Exploring experimental sources of multiple protein conformations in structure-based drug design

Receptor flexibility must be incorporated into structure-based drug design in order to portray a more accurate representation of a protein in solution. Our approach is to generate pharmacophore models based on multiple conformations of a protein and is very similar to solvent mapping of hot spots. Previously, we had success using computer-generated conformations of apo human immunodeficiency virus-1 protease (HIV-1p). Here, we examine the use of an NMR ensemble versus a collection of crystal structures, and we compare back to our previous study based on computer-generated conformations. To our knowledge, this is the first direct comparison of an NMR ensemble and a collection of crystal structures to incorporate protein flexibility in structure-based drug design. To provide an accurate comparison between the experimental sources, we used bound structures for our multiple protein structure (MPS) pharmacophore models. The models from an NMR ensemble and a collection of crystal structures were both able to discriminate known HIV-1p inhibitors from decoy molecules and displayed superior performance over models created from single conformations of the protein. Although the active-site conformations were already predefined by bound ligands, the use of MPS allows us to overcome the cross-docking problem and generate a model that does not simply reproduce the chemical characteristics of a specific ligand class. We show that there is more structural variation between 28 structures in an NMR ensemble than 90 crystal structures bound to a variety of ligands. MPS models from both sources performed well, but the model determined using the NMR ensemble appeared to be the most general yet accurate representation of the active site. This work encourages the use of NMR models in structure-based design.     

Polystyrene models. II. Ab initio study of isobutylbenzene

The structure and stability of the various conformations of isobutylbenzene are studied using ab initio molecular orbital theory. The calculations show that coupling between the structural units is important. The results indicate that complete geometry optimization of the stable and transition structures of isobutylbenzene produce significant changes in geometrical parameters and charge distributions of this molecule when compared with the corresponding results obtained using the rigid-rotor approximation. These changes are particularly noticeable in one of the gauche conformations and in transition structures of isobutylbenzene generated by the phenyl group rotation. For polystyrene, these results present evidence that there is a strong coupling between the chain-backbone folding and the rotation of the phenyl group. Multidimensional potential energy surfaces are displayed using a topological representation. © 1992 John Wiley & Sons, Inc.     

Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure

A procedure that generates random conformations of a protein chain, and then applies energy minimization to find the structure of lowest energy, is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. Each state corresponds to a rectangular region in the ?, ψ map. The conformation of an entire chain is then represented by a sequence of single-residue conformational states. The distinct “chain-states” in this representation correspond to multidimensional rectangular regions in the conformational space of the whole protein. A set of highly-probable chain-states can be predicted from the amino acid sequence using the pattern recognition procedure developed in the first two articles of this series. The importance-sampling minimization procedure of the present article is then used to explore the regions of conformational space corresponding to each of these chain-states. The importance-sampling procedure generates a number of random conformations within a particular multidimensional rectangular region, sampling most densely from the most probable, or “important,” sections of the ?, ψ map. All values of ? and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ? and Φ are generated from bivariate gaussian distributions that are determined from known X-ray structures. Separate gaussian distributions are used for proline residues in the α and ? states, for glycine residues in the α, ?, α*, and ?* states, and for ordinary residues involved in 29 different tripeptide conformations. Energy minimization is then applied to the randomly-generated structures to optimize interactions and to improve packing. The final energy values are used to select the best structures. The importance-sampling minimization procedure is tested on the avian pancreatic polypeptide, using chain-states predicted from the amino acid sequence. The conformation having the lowest energy is very similar to the X-ray conformation.     

Automated flexible ligand docking method and its application for database search

We have developed a new docking program that explores ligand flexibility. This program can be applied to database searches. The program is similar in concept to earlier efforts, but it has been automated and improved. The algorithm begins by selecting an anchor fragment of a ligand. This fragment is protonated, as needed, and then placed in the receptor by the DOCK algorithm, followed by minimization using a simplex method. Finally, the conformations of the remaining parts of the putative ligands are searched by a limited backtrack method and minimized to get the most stable conformation. To test the efficiency of this method, the program was used to regenerate ten ligand–protein complex structures. In all cases, the docked ligands basically reproduced the crystallographic binding modes. The efficiency of this method was further tested by a database search. Ten percent of molecules from the Available Chemicals Directory (ACD) were docked to a dihydrofolate reductase structure. Most of the top-ranking molecules (7 of the top 13 hits) are dihydrofolate or methotrexate derivatives, which are known to be DHFR inhibitors, demonstrating the suitability of this program for screening molecular databases. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1812–1825, 1997     

Generic shapes for the conformation analysis of macrocyclic structures

A new algorithm for the systematic generation of conformations of macrocyclic systems is presented. The procedure is based on the concept of generic shapes that are found in such structures. These shapes are characterized by a selection of harmonics which occur in an approximate Fourier representation of the atomic coordinates of the rings. Following a fixed protocol, a limited set of in-plane and out-of-plane circular harmonics is used to define an ensemble of generic ring shapes. These generic shapes are used as start structures for energy minimizations by a given force-field method. To account for the possibility of having several final conformations originating from the same generic shape, the corresponding initial structure is taken several times and subjected to a randomization step before minimization. The resulting conformations that fall within a preset low-energy band are collected and screened for duplicates and enantiomers. The efficiency of this procedure (ratio between the number of accepted conformations and the total number of energy minimizations) depends on the flexibility of the macrocyclic system. The efficiency is generally quite high for very flexible rings. According to the proposed protocol, the number of generic shapes used as start structures grows as the square of N(lnN), where N is the ring size. The algorithm lends itself to conformational analyses of medium-size and large rings as well as of loops spanned between fixed structural units.     

The Impact of Amino Acid Side Chain Mutations in Conformational Design of Peptides and Proteins

Local energetic effects of amino acid replacements are often considered to have only a moderate influence on the backbone conformation of proteins or peptides. As these effects are difficult to determine experimentally, no comparison has yet been performed. However, knowledge of the influence of side chain mutations is essential in protein homology modeling and in optimizing biologically active peptide ligands in medicinal chemistry. Furthermore, the tool of N‐methylation of peptides is of increasing importance for the design of peptidic drugs to gain oral availability or receptor selectivity. However, N‐methylation is often accompanied by considerable population of cis‐peptide bond structures, resulting in completely different conformations compared with the parent peptide. To retain a favored structure, it might be important to understand the effect of different side chains on the backbone conformation and to enable the introduction of an N‐methylation at the right position without disturbing a biologically active conformation. In order to detect even small energetic effects due to side chain mutations, we employed a trick to investigate the structural equilibrium of a selected cyclic pentapeptide in which two conformations are equally populated. Very small energetic differences between both conformations could easily be determined experimentally by identifying shifts in the population of both isomers.     

Conformational analysis of a flexible oligosaccharide using residual dipolar couplings.

We present a new approach to the analysis of the conformational and the motional properties of an oligosaccharide, methyl 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranoside. The approach relies on an order matrix analysis of residual dipolar couplings in the solution state. By combining a number of different types of couplings, (1)D(CH), (2)D(CH), and D(HH), an order matrix is solved for each ring of the trimannoside. The resulting order parameters indicate the internal motion at the alpha (1,3) linkage to be limited, while significant motion is suggested at the alpha (1,6) linkage. Two structures for the trimannoside were determined by aligning the order tensor principal axes obtained from two different orienting media, bicelles and phage. The very similar conformations at the alpha (1,3) linkage of these two structures confirm that the internal motion at the alpha (1,3) linkage is small and the conformation is a good representation of a single preferred structure. The different conformations at the alpha (1,6) linkage suggest that the motional amplitudes are large and the conformations must be viewed as virtual conformers. Compared with traditional NMR methods, data acquisition is easy and data analysis is straightforward.     

Enhanced sampling method in molecular simulations using genetic algorithm for biomolecular systems

We propose a molecular simulation method using genetic algorithm (GA) for biomolecular systems to obtain ensemble averages efficiently. In this method, we incorporate the genetic crossover, which is one of the operations of GA, to any simulation method such as conventional molecular dynamics (MD), Monte Carlo, and other simulation methods. The genetic crossover proposes candidate conformations by exchanging parts of conformations of a target molecule between a pair of conformations during the simulation. If the candidate conformations are accepted, the simulation resumes from the accepted ones. While conventional simulations are based on local update of conformations, the genetic crossover introduces global update of conformations. As an example of the present approach, we incorporated genetic crossover to MD simulations. We tested the validity of the method by calculating ensemble averages and the sampling efficiency by using two kinds of peptides, ALA3 and (AAQAA)₃. The results show that for ALA3 system, the distribution probabilities of backbone dihedral angles are in good agreement with those of the conventional MD and replica-exchange MD simulations. In the case of (AAQAA)₃ system, our method showed lower structural correlation of α-helix structures than the other two methods and more flexibility in the backbone ψ angles than the conventional MD simulation. These results suggest that our method gives more efficient conformational sampling than conventional simulation methods based on local update of conformations. © 2018 Wiley Periodicals, Inc.     

Rotamer libraries of spin labelled cysteines for protein studies

Studies of structure and dynamics of proteins using site-directed spin labelling rely on explicit modelling of spin label conformations. The large computational effort associated with such modelling with molecular dynamics (MD) simulations can be avoided by a rotamer library approach based on a coarse-grained representation of the conformational space of the spin label. We show here that libraries of about 200 rotamers, obtained by iterative projection of a long MD trajectory of the free spin label onto a set of canonical dihedral angles, provide a representation of the underlying trajectory adequate for EPR distance measurements. Rotamer analysis was performed on selected X-ray structures of spin labelled T4 lysozyme mutants to characterize the spin label rotamer ensemble on a single protein site. Furthermore, predictions based on the rotamer library approach are shown to be in nearly quantitative agreement with electron paramagnetic resonance (EPR) distance data on the Na(+)/H(+) antiporter NhaA and on the light-harvesting complex LHCII whose structures are known from independent cryo electron microscopy and X-ray studies, respectively. Suggestions for the selection of labelling sites in proteins are given, limitations of the approach discussed, and requirements for further development are outlined.     

An evaluation of molecular models of the cytochrome P450 Streptomyces griseolus enzymes P450SU1 and P450SU2

Summary P450SU1 and P450SU2 are herbicide-inducible bacterial cytochrome P450 enzymes from Streptomyces griseolus. They have two of the highest sequence identities to camphor hydroxylase (P450cam from Pseudomonas putida), the cytochrome P450 with the first known crystal structure. We have built several models of these two proteins to investigate the variability in the structures that can occur from using different modeling protocols. We looked at variability due to alignment methods, backbone loop conformations and refinement methods. We have constructed two models for each protein using two alignment algorithms, and then an additional model using an identical alignment but different loop conformations for both buried and surface loops. The alignments used to build the models were created using the Needleman-Wunsch method, adapted for multiple sequences, and a manual method that utilized both a dotmatrix search matrix and the Needleman-Wunsch method. After constructing the initial models, several energy minimization methods were used to explore the variability in the final models caused by the choice of minimization techniques. Features of cytochrome P450cam and the cytochrome P450 superfamily, such as the ferredoxin binding site, the heme binding site and the substrate binding site were used to evaluate the validity of the models. Although the final structures were very similar between the models with different alignments, active-site residues were found to be dependent on the conformations of buried loops and early stages of energy minimization. We show which regions of the active site are the most dependent on the particular methods used, and which parts of the structures seem to be independent of the methods.     

基于超快多维振动光谱技术解析分子体系的三维空间构型

超快多维振动光谱技术目前已经被广泛应用到各种凝聚态分子体系中分子的结构以及快速变化动力学过程的测量之中,并有望成为新一代解析分子体系微观结构及超快行为的常规手段。本文从两个主线出发,介绍如何利用超快多维振动光谱技术解析分子体系的三维空间构型。一方面通过测量分子内各个振动模式跃迁偶极矩间的夹角来获得分子体系内不同基团的相对空间取向,并最终确定分子的空间构型。另一方面,通过详细解析分子间振动能量转移的机理,进而将实验中测得的振动能量转移速率转化为分子之间的距离信息。     

Representing receptor flexibility in ligand docking through relevant normal modes

Inspired by the current representation of the ligand-receptor binding process, a normal-mode-based methodology is presented to incorporate receptor flexibility in ligand docking and virtual screening. However, the systematic representation of the deformation space grows geometrically with the number of modes, and furthermore, midscale loop rearrangements like those found in protein kinase binding pockets cannot be accounted for with the first lowest-frequency modes. We thus introduced a measure of relevance of normal modes on a given region of interest and showed that only very few modes in the low-frequency range are necessary and sufficient to describe loop flexibility in cAMP-dependent protein kinase. We used this approach to generate an ensemble of representative receptor backbone conformations by perturbing the structure along a combination of relevant modes. Each ensemble conformation is complexed with known non-native binders to optimize the position of the binding-pocket side chains through a full flexible docking procedure. The multiple receptor conformations thus obtained are used in a small-scale virtual screening using receptor ensemble docking. We evaluated this algorithm on holo and apo structures of cAMP-dependent protein kinase that exhibit backbone rearrangements on two independent loop regions close to the binding pocket. Docking accuracy is improved, since the ligands considered in the virtual screening docked within 1.5 A to at least one of the structures. The discrimination between binders and nonbinders is also enhanced, as shown by the improvement of the enrichment factor. This constitutes a new step toward the systematic integration of flexible ligand-flexible receptor docking tools in structure-based drug discovery.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Predicting helical hairpins from sequences by Monte Carlo simulations

The key problem in polypeptide‐structure prediction is with regard to thermodynamics. Two factors limit prediction in ab initio computer simulations. First, the thermodynamically dominant conformations must be found from an extremely large number of possible conformations. Second, these low‐energy forms must deviate little from the experimental structures. Here, we report on the application of the diffusion‐controlled Monte Carlo approach to predict four α‐helical hairpins with 34–38 residues by global optimization, using an energy optimized on other supersecondary structures. A total of seven simulations is carried out for each protein starting from fully extended conformations. Three proteins are correctly folded (within 3.0 Å rms from the experimental structures), but the fourth protein cannot distinguish between several equienergetic conformations. Possible improvement of the energy model is suggested. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 582–589, 2000     

Conformational analysis of bradykinin by annealed molecular dynamics and comparison to NMR-derived conformations

Conformational analysis of bradykinin (BK), a nonapeptide of the sequence RPPGFSPFR, was accomplished using annealed molecular dynamics (AMD) at 1000 K in BIOGRAF 2.2. One hundred anneal cycles produced 100 conformations over approximately 2000 ps. These conformations were compared to structures derived by nuclear magnetic resonance (NMR) methods for similar shape and energy. Energy minimization of relevant conformations using both BIOGRAF 2.2 and AMBER 3.0a revealed that the AMD-determined conformations are in the same energy range as the NMR-determined structures. Also, the shape of the relevant conformations appeared similar, suggesting that AMD is a good tool for the conformational analysis of small peptide ligands. © 1993 John Wiley & Sons, Inc.     

Statistically based reduced representation of amino acid side chains

Preferred conformations of amino acid side chains have been well established through statistically obtained rotamer libraries. Typically, these provide bond torsion angles allowing a side chain to be traced atom by atom. In cases where it is desirable to reduce the complexity of a protein representation or prediction, fixing all side-chain atoms may prove unwieldy. Therefore, we introduce a general parametrization to allow positions of representative atoms (in the present study, these are terminal atoms) to be predicted directly given backbone atom coordinates. Using a large, culled data set of amino acid residues from high-resolution protein crystal structures, anywhere from 1 to 7 preferred conformations were observed for each terminal atom of the non-glycine residues. Side-chain length from the backbone C(alpha) is one of the parameters determined for each conformation, which should itself be useful. Prediction of terminal atoms was then carried out for a second, nonredundant set of protein structures to validate the data set. Using four simple probabilistic approaches, the Monte Carlo style prediction of terminal atom locations given only backbone coordinates produced an average root mean-square deviation (RMSD) of approximately 3 A from the experimentally determined terminal atom positions. With prediction using conditional probabilities based on the side-chain chi(1) rotamer, this average RMSD was improved to 1.74 A. The observed terminal atom conformations therefore provide reasonable and potentially highly accurate representations of side-chain conformation, offering a viable alternative to existing all-atom rotamers for any case where reduction in protein model complexity, or in the amount of data to be handled, is desired. One application of this representation with strong potential is the prediction of charge density in proteins. This would likely be especially valuable on protein surfaces, where side chains are much less likely to be fixed in single rotamers. Prediction of ensembles of structures provides a method to determine the probability density of charge and atom location; such a prediction is demonstrated graphically.     

MCCE2: Improving protein pKa calculations with extensive side chain rotamer sampling

Multiconformation continuum electrostatics (MCCE) explores different conformational degrees of freedom in Monte Carlo calculations of protein residue and ligand pK_as. Explicit changes in side chain conformations throughout a titration create a position dependent, heterogeneous dielectric response giving a more accurate picture of coupled ionization and position changes. The MCCE2 methods for choosing a group of input heavy atom and proton positions are described. The pK_as calculated with different isosteric conformers, heavy atom rotamers and proton positions, with different degrees of optimization are tested against a curated group of 305 experimental pK_as in 33 proteins. QUICK calculations, with rotation around Asn and Gln termini, sampling His tautomers and torsion minimum hydroxyls yield an RMSD of 1.34 with 84% of the errors being <1.5 pH units. FULL calculations adding heavy atom rotamers and side chain optimization yield an RMSD of 0.90 with 90% of the errors <1.5 pH unit. Good results are also found for pK_as in the membrane protein bacteriorhodopsin. The inclusion of extra side chain positions distorts the dielectric boundary and also biases the calculated pK_as by creating more neutral than ionized conformers. Methods for correcting these errors are introduced. Calculations are compared with multiple X‐ray and NMR derived structures in 36 soluble proteins. Calculations with X‐ray structures give significantly better pK_as. Results with the default protein dielectric constant of 4 are as good as those using a value of 8. The MCCE2 program can be downloaded from http://www.sci.ccny.cuny.edu/～mcce . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009