Conformation‐Family Monte Carlo (CFMC): An Efficient Computational Method for Identifying the Low‐Energy States of a Macromolecule

A highly efficient method, Conformation‐Family Monte Carlo (CFMC), has been developed for searching the conformational space of a macromolecule and identifying its low‐energy conformations. This method maintains a database of low‐energy conformations that are clustered into families. The conformations in this database are improved iteratively by a Metropolis‐type Monte Carlo procedure, together with energy minimization, in which the search is biased towards investigating the regions of the lowest‐energy families. The CFMC method has the advantages of our earlier potential‐smoothing methods (in that it `coarse‐grains' the conformational space and exploits information about nearby low‐energy states), but avoids their disadvantages (such as the displacement of the global minimum at large smoothings). The CFMC method is applied to a test protein, domain B of Staphylococcal protein A. Independent CFMC runs yielded the same low‐energy families of conformations from random starts, indicating that the thermodynamically relevant conformational space of this protein has been explored thoroughly. The CFMC method is highly efficient, performing as well as or better than competing methods, such as Monte Carlo with minimization, conformational‐space annealing, and the self‐consistent basin‐to‐deformed‐basin method.     

A parallel tabu search for conformational energy optimization of oligopeptides

We have developed and implemented a tabu search heuristic (TS) to determine the best energy minimum for oligopeptides. Our test molecule was Met‐enkephalin, a pentapetide that over the years has been used as a validation model for many global optimizers. The test potential energy function was ECEPP/3. Our tabu search implementation is based on assigning integer values to the variables to be optimized, and in facilitating the diversification and intensification of the search. The final output from the TS is treated with a local optimizer, and our best result competes both in quality and CPU time with those reported in the literature. The results indicate that TS is an efficient algorithm for conformational searches. We present a parallel TS version along with experimental results that show that this algorithm allows significant increases in speed. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 147–156, 2000     

A comparison of a direct search method and a genetic algorithm for conformational searching

We present results from the application of two conformational searching methods: genetic algorithms (GA) and direct search methods for finding low energy conformations of organic molecules. GAs are in a class of biologically motivated optimization methods that evolve a population of individuals in which individuals who are more “fit” have a higher probability of surviving into subsequent generations. The parallel direct search method (PDS) is a type of pattern search method that uses an adaptive grid to search for minima. Both methods found energies equal to or lower than the energy of the relaxed crystal structure in all cases, at a relatively small cost in CPU time. We suggest that either method would be a good candidate to find 3-D conformations in a large scale screening application. © 1996 by John Wiley & Sons, Inc.     

Structural and energetic effects in the molecular recognition of amino acids by 18-crown-6

Absolute 18-crown-6 (18C6) affinities of five amino acids (AAs) are determined using guided ion beam tandem mass spectrometry techniques. The AAs examined in this work include glycine (Gly), alanine (Ala), lysine (Lys), histidine (His), and arginine (Arg). Theoretical electronic structure calculations are performed to determine stable geometries and energetics for neutral and protonated 18C6 and the AAs as well as the proton bound complexes comprised of these species, (AA)H(+)(18C6). The proton affinities (PAs) of Gly and Ala are lower than the PA of 18C6, whereas the PAs of Lys, His, and Arg exceed that of 18C6. Therefore, the collision-induced dissociation (CID) behavior of the (AA)H(+)(18C6) complexes differs markedly across these systems. CID of the complexes to Gly and Ala produces H(+)(18C6) as the dominant and lowest energy pathway. At elevated energies, H(+)(AA) was produced in competition with H(+)(18C6) as a result of the relatively favorable entropy change in the formation of H(+)(AA). In contrast, CID of the complexes to the protonated basic AAs results in the formation of H(+)(AA) as the only direct CID product. H(+)(18C6) was not observed, even at elevated energies, as a result of unfavorable enthalpy and entropy change associated with its formation. Excellent agreement between the measured and calculated (AA)H(+)-18C6 bond dissociation energies (BDEs) is found with M06 theory for all complexes except (His)H(+)(18C6), where theory overestimates the strength of binding. In contrast, B3LYP theory significantly underestimates the (AA)H(+)-18C6 BDEs in all cases. Among the basic AAs, Lys exhibits the highest binding affinity for 18C6, suggesting that the side chains of Lys residues are the preferred binding site for 18C6 complexation in peptides and proteins. Gly and Ala exhibit greater 18C6 binding affinities than Lys, suggesting that the N-terminal amino group provides another favorable binding site for 18C6. Trends in the 18C6 binding affinities among the five AAs examined here exhibit an inverse correlation with the polarizability and proton affinity of the AA. Therefore, the ability of the N-terminal amino group to compete for 18C6 complexation is best for Gly and should become increasing less favorable as the size of the side chain substituent increases.     

Extensive conformational searches of 13 representative dipeptides and an efficient method for dipeptide structure determinations based on amino acid conformers

Conformations of peptides are the basis for their property studies and the predictions of peptide structures are highly important in life science but very complex in practice. Here, thorough searches on the potential energy surfaces of 13 representative dipeptides by considering all possible combinations of the bond rotational degrees of freedom are performed using the density functional theory based methods. Careful analyses of the conformers of the 13 dipeptides and the corresponding amino acids reveal the connections between the structures of dipeptide and amino acids. A method for finding all important dipeptide conformers by optimizing a small number of trial structures generated by suitable superposition of the parent amino acid conformations is thus proposed. Applying the method to another eight dipeptides carefully examined by others shows that the new approach is both highly efficient and reliable by providing the most complete ensembles of dipeptide conformers and much improved agreements between the theoretical and experimental IR spectra. The method opens the door for the determination of the stable structures of all dipeptides with a manageable amount of effort. Preliminary result on the applicability of the method to the tripeptide structure determination is also presented. The results are the first step towards proving Anfinsen's hypothesis by revealing the relationships between the structures of the simplest peptide and its constituting amino acids. It implies that the structures of peptides are not only determined by their amino acid sequences, but also closely linked with the amino acid conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

An unbounded systematic search of conformational space

A new method for searching internal coordinate conformational space systematically via a continuous-process procedure is described. Unlike previous systematic search methods, the new scheme generates torsionally remote conformers early in the search. It is also unbounded in that the extent of the search need not be specified at the outset. The search begins at low resolution (120° in torsion angle space) and then goes to higher and higher resolution as all points in space at a given resolution have been searched. The search may run without end or be terminated when new conformers cease to be found or when all space at some maximum allowable resolution has been explored. Conformational searches on several medium- and large-ring molecules using the new method are described and the results are compared with those from certain previously described search methods. It is found that the new method is significantly more efficient than previous procedures at finding all low energy conformers of organic molecules.     

Highly Constrained Linear Oligopeptides Containing Heterocyclic α‐Amino Carboxylic Acids

Two spiroheterocyclic 2H‐azirin‐3‐amines, 1f and 1g , were shown to be useful synthons for the dipeptides N‐(4‐aminotetrahydro‐2H‐pyran‐4‐yl)prolinate (Thp‐Pro) and the corresponding thiopyran derivative, Tht‐Pro, respectively. By coupling of 4‐bromobenzoic acid with 1f or 1g and saponification, followed by repeating the coupling and saponification steps, oligopeptides of type 4‐BrBz‐(Thp‐Pro)_n‐OMe and 4‐BrBz‐(Tht‐Pro)_n‐OMe were prepared, and their conformations were evaluated in solution by NMR techniques and in the crystalline state by X‐ray crystallography. All of these sterically highly congested oligopeptides adopt fairly rigid helical conformations. It is interesting to note that the hexapeptide with Thp forms a 3₁₀‐helix, whereas the Tht analog has a β‐bend ribbon spiral confirmation.     

Quantum chemical study of cyclic dipeptides

The preferred conformations of cyclic dipeptides were first studied systemically using the density functional theory (DFT) B3LYP method at the 6‐31G(d) level. The structural characteristics of cyclic dipeptides were revealed, most of which have not been confirmed until now. Our studies showed that the six‐member main circles of cyclic dipeptides composed of natural L ‐amino acid residues appeared as boat conformations. The important factors that influence conformations of cyclic dipeptides, such as molecular total energy, nuclear repulsion energy, molecular orbit, spatial effects, and reactive mechanism, are discussed in detail. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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

Understanding 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.     

Conformational searching methods for small molecules. II. Genetic algorithm approach

We demonstrate the use of a genetic algorithm (GA) search procedure for finding low-energy conformations of small to medium organic molecules (1–12 rotatable bonds). GAS are in a class of biologically motivated optimization methods that evolve a population of individuals where individuals who are more “fit” have a higher probability of surviving into subsequent generations. Here, an individual is a conformation of a given molecule and the fitness is the molecule's conformational energy. In the course of a simulated evolution, the population produces conformations having increasingly lower energy. We test the GA method on a suite of 72 molecules and compare the performance against the CSEARCH algorithm in Sybyl. For molecules with more than eight rotatable bonds, the GA method is more efficient computationally and as the number of rotatable bonds increases the relative efficiency of the GA method grows. The GA method also found energies equal to or lower than the energy of the relaxed crystal structure in the large majority of cases. © John Wiley & Sons, Inc.     

Putative One‐Pot Prebiotic Polypeptides with Ribonucleolytic Activity

KIA7, a peptide with a highly restricted set of amino acids (Lys, Ile, Ala, Gly and Tyr), adopts a specifically folded structure. Some amino acids, including Lys, Ile, Ala, Gly and His, form under the same putative prebiotic conditions, whereas different conditions are needed for producing Tyr, Phe and Trp. Herein, we report the 3D structure and conformational stability of the peptide KIA7H, which is composed of only Lys, Ile, Ala, Gly and His. When the imidazole group is neutral, this 20‐mer peptide adopts a four‐helix bundle with a specifically packed hydrophobic core. Therefore, one‐pot prebiotic proteins with well‐defined structures might have arisen early in chemical evolution. The Trp variant, KIA7W, was also studied. It adopts a 3D structure similar to that of KIA7H and its previously studied Tyr and Phe variants, but is remarkably more stable. When tested for ribonucleolytic activity, KIA7H, KIA7W and even short, unstructured peptides rich in His and Lys, in combination with Mg⁺⁺, Mn⁺⁺ or Ni⁺⁺ (but not Cu⁺⁺, Zn⁺⁺ or EDTA) specifically cleave the single‐stranded region in an RNA stem–loop. This suggests that prebiotic peptide–divalent cation complexes with ribonucleolytic activity might have co‐inhabited the RNA world.     

简化的系统搜索法及其在构象分析中的应用

多肽的构象研究除了可以用X-射线晶体学及二维核磁共振等实验方法外,理论计算的方法有系统搜索法、蒙特卡洛方法、距离几何方法、分子动力学方法及能量极小化等.系统搜索法具有构象空间搜索彻底的特点,相对来说找到系统整体极小值的可能性较大,但由于其计算量较大,对于多肽及蛋白质很难实现.我们对系统搜索法进行了简化,不是同时旋转所有的二面角,而是成对地进行,以迭代的方法达到收敛,最后得到可能的构象.     

Predicting bioactive conformations and binding modes of macrocycles

Macrocyclic compounds experience increasing interest in drug discovery. It is often thought that these large and chemically complex molecules provide promising candidates to address difficult targets and interfere with protein–protein interactions. From a computational viewpoint, these molecules are difficult to treat. For example, flexible docking of macrocyclic compounds is hindered by the limited ability of current docking approaches to optimize conformations of extended ring systems for pose prediction. Herein, we report predictions of bioactive conformations of macrocycles using conformational search and binding modes using docking. Conformational ensembles generated using specialized search technique of about 70 % of the tested macrocycles contained accurate bioactive conformations. However, these conformations were difficult to identify on the basis of conformational energies. Moreover, docking calculations with limited ligand flexibility starting from individual low energy conformations rarely yielded highly accurate binding modes. In about 40 % of the test cases, binding modes were approximated with reasonable accuracy. However, when conformational ensembles were subjected to rigid body docking, an increase in meaningful binding mode predictions to more than 50 % of the test cases was observed. Electrostatic effects did not contribute to these predictions in a positive or negative manner. Rather, achieving shape complementarity at macrocycle-target interfaces was a decisive factor. In summary, a combined computational protocol using pre-computed conformational ensembles of macrocycles as a starting point for docking shows promise in modeling binding modes of macrocyclic compounds.     

A new method for fast and accurate derivation of molecular conformations

During molecular simulations, three-dimensional conformations of biomolecules are calculated from the values of their bond angles, bond lengths, and torsional angles. In this paper we study how to efficiently derive three-dimensional molecular conformations from the values of torsional angles. This case is of broad interest as torsional angles greatly affect molecular shape and are always taken into account during simulations. We first review two widely used methods for deriving molecular conformations, the simple rotations scheme and the Denavit-Hartenberg local frames method. We discuss their disadvantages which include extensive bookkeeping, accumulation of numerical errors, and redundancies in the local frames used. Then we introduce a new, fast, and accurate method called the atomgroup local frames method. This new method not only eliminates the disadvantages of earlier approaches but also provides lazy evaluation of atom positions and reduces the computational cost. Our method is especially useful in applications where many conformations are generated or updated such as in energy minimization and conformational search.     

The SAAP force field: Development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

Molecular simulation by using force field parameters has been widely applied in the fields of peptide and protein research for various purposes. We recently proposed a new all‐atom protein force field, called the SAAP force field, which utilizes single amino acid potentials (SAAPs) as the fundamental elements. In this article, whole sets of the SAAP force field parameters in vacuo, in ether, and in water have been developed by ab initio calculation for all 20 proteinogenic amino acids and applied to Monte Carlo molecular simulation for two short peptides. The side‐chain separation approximation method was employed to obtain the SAAP parameters for the amino acids with a long side chain. Monte Carlo simulation for Met‐enkephalin (CHO‐Tyr‐Gly‐Gly‐Phe‐Met‐NH₂) by using the SAAP force field revealed that the conformation in vacuo is mainly controlled by strong electrostatic interactions between the amino acid residues, while the SAAPs and the interamino acid Lennard‐Jones potentials are predominant in water. In ether, the conformation would be determined by the combination of the three components. On the other hand, the SAAP simulation for chignolin (H‐Gly‐Tyr‐Asp‐Pro‐Glu‐Thr‐Gly‐Thr‐Trp‐Gly‐OH) reasonably reproduced a native‐like β‐hairpin structure in water although the C‐terminal and side‐chain conformations were different from the native ones. It was suggested that the SAAP force field is a useful tool for analyzing conformations of polypeptides in terms of intrinsic conformational propensities of the single amino acid units. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Cyclopropane-derived peptidomimetics. Design, synthesis, and evaluation of novel enkephalin analogues

It is known that peptide mimics containing trans-substituted cyclopropanes stabilize extended conformations of oligopeptides, and molecular modeling studies now suggest that the corresponding cis-cyclopropane dipeptide isosteres could stabilize a reverse turn. To begin to assess this possibility, a series of cis-substituted cyclopropanes were incorporated as replacements of the Gly(2)-Gly(3) and Phe(4)-Leu(5) dipeptide subunits in Leu-enkephalin (H(2)N-Tyr-Gly-Gly-Phe-Leu-OH), which is believed to bind to opiod receptors in a conformation containing a beta-turn. General methods for the synthesis of the cyclopropane-containing dipeptide isosteres -XaaPsi[COcpCO]Yaa- and -XaaPsi[NHcpNH]Yaa-were developed by a sequence that featured the enantioselective cyclization of allylic diazoacetates catalyzed by the chiral rhodium complexes Rh(2)[(5S)-MEPY](4) and Rh(2)[(5R)-MEPY](4). A useful modification of the Weinreb amidation procedure was applied to the opening of the intermediate lactones with dipeptides, and a novel method for the synthesis of substituted diaminocyclopropanes was also developed. The Leu-enkephalin analogues were tested in a panel of binding and functional assays, and although those derivatives containing cyclopropane replacements of the Gly(2)-Gly(3) exhibited low micromolar affinity for the mu-receptor, analogues containing such replacements for the Phe(4)-Leu(5) subunit did not bind with significant affinity to any of the opioid receptors. These results are discussed.     

Accurate assessment of the strain energy in a protein-bound drug using QM/MM X-ray refinement and converged quantum chemistry

An ongoing question regarding the energetics of protein‐ligand binding has been; what is the strain energy that a ligand pays (if any) when binding to its protein target? The traditional method to estimate strain energy uses force fields to calculate the energy difference between the ligand bound conformation and its nearest local minimum/global minimum on the gas‐phase or aqueous phase potential energy surface. This makes the implicit assumption that the underlying force field as well as the reference crystal structure is accurate. Herein, we use ibuprofen as a test case and compare MMFF and ab initio QM methods to identify the local and global minimum conformations. Nine low energy conformations were identified with HF/6‐31G* geometry optimization in vacuo. We also obtained highly accurate relative energies for ibuprofen's conformational energy surface based on M06/aug‐cc‐pVXZ (X = D and T), MP2/aug‐cc‐pVXZ (X = D and T) and the MP2/CBS method (with and without solvent corrections). Moreover, we curate and re‐refine the ibuprofen‐protein complex (PDB 2BXG) using QM/MM X‐ray refinement approaches (HF/6‐31G* was the QM method and the MM model was the AMBER force field ff99sb), which were compared with the low energy conformers to calculate the strain energy. The result indicates that there was an 88% reduction in ibuprofen conformation strain using the QM/MM refined structure versus the original PDB ibuprofen conformations. Furthermore, our results indicate that, due to its inherent limitations in estimating electrostatic interactions, force fields are not suitable to gauge strain energy for charged drug molecules like ibuprofen. The present work offers a carefully validated conformational potential energy surface for a drug molecule as well as a reliable QM/MM re‐refined X‐ray structure that can be used to test current structure‐based drug design approaches. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011