Molecular dynamics simulations of a liquid crystalline molecule in the smectic A and E phases and in vacuum

Molecular dynamics simulations are performed in this work at 393 and 323 K for a mesogenic molecule ( R )-1-methylheptyl 4\[4-(2-allyloxyethoxy)biphenyl-4-carbonyloxy]benzoate in the simulated smectics A and E, respectively, and in a vacuum at 300 K, for a period of 1.0ns. The trajectories obtained from molecular dynamics simulations allow us to investigate the dynamical behaviour of this mesogenic molecule in the simulated smectic phases. This dynamical behaviour of a single molecule is presented using the distributions of dihedral angles and rotational diffusion around the C-axis defined by the simulated cells. Simulation results indicate that, except for the bonds near the end of the spacer segment, the dihedral angles all exhibit a single Gaussian-like distribution in the smectic A and E phases. Fluctuations of a dihedral angle about its mean value are more restricted in the smectics A and E than in those simulated in a vacuum. The average value of the fluctuations of the dihedral angles at the bonds in the spacer is found to be about 2 fold larger than that of fluctuations in the tail of the same molecule in the smectic A and E phases. In the smectic A phase, the distribution of orientations of a molecule about its long axis in a 36 molecule cell in which the outer molecules are fixed is found to have three distinct peaks. This result shows that the orientational fluctuations of single molecules are limited by confinement due to neighbouring molecules, i.e. that the layers have short-range structural correlations. The orientational distributions show larger fluctuations at the ends of the molecules.     

Normal mode analysis based on an elastic network model for biomolecules in the Protein Data Bank,which uses dihedral angles as independent variables

We have developed a computer program, named PDBETA, that performs normal mode analysis (NMA) based on an elastic network model that uses dihedral angles as independent variables. Taking advantage of the relatively small number of degrees of freedom required to describe a molecular structure in dihedral angle space and a simple potential-energy function independent of atom types, we aimed to develop a program applicable to a full-atom system of any molecule in the Protein Data Bank (PDB). The algorithm for NMA used in PDBETA is the same as the computer program FEDER/2, developed previously. Therefore, the main challenge in developing PDBETA was to find a method that can automatically convert PDB data into molecular structure information in dihedral angle space. Here, we illustrate the performance of PDBETA with a protein–DNA complex, a protein–tRNA complex, and some non-protein small molecules, and show that the atomic fluctuations calculated by PDBETA reproduce the temperature factor data of these molecules in the PDB. A comparison was also made with elastic-network-model based NMA in a Cartesian-coordinate system.     

Dihedral Angles in Cyclic Molecules

The experimental and quantum-chemical values of dihedral angles are analyzed for mono- and bicyclic molecules. Correlations have been found for the bond and dihedral angles.     

Etude de la conformation des n-aryl azoles par la methode e.h.t. (extended hückel theory)

E.H.T. calculations of total energy as a function of dihedral angle are presented for 8 N-aryl azoles, six with dihedral angle α and two with dihedral angles α and β. The rotational barriers to the planar and to the orthogonal geometries are discussed. The dihedral angles α or β corresponding to the minimum of the calculated potential curve or surface are important; a uniform correction of these values is necessary to find the experimental values.     

Stationary points on the aminomethanol potential energy surface

Summary In this work we study surface fitting equations for a rigid rotor model of aminomethanol. The energies were obtained from the GAUSSIAN88 package using 3-21G bases and fitted on a least square equation, thus generating a Fourier series expansion of the energy as a function of two dihedral angles. The dihedral angles chosen are those that represent rotation around the C-O and N-C axes in the first case, and rotation around C-O and inversion around the amino group in the second case. Results indicate that the hydroxyl hydrogen is subject to almost free rotation around the C-O axis. Further fully relaxed 6-31G* calculations were performed in order to qualify the results obtained for the rigid rotor model.     

Molecular dynamics simulation study on the isomerization and molecular orientation of liquid crystals formed by azobenzene and (1-cyclohexenyl)phenyldiazene

Atomistic molecular dynamics simulations have are used to investigate the liquid crystal systems based on [4-pentyl-(1-cyclohexenyl)]-(4-cyanophenyl)diazene (5CPDCN) and 4-cyano-4'-pentylazobenzene (5AZCN). The results show the growth process of a nematic phase from a disordered phase. Then the phase transition caused by isomerization reaction is studied based on a temporary modification of the dihedral potential. The properties of 5AZCN and 5CPDCN are compared, showing that the orientation of trans-5CPDCN is more highly ordered than trans-5AZCN. This can be attributed to the more extended dihedral angles φ(2) (i.e. the dihedral angle between the ring system and the terminal chain) in trans-5CPDCN enhance the rod-like conformation of the molecules. The orientational correlation functions g(l)(r) (l = 1, 2) are also calculated, by which we find that both 5CPDCN and 5AZCN systems in nematic phase present parallel and anti-parallel dipole correlations. The anti-parallel dipole correlation is localized for the 5CPDCN system; on the contrary, the parallel dipole correlation is weakly localized for the 5AZCN system.     

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.     

An intramolecular induction correction model of the molecular dipole moment

A model for intramolecular polarization is presented. It is used to describe the changes in the molecular charge distribution occurring as a response to changes of dihedral angles in the molecule. The model is based on a multicenter multipole distribution of the molecular charge distribution. The electric field from this charge distribution induce dipole moments in the same molecule. The model contains atom type parameters to describe the damping of the electric field. A total of four atom types are used. The parameters are fitted to a calibration set with various functional groups, and tested against a validation set. The error obtained for the calibration set is reduced by 92% and by 88% for the validation set, if compared to an accurate state-of-the-art force field. It is shown that rotating the non-polarizable multicenter multipole distribution for the equilibrium geometry gives too large dipole moments for dihedral angles deviating from the equilibrium geometry. This will lead to too large long-range attractions in simulations. This problem is overcome by using the dipole polarizability correction suggested here, which gives dipole moments very close to the Hartree-Fock dipole moments obtained from reference calculations.     

24 IPR isomers of fullerene C84: Cage deformation as geometrical characteristic of local strains

The structures of 24 IPR‐isomers of C₈₄ fullerene with distributed single, double and delocalized bonds are presented. Obtained results are fully supported by DFT quantum‐chemical calculations of electronic and geometrical structures of these isomers. Two reasons of instability of fullerene molecules are their radical origin and/or high local strain. Distortion of pentagons as well as hexagons with alternating single and double bonds is the most significant geometrical parameter reflecting local strain of a molecule. These distortions are measured as maximal dihedral angles of those cycles and reach 20 degrees in mostly deformed hexagons and pentagons. In contrast high values of dihedral angles in hexagons with delocalized π‐bonds are typical for stable isomers. Other geometric parameters such as valence angles, sums of valence angles and dihedral angles between approximate planes of fused rings have no marked influence on stability. The development of strain‐related criteria for fullerene stability will be helpful in the prediction which isomers might potentially be observable in experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A computational analysis of the electrostatic potentials and relative bond strengths of hydrazine and some of its 1,1-dimethyl derivatives

We have carried out a computational study of hydrazine and five of its 1,1-dimethyl derivatives, focusing on their electrostatic potentials and relative bond strengths. Our approach has involved the calculation of ab initio self-consistent-field molecular orbital wave functions and molecular properties using the GAUSSIAN 82 system of programs. The electrostatic potentials of the hydrazines possess negative regions of varying sizes and strengths associated with the nitrogens of the α-diamino linkages. Through an analysis of the positions of the most negative potentials of these regions, we have obtained directly the dihedral angles between the nitrogen lone pairs in these systems. Our use of the electrostatic potential to obtain these angles is a direct and general approach, in contrast to indirect procedures used in the past. We find this dihedral angle to be close to 90° in hydrazine, with variations in the substituted hydrazines that depend on the nature of the substituents. A highly polar structure is found for 1-chloromethyl-1-methylhydrazine, which involves a delocalization of electronic charge from the substituted nitrogen towards the CH₂Cl group. We find that substituents able to withdraw significant amounts of electronic density from the central nitrogen lone pair regions, either through resonance or by induction, have a slight bond strengthening effect on the central N-N bond. This is attributed to a decrease in the repulsion between the weakened nitrogen lone pair regions. The difficulties encountered in seeking the controlled oxidation of hydrazine to nitro derivatives may be due, in part, to the fact that two factors which would favor this, highly negative nitrogen potentials and strong N-N bonds, are opposing in nature.     

Effect of torsional potential on the predicted phase behavior of n-alkanes

The effect of torsional potential on the predictions of simulation for vapor–liquid equilibria of n-alkanes is determined. Calculations are performed with histogram-reweighting Monte Carlo simulations in the grand canonical ensemble. Decreasing the magnitude of energy barriers to dihedral rotation or allowing free rotation is found to have no effect on the predicted vapor–liquid equilibria. Restriction of the dihedral angles to a Gaussian distribution around the minimum energy conformation causes an under-prediction of the liquid densities and critical temperatures by a maximum of 7% and 2%, respectively, with discrepancies increasing monotonically with the number of dihedral angles present in a molecule. No significant deviation in vapor pressure is observed for any compound, regardless of torsional potential used. An analysis of the conformational behavior reveals that restriction of the dihedral sampling has a measurable effect on excluded volume of the molecule, and this change of conformational behavior is responsible for the reduction in the predicted saturated liquid densities observed in this work. Similar calculations for force fields employing reduced dihedral potentials or freely jointed chains show little change in the predicted excluded volume compared to the reference force field.     

Small-amplitude protein conformational dynamics: Second-order analytic relation between cartesian coordinates and dihedral angles

An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time-dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second-order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first-order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second-order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second-order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.     

Rotamer decomposition and protein dynamics: Efficiently analyzing dihedral populations from molecular dynamics

Molecular mechanics methods have matured into powerful methods to understand the dynamics and flexibility of macromolecules and especially proteins. As multinanosecond to microsecond length molecular dynamics (MD) simulations become commonplace, advanced analysis tools are required to generate scientifically useful information from large amounts of data. Some of the key degrees of freedom to understand protein flexibility and dynamics are the amino acid residue side chain dihedral angles. In this work, we present an easily automated way to summarize and understand the relevant dihedral populations. A tremendous reduction in complexity is achieved by describing dihedral timeseries in terms of histograms decomposed into Gaussians. Using the familiar and widely studied protein lysozyme, it is demonstrated that our approach captures essential properties of protein structure and dynamics. A simple classification scheme is proposed that indicates the rotational state population for each dihedral angle of interest and allows a decision if a given side chain or peptide backbone fragment remains rigid during the course of an MD simulation, adopts a converged distribution between conformational substates or has not reached convergence yet. © 2012 Wiley Periodicals, Inc.     

Spiroconjugation in orthothiocarbonates

The He(I) photoelectron (PE) spectra of the orthothiocarbonates 1–3 have been investigated. To understand the splitting pattern in the low energy region a comparison with chemically related molecules has been made. In addition, molecular orbital calculations based on a ZDO model and semiempirical calculations were carried out with variation of dihedral angles. The split of the first four orbitais, which depends very much on the geometry, is explicitly discussed. The splitting due to spiroconjugation amounts to 1.1 eV for 1,0.55 eV for 2, and 0.45 eV for 3.     

Conformational analysis of a stereochemically complete set of cis-enediol peptide analogues

A conformational analysis of a stereochemically complete set of peptide analogues based on a cis-enediol unit is presented. The cis-enediol unit, which can replace a two or a three amino acid segment of a peptide, contains two "side chains", four asymmetrical carbon atoms, and six free dihedral angles. To determine the accessible conformational space, the molecules are divided into three fragments, each containing two free dihedral angles. The energy surfaces are computed for all dihedral angle values, and the possible conformations of the cis-enediol unit analogues are built using all combinations of the surface minima. Such a "build-up" procedure, which is very fast, is able to reproduce 75% of the minima obtained from a full dihedral angle exploration of the conformational space. The cis-enediol unit minima are compared with the corresponding di- and tripeptide minima; all peptide minima can be closely matched by a cis-enediol unit minimum of low energy (less than 2.2 kcal/mol above the lowest energy conformer). However, there are low energy minima of the cis-enediol unit that have no corresponding minima in peptides. The results are shown to depend strongly on the chirality of the analogues. The ability of each of the stereoisomers to mimic natural peptides, evaluated by the present approach, is correlated with its experimental activity in a renin inhibition assay.     

Investigation of the polymorphs of dimethyl-3,6-dichloro-2,5-dihydroxyterephthalate by (13)C solid-state NMR spectroscopy.

Two of the three conformational polymorphs of dimethyl-3,6-dichloro-2,5-dihydroxyterephthalate are studied by solid-state NMR techniques. The structural differences between the polymorphs have previously been studied by X-ray. In these two polymorphs named white and yellow due to their color, the major structural difference is the torsional angle between the ester group and the aromatic ring. The yellow form has a dihedral angle of 4 degrees between the plane of the aromatic ring and the plane of the ester group, while the white form has two different molecules per unit cell with dihedral angles of 70 degrees and 85 degrees. This change greatly affects the conjugation in the pi-electronic system. In addition, there are differences in the hydrogen-bonding patterns, with the white form having intermolecular hydrogen bonds and the yellow form having intramolecular hydrogen bonds. In this work, the carbon isotropic chemical shift values and the chlorine electric field gradient (EFG) tensor information are extracted from the (13)C MAS spectra, and the principal values of the chemical shift tensors of the carbons are obtained from 2D FIREMAT experiments. Quantum chemical calculations of the chemical shift tensor data as well as the EFG tensor are performed at the HF and DFT levels of theory on individual molecules and on stacks of three molecules to account for the important intermolecular interactions in the white form. The differences between the spectral data on the two polymorphs are discussed in terms of the known electronic and structural differences.     

Molecular modelling of liquid crystal systems: An internal coordinate Monte Carlo approach

A Monte Carlo scheme is presented which is designed to provide a convenient mechanism to model accurately the internal molecular structure of liquid crystalline molecules. The technique stores atomic positions in terms of bond lengths, bond angles and dihedral angles within a Z-matrix, and the Monte Carlo scheme involves generating trial configurations from changes to the Z-matrix using the MM2 molecular mechanics potential to describe energy changes between different molecular conformations. The technique is applied to the liquid crystal molecule 4-n-pentyl-4'-cyanobiphenyl (5CB), and results are presented for the conformational populations and dihedral angle distributions of 5CB in the gas phase at 300 K. The effect of a nematic mean field on the distribution of molecular conformations is also examined via the addition of a conformation-dependent potential of mean torque to the internal energy.     

Sterically encumbered diphosphaalkenes and a bis(diphosphene) as potential multiredox-active molecular switches: EPR and DFT investigations

The reduction products of two diphosphaalkenes (1 and 2) and a bis(diphosphene) (3) containing sterically encumbered ligands and corresponding to the general formulas Ar-X=Y-Ar'-Y=X-Ar, have been investigated by EPR spectroscopy. Due to steric constraints in these molecules, at least one of the dihedral angles between the CXYC plane and either the Ar plane or the Ar' plane is largely nonzero and, hence, discourages conformations that are optimal for maximal conjugation of P=X (or P=Y) and aromatic pi systems. Comparison of the experimental hyperfine couplings with those calculated by DFT on model systems containing no cumbersome substituents bound to the aromatic rings shows that addition of an electron to the nonplanar neutral systems causes the X=Y-Ar'-Y=X moiety to become planar. In contrast to 1 and 2, 3 can be reduced to relatively stable dianion. Surprisingly the two-electron reduction product of 3 is paramagnetic. Interpretation of its EPR spectra, in the light of DFT calculations on model dianions, shows that in [3](2)(-) the plane of the Ar' ring is perpendicular to the CXYC planes. Due to interplay between steric and electronic preferences, the Ar-X=Y-Ar'-Y=X-Ar array for 3 is therefore dependent upon its redox state and acts as a "molecular switch".     

Ferreting out correlations from trajectory data

Thermally driven materials characterized by complex energy landscapes, such as proteins, exhibit motions on a broad range of space and time scales. Principal component analysis (PCA) is often used to extract modes of motion from protein trajectory data that correspond to coherent, functional motions. In this work, two other methods, maximum covariance analysis (MCA) and canonical correlation analysis (CCA) are formulated in a way appropriate to analyze protein trajectory data. Both methods partition the coordinates used to describe the system into two sets (two measurement domains) and inquire as to the correlations that may exist between them. MCA and CCA provide rotations of the original coordinate system that successively maximize the covariance (MCA) or correlation (CCA) between modes of each measurement domain under suitable constraint conditions. We provide a common framework based on the singular value decomposition of appropriate matrices to derive MCA and CCA. The differences between and strengths and weaknesses of MCA and CCA are discussed and illustrated. The application presented here examines the correlation between the backbone and side chain of the peptide met-enkephalin as it fluctuates between open conformations, found in solution, to closed conformations appropriate to when it is bound to its receptor. Difficulties with PCA carried out in Cartesian coordinates are found and motivate a formulation in terms of dihedral angles for the backbone atoms and selected atom distances for the side chains. These internal coordinates are a more reliable basis for all the methods explored here. MCA uncovers a correlation between combinations of several backbone dihedral angles and selected side chain atom distances of met-enkephalin. It could be used to suggest residues and dihedral angles to focus on to favor specific side chain conformers. These methods could be applied to proteins with domains that, when they rearrange upon ligand binding, may have correlated functional motions or, for multi-subunit proteins, may exhibit correlated subunit motions.