Regions Of Conformational Space Research Articles

PROCEDURE FOR SELECTING STARTING CONFORMATIONS FOR ENERGY MINIMIZATION OF NUCLEOSIDES AND NUCLEOTIDES

ABSTRACT The purpose of this study was to carry out a thorough search of the conformational space of various adenine-containing nucleotides, applying a previously published searching procedure, known as the representative method. This method, which reduces the number of starting conformations required to explore all the important regions of conformational space, appears to be successful in finding all (or nearly all) the putative low-energy conformations of each molecule.

Synthesis and Conformational Analysis of the T-Antigen Disaccharide (β-D-Gal-(1→3)-α-D-GalNAc-OMe)

We report an improved synthesis of the T-antigen disaccharide [β-D-Gal-(1→3)-α-D-GalNAc-OMe], incorporating recycling of the undesired β-glycosyl acceptor [methyl 2-azido-4,6-benzylidene-2-deoxy-β-D-galactopyranoside (9β)] through anomerization by treatment with FeCl3. The conformational analysis of the disaccharide made use of high quality NOE data in combination with extensive Metropolis Monte-Carlo (MMC) and molecular dynamic (MD) simulations. To sample the conformational space sufficiently, 9.5·106 Monte-Carlo steps were collected for the MMC simulations, while the fully solvated MD simulations were performed for 10 ns for comparison. In general, the MMC and MD simulations agreed very well. Comparison of theoretical NOE curves from both MMC and MD simulations with the experimental curves showed that the disaccharide populates two regions of conformational space, with a population of about 95% for the global minimum energy region and about 5% for a local minimum energy region.

A conformational study of the trisaccharide beta-D-Glcp-(1-->2)[beta-D-Glcp-(1-->3)]alpha-D-Glcp-OMe by NMR NOESY and TROESY experiments, computer simulations, and X-ray crystal structure analysis.

Proton-proton cross-relaxation rates have been measured for the trisaccharide beta-D-Glcp-(l --> 2)[beta-D-Glcp-(1 --> 3)]alpha-D-Glcp-OMe in D2O as well as in D2O/[D6]DMSO 7:3 solution at 30 degrees C by means of one-dimensional NMR pulsed field gradient 1H,1H NOESY and TROESY experiments. Interatomic distances for the trisaccharide in D2O were calculated from the cross-relaxation rates for two intraresidue and three interglycosidic proton pairs, using the isolated spin-pair approximation. In the solvent mixture one intraresidue and three interglycosidic distances were derived without the use of a specific molecular model. In this case the distances were calculated from the cross-relaxation rates in combination with "model-free" motional parameters previously derived from 13C relaxation measurements. The proton-proton distances for interglycosidic pairs were compared with those averaged from Metropolis Monte Carlo and Langevin Dynamics simulations with the HSEA, PARM22, and CHEAT95 force fields. The crystal structure of the trisaccharide was solved by analysis of X-ray data. Interresidue proton pairs from the crystal structure and those observed by NMR experiments were similar. However, the corresponding proton-proton distances generated by computer simulations were longer. For the (1 --> 2) linkage the glycosidic torsion angles of the crystal structure were found in a region of conformational space populated by all three force fields, whereas for the (1 --> 3) linkage they occupied a region of low population density, as seen from the simulations.

A Study of Chain-Length Effect on Helical Screw Sense in Peptides Having an N-Terminal L-Leu Residue

In order to clarify which helical screw sense is dominated depending on chain-length of peptides when an L-residue is introduced into the N-terminal position of achiral helical segments, we prepared three kinds of peptides I—III: Boc–L-Leu–(Aib-ΔPhe)n–Aib–OMe (n=2—4) I—III (Boc, t-butoxycarbonyl; Aib, α-aminoisobutyric acid; ΔPhe, Z-dehydrophenylalanine; OMe, methoxy). Here the segment –(Aib–ΔPhe)n–Aib–OMe was used for an achiral backbone composed of two “enantiomeric” (left-/right-handed) helices. Peptides I—III were found to form a 310-type helical conformation in chloroform, from the position of amide I band in FT-IR spectra and solvent accessibility of NH resonances in 1H NMR measurement. CD spectra of peptides I—III showed exciton couplets around 280 nm with a positive peak at longer wavelengths in chloroform, acetonitrile, methanol, and tetrahydrofuran. The sign of exciton couplets indicates that the main-chains prefer a left-handed screw sense. Consequently, an N-terminal L-Leu residue induces a left-handed screw sense preferentially, irrespective of chain lengths for achiral helical segments (5—9 residues).This result could be supported by conformational energy calculation on acetyl–L-Leu–(Aib–ΔPhe)4–Aib–OMe, in which a left-handed helical conformation was predominant. Also, in the lowest-energy left-handed helix, an N-terminal L-Leu residue takes an irregular conformation that deviates from a left-handed 310-/α-helical region in conformational space of (φ, ψ).

Macrostates of classical stochastic systems

The thermodynamic and dynamic properties of a stochastic system can be determined from the underlying microscopic description once appropriate macroscopic states (‘‘macrostates’’) have been identified. Macrostates correspond to temperature-dependent regions of conformation space that are effectively isolated by potential energy barriers. However, there is no rigorous procedure for defining them and they are generally specified by ad hoc temperature-independent prescriptions. This is inadequate for complicated multidimensional systems like proteins. Here we provide a rigorous definition of macrostates of diffusive stochastic systems by relating the eigenfunction expansion of the Smoluchowski equation to a macrostate expansion via a ‘‘Minimum Uncertainty Condition.’’ We develop a general computational bootstrap procedure for identifying macrostates in multiple dimensions and computing their thermal and dynamic properties. This employs nonlinear ‘‘characteristic packet equations’’ to identify anisotropic Gaussian packets that provide a coarse-grained representation of the equilibrium probability distribution. These provide starting points for a variational method for calculating transition rates between macrostates and for a perturbative method for describing relaxations within macrostates.

An investigation into intramolecular hydrogen bonding: impact of basis set and electron correlation on the ab initio conformational analysis of 1,2-ethanediol and 1,2,3-propanetriol

Electron correlation effects are especially important in systems with strong nonbonded interactions. Despite this, very few ab initio studies of polyfunctional alcohols have included correlation effects in their geometry optimizations. In order to better understand intramolecular hydrogen bonding and to develop more reliable energy and geometric parameters for future molecular modeling, we optimized the geometries of 10 conformers of 1,2-ethanediol (ethylene glycol) and 11 conformers of 1,2,3-propanetriol (glycerol) at the HF/4-21G, HF/6-311G ∗∗ and MP2/6-311G ∗∗ levels of theory. All three computational methods are able to predict differences between internal coordinates optimized in different regions of conformational space, to within typical experimental accuracies. However, the inclusion of electron correlation has a major impact on the absolute values of these internal coordinates and on the depths of the associated energy minima. Compared with our HF/6-311G ∗∗ results, the MP2-optimized structures have longer CO bonds by up to 0.020 Å, OH bonds that are up to 0.023 Å longer, OCC angles that are often 1 ° smaller, HOC angles in excess of 4 ° smaller, and torsional angles that may deviate from ideal trans or gauche values by an additional 5 ° for heavy-atom torsions and 8 ° for HOCC torsions. The net effect of all these conformational rearrangements is to greatly enhance intramolecular hydrogen bonding. Nonbonded O … H distances invariably decrease, by up to 0.19 Å, and the alignments of hydrogens with hypothetical lone-pair orbitals on oxygen acceptors improve. Electron correlation selectively stabilizes those conformers with more intramolecular hydrogen bonds, but decreases the energy differences among conformers with the same number of hydrogen bonds. The errors associated with single-point MP2 energy calculations at HF-optimized geometries appear to increase with the size of the system, as do differences between MP2- and HF-optimized OCCO torsional angles. Thus, molecular mechanics parameters derived from MP2/6-311G ∗∗ optimizations of prototypical small molecules such as ethylene glycol and glycerol are expected to result in significantly different macromolecular energies and structures than those based on HF/6-311G ∗∗ optimizations.

Solution Structure of Bound Trimethoprim in Its Complex with Lactobacillus casei Dihydrofolate Reductase

Two- and three-dimensional (2D and 3D) NMR techniques have been used to assign the signals from nearly all of the protons in Lactobacillus casei dihydrofolate reductase (DHFR) (M(r) 18,300) in its 1:1 complex with the antibacterial drug trimethoprim. A sample of uniformly 15N-labeled protein was examined using 3D 15N/1H experiments [nuclear Overhauser, heteronuclear multiple quantum coherence (NOESY-HMQC) and total correlation, heteronuclear multiple quantum coherence (TOCSY-HMQC) experiments]. Twenty-two intermolecular NOEs between trimethoprim and protein protons and four intramolecular NOEs in the ligand have been detected. Some were obtained by using heteronuclear editing and 2D HMQC-NOESY experiments on complexes formed with 15N-and 13C-labeled trimethoprim molecules ([1,3-15N2,2-amino-15N]-and [7-13C,4'-methoxy-13C]trimethoprim) bound to unlabeled protein. The ligand-protein NOEs were used as distance constraints in conjunction with minimum energy and simulated annealing calculations (carried out with X-PLOR) to dock the trimethoprim ligand into dihydrofolate reductase, using as a starting structure the crystal coordinates from a related complex with a similar overall protein structure. The restrained minimum energy calculations and the simulated annealing calculations gave 83 calculated structures with distance violations of < 0.1 A. In all of these, the two aromatic rings of trimethoprim occupied essentially the same region of conformational space in the binding site (RMSD = 0.63 A). The protein residues nearest to the bound trimethoprim were found to be very similar in all of the structures and agreed well with corresponding contact residues observed in the X-ray crystal studies on trimethoprim complexes formed with Escherichia coli and chicken liver DHFRs.

Conformations of arginine and lysine side chains in association with anions

The side chain conformations shown by arginine and lysine in amino-acid and peptide crystal structures and bound to oxyanions in proteins have been analyzed in an attempt to understand the behaviour of these long-chain amino acids in an ionic environment. Except for chi 1, torsions have a preference for the trans conformation. However, for arginine in protein structures, chi 3 and chi 4 appear to be flexible and can be tuned for optimal anion binding. For chi 4, values in the range -80 to 80 degrees are excluded for steric reasons; the remaining region in conformational space is accessible. This orientational variety exhibited by chi 4 has not been hitherto appreciated. Factors that can forbid a chi-angle to be in the trans geometry are the simultaneous binding of the anion by the main- and side-chain atoms, or the sharing of the anion between two different molecules in the crystal structure. Small molecules containing arginine have a distinct tendency to crystallize with two molecules in the asymmetric unit. This may be a general phenomenon for all extended molecules which have hydrogen-bond donors (or acceptors) embedded in a rigid set-up.

Solution conformations of the gamma-carboxyglutamic acid domain of bovine prothrombin fragment 1, residues 1-65.

Molecular dynamics simulations have been performed (AMBER version 3.1) on solvated residues 1-65 of bovine prothrombin fragment 1 (BF1) by using the 2.8-A resolution crystallographic coordinates as the starting conformation for understanding calcium ion-induced conformational changes that precede experimentally observable phospholipid binding. Simulations were performed on the non-metal-bound crystal structure, the form resulting from addition of eight calcium ions to the 1-65 region of the crystal structure, the form resulting from removal of calcium ions after 107 ps and continuing the simulation, and an isolated hexapeptide loop (residues 18-23). In all cases, the 100-ps time scale seemed adequate to sample an ensemble of solution conformers within a particular region of conformation space. The non-metal-containing BF1 did not unfold appreciably during a 106-ps simulation starting from the crystallographic geometry. The calcium ion-containing structure (Ca-BF1) underwent an interesting conformational reorganization during its evolution from the crystal structure: during the time course of a 107-ps simulation, Ca-BF1 experienced a trans----cis isomerization of the gamma-carboxyglutamic acid-21 (Gla-21)-Pro-22 peptide bond. Removal of the calcium ions from this structure followed by 114 ps of additional molecular dynamics showed significant unfolding relative to the final 20-ps average structure of the 107-ps simulation; however, the Gla-21-Pro-22 peptide bond remained cis. A 265-ps simulation on the termini-protected hexapeptide loop (Cys-18 to Cys-23) containing two calcium ions also did not undergo a trans----cis isomerization. It is believed that the necessary activation energy for the transitional event observed in the Ca-BF1 simulation was largely supplied by global conformational events with a possible assist from relief of intermolecular crystal packing forces. The presence of a Gla preceding Pro-22, the inclusion of Pro-22 in a highly strained loop structure, and the formation of two long-lived salt bridges prior to isomerization may all contribute to this finding.

The dependence of a protein solution structure on the quality of the input NMR data. Application of the double-iterated Kalman filter technique to oxytocin

The determination of a three-dimensional protein structure in solution from twodimensional NMR NOE distance data has been attempted in recent years by a variety of computational methods. In particular, the distance geometry algorithm (1, 2) has been extensively used (3~2-3 d), as well as a minimization of dihedral angles only, using a variable target function (4)) simulated annealing (5)) restrained molecular dynamics (6)) systematic conformational search ( 7-9)) and Monte Carlo simulations (IO). However, problems arise in all of these approaches. Recently, there have been increased efforts in defining the limitations and computational characteristics of the algorithms. Results on BPTI and on several peptides ( 11) indicate that some implementations of the distance geometry technique can generate incorrect extended structures, and sample only a small region of conformational space. Moreover, recent distance geometry calculations of Neutrophil peptide 5 (12) further reveal the sampling limitations of the algorithms used. We have recently developed a different methodology for protein structure determination, namely the double-iterated Kalman filter (DIKF) technique ( 13, 14), which addresses some of these problems by quantifying an upper bound on the set of atomic positions that are compatible with the data. This method enables both a structure determination and a definitive estimate of its uncertainty, and thus provides significant additional knowledge and insight on those regions of the protein which correspond to nonunique conformations, e.g., for the Zuc repressor headpiece (15). In general, it is of importance that any study of a protein solution structure from NMR NOE data is accompanied by an investigation of the dependence of the final structure on the quality of the input distance data. This consists primarily of a controlled application of the technique to a small molecule of a known structure with data sets of varying quantity and quality. The variables tested are: ( 1) abundance of the input data; (2) precision of the input data; and (3) the computation time, or the number of double-iterated cycles. The precision and accuracy of the results are recorded as a function of these variables. It is the purpose of this Note to offer a validation of the DIKF algorithm for protein structure determination by an application to the crystal structure of oxytocin. The approach has already proven successful in an NMR solution structure determination of a larger protein, i.e., the lac repressor headpiece (13-1.5),

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability‐directed search procedure

AbstractA procedure that finds the most probable conformational states of a protein chain is described. Single‐residue conformations are represented in terms of four conformational states, α, ϵ, α*, and ϵ*. The conformation of the entire chain is represented by a sequence of single‐residue conformational states; the distinct conformations in this representation are called “chain‐states.” The first article in this series described a procedure that computes tripeptide conformational probabilities from the amino acid sequence using pattern recognition techniques. The procedure described in this article uses the tripeptide probabilities to estimate the probabilities of the chain‐states. The chain‐state probability estimator is a product of conditional and marginal probabilities (obtained from the tripeptide probabilities), with a penalty factor to eliminate conformations containing α‐helices and ϵ‐strands of excessive length. The probability estimator considers short‐range conformational information, medium‐range sequence information and some simple long‐range information (through the restrictions on helix and strand lengths). Energy minimization calculations can be carried out in the region of conformational space corresponding to a particular chain‐state. By selecting the most probable chain‐states, the search can be focused on the most probable, or “important,” regions of the conformational space. These energy calculations are described in the third article of the series. The complete procedure described by the three articles is called PRISM, for pattern recognition‐based importance sampling minimization.

An approach to the multiple-minima problem in protein folding by relaxing dimensionality: Tests on enkephalin

An algorithm for locating the region in conformational space containing the global energy minimum of a polypeptide is described. Distances are used as the primary variables in the minimization of an objective function that incorporates both energetic and distancegeometric terms. The latter are obtained from geometry and energy functions, rather than nuclear magnetic resonance experiments, although the algorithm can incorporate distances from nuclear magnetic resonance data if desired. The polypeptide is generated originally in a space of high dimensionality. This has two important consequences. First, all interatomic distances are initially at their energetically most favorable values; i.e. the polypeptide is initially at a global minimum-energy conformation, albeit a high-dimensional one. Second, the relaxation of dimensionality constraints in the early stages of the minimization removes many potential energy barriers that exist in three dimensions, thereby allowing a means of escaping from three-dimensional local minima. These features are used in an algorithm that produces short trajectories of three-dimensional minimum-energy conformations. A conformation in the trajectory is generated by allowing the previous conformation in the trajectory to evolve in a high-dimensional space before returning to three dimensions. The resulting three-dimensional structure is taken to be the next conformation in the trajectory, and the process is iterated. This sequence of conformations results in a limited but efficient sampling of conformational space. Results for test calculations on Met-enkephalin, a pentapeptide with the amino acid sequence H-Tyr-Gly-Gly-Phe-Met-OH, are presented. A tight cluster of conformations (in three-dimensional space) is found with ECEPP energies (Empirical Conformational Energy Program for Peptides) lower than any previously reported. This cluster of conformations defines a region in conformational space in which the global-minimum-energy conformation of enkephalin appears to lie.

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. III. Probable and average conformations of enkephalin.

AbstractThe program SMAPPS (Statistical‐Mechanical Algorithm for Predicting Protein Structure) was originally designed to determine the probable and average backbone (ϕ, ψ) conformations of a polypeptide by the application of equilibrium statistical mechanics in conjunction with an adaptive importance sampling Monte Carlo procedure. In the present paper, the algorithm has been extended to include the variation of all side‐chain (χ) and peptide‐bond (ω) dihedral angles of a polypeptide during the Monte Carlo search of the conformational space. To test the effectiveness of the generalized algorithm, SMAPPS was used to calculate the probable and average conformations of Met‐enkephalin for which all dihedral angles of the pentapeptide were allowed to vary. The total conformational energy for each randomly generated structure of Met‐enkephalin was obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. The interaction energies were computed by the program ECEPP /2 (Empirical Conformational Energy Program for Peptides). Solvent effects were not included in the computation. The results of the Monte Carlo calculation of the structure of Met‐enkephalin indicate that the thermodynamically preferred conformation of the pentapeptide contains a γ‐turn involving the three residues Gly2‐Gly3‐Phe4. The γ‐turn conformation, however, does not correspond to the structure of lowest conformational energy. Rather, the global minimum‐energy conformation, recently determined by a new optimization technique developed in this laboratory, contains a type II′ β‐bend that is formed by the interaction of the four residues Gly2‐Gly3‐Phe4‐Met5. A similar minimum‐energy conformation is found by the SMAPPS procedure. The thermodynamically preferred γ‐turn structure has a conformational energy of 4.93 kcal/mole higher than the β‐bend structure of lowest energy but, because of the inclusion of entropy in the SMAPPS procedure, it is estimated to be ∼ 9 kcal/mole lower in free energy. The calculation of the average conformation of Met‐enkephalin was repeated until a total of ten independent average conformations were established. As far as the phenylalanine residue of the pentapeptide is concerned, the results of the ten independent average conformations were all found to lie in the region of conformational space corresponding to the γ‐turn. These results further support the conclusion that the γturn conformation is thermodynamically favored.

AN ANALYSIS OF SIDE‐CHAIN CONFORMATION IN PROTEINS*

The crystal structures of a number of globular proteins are currently available. An analysis of the distribution of side-chains among different allowed conformations in these proteins has been carried out. The observed conformations of individual residues are discussed on the basis of well-known stereochemical criteria. The population distribution of side-chains in different allowed regions in conformational space can be explained largely on the basis of simple steric considerations. In addition to examining the conformational behaviour of individual residues, some population distributions of conformational angles of general interest involving groups of residues have also been analyzed.

Conformation of polypeptide chains containing both L- and D-residues. II. Double-helical structures of poly-LD-peptides.

Polypeptides with alternating L- and D-amino acid residues can take up stereo-chemically satisfactory coaxial double-helical structures, both antiparallel and parallel, which are stabilized by systematic interchain NH...O hydrogen bonds. Semiempirical energy calculations over allowed regions of conformational space have yielded the characteristics of these double-helices. There are four possible types of antiparallel double-helices - A3, A4, A5 and A6, with n, the number of LD peptide units per turn, around 2.8, 3.6, 4.5 and 5.5 respectively, while for the parallel double-helices there are two types, P3 and P4, having similar helical parameters as in A3 and A4. The hydrogen-bonding scheme restricts the pitch in all the models to the narrow range of 10.0 to 11.5 A. All these helices have large central cores whose radii increase proportionately with n. In this respect, A3 and A4 are suitable models for the structure of gramicidin A. In terms of their relative energies, antiparallel double-helices are marginally more stable than those with parallel strands. Our results indicate that the energy differences amongst the members in the antiparallel family are not significant and thus provide an explanation for the polymorphism reported for poly (gamma-benzyl-LD-glutamate).

Nuclear magnetic resonance study of the conformations of atropine and scopolamine cations in aqueous solution

We have measured the 1H and 13C chemical shifts and 1H–1H coupling constants from the n.m.r. spectra of atropine and scopolamine cations. For both species, nuclei in symmetrical positions in the tropane ring shown non-equivalence because they experience different shielding effects from the aromatic substituent. We have estimated the different ring current shift contributions at the tropane ring nuclei for a wide range of conformations (varying the torsion angles ϕ2–ϕ5) and searched for the conformations which give the best fit to the measured chemical shift differences for the symmetrical pairs of nuclei. We find that the aromatic ring in atropine and scopolamine occupies approximately the same region of conformational space in both the crystal and solution states. In this special case where we are calculating several shielding differences (which can be measured accurately) attributed to ring current shifts this method of conformational analysis would be expected to give reliable results.

Conformational stability in dinucleoside phosphate crystals. Semiempirical potential energy calculations for uridylyl-3'-5'-adenosine monophosphate (UpA) and guanylyl-3',5'-cytidine monophosphate (GpC).

AbstractClassical potential energy calculations were performed for the dinucleoside phosphates UpA and GpC. Two widely accessible low‐energy regions of conformation space were found for the ω′, ω pair. That of lowest energy contains conformations similar to helical RNA, with ω′ and ω in the vicinity of 300° and 280°, respectively. All five experimental observations of crystalline GpC, two of ApU, and the helical fragment of ApApA fall in this range. The second lowest region has ω′ and ω at about 20° and 80°, respectively, which is in the general region of one experimentally observed crystalline conformer of UpA, and the nonhelical region of ApApA.It is concluded that GpC and ApU, which were crystallized as either sodium or calcium salts, are shielded from each other in the crystal by the water of hydration and are therefore free to adopt their predicted in vacuo minimum energy helical conformations. By contrast, crystalline UpA had only 1/2 water per molecule, and was forced into higher energy conformations in order to maximize intermolecular hydrogen bonding.

An EHT re-examination of Acetylcholine

The results of EHT calculations on the most stable conformations of the neurotransmitter molecule acetylcholine (ACh) are reported. These results are compared with those obtained with other semiempirical quantum mechanical methods CNDO/2, INDO and PCILO, and with those obtained by the classical partitioning of the energy method (PEM). From this comparison it becomes evident a wide agreement between the results of PCILO, EHT and PEM, all these methods allowing accessibility to discrete regions in conformational space.

Minimization of polypeptide energy: X. A global search algorithm

In order to find the global minimum of the energy of a polypeptide, it is necessary to perform a global search, rather than a local one as is carried out by most standard minimization algorithms. A technique is described for locating the global minimum by means of a relatively efficient search over all possible conformations; after investigation, it eliminates whole regions of conformation space not likely to contain the lowestative minimum. An illustr test of it on “tetraglycine” is presented.