Search Of Conformational Space Research Articles

Computational studies on carbohydrates: I. Density functional ab initio geometry optimization on maltose conformations

Ab initio geometry optimization was carried out on 10 selected conformations of maltose and two 2-methoxytetrahydropyran conformations using the density functional denoted B3LYP combined with two basis sets. The 6-31G* and 6-311++G** basis sets make up the B3LYP/6-31G* and B3LYP/6-311++G** procedures. Internal coordinates were fully relaxed, and structures were gradient optimized at both levels of theory. Ten conformations were studied at the B3LYP/6-31G* level, and five of these were continued with full gradient optimization at the B3LYP/6-311++G** level of theory. The details of the ab initio optimized geometries are presented here, with particular attention given to the positions of the atoms around the anomeric center and the effect of the particular anomer and hydrogen bonding pattern on the maltose ring structures and relative conformational energies. The size and complexity of the hydrogen-bonding network prevented a rigorous search of conformational space by ab initio calculations. However, using empirical force fields, low-energy conformers of maltose were found that were subsequently gradient optimized at the two ab initio levels of theory. Three classes of conformations were studied, as defined by the clockwise or counterclockwise direction of the hydroxyl groups, or a flipped conformer in which the ψ-dihedral is rotated by ∼180°. Different combinations of ω side-chain rotations gave energy differences of more than 6 kcal/mol above the lowest energy structure found. The lowest energy structures bear remarkably close resemblance to the neutron and X-ray diffraction crystal structures. © 2000 John Wiley & Sons, Inc.* J Comput Chem 21: 1204–1219, 2000

Simplified models of protein folding exploiting the Lagrange radius of gyration of the hydrophobic component

Studies are performed using an early proposed, but relatively little investigated, model that efficiently emulates a hydrophobic funneling effect in protein folding. Its simple form, introduced as a further interaction term going as the square of the separation distance, is suitable for initial searches of conformational space by parallel computation and special processors which use polynomial representation of pair-wise interactions. Use of such a term implies calculation of the square of the Lagrange radius of gyration, but weighted by hydrophobicity rather than the masses of the constituent particles. The unusual choice is justified by the observation that experimental protein structures have forms consistent with this Lagrange formalism for hydrophobic residues, and so compact model structures have appropriate density. However, since the long-range and square-power form strains open structures and leads to rapid generation of compact structures, such that for most of the simulation chain the movements result in intra-chain clashes, a rapid rejection algorithm is employed that prunes out similar but high energy structures. The studies also explore the choice of the simplest possible models which might be used to explore folding. Hence pancreatic trypsin inhibitor is modeled as a ‘string-of-beads’, where the beads represent residues of differing hydrophobicity. This model has only limited success, and because there are no identifiable common centers of interaction between the ‘string-of-beads’ model and all-atom protein representations, it encounters the difficulties: (a) of comparing such highly simplified models with observed structures, and (b) of using such models as a starting point for conversion to all-atom models. The conclusion is that this solvent treatment is best applied to all-atom simulations from the outset. Nonetheless, low energy predictions obtained in this simple study can be considered as having promising features, and provide interesting insight into protein folding and the funneling contribution.

Structures of Furanosides: A Study of the Conformational Space of Methyl α-d-Lyxofuranoside by Density Functional Methods

A search of the gas phase conformational space of methyl α-d-lyxofuranoside was carried out at the B3LYP/cc-pVDZ level. Relative energies of the local minima were computed using the larger aug-cc-pVDZ basis set and the recent mPW1LYP exchange-correlation functional. Local minima include structures with zero, one, two, three, or four internal hydrogen bonds and conformational energies of 12−2 kcal/mol relative to the “strain-free” methyl α-d-lyxopyranoside. The two most stable structures, with three and four internal hydrogen bonds, have conformational energies of approximately 2 kcal/mol. The relevance of these results to the conformational behavior of furanosides in the crystalline state and in solution is discussed. An efficient and accurate general procedure for searching the conformational space of furanosides is proposed.

Computational studies on carbohydrates: I. Density functionalab initio geometry optimization on maltose conformations

Ab initio geometry optimization was carried out on 10 selected conformations of maltose and two 2-methoxytetrahydropyran conformations using the density functional denoted B3LYP combined with two basis sets. The 6-31G and 6-311CCG basis sets make up the B3LYP/6-31G and B3LYP/6-311CCG procedures. Internal coordinates were fully relaxed, and structures were gradient optimized at both levels of theory. Ten conformations were studied at the B3LYP/6-31G level, and five of these were continued with full gradient optimization at the B3LYP/6-311CCG level of theory. The details of the ab initio optimized geometries are presented here, with particular attention given to the positions of the atoms around the anomeric center and the effect of the particular anomer and hydrogen bonding pattern on the maltose ring structures and relative conformational energies. The size and complexity of the hydrogen-bonding network prevented a rigorous search of conformational space by ab initio calculations. However, using empirical force fields, low-energy conformers of maltose were found that were subsequently gradient optimized at the two ab initio levels of theory. Three classes of conformations were studied, as defined by the clockwise or counterclockwise direction of the hydroxyl groups, or a flipped conformer in which the -dihedral is rotated by180 .D ifferent combinations of! side-chain rotations gave energy differences of more than 6 kcal/mol above the lowest energy structure found. The lowest energy structures bear remarkably close resemblance to the neutron and X-ray diffraction crystal structures. c 2000 John Wiley & Sons, Inc. JC omput Chem 21: 1204-1219, 2000

How large should proteins be? The minimal size of a good structure seeker

This work deals with the determination of the minimum length of a protein chain required for expeditious and robust folding into a specific target structural motif. Our goal requires that we explore the relationship between the size of a protein and its ability to fold from the statistical mechanics perspective. A coarse partition of the soft-mode conformation space in basins of attraction of the potential energy surface (PES) associated to different contact patterns (CPs) is assumed. This coarse description is consistent with low-temperature experimental probes, revealing the fine resolution of each PES basin, a feature known to be washed out at typical renaturation temperatures. This experimental observation provides the signature of an entrainment of fast-relaxing variables by a coarse CP-resolution of the dynamics. Our statistical analysis is thus focused on the size-dependent energy dispersion within basins and the observation that large energy-level dispersions prevent the entrainment of long-time torsional dynamics by CP transitions due to the breakdown of relaxation timescale separation. The entrainment by coarse dynamics is required by a good structure seeker, since it renders adiabatically the search in conformation space, a regime warranted by a relatively fast equilibration within each CP-basin. This drastic reduction in the number of dominant variables, probed for real proteins at low unphysiological temperatures, is reasonably assumed to be responsible for the robustness and expediency of the folding process, which is thus no longer dependent on the fine details of the torsional dynamics. Finding the minimal size of a protein chain fulfilling such requirements is precisely the goal of this work. If the chain is not long enough, the large relative dispersion of energy levels within a basin introduces correlations between substates of different basins and leads to a breakdown of the dynamic entrainment, rendering the folding process ineffective, and considerably decreasing its expediency. This is so since energy fluctuations within a CP-basin relax on timescales which are no longer incommensurably shorter than those of CP-transitions and intra-CP-basin relaxation interferes with the folding process as viewed from the coarser perspective.

A variational approach to relaxation in ultrametric spaces

We investigate the relaxation behavior of complex systems endowed with a rugged free energy landscape from a variational perspective. We focus first on the dynamics in generic ultrametric spaces and then we specialize our generic results to a coarse-grained description of RNA folding, where ultrametricity holds as a limit description of conformation space. Using variational calculus in the generic context, we obtain the brachistochrone or fastest relaxation pathway for the ultrametric distance as a function of the barrier size and conclude that the brachistochrone may only be realized by those systems that follow the exponential or Debye law. Our approach not only reproduces the phenomenological generic relaxation law in the ultrametric limit, but is also justified a posteriori in specialized contexts: It reproduces meaningful folding pathways for the search in conformational space performed by renaturing RNA molecules which are targets of natural selection, reflecting a maximization in the efficiency of the folding process.

Flexible docking allowing induced fit in proteins: Insights from an open to closed conformational isomers

Here we dock a ligand onto a receptor surface allowing hinge-bending domain/substructural movements. Our approach mimics and manifests induced fit in molecular recognition. All angular rotations are allowed on the one hand, while a conformational space search is avoided on the other. Rather than dock each of the molecular parts separately with subsequent reconstruction of the consistently docked molecules, all parts are docked simultaneously while still utilizing the position of the hinge from the start. Like pliers closing on a screw, the receptor automatically closes on its ligand in the best surface-matching way. Movements are allowed either in the ligand or in the larger receptor, hence reproducing induced molecular fit. Hinge bending movements are frequently observed when molecules associate. There are numerous examples of open versus closed conformations taking place upon binding. Such movements are observed when the substrate binds to its respective enzyme. In particular, such movements are of interest in allosteric enzymes. The movements can involve entire domains, subdomains, loops, (other) secondary structure elements, or between any groups of atoms connected by flexible joints. We have implemented the hinges at points and at bonds. By allowing 3-dimensional (3-D) rotation at the hinge, several rotations about (consecutive or nearby) bonds are implicitly taken into account. Alternatively, if required, the point rotation can be restricted to bond rotation. Here we illustrate this hinge-bending docking approach and the insight into flexibility it provides on a complex of the calmodulin with its M13 ligand, positioning the hinges either in the ligand or in the larger receptor. This automated and efficient method is adapted from computer vision and robotics. It enables utilizing entire molecular surfaces rather than focusing a priori on active sites. Hence, allows attaining the overall optimally matching surfaces, the extent and type of motions which are involved. Here we do not treat the conformational flexibility of side-chains or of very small pieces of the molecules. Therefore, currently available methods addressing these issues and the method presented here, are complementary to each other, expanding the repertoire of computational docking tools foreseen to aid in studies of recognition, conformational flexibility and drug design. Proteins 32:159–174, 1998. © 1998 Wiley-Liss, Inc.

Flexible docking allowing induced fit in proteins: Insights from an open to closed conformational isomers

Here we dock a ligand onto a receptor surface allowing hinge-bending domain/substructural movements. Our approach mimics and manifests induced fit in molecular recognition. All angular rotations are allowed on the one hand, while a conformational space search is avoided on the other. Rather than dock each of the molecular parts separately with subsequent reconstruction of the consistently docked molecules, all parts are docked simultaneously while still utilizing the position of the hinge from the start. Like pliers closing on a screw, the receptor automatically closes on its ligand in the best surface-matching way. Movements are allowed either in the ligand or in the larger receptor, hence reproducing induced molecular fit. Hinge bending movements are frequently observed when molecules associate. There are numerous examples of open versus closed conformations taking place upon binding. Such movements are observed when the substrate binds to its respective enzyme. In particular, such movements are of interest in allosteric enzymes. The movements can involve entire domains, subdomains, loops, (other) secondary structure elements, or between any groups of atoms connected by flexible joints. We have implemented the hinges at points and at bonds. By allowing 3-dimensional (3-D) rotation at the hinge, several rotations about (consecutive or nearby) bonds are implicitly taken into account. Alternatively, if required, the point rotation can be restricted to bond rotation. Here we illustrate this hinge-bending docking approach and the insight into flexibility it provides on a complex of the calmodulin with its M13 ligand, positioning the hinges either in the ligand or in the larger receptor. This automated and efficient method is adapted from computer vision and robotics. It enables utilizing entire molecular surfaces rather than focusing a priori on active sites. Hence, allows attaining the overall optimally matching surfaces, the extent and type of motions which are involved. Here we do not treat the conformational flexibility of side-chains or of very small pieces of the molecules. Therefore, currently available methods addressing these issues and the method presented here, are complementary to each other, expanding the repertoire of computational docking tools foreseen to aid in studies of recognition, conformational flexibility and drug design.

Essential structural factors of annonaceous acetogenins as potent inhibitors of mitochondrial complex I

The annonaceous acetogenins are the most potent of the known inhibitors of bovine heart mitochondrial complex I. These inhibitors act, at the terminal electron transfer step of the enzyme, in a similar way to the usual complex I inhibitors, such as piericidin A and rotenone; however, structural similarities are not apparent between the acetogenins and these known complex I inhibitors. A systematic set of isolated natural acetogenins was prepared and examined for their inhibitory actions with bovine heart mitochondrial complex I to identify the essential structural factors of these inhibitors for the exhibition of potent activity. Despite their very potent activity, the structural requirements of the acetogenins are not particularly rigid and remain somewhat ambiguous. The most common structural units, such as adjacent bis-tetrahydrofuran (THF) rings and hydroxyl groups in the 4- and/or 10-positions, were not essential for exhibiting potent activity. The stereochemistry surrounding the THF rings, surprisingly, seemed to be unimportant, which was corroborated by an exhaustive conformational space search analysis, indicating that the model compounds, with different stereochemical arrangements around the THF moieties, were in fairly good superimposition. Proper length and flexibility of the alkyl spacer moiety, which links the THF and the α,β-unsaturated γ-lactone ring moieties, were essential for the potent activity. This probably results from some sort of specific conformation of the spacer moiety which regulates the two ring moieties to locate into an optimal spatial position on the enzyme. It is, therefore, suggested that the structural specificity of the acetogenins, required for optimum inhibition, differs significantly from that of the common complex I inhibitors in which essential structural units are compactly arranged and conveniently defined. The structure–activity profile for complex I inhibition is discussed in comparison with those for other biological activities.

Cluster conformational analysis of a seco acid used in Woodward's total synthesis of erythromycin A

An efficient conformational space search algorithm CONFLEX augmented with a clustering technique was applied to a model of that particular seco acid which successfully cyclized to macrocyclic lactone in Woodward's total synthesis of erythromycin A, with the purpose of finding the folded conformation long supposed to exist in this seco acid. Among 4999 energy minima that have been generated, 270 of them had conformations almost superimposable with those of the dominant forms of the cyclized model, but the combined population of the reactive conformers was only 3.2% of the total. The implications of these observations are discussed.

Conformational analysis on segments of charged polysaccharides. The case of hyaluronic acid dimer and chondrosine

The conformations of two differently charged carbohydrate systems, namely hyaluronic acid dimer and chondrosine, were studied by various methods of molecular modelling. The effects of protonation, ionization, solvent polarity and the presence of counter-ions on the conformational behaviour were evaluated. Two different generic force fields (CVFF and DII) and different methodologies (grid search, Monte Carlo, quenched molecular dynamics) were adopted for the search of stable conformers and conformational space. Data obtained from molecular modelling were compared with those derived from one-dimensional nuclear Overhauser spectroscopy (NOESY) experiments.

Full ab Initio Conformational Spectrum of α,α‘-Diaminoacetone

The ab initio conformational spectrum of α,α‘-diaminoacetone, (NH2CH2)2CO, is obtained by systematic conformational space search at the HF/6-31+G* level. The 15 conformers are discussed in terms of...

Application of a genetic algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: comparison with distance geometry calculations.

The three-dimensional spatial structure of a methylene-acetal-linked thymine dimer present in a 10 basepair (bp) sense-antisense DNA duplex was studied with a genetic algorithm designed to interpret NOE distance restraints. Trial solutions were represented by torsion angles. This means that bond angles for the dimer trial structures are kept fixed during the genetic algorithm optimization. Bond angle values were extracted from a 10 bp sense-antisense duplex model that was subjected to energy minimization by means of a modified AMBER force field. A set of 63 proton-proton distance restraints defining the methylene-acetal-linked thymine dimer was available. The genetic algorithm minimizes the difference between distances in the trial structures and distance restraints. A large conformational search space could be covered in the genetic algorithm optimization by allowing a wide range of torsion angles. The genetic algorithm optimization in all cases led to one family of structures. This family of the methylene-acetal-linked thymine dimer in the duplex differs from the family that was suggested from distance geometry calculations. It is demonstrated that the bond angle geometry around the methylene-acetal linkage plays an important role in the optimization.

Modelling constrained calcitonin gene-related peptide analogues.

The calcitonin gene-related peptide (CGRP) is a 37-residue peptide with pronounced physiological activities, making it an interesting lead for drug development. In our previous work, we designed constrained analogues of the peptide. The biological activities of these proved that the disulfide bridges created favoured the active conformations of the peptide. Here we report the molecular modelling of the conformation of domains involved in receptor activation. Our approach was to create sets of possible conformations for three differently constrained bioactive regions by a random search of conformational space and molecular modelling. The conformations were compared, and those allowed for all derivatives were considered relevant for receptor activation. This approach resulted in one favoured group of conformations characterized by an inverse gamma-turn followed by a gamma-turn, defining the conformation of the tripeptide region with a similar sequence in all active analogues. The models may also be used for the design of peptide and non-peptide analogues of CGRP.

Flexible ligand docking without parameter adjustment across four ligand–receptor complexes

AbstractUnderstanding molecular recognition is one of the fundamental problems in molecular biology. Computationally, molecular recognition is formulated as a docking problem. Ideally, a molecular docking algorithm should be computationally efficient, provide reasonably thorough search of conformational space, obtain solutions with reasonable consistency, and not require parameter adjustments. With these goals in mind, we developed DIVALI (Docking wIth eVolutionary AlgorIthms), a program which efficiently and reliably searches for the possible binding modes of a ligand within a fixed receptor. We use an AMBER‐type potential function and search for good ligand conformations using a genetic algorithm (GA). We apply our system to study the docking of both rigid and flexible ligands in four different complexes. Our results indicate that it is possible to find diverse binding modes, including structures like the crystal structure, all with comparable potential function values. To achieve this, certain modifications to the standard GA recipe are essential. © 1995 John Wiley & Sons, Inc.

Ascribing weights to folding histories: explaining the expediency of biopolymer folding

The author develops a novel scheme of statistical inference whereby statistical weights are assigned to folding pathways. Evidence is presented that supports the fact that this scheme accounts for the robustness and expediency of biopolymer folding processes. The essential properties of folding are captured by showing that the weight is concentrated over a very limited domain of closely related folding pathways. To make probabilistic inferences, the author constructively defines a measure eta over the space of folding pathways. Such a scheme stands in contrast to traditional methods built upon a Boltzmann measure over conformation space. In order to implement and validate this new approach the author combines analytical theory and computations that successfully reproduce pulse-chase kinetic experiments. The author first presents a rigorous analytical result by proving that an appropriate measure exists over the space of folding pathways. This existence theorem is shown to hold in two general scenarios: (i) the unbiased folding (UF) scenario, in which the complete chain starts its search in conformation space in an unbiased manner; (ii) the sequential folding (SF) scenario, in which the chain starts searching in conformation space concurrently with its own sequential assembling by progressive incorporation of monomers. A systematic coarse-graining simplification of the space of folding pathways is implemented to make the computations feasible and to validate the author's theory as a means of accounting for the expedient way of searching for the functionally competent conformation.

Shape complementarity at protein–protein interfaces

A matching algorithm using surface complementarity between receptor and ligand protein molecules is outlined. The molecular surfaces are represented by "critical points," describing holes and knobs. Holes (maxima of a shape function) are matched with knobs (minima). This simple and appealing surface representation has been previously described by Connolly [(1986) Biopolymers, Vol. 25, pp. 1229-1247]. However, attempts to implement this description in a docking scheme have been unsuccessful (e.g., Connolly, ibid.). In order to decrease the combinatorial complexity, and to make the execution time affordable, four critical hole/knob point matches were sought. This approach failed since some bound interfaces are relatively flat and do not possess four critical point matches. On the otherhand, matchings of fewer critical points require a very time-consuming, full conformational (grid) space search [Wang, (1991) Journal of Computational Chemistry, Vol. 12, pp. 746-750]. Here we show that despite the initial failure of this approach, with a simple and straightforward modification in the matching algorithm, this surface representation works well. Out of the 16 protein-protein complexes we have tried, 15 were successfully docked, including two immunoglobulins. The entire molecular surfaces were considered, with absolutely no additional information regarding the binding sites. The whole process is completely automated, with no manual intervention, either in the input atomic coordinate data, or in the matching. We have been able to reach this level of performance with the hole/knob surface description by using pairs of critical points along with their surface normals in the calculation of the transformation matrix. The success of this approach suggests that future docking methods should use geometric docking as the first screening filter.(ABSTRACT TRUNCATED AT 250 WORDS)

Heuristic methods in conformational space search of peptides

Heuristic methods for combinatorial optimization problems can be helpful in searching for the lowest energy conformation of molecules. Among them, genetic algorithms are still in their infancy when dealing with this problem. Instead, simulated annealing and its variations like threshold accepting have proved to be competitive when compared to other optimization methods. We present here satisfactory results when applying the threshold accepting algorithm to small size peptide molecules.

Memorizing all significant foldings of a random RNA chain

We implement a synchronous parallel neural network associating a two-state unit to each pair of bases in a random RNA chain in such a way that a Watson-Crick base-pair corresponds to an activated unit and the phase space flow realizes the search in the conformation space for the RNA chain. Accordingly, all significant secondary structures are associated to metastable or stable neural patterns and exploration of conformation space emerges as a collective property of a neural-like system made up of equivalent components. The synaptic tensor is constructed taking into account the cooperativity principles of secondary structure formation, incorporating nucleation effects for initiation of intra-chain duplex formation and stacking of base pairs. This tensor is readily reducible to Moore-Penrose normal form since al metastable patterns become stable and orthogonal in the T = 0 limit. The dynamics of the exploration of metastable patterns by the network are shown to follow a random energy model in accord with the already-established uncorrelated energy landscape for random RNA foldings.

Modelling the structure of the calcitonin gene-related peptide.

The calcitonin gene-related peptide (CGRP) is a 37 residue neuropeptide which causes vasodilatation, increases heart rate and inhibits bone resorption. These effects make it an interesting lead for drug discovery. We have combined current structural and biological information to model the structure of hCGRP-beta to be used as a basis for the rational design of novel analogues. Distinct regions of CGRP have been shown to be responsible for the activity of the whole molecule. Thus, the structure of the peptide was modelled in four parts which were finally combined. A random search of conformational space was performed for the fragments CGRP1-8 and CGRP30-37 which have been shown to be central for receptor activation and binding, respectively. Five low-energy hCGRP-beta structures were obtained from modelled fragments by molecular dynamics. The relevance of the approach was verified by comparing the models with NMR structures of CGRP and calcitonin. The models obtained for the N- and C-terminal fragments should enable the design of novel agonists and antagonists of the CGRP receptor, respectively. Models of the whole molecule may be used in the design of peptides with shortened spacers between the receptor-bound regions. The approach described is applicable to several related peptide hormones, like growth hormone-releasing hormone and secretin.