Investigation of the Potential Surface of Tetraalanine-Peptide by Sequentially Locking the Molecular Dynamic Trajectory of the System in Attraction Basins

A new approach to investigation of finite polyatomic systems such as clusters and biomolecules is suggested. The molecular dynamic trajectory of the system is sequentially locked in attraction basins on the potential energy surface (PES) subject to a certain strategy of system dislocation over the surface. The approach is illustrated by investigating the PES of the tetraalanine-peptide N-acetyl-(Ala)₃-methylamide in aqueous solution. It is indicated that the PES of the system consists of a great number of local minima united in clusters, which correspond to different trans/cis conformations of the molecule and are separated by barriers with a height of 14 kcal/mole or more.     

Analysis of the genetic algorithm method of molecular conformation determination

Many important problems in chemistry require knowledge of the 3-D conformation of a molecule. A commonly used computational approach is to search for a variety of low-energy conformations. Here, we study the behavior of the genetic algorithm (GA) method as a global search technique for finding these low-energy conformations. Our test molecule is cyclic hexaglycine. The goal of this study is to determine how to best utilize GAs to find low-energy populations of conformations given a fixed amount of CPU time. Two measures are presented that help monitor the improvement in the GA populations and their loss of diversity. Different hybrid methods that combine coarse GA global search with local gradient minimization are evaluated. We present several specific recommendations about trade-offs when choosing GA parameters such as population size, number of generations, rate of interaction between subpopulations, and combinations of GA and gradient minimization. In particular, our results illustrate why approaches that emphasize convergence of the GA can actually decrease its effectiveness as a global conformation search method. © John Wiley & Sons, Inc.     

Conformational sampling via a self-regulating effective energy surface

The difficulty of efficiently sampling the phase space of complex systems with rough energy surfaces is well known. Typical solutions to the problem involve accelerating the crossing of barriers, but such methods often have the secondary problem that the low-energy states of interest are inadequately sampled, unless the parameters of the search algorithm are modified as the system evolves. A method is presented to improve the sampling with particular emphasis on the low-energy conformations, which make the most important contributions to the thermodynamics of the system. The algorithm proposed here samples the details of the minima, while easily surmounting barriers. This is achieved by introducing a self-regulating sampling variable which depends on the current state of the system. Two replicas of the system are introduced and the sampling variable is treated as a particle coupled to the physical system. The method is illustrated with a simple model system and is applied to the realistic example of barrier crossing in a protein-ligand complex.     

Folding–Unfolding Equilibrium of a Methylidene‐Substituted β‐Peptide

β‐Peptides possess the ability to fold into secondary structure elements, and this property, together with resistance to biodegradation, makes these compounds interesting for pharmaceutical applications. Recently, a novel class of β‐peptides containing methylidene moieties was described. The GROMOS 53A6 force field was used to simulate the folding equilibrium of a β³‐hexapeptide with methylidene (CH₂?) groups at all six CA‐atoms. Due to the rotational barriers induced by these methylidene groups, the helical secondary‐structure elements, normally found in β³‐peptides, are disfavored in this molecule. Simulations, started from fully extended and 3₁₄‐helical conformations, showed that the molecule adopts a complete 2₈‐helix for ca. 5% of the time and partial 2₈‐helical conformations for ca. 20% of the time. Yet, as suggested by experiments, the folding equilibrium is dominated by unfolded conformations.     

Molecular mechanics conformational analysis of cyclononane using the RIPS method and comparison with quantum-mechanical calculations

The recently reported Random Incremental Pulse Search (RIPS) technique has been used to probe the conformational energy surface of cyclononane. The stochastic method permits searching of the potential energy surface for all minimum-energy conformations. The search located all previously reported structures together with three additional conformations that were not found by earlier, primitive searching techniques. Two of these structures are high-nergy skew forms, and the third is a low-energy conformer that should contribute significantly to the overall equilibrium set of cyclononane conformations. The global minimum has been found to be the D₃ symmetrical twist chair-boat (TBC) form in accordance with previous studies. The newly discovered low-energy structure, which lies only 2.2 kcal/mol above the global minimum, has been designated twist chair-twist chair (TCTC). The two higher energy conformers are skewed chair-chair (SCC) and skewed boat-boat (SBB) forms that are 5.7 kcal/mol and 10.4 kcal/mol above the global minimum, respectively. The seven reported conformations were reanalyzed quantum mechanically (AM 1), and a comparison between MM 2 and AM 1 results is presented.     

MM3 MODELING OF ALDOPENTOSE PYRANOSE RINGS

MM3 (version 1992, ?=3.0) was used to study the ring conformations of d-xylopyranose, d-lyxopyranose and d-arabinopyranose. The energy surfaces exhibit low-energy regions corresponding to chair and skew forms with high-energy barriers between these regions corresponding to envelope and half-chair forms. The lowest energy conformer is ⁴ C ₁ for α- and β-xylopyranose and α- and β-lyxopyranose, and the lowest energy conformer is ¹ C ₄ for α- and β-arabinopyranose. Only α-lyxopyranose exhibits a secondary low-energy region (¹ C ₄) within 1 kcal/mol of its global minimum. Overall, the results are in good agreement with NMR and crystallographic results. For many of these molecules, skew conformations are found with relatively low energies (2.5 to 4 kcal/mol above lowest energy chair form). The ² S _O and ¹ C ₄ conformers of crystalline benzoyl derivatives of xylopyranose are in secondary low-energy regions on the β-xylopyranose surface, within 3.8 kcal/mol of the global ⁴ C ₁ minimum.     

Structural and quantum chemical analysis on 4,4′-di(2-hydroxybenzylamino)diphenylmethane

The title compound is analyzed by X-ray diffraction. ONIOM(B3LYP/6-31G(d,p):PM3) is used to investigate the optimized calculation and the frequency analysis of the molecule, in which the PM3 method was used for carbon and hydrogen atoms of the benzene ring and the B3LYP/6-31G(d,p) method was used for the other parts. Energy changes in the molecule are numerically investigated by the flexible scan at PM3 level. The nature of intramolecular interactions that stabilize the structure in vacuo and solid is studied. The results reveal that the molecule is flexible and molecular conformations can easily be mutually transformed through very small potential barriers.     

Iterative method for finding the low‐energy conformations based on the concept of molecular volumes

The recently proposed overlapping spheres (OS) method (Raos, N. Croat Chem Acta 1999, 72, 727) finds low‐energy conformations by minimizing the repulsion potential dependent on the free molecular volume inside the sphere with radius R_v. The sphere is situated at the geometrical center of the molecule or at the center of a molecular segment. The method was checked on branched alkanes and cyclic molecules (1,4‐diethylcyclohexane and copper(II) monochelates with N‐alkylated amino acids), yielding in all cases stable conformations with usually lower conformational energy than the “seed” conformations. The simple rules for segmentation of a molecule, based mostly on the topological considerations, were derived from the results of successfull optimizations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1353–1360, 2000     

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.     

Synthesis of a Type-VIβ-Turn Peptide Mimetic and Its Incorporation into a High-Affinity Somatostatin Receptor Ligand

The synthesis of a cis-Phe-Pro dipeptide mimetic is described, which adopts a type-VIβ-turn conformation. In this mimetic, the α-positions of Phe and Pro are joined by a CH₂CH₂ bridge, thereby forming a fused bicyclic system, and fixing a geometry similar to that seen in cis-Phe-Pro units in protein crystal structures. The dipeptide mimetic 20 was synthesized in optically pure form starting from (R)-α-allylproline ( 6 ; Schemes 1, 3, and 4), with a free carboxylic acid and an Fmoc-protected N-terminus, thereby allowing its incorporation into linear and cyclic peptides using standard solid-phase methods. The mimetic 20 was incorporated into the cyclic somatostatin analogue cyclo(-Phe = Pro-Phe-D -Trp-Lys-Thr-), where Phe = Pro represents the mimetic. This analogue shows a high affinity (pIC₅₀ 8.6) for somatostatin receptors on rat-brain cortex membranes. Based on NMR studies in aqueous solution, likely low-energy conformations for this analogue were deduced using restrained dynamic simulated annealing. The conformations found, which include a distorted type-II′ turn at D -Trp-Lys, are similar to low-energy conformations deduced elsewhere for cyclo(-Phe-Pro-Phe-D -Trp-Lys-Thr-), as well as to those seen in crystal structures of the somatostatin analogue octreotide.     

Prediction of the crystal structure of a cyclic tetrapeptide

Prediction of the known crystal structure of cyclic-L-Ser(O-t-Bu)-β-Ala-Gly-L-β-Asp(OMe) has been attempted by establishing the low-energy conformations of the isolated molecule by conformational analysis, and then regarding each of these as a rigid molecule, by establishing the favorable crystal packing arrangements by molecular packing analysis. The theoretical model closest to the observed structure was one of the lowest-energy solutions and was recognized as essentially correct by reference to the x-ray data. The limitations of the model follow from the fact that the side chain conformations are somewhat affected by packing interactions.     

Ab initio SCF calculations on low-energy conformers of cyclohexaglycine

Results from ab initio self-consistent field (SCF) calculations with a 3-21G and a double-zeta-plus polarization (DZP) basis set on four low-energy conformations of cyclohexaglycine are reported. In agreement with results from semiempirical and molecular mechanics force field calculations, the lowest-energy conformation found at the DZP level is a conformation forming six C₇ turns. However, the energy difference to the β-turn conformers is significantly smaller at the ab initio DZP level than calculated by the other methods. In contrast to the results obtained with some of the other methods, the present ab initio calculations show that both the double-type-I β turn and the double-type-II β-turn conformer of cyclohexaglycine are stable low-energy structures. © 1995 by John Wiley & Sons, Inc.     

Angular distribution of intensity of rayleigh scattering from comblike branched molecules

The angular distribution function P(θ) for intensity of light scattered by a dilute solution of comblike branched molecules has been determined for three situations of some interest for evaluation of experimental data: (1) the molecules are identical with branches of equal length attached equidistantly along linear backbone chains; (2) the molecules are homogeneous in mass, with the same number of branches on each molecule, but the branches are distributed at random along the chain; (3) branches and main chains are still uniform, but the molecules are heterogeneous in mass with the number of branches per molecule distributed according to the binomial distribution and the branches in any molecule spaced randomly along the backbone. Examination of numerical results shows that the scattering functions for models (1) and (2) are not very different. The function for case (3) is somewhat different from the others when the mean number of branches per molecule is small but they contain a large fraction of the mass of the molecule. Over a limited range of the pertinent variables (corresponding roughly to observations on typical vinyl polymers of molecular weights up to 10⁶) all three functions agree quite well with P(θ) for homogeneous linear chains with the same mean-square radius of gyration.     

Design of Peptides with α,β-Dehydro Residues: Synthesis,Crystal Structure and Molecular Conformation of a Peptide N-Boc-Phe-ΔPhe-Ile-OCH<Subscript>3</Subscript>

To develop a complete set of design rules with α,β-dehydro residues, a tripeptide N-Boc-Phe-ΔPhe-Ile-OCH₃ was synthesized. The synthesis was carried out in solution phase using azlactone procedure. The three-dimensional structure of the peptide was determined by X-ray diffraction method and refined to an R-factor of 0.085. The structure contains three peptide molecules in the asymmetric unit. In all the three crystallographically independent molecules ΔPhe residue adopts one of the three conformations that have been reported for a ΔPhe residue. The overall conformations of three peptide molecules in the asymmetric unit are not similar. Two out of three crystallographically independent molecules adopt type II β-turn conformations whereas the third molecule is found having the characteristic S-shaped conformation in which the values of dihedral angles φ, ψ have opposite signs alternately. One of these two types of conformations has been observed when a ΔPhe is introduced at (i+2) position of a tetrapeptide. The β-turn conformation is stabilized by a 4→1 hydrogen bond where the hydrophobic side chains of residues at (i+1) and (i+3) positions stabilized the unfolded conformation with van der Waals interactions. The three independent molecules are locked together by three hydrogen bonds between molecules A and B and two hydrogen bonds between molecules B and C.     

Synthesis of a New pH-Dependent Ligand: Conformational and Complexation Studies

A new macrocyclic ligand, 3, which exhibits pH-induced conformational changes, has been prepared. This ligand consists of a crown ether derived from a trans-anti-trans 1,2,4,5-tetrasubstituted cyclohexane. Due to the stereochemistry of the substituents on the carbocyclic ring, two different low-energy conformations of the crown ether are possible. Ligand 3 has been studied in solution by ¹H NMR spectroscopy at different values of pH and temperature, showing that the conformation of the crown ether, and thus its complexing ability, is strongly pH-dependent. The solid-state structure of the ligand has been determined by X-ray diffraction.     

Conformational study of Met-enkephalin in its zwitterionic form

An extensive exploration of Met-enkephalin in its zwitterionic form has been carried out, in order to characterize the different low-energy conformational domains accessible to this pentapeptide. The study builds on previous studies carried out in our lab for the neutral molecule, which provided the initial geometries from which the conformational space of the charged molecule could be scanned. The initial conformations were subjected to a series of high- and lowtemperature molecular dynamics simulations. Snapshots along each trajectory were taken, minimized, and used as starting points in further MD trajectories until no lower-energy conformers could be characterized. The CHARMm force field was used throughout the study for this purpose. The same search strategy was used in these studies simulating two different environmental conditions, a distance-dependent dielectric ? = r and a high constant dielectric ? = 80. In the low dielectric environment, the formation of the salt bridge dominates the structure. In the high dielectric environment, the screening of the electrostatic interactions results in weaker intramolecular interactions. In both cases, the Gly²–Gly³ β-turn-type structures are preferred over the Gly³–Phe⁴ turns, in marked contrast to what is found for the neutral molecule. The lowest-energy structures from both environmental conditions were reoptimized in the presence of a cluster of explicit water molecules. Reoptimization of the structures considering explicit water structures did not result in significant conformational changes for the structures characterized with the ε = r or ε = 80 environments.     

A Crystalline π‐Stack Containing Five Stereoisomers: Insights into Conformational Isomorphism,Chirality Inversion,and Disorder

An unprecedented crystal‐packing arrangement of a tetramethoxy‐bay‐substituted perylene bisimide (PBI) consists of three crystallographically independent molecules, that is, an achiral ( AC ) PBI of saddle‐shaped geometry along with two pairs of propeller‐like twisted (P )‐ and (M )‐enantiomeric PBI frameworks. All these five conformations are observed within a single π‐stack revealing an intriguing packing sequence with an inversion of chirality from P to M via AC . Nudged elastic band calculations for the isolated molecule show that AC is a local minimum of the P to M interconversion path. In addition, two minor conformations were observed in the crystal, one of which resembles a transition‐state molecule. Theoretical studies of dimeric and trimeric stacks reveal that the coexistence of all these structures in the crystal lattice is aided by the strong dispersion interactions between PBI cores and perfectly interdigitated dodecyl chains which stabilize energetically higher conformations.     

A Crystalline π‐Stack Containing Five Stereoisomers: Insights into Conformational Isomorphism,Chirality Inversion,and Disorder

An unprecedented crystal‐packing arrangement of a tetramethoxy‐bay‐substituted perylene bisimide (PBI) consists of three crystallographically independent molecules, that is, an achiral ( AC ) PBI of saddle‐shaped geometry along with two pairs of propeller‐like twisted (P )‐ and (M )‐enantiomeric PBI frameworks. All these five conformations are observed within a single π‐stack revealing an intriguing packing sequence with an inversion of chirality from P to M via AC . Nudged elastic band calculations for the isolated molecule show that AC is a local minimum of the P to M interconversion path. In addition, two minor conformations were observed in the crystal, one of which resembles a transition‐state molecule. Theoretical studies of dimeric and trimeric stacks reveal that the coexistence of all these structures in the crystal lattice is aided by the strong dispersion interactions between PBI cores and perfectly interdigitated dodecyl chains which stabilize energetically higher conformations.