Preference of small molecules for local minimum conformations when binding to proteins

It is well known that small molecules (ligands) do not necessarily adopt their lowest potential energy conformations when binding to proteins. Analyses of protein-bound ligand crystal structures have reportedly shown that many of them do not even adopt the conformations at local minima of their potential energy surfaces (local minimum conformations). The results of these analyses raise a concern regarding the validity of virtual screening methods that use ligands in local minimum conformations. Here we report a normal-mode-analysis (NMA) study of 100 crystal structures of protein-bound ligands. Our data show that the energy minimization of a ligand alone does not automatically stop at a local minimum conformation if the minimum of the potential energy surface is shallow, thus leading to the folding of the ligand. Furthermore, our data show that all 100 ligand conformations in their protein-bound ligand crystal structures are nearly identical to their local minimum conformations obtained from NMA-monitored energy minimization, suggesting that ligands prefer to adopt local minimum conformations when binding to proteins. These results both support virtual screening methods that use ligands in local minimum conformations and caution about possible adverse effect of excessive energy minimization when generating a database of ligand conformations for virtual screening.     

Influence of environment on the antifolate drug trimethoprim: energy minimization studies

Environmental effects on trimethoprim (TMP), an inhibitor of bacterial dihydrofolate reductase (DHFR), were investigated with energy minimizations in vacuo, in the crystal, and in aqueous solution. The conformations, harmonic dynamics, and energetics of the antibacterial drug calculated in these environments were compared with each other and with those of two enzyme-bound drugs. Valence and torsion angles and their energies and overall intra- and intermolecular energies compensated one another in the minimized TMP structures. The conformations of the isolated and aqueous molecules were similar to that of TMP bound to chicken liver DHFR, while the structures from the TMP crystal and from the Escherichia coli DHFR complex were unique. Since neither the small-molecule crystal nor a local minimum of the isolated molecule gave the conformation of TMP bound to the bacterial enzyme, a combination of several experimental and theoretical techniques may be necessary to probe accessible conformations of a molecule.     

Polar hydrogen positions in proteins: Empirical energy placement and neutron diffraction comparison

A method for the prediction of hydrogen positions in proteins is presented. The method is based on the knowledge of the heavy atom positions obtained, for instance, from X-ray crystallography. It employs an energy minimization limited to the environment of the hydrogen atoms bound to a common heavy atom or to a single water molecule. The method is not restricted to proteins and can be applied without modification to nonpolar hydrogens and to nucleic acids. The method has been applied to the neutron diffraction structures of trypsin ribonuclease A, and bovine pancreatic trypsin inhibitor. A comparison of the constructed and the observed hydrogen positions shows few deviations except in situations in which several energetically similar conformations are possible. Analysis of the potential energy of rotation of Lys amino and Ser, Thr, Tyr hydroxyl groups reveals that the conformations of lowest intrinsic torsion energies are statistically favored in both the crystal and the constructed structures.     

Disaccharide conformational flexibility. I. An adiabatic potential energy map for sucrose

Constrained conformational energy minimizations have been used to calculate an adiabatic (phi, psi) potential energy surface for the disaccharide sucrose. The inclusion of molecular flexibility in the conformational energy analysis of this disaccharide was found to have a significant effect upon the allowed conformational space of the molecule. Three low-energy regions were identified on the adiabatic energy surface, and two of these regions were found to contain two related local minimum-energy conformations, with similar energies, differing only in the directionality of the intra-residue hydrogen bonds of the glucose portion of the molecule. The known crystal structures of seven molecules containing the sucrose moiety all fall within the region of the primary allowed minimum and are consistent with the relaxed energy map, while these crystal conformations could not be rationalized using energy maps for rigid residue geometries. The greater flexibility of the furanoid ring relative to that of the pyranoid ring contributed significantly to the enlargement of the low-energy region on the adiabatic map. However, in spite of the importance of limited flexibility in understanding the conformation and fluctuations of sucrose, this molecule was found to be considerably more rigid that some other disaccharides, such as maltose and cellobiose, in accord with experimental studies.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Conformational preferences of 1,4,7-trithiacyclononane: a molecular mechanics and density functional theory study

Conformational preferences of 1,4,7-trithiacyclononane were studied using a highly efficient sampling technique based on local nonstochastic deformations and the MM2(91) force field. The results show that conformers that the molecule adopts in the crystal state were found to be low-energy conformers (LECs) within 5 kcal mol(-1) of the global minimum. A conformation with C1 symmetry was the global minimum and the C3 and C2 conformations were calculated to be 0.03 and 1.78 kcal mol(-1) higher in energy, respectively. The structures were further minimized using Density Functional Theory (DFT) calculations with two different functionals. The C2 and the C1 conformations were found to be LECs with the C3 conformation more than 4.0 kcal mol(-1) above the global minimum. The relative energies and structural ordering obtained using the BP86 functional are in agreement with the previously reported relative energies calculated using second-order Moller-Plesset (MP2) ab initio calculations. With the energy ordering being dependent on the molecular mechanics force field used, the approach of MM-->DFT (searching exhaustively the available conformational space at the MM level followed by generating the energy ordering through DFT calculations) appears to be appropriate for thiacrown ethers.     

Necessary conditions for avoiding incorrect polypeptide folds in conformational search by energy minimization

Low energy conformations have been generated for melittin, pancreatic polypeptide, and ribonuclease S-peptide, both in the vicinity of x-ray structures by energy refinement and by an unconstrained search over the entire conformational space. Since the structural polymorphism of these medium-sized peptides in crystal and solution is moderate, comparing the calculated conformations to x-ray and nmr data provides information on local and global behavior of potential functions. Local analysis includes standardization calculations, which show that models with standard geometry can approximate good resolution x-ray data with less than 0.5 Å rms deviation (RMSD). However, the atomic coordinates are shifted up to 2 Å RMSD by local energy minimization, and thus 2 Å is generally the smallest RMSD value one can target in a conformational search using the same energy evaluation models. The unconstrained search was performed by a buildup-type method based on dynamic programming. To accelerate the generation of structures in the conformational search, we used the ECEPP potential, defined in terms of standard polypeptide geometry. A number of low energy conformations were further refined by relaxing the assumption of standard bond lengths and bond angles through the use of the CHARMM potential, and the hydrophobic folding energies of Eisenberg and McLachlan were calculated. Each conformation is described in terms of the RMSD from the native, hydrogen-bonding structure, solvent-acessible surface area, and the ratio of surfaces corresponding to nonpolar and polar residues. The unconstrained search finds conformations that are different from the native, sometimes substantially, and in addition, have lower conformational energies than the native. The origin of deviations is different for each of the three peptides, but in all examples the refined x-ray structures have lower energies than the calculated incorrect folds when (1) the assumption of standard bond lengths and bond angles is relaxed; (2) a small and constant effective dielectric permittivity (ε < 10) is used; and (3) the hydrophobic folding energy is incorporated into the potential. © 1993 John Wiley & Sons, Inc.     

Determining minimum energy conformations of polypeptides by dynamic programming

A combinatorial optimization approach is used for solving the multiple-minima problem when determining the low-energy conformations of short polypeptides. Each residue is represented by a finite number of discrete states corresponding to single residue local minima of the energy function. These precomputed values constitute a search table and define the conformational space for discrete minimization by a generalized dynamic programming algorithm that significantly limits the number of intermediate conformations to be generated during the search. Since dynamic programming involves stagewise decisions, it results in buildup-type procedures implemented in two different forms. The first procedure predicts a number of conformations by a completely discrete search and these are subsequently refined by local minimization. The second involves limited continuous local minimization within the combinatorial algorithm, generally restricted to two dihedral angles in a buildup step. Both procedures are tested on 17 short peptides previously studied by other global minimization methods but involving the same potential energy function. The discrete method is extremely fast, but proves to be successful only in 14 of the 17 test problems. The version with limited local minimization finds, however, conformations in all the 17 examples that are close to the ones previously presented in the literature or have lower energies. In addition, results are almost independent of the cutoff energy, the most important parameter governing the search. Although the limited local minimization increases the number of energy evaluations, the method still offers substantial advantages in speed.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. II. Average backbone structure of enkephalin

The average conformation of Met-enkephalin was determined by using an adaptive, importance-sampling Monte Carlo algorithm (SMAPPS—Statistical Mechanical Algorithm for Predicting Protein Structure). In the calculation, only the backbone dihedral angles (? and ψ) were allowed to vary; i.e., all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to a low-energy structure of the pentapeptide. The total conformational energy for each randomly generated structure of the polypeptide 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 calculation was repeated until a total of 10 independent average conformations were established. The regions of conformational space occupied by the average structures were compared with the regions of low conditional free energy obtained by SMAPPS in the first paper of this series. Such a comparison provides an analysis of the capacity of SMAPPS to adjust the Monte Carlo search to regions of highest probability. The results demonstrate that the ability of SMAPPS to focus the Monte Carlo search is excellent. Finally, the 10 independent average conformations and the mean of the 10 average structures were utilized as the initial conformations for a direct energy minimization of the pentapeptide. Of the 11 final energy-minimized structures, three of the conformations were found to be equivalent to the conformation of lowest energy determined previously. In addition, all but two of the remaining energy-minimized structures were found to correspond to one of the two other conformations of high probability obtained in the first paper of this series. These results indicate that a set of independent average conformations can provide a rational, unbiased choice for the initial conformation, to be used in a direct energy minimization of a polypeptide. The final energy-minimized structures consequently constitute a set of low-energy conformations, which include the global energy minimum.     

A Monte Carlo method for generating structures of short single-stranded DNA sequences

A Monte Carlo method has been developed for generating the conformations of short single-stranded DNAs from arbitrary starting states. The chain conformers are constructed from energetically favorable arrangements of the constituent mononucleotides. Minimum energy states of individual dinucleotide monophosphate molecules are identified using a torsion angle minimizer. The glycosyl and acyclic backbone torsions of the dimers are allowed to vary, while the sugar rings are held fixed in one of the two preferred puckered forms. A total of 108 conformationally distinct states per dimer are considered in this first stage of minimization. The torsion angles within 5 kcal/mole of the global minimum in the resulting optimized states are then allowed to vary by ±10° in an effort to estimate the breadth of the different local minima. The energies of a total of 2187 (3⁷) angle combinations are examined per local conformational minimum. Finally, the energies of all dinucleotide conformers are scaled so that the populations of differently puckered sugar rings in the theoretical sample match those found in nmr solution studies. This last step is necessitated by limitations in the theoretical methods to predict DNA sugar puckering accurately. The conformer populations of the individual acyclic torsion angles in the composite dimer ensembles are found to be in good agreement with the distributions of backbone conformations deduced from nmr coupling constants and the frequencies of glycosyl conformations in x-ray crystal structures, suggesting that the low energy states are reasonable. The low energy dimer forms (consisting of 150–325 conformational states per dimer step) are next used as variables in a Monte Carlo algorithm, which generates the conformations of single-stranded d(CX_nG) chains, where X = A, T and n = 3, 4, 5. The oligonucleotides are built sequentially from the 5′ end of the chain using random numbers to select the conformations of overlapping dimer units. The simulations are very fast, involving a total of 10⁶ conformations per chain sequence. The potential errors in the buildup procedure are minimized by taking advantage of known rotational interdependences in the sugar–phosphate backbone. The distributions of oligonucleotide conformations are examined in terms of the magnitudes, positions, and orientations of the end-to-end vectors of the chains. The differences in overall flexibility and extension of the oligomers are discussed in terms of the conformations of the constituent dinucleotide steps, while the general methodology is discussed and compared with other nucleic acid model building techniques. © 1993 John Wiley & Sons, Inc.     

Stereochemical studies on cyclic peptides: Detailed energy minimization studies on hydrogen bonded all-trans cyclic pentapeptide backbones

Conformational studies have been carried out on hydrogenbonded all-trans cyclic pentapeptide backbone. Application of a combination of grid search and energy minimization on this system has resulted in obtaining 23 minimum energy conformations, which are characterized by unique patterns of hydrogen bonding comprising of β- and γ-turns. A study of the minimum energy conformationsvis-a-vis non-planar deviation of the peptide units reveals that non-planarity is an inherent feature in many cases. A study on conformational clustering of minimum energy conformations shows that the minimum energy conformations fall into 6 distinct conformational families. Preliminary comparison with available X-ray structures of cyclic pentapeptide indicates that only some of the minimum energy conformations have formed crystal structures. The set of minimum energy conformations worked out in the present study can form a consolidated database of prototypes for hydrogen bonded backbone and be useful for modelling cyclic pentapeptides both synthetic and bioactive in nature. This is part XV of the series. Part XIV in this series is Ramakrishnanet al 1987.     

On the multiple-minima problem in the conformational analysis of polypeptides. II. An electrostatically driven Monte Carlo method--tests on poly(L-alanine)

A new approach to the multiple-minima problem in protein folding is presented. It is assumed that the molecule is driven toward the native structure by three types of mechanism. The first one involves an optimization of the electrostatic interactions, whereby the molecule evolves toward conformations in which the charge distribution becomes energetically more favorable. The second mechanism involves a Monte Carlo–energy minimization approach, and the third one is a backtrack mechanism that acts in the opposite direction, increasing the energy—the third type of movement provides a means to perturb the molecule when it is trapped in a stable but energetically unfavorable local energy minimum. This paper describes the implementation of a model based on these mechanisms, and illustrates its effectiveness by computations on different arbitrary starting conformations of a terminally blocked 19-residue chain of poly(L -alanine) for which the global minimum apparently corresponds to the right-handed α-helix. In all cases, the global minimum was attained, even when the starting conformation was a left-handed α-helix. In the latter case, the trajectory of conformations passed through partially melted forms of the left-handed α-helix (because of electrostatic defects at the ends), and then through the formation of structures leading to the more stable right-handed α-helix.     

Potential energy function for continuous state models of globular proteins.

One of the approaches to protein structure prediction is to obtain energy functions which can recognize the native conformation of a given sequence among a zoo of conformations. The discriminations can be done by assigning the lowest energy to the native conformation, with the guarantee that the native is in the zoo. Well-adjusted functions, then, can be used in the search for other (near-) natives. Here the aim is the discrimination at relatively high resolution (RMSD difference between the native and the closest nonnative is around 1 A) by pairwise energy potentials. The potential is trained using the experimentally determined native conformation of only one protein, instead of the usual large survey over many proteins. The novel feature is that the native structure is compared to a vastly wider and more challenging array of nonnative structures found not only by the usual threading procedure, but by wide-ranging local minimization of the potential. Because of this extremely demanding search, the native is very close to the apparent global minimum of the potential function. The global minimum property holds up for one other protein having 60% sequence identity, but its performance on completely dissimilar proteins is of course much weaker.     

Improving conformational searches by geometric screening

MOTIVATION: Conformational searches in molecular docking are a time-consuming process with wide range of applications. Favorable conformations of the ligands that successfully bind with receptors are sought to form stable ligand-receptor complexes. Usually a large number of conformations are generated and their binding energies are examined. We propose adding a geometric screening phase before an energy minimization procedure so that only conformations that geometrically fit in the binding site will be prompted for energy calculation. RESULTS: Geometric screening can drastically reduce the number of conformations to be examined from millions (or higher) to thousands (or lower). The method can also handle cases when there are more variables than geometric constraints. An early-stage implementation is able to finish the geometric filtering of conformations for molecules with up to nine variables in 1 min. To the best of our knowledge, this is the first time such results are reported deterministically. CONTACT: mzhang@mdanderson.org.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. I. Backbone structure of enkephalin

A new methodology for theoretically predicting the native, three-dimensional structure of a polypeptide is presented. Based on equilibrium statistical mechanics, an algorithm has been designed to determine the probable conformation of a polypeptide by calculating conditional free-energy maps for each residue of the macromolecule. The conditional free-energy map of each residue is computed from a set of probability integrals, obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. By locating the region(s) of lowest free energy for each map, the probable conformation for each residue can be identified. The native structure of the polypeptide is assumed to be the combination of the probable conformations of the individual residues. All multidimensional probability integrals are evaluated by an adaptive Monte Carlo algorithm (SMAPPS —Statistical-Mechanical Algorithm for Predicting Protein Structure). The Monte Carlo algorithm searches the entire conformational space, adjusting itself automatically to concentrate its sampling in regions where the magnitude of the integrand is largest (“importance sampling”). No assumptions are made about the native conformation. The only prior knowledge necessary for the prediction of the native conformation is the amino acid sequence of the polypeptide. To test the effectiveness of the algorithm, SMAPPS was applied to the prediction of the native conformation of the backbone of Met-enkephalin, a pentapeptide. In the calculations, only the backbone dihedral angles (? and ψ) were allowed to vary; all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to the alleged global minimum energy previously determined by direct energy minimization. For each conformation generated randomly by the Monte Carlo algorithm, the total conformational energy of the polypeptide was obtained from established empirical potential energy functions. Solvent effects were not included in the computations. With this initial application of SMAPPS , three distinct low-free-energy β-bend structures of Met-enkephalin were found. In particular, one of the structures has a conformation remarkably similar to the one associated with the previously alleged global minimum energy. The two additional structures of the pentapeptide have conformational energies lower than the previously computed low-energy structure. However, the Monte Carlo results are in agreement with an improved energy-minimization procedure. These initial results on the backbone structure of Met-enkephalin indicate that an equilibrium statistical-mechanical procedure, coupled with an adaptive Monte Carlo algorithm, can overcome many of the problems associated with the standard methods of direct energy minimization.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Effects of electric field on alamethicin bound at the lipid-water interface: a molecular mechanics study.

A systematic molecular mechanics study of the alamethicin molecule was made to determine a set of low-energy conformers in vacuo and in aqueous environment. The behavior of these conformers was investigated at the phase boundary which was modeled as a plane dividing two compartments with solvation properties of water and octanol with a constant electric field applied normal to the boundary. The calculations were performed with a molecular mechanics program for calculation of stable conformations at the phase boundary utilizing the Empiric Conformational Energy Program for Peptides force field and the Hopfinger-Scheraga solvation model. 371 minimum energy conformers of alamethicin, determined in vacuo with the build-up procedure, were used as starting conformations for energy minimization in aqueous environment and at the phase boundary. Only 49 interphase-bound structures were within 12 kcal/mol of the minima which was found. No helical structures having values close to the canonical parameters for an alpha- or 3(10)-helix were found despite the presence of eight alpha-methylalanine residues which favor the formation of these helices; four helix-like structures were found, having all negative phi, psi values. All the helical conformers have very high energies in water (approximately 14 kcal/mol), but are quite stable at the phase boundary (3.7-6.8 kcal/mol above the lowest minima found). The implications of these results for proposed mechanisms for membrane-binding and voltage-dependent gating are considered.     

A novel parameterization scheme for energy equations and its use to calculate the structure of protein molecules

A novel scheme for the parameterization of a type of “potential energy” function for protein molecules is introduced. The function is parameterized based on the known conformations of previously determined protein structures and their sequence similarity to a molecule whose conformation is to be calculated. Once parameterized, minima of the potential energy function can be located using a version of simulated annealing which has been previously shown to locate global and near-global minima with the given functional form. As a test problem, the potential was parameterized based on the known structures of the rubredoxins from Desulfovibrio vulgaris, Desulfovibrio desulfuricans, and Clostridium pasteurianum, which vary from 45 to 54 amino acids in length, and the sequence alignments of these molecules with the rubredoxin sequence from Desulfovibrio gigas. Since the Desulfovibrio gigas rubredeoxin conformation has also been determined, it is possible to check the accuracy of the results. Ten simulated-annealing runs from random starting conformations were performed. Seven of the 10 resultant conformations have an all-C_α rms deviation from the crystallographically determined conformation of less than 1.7 Å. For five of the structures, the rms deviation is less than 0.8 Å. Four of the structures have conformations which are virtually identical to each other except for the position of the carboxy-terminal residue. This is also the conformation which is achieved if the determined crystal structure is minimized with the same potential. The all-C_α rms difference between the crystal and minimized crystal structures is 0.6 Å. It is further observed that the “energies” of the structures according to the potential function exhibit a strong correlation with rms deviation from the native structure. The conformations of the individual model structures and the computational aspects of the modeling procedure are discussed. © 1993 Wiley-Liss, Inc.     

Extracting contact energies from protein structures: A study using a simplified model

In this study, we exploited an elementary 2-dimensional square lattice model of HP polymers to test the premise of extracting contact energies from protein structures. Given a set of prespecified energies for H–H, H–P, and P–P contacts, all possible sequences of various lengths were exhaustively enumerated to find sequences that have unique lowest-energy conformations. The lowest-energy structures (or native structures) of such (native) sequences were used to extract contact energies using the Miyazawa-Jernigan procedure and here-defined reference state. The relative magnitudes of the original energies were restored reasonably well, but the extracted contact energies were independent of the absolute magnitudes of the initial energies. We turned to a more detailed characterization of the energy landscapes of the native sequences in light of a new theoretical framework on protein folding. Foldability of such sequences imposes two limits on the absolute value of the prespecified energies: a lower bound entailed by the minimum requirement for thermodynamic stability and an upper bound associated with the entrapment of the chain to local minima. We found that these two limits confine the prespecified energy values to a rather narrow range which, surprisingly, also contains the extracted energies in all the cases examined. These results indicate that the quasi-chemical approximation can be used to connect quantitatively the occurrence of various residue–residue contacts in an ensemble of native structures with the energies of the contacts. More importantly, they suggest that the extracted contact energies do contain information on structural stability and can be used to estimate actual structural energetics. This study also encourages the use of structure-derived contact energies in threading. The finding that there is a rather narrow range of energies that are optimal for folding a sequence also cautions the use of arbitrary energy Hamiltonion in minimal folding models. Proteins 31:299–308, 1998. © 1998 Wiley-Liss, Inc.     

Study of conformations of the adenosine phosphates. II: Adenosine tri- and diphosphate (ATP,ADP)

Using extended Hückel theory (EHT), a theoretical study of the preferred conformations of ATP and ADP are compared with the experimentally observed structures, as the second of a set of studies on the molecular conformations of AMP, ATP and ADP. Results show that EHT yields a minimum energy ATP configuration that corresponds to the observed structure when atoms from the crystal are included in the calculations. Eight torsional angles were examined for ATP and six for ADP with all atoms included in the calculations. Results indicate that torsional rotations involving the adenosine part of the molecule show well-defined local minima. The predominant feature of the pyrophosphate section, however, is a low energy profile enabling the molecule to adapt its conformation to the environmental conditions.