Comparison of computer modelling and X-ray results of the binding of a pyrazole derivative to liver alcohol dehydrogenase

The binding to liver alcohol dehydrogenase of the inhibitor 2,4-(4-pyrazolyl)-butylisothiourea has been studied both by modelling experiments using computer graphics with interactive energy minimization and by X-ray crystallographic structure determination. For the modelling experiments, we used the program system TOM, which was developed in our laboratory as an extension of the program FRODO. Different strategies for using computer graphics with interactive energy minimization were tested. Two essentially different binding modes were found. One of these was favoured from energy minimizations using a potential energy function which was the sum of a Coulomb interaction term and two different van der Waals' interaction terms for non-bonded and torsional interactions. This binding mode was close to the crystallographic observed structure. The results show that flexibility of both ligand and receptor side-chains as well as main-chain conformations are important for docking to the active site of liver alcohol dehydrogenase.     

Fold helical proteins by energy minimization in dihedral space and a DFIRE-based statistical energy function

Statistical energy functions are discrete (or stepwise) energy functions that lack van der Waals repulsion. As a result, they are often applied directly to a given structure (native or decoy) without further energy minimization being performed to the structure. However, the full benefit (or hidden defect) of an energy function cannot be revealed without energy minimization. This paper tests a recently developed, all-atom statistical energy function by energy minimization with a fixed secondary helical structure in dihedral space. This is accomplished by combining the statistical energy function based on a distance-scaled finite ideal-gas reference (DFIRE) state with a simple repulsive interaction and an improper torsion energy function. The energy function was used to minimize 2000 random initial structures of 41 small and medium-sized helical proteins in a dihedral space with a fixed helical region. Results indicate that near-native structures for most studied proteins can be obtained by minimization alone. The average minimum root-mean-squared distance (rmsd) from the native structure for all 41 proteins is 4.1 A. The energy function (together with a simple clustering of similar structures) also makes a reasonable selection of near-native structures from minimized structures. The average rmsd value and the average rank for the best structure in the top five is 6.8 A and 2.4, respectively. The accuracy of the structures sampled and the structure selections can be improved significantly with the removal of flexible terminal regions in rmsd calculations and in minimization and with the increase in the number of minimizations. The minimized structures form an excellent decoy set for testing other energy functions because most structures are well-packed with minimum hard-core overlaps with correct hydrophobic/hydrophilic partitioning. They are available online at http://theory.med.buffalo.edu.     

Improved AMYR program: an algorithm for the theoretical simulation of molecular associations,including geometrical and topological characterization of the dimers

Program AMYR, originally written by S. Fraga (University of Alberta, Canada), allows for the calculation of molecular associations using a pair-wise atom-atom potential. The interaction energy is evaluated through a 1/R expansion. Our improved version includes a dispersion energy term in the potential corrected by damping functions, the possibility of carrying out energy minimizations through variable metric methods, as well as the optional calculation of geometrical and topological indices. Program AMYR has been adapted also for high-performance computing and vectorization. An interactive version of the program carries out real-time molecular graphics showing simultaneously the energy profile of the calculations.     

An easy way to include weak alignment constraints into NMR structure calculations

We have recently shown that an energy penalty for the incorporation of residual tensorial constraints into molecular structure calculations can be formulated without the explicit knowledge of the Saupe orientation tensor (Moltke and Grzesiek, J. Biomol. NMR, 1999, 15, 77–82). Here we report the implementation of such an algorithm into the program X-PLOR. The new algorithm is easy to use and has good convergence properties. The algorithm is used for the structure refinement of the HIV-1 Nef protein using 252 dipolar coupling restraints. The approach is compared to the conventional penalty function with explicit knowledge of the orientation tensor's amplitude and rhombicity. No significant differences are found with respect to speed, Ramachandran core quality or coordinate precision.     

Accurate ab initio calculation of the Ar–CF4 intermolecular potential energy surface

Ar–CF₄ intermolecular interaction potential is studied by ab initio calculations at the MP2 and CCSD(T) levels of theory containing the so-called bond functions ({3s3p2d1f} basis set was chosen) both with and without a correction for the basis-set superposition error. The calculations were performed with Dunning's correlation consistent basis sets (aug-cc-pVXZ, X = D, T, Q, 5) to extrapolate the Ar–CF₄ potential energy minimum and intermolecular distance to their complete basis set (CBS) limits. It is shown that the addition of bond functions results in a dramatic improvement in the convergence of the calculated interaction energies at the MP2/aug-cc-pVTZ level. The MP2/{3s3p2d1f}-aug-cc-pVTZ potential energy surface even approaches the CCSD(T)/aug-cc-pVQZ potential energy surface. The potential energy minima and the intermolecular distances are both significantly closer to the CBS limit when using the bond functions, and it implies that adding bond functions in the calculation has a great effect on the interaction energies. We also find that with bond functions included in the CCSD(T)/aug-cc-pVDZ model chemistry, the potential energy minima are extremely close to the CBS limit and are better than the CCSD(T)/aug-cc-pVQZ values. Several levels of theory described in the text were used to determine pairwise analytic potential energy surfaces for Ar+CF₄. The analytic potential energy surfaces are in very good agreement with the ab initio values.     

Discrimination of near-native structures in protein-protein docking by testing the stability of local minima

Fast Fourier transform (FFT) correlation methods of protein-protein docking, combined with the clustering of low energy conformations, can find a number of local minima on the energy surface. For most complexes, the locations of the near-native structures can be constrained to the 30 largest clusters, each surrounding a local minimum. However, no reliable further discrimination can be obtained by energy measures because the differences in the energy levels between the minima are comparable with the errors in the energy evaluation. In fact, no current scoring function accounts for the entropic contributions that relate to the width rather than the depth of the minima. Since structures at narrow minima loose more entropy, some of the nonnative states can be detected by determining whether or not a local minimum is surrounded by a broad region of attraction on the energy surface. The analysis is based on starting Monte Carlo Minimization (MCM) runs from random points around each minimum, and observing whether a certain fraction of trajectories converge to a small region within the cluster. The cluster is considered stable if such a strong attractor exists, has at least 10 convergent trajectories, is relatively close to the original cluster center, and contains a low energy structure. We studied the stability of clusters for enzyme-inhibitor and antibody-antigen complexes in the Protein Docking Benchmark. The analysis yields three main results. First, all clusters that are close to the native structure are stable. Second, restricting considerations to stable clusters eliminates around half of the false positives, that is, solutions that are low in energy but far from the native structure of the complex. Third, dividing the conformational space into clusters and determining the stability of each cluster, the combined approach is less dependent on a priori information than exploring the potential conformational space by Monte Carlo minimizations.     

Accurate representation of B-DNA double helical structure with implicit solvent and counterions

High-resolution nuclear magnetic resonance (NMR) and crystallographic data have been taken to refine the force field used in the torsion angle space nucleic acids molecular mechanics program DUPLEX. The population balance deduced from NMR studies of two carcinogen-modified DNA conformers in equilibrium was used to fine tune a sigmoidal, distance-dependent dielectric function so that reasonable relative energies could be obtained. In addition, the base-pair and backbone geometry from high-resolution crystal structures of the Dickerson-Drew dodecamer was used to re-evaluate the deoxyribose pseudorotation profile and the Lennard-Jones nonbonded energy terms. With a modified dielectric function that assumes a very steep distance-dependent form, a deoxyribose pseudorotation profile with reduced energy barriers between C2'- and C3'-endo minima, and a shift of the Lennard-Jones potential energy minimum to a distance approximately 0.4 A greater than the sum of the van der Waals' radii, the sequence-dependent conformational features of the Dickerson-Drew dodecamer in both the solid state and the aqueous liquid crystalline phase are well reproduced. The robust performance of the revised force field, in conjunction with its efficiency through implicit treatment of solvent and counterions, provides a valuable tool for elucidating conformations and structure-function relationships of DNA, including those of molecules modified by carcinogens and other ligands.     

Simulated annealing approach to the study of protein structures

One of the most difficult problems in predicting the three dimensional structure of proteins is how to deal with the local minimum problem. In many cases of practical interest this problem has been reduced to how to select an appropriate set of starting conformations for carrying out energy minimizations. How these starting conformations are selected, however, is often based on the physical intuition of the person doing the calculations, and hence it is hard to avoid bearing some sort of arbitrariness. To improve such a situation, we introduced the simulated annealing Monte Carlo algorithm to locate the optimal starting conformations for energy minimizations. The method developed here is valid for both single and multiple polypeptide chain systems. The annealing process can be conducted with respect to either the internal dihedral angles of a polypeptide chain or the external rotations and translations of various constituent polypeptide chains, and hence is particularly useful for studying the packing arrangements of secondary structures in proteins, such as helix/helix packing, helix/sheet packing and sheet/sheet packing. It was shown via a number of comparative calculations that the final structures obtained through the annealing process not only had lower energies than the corresponding energy-minimized structures reported previously, but also assumed the forms closer to the observations in proteins. All these results indicate that a better result can be obtained in search of low-energy structures of proteins by incorporating the simulated annealing approach.(ABSTRACT TRUNCATED AT 250 WORDS)     

Distortions of the DNA Double Helix Induced by 1,3-trans-Diamminedichloroplatinum(II)-intrastrand Cross-link: An Internal Coordinate Molecular Modeling Study

Abstract

A trans-diamminedichloroplatinum(II) (trans-DDP) intrastrand adduct within the sequence d(TCTG*TG*TC)·d(GACACAGA) (where G* represents a platinated guanine) is modeled on the basis of qualitative experimental data concerning global unwinding and curvature as well as information on base pairing. Modeling is performed using the internal coordinate JUMNA program, specific to nucleic acids, and modified to include the possibility of covalently bound ligands. Calibration of the energy functions representing the Pt-N7 bond with guanine is described. The platinum atom and the platinum-nitrogen bonds are parameterized for use in the Hückel Del Re method to calculate monopoles at each atom. These monopoles are consistent with the Flex force field included in Jumna. By developing an appropriate minimization protocol we are able to generate stable, distorted three-dimensional structures compatible with the experimental data and including an unusually high global unwinding. No a priori geometric assumptions are made in generating these structures.     

Energetic approach to the folding of four alpha-helices connected sequentially

The packing of four alpha-helices, which each consist of 12 Ala residues and are sequentially connected to each other by a segment of 10 Ala residues, has been investigated by means of energy minimizations. For the lowest energy structure thus obtained, the following features have been found: (i) the four alpha-helices are intimately packed to form an assembly with an approximately square section; (ii) the distances of closest approach between two adjacent interhelix axes are 7.7 +/- 0.2 A and those between two diagonal interhelix axes are 11.2 +/- 0.2 A; (iii) the adjacent interhelix angles are -163 +/- 2 degrees; and (iv) the diagonal interhelix angles are 24 +/- 4 degrees. These results indicate that the polypeptide chain, driven by energetics (nonbonded and electrostatic interactions), is folded into a typical left-handed twisted four-helix bundle with an approximately 4-fold symmetric array, as observed in most four alpha-helix proteins. Furthermore, it has been found that the interaction between the loops formed by the connecting segments and the other part of molecule plays a significant role in stabilizing such a bundle structure. The technology developed here and the relevant knowledge obtained through this study are very useful for the study of modeling four-helix bundle proteins.     

The multiple-minima problem in the conformational analysis of polypeptides. III. An Electrostatically Driven Monte Carlo Method: Tests on enkephalin

The three-dimensional conformation of Met-enkephalin, corresponding to the lowest minimum of the empirical potential energy function ECEPP/2 (empirical conformational energy program for peptides), has been determined using a new algorithm, viz. the Electrostatically Driven Monte Carlo Method. This methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. These features are included in the algorithm that produces a Monte Carlo search in the conformational hyperspace of the polypeptide, using electrostatic predictions and a random sampling technique to locate low-energy conformations. In addition, we have incorporated an alternative mechanism that allows the structure to escape from some conformational regions representing metastable local energy minima and even from regions of the conformational space with great stability. In 33 test calculations on Met-enkephalin, starting from arbitrary or completely random conformations, the structure corresponding to the global energy minimum was found inall the cases analyzed, with a relatively small search of the conformational space. Some of these starting conformations wereright orleft-handed -helices, characterized by good electrostatic interactions involving their backbone peptide dipoles; nevertheless, the procedure was able to convert such locally stable structures to the global-minimum conformation.On leave from the National University of San Luis, Faculty of Sciences and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Instituto de Matemática Aplicada, San Luis, Ejército de los Andes 950, 5700 San Luis, Argentina.     

Energy allocation strategy modifies growth–survival trade-offs in juvenile fish across ecological and environmental gradients

In young temperate zone fishes, conflicting energy demands lead to variability in growing season and winter survival. Growing season survival is driven by size-dependent predation risk whereas winter survival is constrained by autumn body size, energy storage and winter duration. We developed a model of the seasonality of energetics coupled to empirical measures of resource availability, size-dependent predation and temperature seasonality for rainbow trout (Oncorhynchus mykiss) in two sets of lakes in British Columbia, Canada, representing endpoints of a gradient of temperature, growing season duration and winter duration. This model was used to determine the energy allocation strategy which maximized first-year survival across these gradients. Survival was sensitive to the timing of the switch from somatic to storage strategies in cold, short growing season, low resource environments. A broader range of energy allocation strategies were viable in warmer, longer growing season and higher resource lakes. We used empirical observations of autumn energy storage and our modeled values for size-dependent minimal lipid levels needed to survive winter in each system to estimate winter survival for juvenile rainbow trout. Winter survival estimates were 6% in cold lakes with low resources, 82% in warm, lakes with low resources and 100% in warm lakes with high resources. Fish in warm lakes with ample resources allocated substantially more to storage than the minimum required to survive winter generated from our model, suggesting additional selection pressures for increased storage when there was ample surplus energy. We concluded that growth–survival trade-offs, modified by seasonality of the environment, influenced the growing season energy allocation strategies for young-of-the-year fish, and suggested this may be important for understanding population viability across environmental gradients.     

Binding of Net-Fla,a Netropsin-Flavin Hybrid Molecule,to DNA: Molecular Mechanics and Dynamics Studies in vacuo and in Water Solution

Abstract

We have studied the binding of the hybrid netropsin-flavin (Net-Fla) molecule onto four sequences containing four A.T base pairs. Molecular mechanics minimizations in vacuo show numerous minimal conformations separated by one base pair. 400 ps molecular dynamics simulations in vacuo have been performed using the lowest minima as the starting conformations. During these simulations, the flavin moiety of the drug makes two hydrogen bonds with an amino group of a neighboring guanine. A 200 ps molecular dynamics simulation in explicit water solution suggests that the binding of Net-Fla upon the DNA substrate is enhanced by water bridges. A water molecule bridging the amidinium of Net-Fla to the N3 atom of an adenine seems to be stuck in the dmg-DNA complex during the whole simulation. The fluctuations of the DNA helical parameters and of the torsion angles of the sugar-phosphate backbone are very similar in the simulations in vacuo and in water. The time auto-correlation functions for the DNA helical parameters decrease rapidly in the picosecond range in vacuo. The same functions computed from the water solution molecular dynamics simulations seem to have two modes: the rapid mode is similar to the behavior in vacuo, and is followed by a slower mode in the 10 ps range.     

Energy Minimization for Tertiary Structure Prediction of Homologous Proteins: α1-purothionin and Viscotoxin A3 Models from Crambin

Abstract

Homologous proteins may fold into similar three-dimensional structures. Spectroscopic evidence suggests this is true for the cereal grain thionins, the mistletoe toxins, and for crambin, three classes of plant proteins. We have combined primary sequence homology and energy minimization to predict the structures α₁-purothionin (from Durum wheat) and viscotoxin A3 (from Viscum album, European mistletoe) from the high resolution (0.945 Å) crystal structure of crambin (from Crambe abyssinica). Our predictions will be verifiable because we have diffraction-quality crystals of α₁-purothionin whose structure we are have predicted. The potential energy minimizations for each protein were performed both with and without harmonic constraints to its initial backbone to explore the existence of local minima for the predicted proteins. Crambin was run as a control to examine the effects of the potential energy minimization on a protein with a well-known structure. Only α₁-purothionin which has one fewer residue in a turn region shows a significant difference for the two minimization paths. The results of these predictions suggest that α₁-purothionin and viscotoxin are amphipathic proteins, and this character may relate to the mechanism of action for these proteins. Both are mildly membrane-active and their amphipathic character is well suited for interaction with a lipid bilayer.     

Stable equilibrium strategies and penalty functions in a game of attrition

Maynard-Smith (1974) has presented a game of attrition model for animal conflict. He assumed that the penalty function, giving the cost in terms of fitness, of displaying for a given time period, is a linear function of the time of display. Under this assumption he shows that an evolutionary stable strategy (ESS) always exists: one such is a mixed strategy for which display times have a negative exponential distribution. Given the diversity of reproductive strategies and patterns of agonistic behavior in nature, it is reasonable to consider games with different types of cost functions. In this paper it is shown that if more general cost functions are allowed (not necessarily linear), then ESS's still exist and give a great variety of distributions of display time. Supporting data are presented to suggest that these distributions may be found in nature. It is suggested that the interrelations between an animal's fitness budget and the game's penalty function will determine the nature of an ESS for different kinds of games.     

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.     

Stereochemistry of nucleic acids and polynucleotides. VI. Minimum energy conformations of dimethyl phosphate

As part of a study on the conformation of polynucleotides and nucleic acids the preferred conformations of the model conpound dimethyl phosphate are worked out using potential energy functions. In calculating the total potential energy associated with the conformation, nonbonded, torsional, and electrostatic terms have been considered. The variation of the total conformational energy is represented as a function of two torsion angles ? and ψ which are the rotations about the two phosphoester bonds. The most stable conformations are found to be the gauche–gauche conformations about these bonds. The conformations observed for phosphodiesters in the solid state and in the proposed structures of polynucleotides and nucleic acids cluster around the minimum. Also, regions of minimum energy correspond well with the typical allowed regions of a representative dinucleotide.     

A variable gap penalty function and feature weights for protein 3-D structure comparisons.

We have developed a variable gap penalty function for use in the comparison program COMPARER which aligns protein sequences on the basis of their 3-D structures. For deletions and insertions, components are a function of structural features of individual amino acid residues (e.g. secondary structure and accessibility). We have also obtained relative weights for different features used in the comparison by examining the equivalent residues in weight matrices and in alignments for pairs of 3-D structures where the equivalencies are relatively unambiguous. We have used the new parameters and the variable gap penalty function in COMPARER to align protein structures in the Brookhaven Data Bank. The variable gap penalty function is useful especially in avoiding gaps in secondary structure elements and the new feature weights give improved alignments. The alignments for both azurins and plastocyanins and N- and C-terminal lobes for aspartic proteinases are discussed.     

Ant colony optimization for multicasting in static wireless ad-hoc networks

Nodes of wireless ad-hoc networks are generally equipped with batteries. This makes energy a scarce resource. Therefore, power consumption of network operations is critical and subject to optimization. One of the fundamental problems in ad-hoc networks is multicasting. In this work, we consider the so-called minimum energy multicast (MEM) problem in static ad-hoc networks. This problem can be stated as a combinatorial optimization problem. We develop an ant colony optimization algorithm for networks with omni-directional as well as directional antennas. The results show that our algorithm consistently outperforms existing techniques. This work was supported by grant TIN2007-66523 (FORMALISM) of the Spanish Government, and by the EU project FRONTS (FP7-ICT-2007-1) funded by the European Commission under the FET Proactive Initiative Pervasive Adaptation. In addition, Christian Blum acknowledges support from the Ramón y Cajal program of the Spanish Ministry of Science and Innovation, and Hugo Hernández acknowledges support from the Catalan Government through an FI grant.     

Minimum requirements of hydrophobic and hydrophilic features in cationic peptide antibiotics (CPAs): pharmacophore generation and validation with cationic steroid antibiotics (CSAs)

Cationic peptide antibiotics (CPAs) are known to possess amphiphilic structure, by virtue of which they display lytic activity against bacterial cell membranes. Naturally occurring antimicrobial peptides contain a large number of amino acid residues, which limits their clinical applicability. Recent studies indicate that it is possible to decrease the chain-length of these peptides without loss of activity, and suggest that a minimum of two positive ionizable (hydrophilic) and two bulky groups (hydrophobic) are required for antimicrobial activity. By employing the HipHop module of the software package CATALYST, we have translated these experimental findings into 3-D pharmacophore models by finding common features among active peptides. Positively ionizable (PI) and hydrophobic (HYD) features are the important characteristics of compounds used for pharmacophore model development. Based on the highest score and the presence of amphiphilic structure, two separate hypothesis, Ec-2 and Sa-6 for Escherichia coli and Staphylococcus aureus, respectively, were selected for mapping analysis of active and inactive peptides against these organisms. The resulting models not only provided information on the minimum requirement of PI and HYD features but also indicated the importance of their relative arrangement in space. The minimum requirement for PI features was two in both cases but the number of HYD features required in the case of E. coli was four while for S. aureus it was found to be three. These hypotheses were able to differentiate between active and inactive CPAs against both organisms and were able to explain the experimental results. The hypotheses were further validated using cationic steroid antibiotics (CSAs), a different class of facial amphiphiles with same mechanism of antimicrobial action as that of CPAs. The results showed that CSAs also require similar minimum features to be active against both E. coli and S. aureus. These studies also indicate that the minimum feature requirements may be conserved for different strains of the same organism. Figure shows the mapping of an active cationic peptide antibiotic (CPA) mapped to the most acceptable hypothesis Sa6 against S. aureus