Structural basis of hierarchical multiple substates of a protein. III: Side chain and main chain local conformations

An analysis is carried out of differences in the minimum energy conformations obtained in the previous paper by energy minimization starting from conformations sampled by a Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. Main conformational differences in each pair of energy minima are found usually localized in several side chains and in a few local main chain segments. Such side chains and local main chain segments are found to take a few distinct local conformations in the minimum energy conformations. Energy minimum conformations can thus be described in terms of combinations of these multiple local conformations.     

NMR studies of bipyrimidine cyclobutane photodimers

Cyclobutane-type photodimers of dinucleoside monophosphates dCpdT, dTpdC and dTpdT were prepared by ultraviolet irradiation in the presence of acetophenone as photosensitizer. The cytosine-containing derivatives were found to deaminate forming uracil products. Using one- and two-dimensional NMR, the photoproducts were characterized as cis-syn and trans-syn cyclobutane photodimers. On the basis of NOE data the structures of the cis-syn and trans-syn products of dUpdT were determined using distance-geometry and restrained-energy-minimization methods. The cis-syn structures showed (high-ANTI/SYN)/high-ANTI glycosidic linkages while the trans-syn structures were in the SYN-ANTI region. The backbone conformations of both structures were in fair agreement with the coupling-constant-data. The trans-syn structures were found to be very rigid and similar in all three products. For the three cis-syn structures more conformational freedom and more variation among the three structures was observed.     

Conformations of dinucleoside phosphates in aqueous solution

The conformations of dinucleoside phosphates have been reexamined by semiempirical potential energy calculations. Conformations I, II, and III, proposed by Lee & Tinoco [Lee, C. H., & Tinoco, I., Jr. (1977) Biochemistry 16, 5403], are possible species after refinement of their structures by potential energy minimization. These three conformers can represent three types of dinucleoside phosphate species in solution. Dhingra et al. [Dhingra, M. M., Sarma, R. H., Giessner-Prettre, C., & Pullman, B. (1978) Biochemistry 17, 5815] had concluded that conformations of type II and III were unlikely or impossible. They favored conformations g-g- (equivalent to I), g+g+,g+t, and tg+; the last three conformations have little stacking and are calculated to be energetically less favorable by more than 5 kcal/mol. Common structures of the types I, II, and III are found for dinucleoside phosphates with different purine-pyrimidine sequences. The sequence dependence of the potential energy of these three conformers has been calculated. The experimental nuclear magnetic resonance data of dinucleoside phosphates are consistent with these three conformations.     

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

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

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.     

Circular dichroism study of 2'-5' dinucleoside monophosphates modified with N-2-acetylaminofluorene.

The conformational properties of four 2′ – 5′ dinucleoside monophosphates modified with $\text{N}$-2-acetylaminofluorene have been studied by circular dichroism spectroscopy. Covalent binding of this chemical carcinogen at the C₈ position of guanosine in the 2′ – 5′ dinucleoside monophosphates induces striking changes in their circular dichroic spectra depending on their base sequence and composition. The changes in CD spectra, redshift of the extrema and change of their polarity, not observed in the spectra of corresponding 3′ – 5′ derivatives modified with $\text{N}$-2-acetylaminofluorene are correlated with the difference in the configuration of 2′ – 5′ and 3′ – 5′ dinucleoside monophosphates and discussed in respect to the intramolecular stacking interactions.     

On the multiple-minima problem in the conformational analysis of polypeptides. IV. Application of the electrostatically driven Monte Carlo method to the 20-residue membrane-bound portion of melittin

The conformational space of the membrane-bound portion of melittin has been searched using the electrostatically driven Monte Carlo (EDMC) method with the ECEPP/2 (empirical conformational energy program for peptides) algorithm. The former 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. The algorithm produces a Monte Carlo search in the conformational hyperspace of the polypeptide using electrostatic predictions and a random sampling technique, combined with local minimization of the energy function, to locate low-energy conformations. As a result of 8 test calculations on the 20-residue membrane-bound portion of melittin, starting from six arbitrary and two completely random conformations, the method was able to locate a very low-energy region of the potential with a well-defined structure for the backbone. In all of the cases under study, the method found a cluster of similar low-energy conformations that agree well with the structure deduced from x-ray diffraction experiments and with one computed earlier by the build-up procedure.     

X-ray crystallographic analysis of a ternary intercalation complex between proflavine and the dinucleoside monophosphates CpA and UpG

We report the crystal-structure analysis of a complex involving the drug proflavine and the two dinucleoside monophosphates cytidylyl-3′,5′-adenosine (CpA) and uridylyl-3′,5′-guanosine (UpG). The planar drug molecule is intercalated between C ?G and U ?A Watson-Crick base pairs, in a double-helical fragmentlike arrangement. Sugar conformations at the 3′-ends of the two strands are dissimilar. The backbone conformations fall within the ranges of values noted previously for dinucleoside intercalation complexes, and some correlations involving these are noted. The separation of the two strands and the basic twist angle of 16°, compared to other reported complexes, are indicative of sequence-dependent effects of the drug binding.     

Interaction of cardiotoxin A5 with a membrane: role of conformational heterogeneity and hydrophilic properties

The hypothesis that local conformational differences of snake venom cardiotoxins (cytotoxins, CTs) may play a significant role in their interaction with membrane was tested by molecular modeling of the behavior of the CT A5 from the venom of Naja atra in water and at the water-membrane interface. Two models of the CT A5 spatial structure are known: the first was obtained by X-ray analysis and the second, by NMR studies in solution. A molecular dynamics (MD) analysis demonstrated that loop II of the toxin has a fixed omega-like shape in water, which does not depend on its initial structure. Interaction of the experimentally derived (X-ray and NMR) conformations and MD-simulated conformations of CT A5 with the lipid bilayer was studied by the Monte Carlo method using the previously developed model of the implicit membrane. The following was found: (1) Unlike the previously studied CT2 from the venom of cobra Naja oxiana, CT A5 has only loops I and II bound to the membrane, with the involvement of a lesser number of hydrophobic residues. (2) A long hydrophobic area is formed on the surface of CT A5 due to the omega-like shape of loop II and the arrangement of loop I in proximity to loop II. This hydrophobic area favors the toxin embedding into the lipid bilayer. (3) The toxin retains its conformation upon interaction with the membrane. (4). The CT A5 molecule has close values of the potential energy in the membrane and in an aqueous environment, which suggests a dynamic character of the binding. The results of the molecular modeling indicate a definite configuration of loops I and II and, consequently, a specific character of distribution of polar and apolar properties on the toxin surface, which turns out to be the most energetically favorable. The English version of the paper: Russian Journal of Bioorganic Chemistry, 2003, vol. 29, no. 6; see also http://www.maik.ru.     

Using robotics to fold proteins and dock ligands

The problems of protein folding and ligand docking have been explored largely using molecular dynamics or Monte Carlo methods. These methods are very compute intensive because they often explore a much wider range of energies, conformations and time than necessary. In addition, Monte Carlo methods often get trapped in local minima. We initially showed that robotic motion planning permitted one to determine the energy of binding and dissociation of ligands from protein binding sites (Singh et al., 1999). The robotic motion planning method maps complicated three-dimensional conformational states into a much simpler, but higher dimensional space in which conformational rearrangements can be represented as linear paths. The dimensionality of the conformation space is of the same order as the number of degrees of conformational freedom in three-dimensional space. We were able to determine the relative energy of association and dissociation of a ligand to a protein by calculating the energetics of interaction for a few thousand conformational states in the vicinity of the protein and choosing the best path from the roadmap. More recently, we have applied roadmap planning to the problem of protein folding (Apaydin et al., 2002a). We represented multiple conformations of a protein as nodes in a compact graph with the edges representing the probability of moving between neighboring states. Instead of using Monte Carlo simulation to simulate thousands of possible paths through various conformational states, we were able to use Markov methods to calculate the steady state occupancy of each conformation, needing to calculate the energy of each conformation only once. We referred to this Markov method of representing multiple conformations and transitions as stochastic roadmap simulation or SRS. We demonstrated that the distribution of conformational states calculated with exhaustive Monte Carlo simulations asymptotically approached the Markov steady state if the same Boltzman energy distribution was used in both methods. SRS permits one to calculate contributions from all possible paths simultaneously with far fewer energy calculations than Monte Carlo or molecular dynamics methods. The SRS method also permits one to represent multiple unfolded starting states and multiple, near-native, folded states and all possible paths between them simultaneously. The SRS method is also independent of the function used to calculate the energy of the various conformational states. In a paper to be presented at this conference (Apaydin et al., 2002b) we have also applied SRS to ligand docking in which we calculate the dynamics of ligand-protein association and dissociation in the region of various binding sites on a number of proteins. SRS permits us to determine the relative times of association to and dissociation from various catalytic and non-catalytic binding sites on protein surfaces. Instead of just following the best path in a roadmap, we can calculate the contribution of all the possible binding or dissociation paths and their relative probabilities and energies simultaneously.     

Interaction of Cardiotoxin A5 with Membrane: Role of Conformational Heterogeneity and Hydrophobic Properties

The hypothesis that local conformational differences of the snake venom cardiotoxins (cytotoxins, CT) may play a significant role in their interaction with membrane was tested by molecular modeling of the behavior of the CT A5 from the venom of Naja atra in water and at the water–membrane interface. Two models of the CT A5 spatial structure are known: the first was obtained by X-ray analysis and the second, by NMR studies in solution. A molecular dynamics (MD) analysis demonstrated that loop II of the toxin has a fixed -like shape in water, which does not depend on its initial structure. An interaction of the experimentally derived (X-ray and NMR) conformations and MD simulated conformations of CT A5 with the lipid bilayer was studied by the Monte Carlo method using the previously developed model of the implicit membrane. It is found that: (1) unlike the previously studied CT2 from the venom of cobra Naja oxiana, CT A5 has only loops I and II bound to the membrane with the involvement of a lesser number of hydrophobic residues. (2) A long hydrophobic area is formed on the surface of CT A5 due to the -like shape of loop II and the arrangement of loop I in proximity to loop II. This hydrophobic area favors the toxin embedding into the lipid bilayer. (3) The toxin retains its conformation upon interaction with the membrane. (4) The CT A5 molecule has close values of the potential energy in the membrane and in aqueous environment, which suggests dynamic character of the binding. The results of the molecular modeling indicate a definite configuration of loops I and II and, consequently, a specific character of distribution of polar and apolar properties on the toxin surface, which turns out to be the most energetically favorable.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.     

Conformational study of a peptide epitope shows large preferences for beta-turn conformations.

The conformational preferences of the 7-residue peptide Glu-Val-Val-Pro-His-Lys-Lys was investigated using a global search algorithm, namely the Electrostatically Driven Monte Carlo (EDMC) method, and the ECEPP/2 potential energy function. This particular sequence corresponds to the N-terminal portion of a 19-residue peptide antigen whose three dimensional structure, when complexed to a cognate antibody, was reported recently. As a result of this study a series of low-energy conformations were identified showing a common folding pattern with residues Val-3, Pro-4, His-5 and Lys-6 forming a beta turn. A comparison of the computed conformations with the one determined by X-ray crystallography in the antibody-antigen complex reveals marked similarities. In most of the cases rms deviations smaller than 1.1 A were found for the backbone atoms of the four residues forming the turn. These results suggest that the recognition process is accomplished in this case through the interaction of the antibody with relatively stable conformers of the antigenic peptide.     

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.     

Nature of the stacking of nucleic acid bases in water: a Monte Carlo simulation

The results of a Monte Carlo simulation of the hydration of uracil and thymine molecules, their stacked dimers and hydrogen-bonded base pairs are presented. Simulations have been performed in a cluster approximation. The semiempirical atom-atom potential functions have been used (cluster consisting of 200 water molecules). It has been shown that the stacking interactions of uracil and thymine molecules in water arise mainly due to the increase in the water-water interaction during the transition from monomers to dimer. It has been found out that stacked base associates are more preferable than base pairs in water. This preference is mainly due to the energetically more favourable structure of water around the stack.     

Conformational analysis of the 20-residue membrane-bound portion of melittin by conformational space annealing

The conformational space of the 20-residue membrane-bound portion of melittin has been investigated extensively with the conformational space annealing (CSA) method and the ECEPP/3 (Empirical Conformational Energy Program for Peptides) algorithm. Starting from random conformations, the CSA method finds that there are at least five different classes of conformations, within 4 kcal/mol, which have distinct backbone structures. We find that the lowest energy conformation of this peptide from previous investigations is not the global minimum-energy conformation (GMEC); but it belongs to the second lowest energy class of the five classes found here. In four independent runs, one conformation is found repeatedly as the lowest energy conformation of the peptide (two of the four lowest energy conformations are identical; the other two have essentially identical backbone conformations but slightly different side-chain conformations). We propose this conformation, whose energy is lower than that found previously by 1.9 kcal/mol, as the GMEC of the ECEPP/3 force field. The structure of the proposed GMEC is less helical and more compact than the previous one. It appears that the CSA method can find several classes of conformations of a 20-residue peptide starting from random conformations utilizing only its amino acid sequence information. The proposed GMEC has also been found with a modified electrostatically driven Monte Carlo method [D. R. Ripoll, A. Liwo, and H.A. Scheraga (1998) “New Developments of the Electrostatically Driven Monte Carlo Method: Test on the Membrane-Bound Portion of Melittin,” Biopolymers, Vol. 46, pp. 117–126]. © 1998 John Wiley & Sons, Inc. Biopoly 46: 103–115, 1998     

Correlation between the backbone and side chain conformations in 5′-nucleotides. The concept of a ‘rigid’ nucleotide conformation

Conformational energies of the 5′-adenosine monophosphate have been computed as a function of χ and ψ, of the torsion angles about the side-chain glycosyl C(1′)–N(9) and of the main-chain exocyclic C(4′)–C(5′) bonds by considering nonbonded, torsion, and electrostatic interactions. The two primary modes of sugar puckering, namely, C(2′)-endo and C(3′)-endo have been considered. The results indicate that there is a striking correlation between the conformations about the side-chain glyocsyl bond and the backbone C(4′)–C(5′) bond of the nucleotide unit. It is found that the anti and the Gauche–Gauche (gg), conformations about the glycosyl and the C(4′)–C(5′) bonds, respectively, are energetically the most favored conformations for 5′-adenine nucleotide irrespective of whether the puckering of the ribose is C(2′)-endo or C(3′)-endo. Calculations have also shown that the other common 5′-pyrimidine nucleotides will show similar preferences for the glycosyl and C(4′)–C(5′) bond conformations. These results are in remarkable agreement with the concept of the “rigid” nucleotide unit that has been developed from available data on mononucleotides and dinucleoside monophosphates. It is found that the conformational ‘rigidity’ in 5′-nucleotides compared with that of nucleosides is a consequence of, predominantly, the coulombic interactions between the negatively charged phosphate group and the base. The above result permits one to consider polynucleotide conformations in terms of a “rigid” C(2′)-endo or C(3′)-endo nucleotide unit with the major conformational changes being brought about by rotations about the P–O bonds linking the internucleotide phosphorus atom. IT is predicted that the anti and the gg conformations about the glycosyl and the C(4′)–C(5′) bonds would be strongly preferred in the mononucleotide components of different purine and pyrimidine coenzymes and also in the nucleotide phosphates like adenodine di- and triphosphates.     

Backbone conformations in deoxyribonucleic acids. Conformational role of the 2′-hydroxyl group on the internucleotide phosphodiester conformations

The conformations accessible to the internucleotide phosphodiester group in deoxydinucleoside monophosphates, deoxydinucleoside triphosphates, and deoxypolynucleotides have been explored in detail by potential energy calculations. The two most predominant conformations for the nucleotide moiety (³E and ²E) and their possible combinations (³E^?3E, ³E^?2E, ²E^?2E, ²E^?3E) have been employed, similar to our earlier studies on polyribonucleotides. The internucleotide P-O bond torsions are very sensitive to the sugar pucker (³E and ²E) and sugar type (ribose and 2′-deoxyribose) on the 3′-residue of dinucleoside phosphates. The preferred phosphodiester conformations found for the deoxydinucleoside monophosphates and triphosphates, in general, follow the same pattern as those obtained for ribose sugars when the sugar on the 3′-side of the molecule has the ³E sugar-ring conformation. The internucleotide P-O bonds show a greater degree of conformational freedom when the 3′-sugar has the ²E pucker. The double gauche g^?g^? conformation for the phosphodiester, which leads to the overlap of the adjacent bases, is shown to be one of the energetically most favored conformations for all the sequence of sugar puckers. It is found that the ²E^?2E sequence of sugar puckers shows a greater energetic preference for the stacked helical conformation (g^?g^?) than the (³E^?3E) and the mixed sugar-pucker combinations. This effect becomes more pronounced in going from a dinucleoside monophosphate to a dinucleoside triphosphate suggesting that the 2′-deoxy sugars favor the ²E sugar pucker in di-, oligo-, and polydeoxyribonucleotide structures. In addition to g^?g^?, the conformations g⁺g^?, tg^?, g^?t, tg⁺, and g⁺t are also found to be possible for the phosphodiester in a polydeoxyribonucleotide and their populations depend to some extent on the sugar-pucker sequence. It is shown that the short-range intramolecular interactions involving the sugar and the phosphate groups dictate to a large extent the backbone conformations of nucleic acids and polynucleotides.