Consequences of Strain for the Structure of Aliphatic Molecules

The chemist is accustomed to deriving structures and preferred conformations of organic compounds from rigid molecular models and standard values for bond lengths, bond angles, and torsional profiles. In the case of strained compounds, this rigid structural model has to be abandoned and replaced by a flexible one which takes individual conditions of strain into consideration. It is shown, on the basis of new experimental structure data, that the force field method is suitable and highly reliable for the calculation of structural parameters and preferred conformations of strained compounds. It is, therefore, capable of replacing the rigid molecular model. Furthermore, the systematic analysis of strain induced angle and bond deformation gives a new pivot for the development of a qualitative discussion of deformation in strained molecules and hence for improved conformational analysis. — In the course of this work we were able to isolate two rotamers of D,L -3,4-di(1-adamantyl)-2,2,5,5-tetramethylhexane; this is the first isolation of a rotamer pair of an aliphatic hydrocarbon.     

Force field parametrization and molecular dynamics simulation of flexible POSS-linked (NHC; phosphine) Ru catalytic complexes

In recent years, N-heterocyclic carbene (NHC) or phospine groups have been put forward as candidate catalysts ligands for olefin metathesis reactions to be performed using multistep methods. Some of these proposed ligands contain polyhedral oligomeric silsesquioxane (POSS) structures linked to NHC rings by means of alkyl chains. Some important properties for the prediction of catalytic activity, such as the theoretically defined buried volume, are related to the conformational characteristics of these complex ligands that can be studied through molecular dynamics simulations. However, the chemical structure of resulting catalytic complexes usually contains atoms or groups that are not included in the common forcefields used in simulations. In this work we focus on complexes formed by a catalytic metal center (Ru) with both phospine and POSS-linked NHC groups. The central part of the complexes contain atoms and groups that have bonds, bond angles, and torsional angles whose parameters have not been previously evaluated and included in existing force fields. We have performed basic ab initio quantum mechanical calculations based on the density functional theory to obtain energies for this central section. The force field parameters for bonds, bond angles, and torsional angles are then calculated from an analysis of energies calculated for the equilibrium and different locally deformed structures. Nonbonded interactions are also conveniently evaluated. From subsequent molecular dynamics simulations, we have obtained results that illustrate the conformational characteristics most closely connected with the catalytic activity.     

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.     

Fluidic assembly and packing of microspheres in confined channels

We study fluidic assembly and packing of spherical particles in rectilinear microchannels that are terminated by a flow constriction. First, we introduce a method for active assembly of particles in the confined microchannels by triggering a local constriction in the fluid channel using a partially closed membrane valve. This microfluidic valve allows active, on-demand particle assembly as opposed to previous passive assembly methods based on terminal channels and weirs. Second, we study the three-dimensional assembly and packing of particles against a weir in confined rectilinear microchannels. The packings result in achiral particle chains with alternating (zigzag) structure. This structure is characterized by a single, repeated bond angle whose components projected into the frame of the channel are quantified by confocal microscopy and image processing. Brownian dynamics simulation of the packing comprehensively delineates the range of bond angles possible in narrow, rectilinear microchannels as well as the complex dependence of these angles on the relative dimensions of the channel and particles. The simulations of the three-dimensional packings are accurately modeled by a compact theory based on trigonometric relationships. The experimentally measured bond angles show excellent agreement with the simulations, thereby validating the functional dependence of the achiral packing bond angles on channel dimensions. This functional relationship is immediately useful for the design of anisotropic particles by microfluidic synthesis.     

The effects of biasing torsional mutations in a conformational GA

This paper describes the effects of incorporating torsional bias into a conformational Genetic Algorithm (GA) such as that found in the GASP program. Several major conclusions can be drawn. Biasing torsional angles toward values associated with local energy minima increases the rate of convergence of the fitness function (consisting of energy, steric, and pharmacophoric compatibility terms) for a set of molecules, but a definite tradeoff exists between total model energy and the steric and pharmacophoric compatibility terms in the fitness score. Biasing torsions in favor of sets of angles drawn from low-energy conformations does not guarantee low total energy, but biased torsional sampling does generally produce less strained models than does the uniform torsional sampling in classical GASP. Overall, torsionally biased sampling produces good models comprised of energetically favorable ligand conformations.     

Interpreting protein structural dynamics from NMR chemical shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged (1)H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail.     

Ab initio structural investigation of methyl and ethyl carbamate, and carbamyl choline

The molecular structures of four conformations of methylcarbamate, three forms of ethylcarbamate, four forms of ethylacetate, and of the trans-form of carbamylcholine, were determined by ab initio gradient geometry refinement on the 4-21G level, and the results are compared with the geometries of homologous systems. Significant changes in bond distances and angles are observed with torsional changes, but, barring long-range non-bonded interactions, they are to a large extent localized in that part of the system which is directly involved with the torsional transition; i.e., through-bond effects in a bond distance chain begin to be insignificant after a sequence of three bonds.     

Alternative expressions for energies and forces due to angle bending and torsional energy

We have derived alternative expressions for computing the energies and forces associated with angle bending and torsional energy terms commonly used in molecular mechanics and molecular dynamics computer programs. Our expressions address the problems of singularities that are intrinsic in popular angle energy functions and that occur from other chain rule derivations of force expressions. Most chain rule derivations of expressions for Cartesian forces due to angle energies make use of relations such as where ? is a bond or torsion angle, E(?) is energy, and ?/?x represents a derivative with respect to some Cartesian coordinate. This expression leads to singularities from the middle term, ?1/sin ?, when ? is 0 or π. This is a problem that prevents the use of torsional energy expressions that have phase angles, ?°, other than 0 or π, such as in E(?) = κ[1 + cos(n? ? phsi;°)]. Our derivations make use of a different, but equivalent, form of the chain rule: This form still possesses singularities for the bond angle forces since the last factor is undefined when ? is 0 or π. However, the alternate form may be used to great advantage for the torsional angle forces where no such problem arises. The new expressions are necessary if one desires the use of torsional energy expressions with general phase angles. Even for energy expressions in common use, i.e., with phase angles of 0 or π, our force expressions are as computationally efficient as the standard ones. The new expressions are applicable to all molecular simulations that employ restrained, or phase-shifted, torsional angle energy expressions.     

Molecular dynamics simulation of cellobiose in water

The conformational behavior of cellobiose was studied by molecular dynamics simulation in a periodic box of waters. Several different initial conformations were used and the results compared with equivalent vacuum simulations. The average positions and rms fluctuations within single torsional conformations of cellobiose were affected only slightly by the solvent. However, water damped local torsional librations and transitions. The conformational energies of the solute and their fluctuations were also sensitive to the presence of solvent. Intramolecular hydrogen bonding was weakened relative to that observed in vacuo due to competition with solvating waters. All cellobiose hydroxyl groups participated in intermolecular hydrogen bonds with water, with approximately eight hydrogen bonds formed per glucose ring. The hydrogen bonding was predominantly between water hydrogens and solute hydroxyl oxygens. Intermolecular hydrogen bonding to ring and bridge oxygens was seldom present. The diffusion coefficients of both water and solute agree closely with experimental values. Water interchanged rapidly between the solvating first shell and the bulk on the picosecond time scale. © 1993 John Wiley & Sons, Inc.     

Singular value decomposition of torsional angles of analogs of the dopamine reuptake inhibitor GBR 12909

Analysis of large, flexible molecules, such as the dopamine reuptake inhibitor GBR 12909 (1), is complicated by the fact that they can take on a wide range of closely related conformations. The first step in the analysis is to classify the conformers into groups. Here, Singular Value Decomposition (SVD) was used to group conformations of GBR 12909 analogs by the similarity of their nonring torsional angles. The significance of the present work, the first application of SVD to the analysis of very flexible molecules, lies in the development of a novel scaling technique for circular data and in the grouping of molecular conformations using a technique that is independent of molecular alignment. Over 700 conformers each of a piperazine (2) and piperidine (3) analog of 1 were studied. Analysis of the score and loading plots showed that the conformers of 2 separate into three large groups due to torsional angles on the naphthalene side of the molecule, whereas those of 3 separate into nine groups due to torsional angles on the bisphenyl side of the molecule. These differences are due to nitrogen inversion at the unprotonated piperazinyl nitrogen of 2, which results in a different ensemble of conformers than those of 3, where no inversion is possible at the corresponding piperidinyl carbon.     

Calculation of fully optimized geometries of five- and six-membered heterocycles by the CNDO force method

Equilibrium geometries of five- and six-membered aromatic molecules have been calculated by applying the force method of the CNDO/2 procedure. The calculated and experimental geometries agree surprisingly well. The reliable values obtained for bond angles are of special importance in calculating molecular conformations.     

Konformative Beweglichkeit Flexibler Ringsysteme–XII Modellrechnungen zur Ringinversion bei Methylsubstituierten Cyclohexanen

For the interpretation of experimental data on the activation energy and free activation enthalpy for the inversion of cyclohexane and its di-, tetra- and hexa-methyl derivatives, model calculations were made to determine the ‘relative’ energies of the ground, intermediate and transition states of the molecules. For this purpose Hendrickson's model was extended so that with internal molecular variables (bond lengths, valence and torsional angles) the topography and the ‘relative’ energy of every possible unsymmetrical conformation could be included. To obtain optimal agreement between the calculated values and the experimental results a total of 17 different combinations of potential functions for deformation of valence angles, torsional angles and H? H interactions were used. By application of the extended calculating procedure it was found that for cyclohexane the half-chair conformation is not, as until now assumed, the only transition conformation in chair inversion, but that there are numerous other unsymmetrical transition conformations with similar energies. The calculations for methyl cyclohexanes showed that for molecules with synaxial arrangement of methyl groups the relative energy of the chair form is considerably increased. The chair form is however still the most stable, even in the case of 1,1,3,3,5,5-hexamethylcyclohexane. The most favourable twist conformations are about 2.6 to 6.5 kcal/mole energy richer. Calculation of activation energies showed that, with synaxial arrangement of two or more methyl groups, the relative energy of the transition conformation is less markedly increased than is that of the ground state, with the result that the activation energy is reduced in comparison with that for cyclohexane.     

Effect of double bond position on lipid bilayer properties: insight through atomistic simulations

Phosphatidylcholines (PCs) are among the most common phospholipids in plasma membranes. Their structural and dynamic properties are known to be strongly affected by unsaturation of lipid hydrocarbon chains, yet the role of the exact positions of the double bonds is poorly understood. In this work, we shed light on this matter through atomic-scale molecular dynamics simulations of eight different one-component lipid bilayers comprised of PCs with 18 carbons in their acyl chains. By introducing a single double bond in each acyl chain and varying its position in a systematic manner, we elucidate the effects of a double bond on various membrane properties. Studies in the fluid phase show that a number of membrane properties depend on the double bond position. In particular, when the double bond in an acyl chain is located close to the membrane-water interface, the area per lipid is considerably larger than that found for a saturated lipid. Further, when the double bond is shifted from the interfacial region toward membrane center, the area per lipid is observed to increase and have a maximum when the double bond is in the middle of the chain. Beyond this point, the surface area decreases systematically as the double bond approaches membrane center. These changes in area per lipid are accompanied by corresponding changes in membrane thickness and ordering of the chains. Further changes are observed in the tilt angles of the chains, membrane hydration together with changes in the number of gauche conformations, and direct head group interactions. All of these effects can be associated with changes in acyl chain conformations and local effects of the double bond on the packing of the surrounding atoms.     

A fast and efficient method to generate biologically relevant conformations

Summary Mutual binding between a ligand of low molecular weight and its macromolecular receptor demands structural complementarity of both species at the recognition site. To predict binding properties of new molecules before synthesis, information about possible conformations of drug molecules at the active site is required, especially if the 3D structure of the receptor is not known. The statistical analysis of small-molecule crystal data allows one to elucidate conformational preferences of molecular fragments and accordingly to compile libraries of putative ligand conformations. A comparison of geometries adopted by corresponding fragments in ligands bound to proteins shows similar distributions in conformation space. We have developed an automatic procedure that generates different conformers of a given ligand. The entire molecule is decomposed into its individual ring and open-chain torsional fragments, each used in a variety of favorable conformations. The latter ones are produced according to the library information about conformational preferences. During this building process, an extensive energy ranking is applied. Conformers ranked as energetically favorable are subjected to an optimization in torsion angle space. During minimization, unfavorable van der Waals interactions are removed while keeping the open-chain torsion angles as close as possible to the experimentally most frequently observed values. In order to assess how well the generated conformers map conformation space, a comparison with experimental data has been performed. This comparison gives some confidence in the efficiency and completeness of this approach. For some ligands that had been structurally characterized by protein crystallography, the program was used to generate sets of some 10 to 100 conformers. Among these, geometries are found that fall convincingly close to the conformations actually adopted by these ligands at the binding site.     

Development and validation of empirical force field parameters for netropsin

The netropsin molecule preferentially binds to the four consecutive A.T base pairs of the DNA minor groove and could therefore inhibit the expression of specific genes. The understanding of its binding on a molecular level is indispensable for computer-aided design of new antitumor agents. This knowledge could be obtained via molecular dynamics (MD) and docking simulations, but in this case appropriate force field parameters for the netropsin molecule should be explicitly defined. Our parametrization was based on the results of quantum chemical calculations. The resulting set of parameters was able to reproduce bond lengths, bond angles, torsional angles of the ab initio minimized geometry within 0.03 A, 3 deg and 5 deg, respectively, and its vibrational frequencies with a relative error of 4.3% for low and 2.8% for high energy modes. To show the accuracy of the developed parameters we calculated an IR spectrum of the netropsin molecule using MD simulation and found it to be in good agreement with the experimental one. Finally, we performed a 10 ns long MD simulation of the netropsin-DNA complex immersed in explicit water. The overall complex conformation remained stable at all times, and its secondary structure was well retained.     

A kinematic view of loop closure

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.     

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。     

Monte Carlo simulations on short single-stranded oligonucleotides. I. Application to RNA trimers

Monte Carlo (MC) structural simulation of short RNA sequences has been carried out by random variations of the nucleotide conformational angles (i.e., phosphodiester chain torsional angles and sugar pucker pseudorotational angles). All of the chemical bond lengths and valence angles remained fixed during the structural simulation, except those of the sugar pucker ring. In this article we present the simulated structures of RNA trimers—r(AAA) and r(AAG)—obtained at 11°C and 70°C. The influence of various initial conformations (selected as starting points in the MC simulations) on the equilibrium conformations has been discussed. The simulated conformational angles have been compared with those estimated by nuclear magnetic resonance (NMR) spectroscopy. For both of the oligonucleotides studied here, the most stable structures are helical conformations with stacked bases, at 11°C and 70°C. However, when the starting point is a stretched chain, it is found that r(AAA) adopts a reverse-stacked structure at low temperature (11°C), in which the A3 base is located between the A1 and A2 bases. Although the energies of these conformations (helical and reverse stacked) are very close to each other, the potential barrier between them is extremely high (close to 30 kcal/mol). This hinders the conformational transition from one structure to the other at a given temperature (and in the course of a same MC simulation). However, it is possible to simulate this structural transition by heating the reverse-stacked structure up to 500°C and cooling down progressively to 70°C and 11°C: Canonical helical structures have been obtained by this procedure. © 1994 by john Wiley & Sons, Inc.