

A detailed stereochemical analysis of known protein structures has been made which shows that: (1) irregular regions of proteins consist of a limited number of standard structures formed by three, four of more residues; (2) an amino acid residue of a protein can adopt one of the six sterically allowed conformations designated here as alpha, alpha L, beta, gamma, delta, and epsilon. It is shown that there are two allowed conformations of a polypeptide chain at the N-end of an alpha-helix, beta alpha n- and beta gamma alpha n-conformations, where n is a number of residues in the alpha-helix. At the C-end of the alpha-helix there are two conformations as well, alpha n gamma beta- and alpha n gamma alpha L beta-ones. Two beta-strands in a beta-hairpin can be joined, for example, by standard structures with beta beta alpha L beta-, beta alpha gamma alpha L beta-, beta alpha alpha gamma alpha L beta-conformations which are referred to as turns. In the regions where a polypeptide chain passes from one layer to another there are standard structures with beta gamma beta-, beta alpha beta beta-, beta alpha gamma beta-conformations etc., referred to as cross-overs. A structure of any protein irregular region can be represented as a combination of these and other standard turns and cross-overs considered in the paper. The major part of the turns and cross-overs has residues in alpha L- or epsilon-conformations which must be glycine or other residues with small or flexible side chains. Massive hydrophobic residues must not occupy the first beta-positions of the most standard structures. The results obtained can be successfully applied for prediction of the location of the turns and cross-overs in proteins from their amino acid sequences and for interpretation of electron density maps.     

Variable-target-function and build-up procedures for the calculation of protein conformation. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data

An implementation of the variable-target-function procedure, first introduced by Braun and Go [W. Braun and N. Go, J. Mol. Biol. 186, 611-626 (1985)], has been used to generate conformations of the small protein bovine pancreatic trypsin inhibitor (BPTI), given a limited set of simulated data that could be obtained by nuclear magnetic resonance (NMR) techniques. A hybrid strategy was also used to calculate conformations of BPTI, given the same information. In the hybrid strategy, low-energy structures of medium-size fragments (decapeptides) of BPTI were generated using the variable-target-function method, followed by restrained energy optimization. The low-energy conformations were used as a basis to build up the complete fifty-eight-residue BPTI molecule. By using the variable-target-function approach, in which energy considerations were not introduced until full conformations of the entire BPTI molecule had been generated, it was not possible to obtain calculated structures with rms deviations from the X-ray conformation of less than 1.6 A for the alpha-carbons. On the other hand, with the hybrid strategy, which involved the consideration of realistic energy terms in the early stages of the calculations, it was possible to calculate low-energy conformations of BPTI with rms deviations from the X-ray structure of 1.06 to 1.50 A for the alpha-carbons. When the rms deviations were computed along the amino acid sequence, it was found that there was a good correlation between deviations among the calculated structures and deviations from the X-ray structure.     

Three-dimensional structure of potato carboxypeptidase inhibitor in solution. A study using nuclear magnetic resonance, distance geometry, and restrained molecular dynamics

The solution conformation of potato carboxypeptidase inhibitor (CPI) has been investigated by 1H NMR spectroscopy. The spectrum is assigned in a sequential manner by using two-dimensional NMR techniques to identify through-bond and through-space (less than 5 A) connectivities. A set of 309 approximate interproton distance restraints is derived from the two-dimensional nuclear Overhauser enhancement spectra and used as the basis of a three-dimensional structure determination by a combination of metric matrix distance geometry and restrained molecular dynamics calculations. A total of 11 converged distance geometry structures were computed and refined by using restrained molecular dynamics. The average atomic root mean square (rms) difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.3 A for residues 2-39 and 0.9 +/- 0.2 A for residues 5-37. The corresponding values for all atoms are 1.9 +/- 0.3 and 1.4 +/- 0.2 A, respectively. The larger values for residues 2-38 relative to those for residues 5-37 arise from the fact that the positions of the N- (residues 1-4) and C- (residues 38-39) terminal tails are rather poorly determined, whereas those of the core of the protein (residues 5-37) are well determined by the experimental interproton distance data. The computed structures are very close to the X-ray structure of CPI in its complex with carboxypeptidase, and the backbone atomic rms difference between the mean of the computed structures and the X-ray structure is only 1.2 A. Nevertheless, there are some real differences present which are evidenced by significant deviations between the experimental upper interproton distance limits and the corresponding interproton distances derived from the X-ray structure. These principally occur in two regions, residues 18-20 and residues 28-30, the latter comprising part of the region of secondary contacts between CPI and carboxypeptidase in the X-ray structure.     

Conformational flexibility and loss of structural rigidity for a model hexapeptide,GRGDTP: 1H‐NMR and molecular dynamics studies

The NMR and molecular dynamics methods are used to study the conformations of a hexapeptide, GRGDTP, which has been shown to be accessible to various types of cell‐adhesion based cellular behaviors such as cell‐to‐matrix interactions, cell differentiation, immunogenicity development, gene expression, angiogenesis, metastasis, sex determination and gamete fusion. ¹H‐NMR results indicate the existence of weak 5→2 hydrogen bonded β‐turn type‐III. Molecular simulation studies using a mixed protocol of distance geometry, constrained minimization, restrained molecular dynamics followed by energy minimization resulted additional conformations that include about 64% of population of inverse γ‐turn (HB, 3→1) and about 35% population of γ‐turn (HB, 4→2). The inter‐proton distances observed in γ‐and inverse γ‐turns are also consistent with the NMR constraints. The variable internal hydrogen bonding due to γ‐turns initiated at Gly 1 and Arg 2 , and its tendency to inter‐convert between γ‐and inverse γ‐turn conformations imply that the peptide is flexible in nature. © 2013 Wiley Periodicals, Inc. Biopolymers 99: 460–471, 2013.     

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.     

Variable-Target-Function and Build-up Procedures for the Calculation of Protein Conformation. Application to Bovine Pancreatic Trypsin Inhibitor Using Limited Simulated Nuclear Magnetic Resonance Data

Abstract

An implementation of the variable-target-function procedure, first introduced by Braun and Gō [W. Braun and N. Gō, J. Mol. Biol. 186, 611–626 (1985)], has been used to generate conformations of the small protein bovine pancreatic trypsin inhibitor (BPTI), given a limited set of simulated data that could be obtained by nuclear magnetic resonance (NMR) techniques. A hybrid strategy was also used to calculate conformations of BPTI, given the same information. In the hybrid strategy, low-energy structures of medium-size fragments (decapeptides) of BPTI were generated using the variable-target-function method, followed by restrained energy optimization. The low-energy conformations were used as a basis to build up the complete fifty-eight-residue BPTI molecule. By using the variable-target-function approach, in which energy considerations were not introduced until full conformations of the entire BPTI molecule had been generated, it was not possible to obtain calculated structures with rms deviations from the X-ray conformation of less than 1.6 Å for the α-carbons. On the other hand, with the hybrid strategy, which involved the consideration of realistic energy terms in the early stages of the calculations, it was possible to calculate low-energy conformations of BPTI with rms deviations from the X-ray structure of 1.06 to 1.50 Å for the α-carbons. When the rms deviations were computed along the amino acid sequence, it was found that there was a good correlation between deviations among the calculated structures and deviations from the X-ray structure.     

Structure refinement of oligonucleotides by molecular dynamics with nuclear Overhauser effect interproton distance restraints: application to 5' d(C-G-T-A-C-G)2

The solution structure of the self-complementary DNA hexamer 5' d(C-G-T-A-C-G)2 is refined by restrained molecular dynamics in which 192 interproton distances, determined from pre-steady-state nuclear Overhauser enhancement measurements, are incorporated into the total energy of the system in the form of effective potentials. First the method is tested by applying an idealized set of distance restraints taken from classical B-DNA to a simulation starting off from A-DNA and vice versa. It is shown that in both cases the expected transition between A- and B-DNA occurs. Second, a set of restrained molecular dynamics calculations is carried out starting from both A- and B-DNA with the experimental interproton distances for 5' d(C-G-T-A-C-G)2 as restraints. Convergence to the same B-type structure is achieved with the interproton distances equal to the measured values within experimental error. The root-mean-square atomic difference between the two average restrained dynamics structures (less than 1 A) is approximately the same as the root-mean-square fluctuations of the atoms.     

Application of molecular dynamics with interproton distance restraints to three-dimensional protein structure determination. A model study of crambin

The applicability of restrained molecular dynamics for the determination of three-dimensional protein structures on the basis of short interproton distances (less than 4 A) that can be realistically determined from nuclear magnetic resonance measurements in solution is assessed. The model system used is the 1.2 A resolution crystal structure of the 46 residue protein crambin, from which a set of 240 approximate distance restraints, divided into three ranges (2.5 +/- 0.5, 3.0+0.5(-1.0) and 4 +/- 1 A), is derived. This interproton distance set comprises 159 short-range ([i-j] less than or equal to 5) and 56 ([i-j] greater than 5) long-range inter-residue distances and 25 intra-residue distances. Restrained molecular dynamics are carried out using a number of different protocols starting from two initial structures: a completely extended beta-strand; and an extended structure with two alpha-helices in the same positions as in the crystal structure (residues 7 to 19, and 23 to 30) and all other residues in the form of extended beta-strands. The root-mean-square (r.m.s.) atomic differences between these two initial structures and the crystal structure are 43 A and 23 A, respectively. It is shown that, provided protocols are used that permit the secondary structure elements to form at least partially prior to folding into a tertiary structure, convergence to the correct final structure, both globally and locally, is achieved. The r.m.s. atomic differences between the converged restrained dynamics structures and the crystal structure range from 1.5 to 2.2 A for the backbone atoms and from 2.0 to 2.8 A for all atoms. The r.m.s. atomic difference between the X-ray structure and the structure obtained by first averaging the co-ordinates of the converged restrained dynamics structures is even smaller: 1.0 A for the backbone atoms and 1.6 A for all atoms. These results provide a measure with which to judge future experimental results on proteins whose crystal structures are unknown. In addition, from an examination of the dynamics trajectories, it is shown that the convergence pathways followed by the various simulations are different.     

Impact of a micellar environment on the conformations of two cyclic pentapeptides.

In an effort to explore the influence of interfacial environments on reverse turns, we have performed a detailed analysis by nmr of the solution conformations of two cyclic pentapeptides in sodium dodecyl sulfate (SDS) micelles. The first peptide, cyclo (D-Phe1-Pro2-Gly3-D-Ala4-Pro5), adopts a single rigid conformation in solution (either chloroform or dimethylsulfoxide) and in crystals, whereas the second, cyclo (Gly1-Pro2-D-Phe3-Gly4-Val5), is much more flexible and adopts different conformations in the crystal and in solution. Both of these peptides are solubilized by SDS micelles, and nmr relaxation rates indicate that they are both partially immobilized by interaction with the micelles. Furthermore, some amide protons in both peptides participate in hydrogen bonds with water. In the presence of micelles, the former peptide retains a conformation essentially the same as that found in crystals and in solution, which consists of a beta turn and an inverse gamma turn. However, the micellar environment has a significant effect on the latter peptide. In particular, the population of a conformer containing a cis Gly-Pro peptide bond is increased significantly. The most likely conformation of the cis isomer, determined by a combination of nmr and restrained molecular dynamics, contains a Gly1-Pro2 delta turn and a gamma turn about D-Phe3. The nmr data on the trans isomer indicate that this isomer is averaging between two conformations that differ mainly in the orientation of the D-Phe3-Gly4 peptide bond.     

Molecular dynamics study of disulfide bond influence on properties of an RGD peptide.

Three 1 ns length molecular dynamics simulations of an RGD peptide (Ac-Pen-Arg-Gly-Asp-Cys-NH2, with Pen denoting penicillamine) have been performed in aqueous solution, one for the disulfide bridged, and two for the unbridged form. The trajectories were analyzed to identify conformations explored by the two forms and to calculate several properties: NMR vicinal coupling constants, order parameters, dipole moments and diffusion coefficients, in an effort to describe the physical role of the disulfide bond. The cyclic peptide was able to explore several distinct backbone conformations centered around a turn-extended-turn structure. However, its flexibility was limited and it appeared to be 'locked in' into a a family of structures characterized by a high dipole moment and a well-defined conformation of the pharmacophore, which has been previously identified as biologically active. Excellent agreement between the simulated and observed NMR vicinal coupling constants indicates that realistic structures were sampled in the cyclic peptide simulation. The linear form of the peptide was much more flexible than the cyclic one. In the two independent 1 ns simulations of the linear form the explored conformations could be roughly grouped into two classes, of cyclic-like and extended type. Within each simulation the peptide switched between the two classes of structures several times. Exact matches between conformations in the two linear peptide simulations were not found; several conformational regions with backbone rms deviations below 1A were identified, suggesting that representative structures of the linear form have also been identified. In the linear peptide simulations the RGD pharmacophore is able to adopt a wide range of conformations, including the one preferred by the cyclic form. The lower biological activity of the linear peptide compared to the cyclic one may be correlated with the lower population of this structure in the absence of the disulfide bond.     

The reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.     

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.     

Comparison of the solution and X-ray structures of barley serine proteinase inhibitor 2

A comparison of the solution n.m.r. structures of barley serine protease inhibitor 2 (BSPI-2) with the X-ray structures of both subtilisin complexed and native BSPI-2 is presented. It is shown that the n.m.r. and X-ray structures are very similar in terms of overall shape, size, polypeptide fold and secondary structure. The average atomic rms difference between the 11 restrained dynamics structures on the one hand and the two X-ray structures on the other is 1.9 +/- 0.2 A for the backbone atoms and 3.0 +/- 0.3 A for all atoms. The corresponding values for the restrained energy minimized mean dynamics structure are 1.5 and 2.4 A, respectively.     

Fuzzy cluster analysis of molecular dynamics trajectories.

We propose fuzzy clustering as a method to analyze molecular dynamics (MD) trajectories, especially of proteins and polypeptides. A fuzzy cluster analysis locates classes of similar three-dimensional conformations explored during a molecular dynamics simulation. The method can be readily applied to results from both equilibrium and nonequilibrium simulations, with clustering on either global or local structural parameters. The potential of this technique is illustrated by results from fuzzy cluster analyses of trajectories from MD simulations of various fragments of human parathyroid hormone (PTH). For large molecules, it is more efficient to analyze the clustering of root-mean-square distances between conformations comprising the trajectory. We found that the results of the clustering analysis were unambiguous, in terms of the optimal number of clusters of conformations, for the majority of the trajectories examined. The conformation closest to the cluster center can be chosen as being representative of the class of structures making up the cluster, and can be further analyzed, for example, in terms of its secondary structure. The CPU time used by the cluster analysis was negligible compared to the MD simulation time.