Pitfalls in the use of the torsion angle driving method for the calculation of conformational interconversions

Several deficiencies and potential sources of error in the torsion angle driving method, the approach employed most frequently for the simulation of conformational interconversions, have been studied. A general explanation of the observed effects is given in terms of the energy surface and of the effects brought about by “side valleys.” Several examples of molecular mechanics calculations of conformational interconversions, among them the cyclohexane ring inversion, illustrate the problems.     

Convergence of replica exchange molecular dynamics

Replica exchange molecular dynamics (REMD) method is one of the generalized-ensemble algorithms which performs random walk in energy space and helps a system to escape from local energy traps. In this work, we studied the accuracy and efficiency of REMD by examining its ability to reproduce the results of multiple extended conventional molecular dynamics (MD) simulations and to enhance conformational sampling. Two sets of REMD simulations with different initial configurations, one from the fully extended and the other from fully helical conformations, were conducted on a fast-folding 21-amino-acid peptide with a continuum solvent model. Remarkably, the two REMD simulation sets started to converge even within 1.0 ns, despite their dramatically different starting conformations. In contrast, the conventional MD within the same time and with identical starting conformations did not show obvious signs of convergence. Excellent convergence between the REMD sets for T>300 K was observed after 14.0 ns REMD simulations as measured by the average helicity and free-energy profiles. We also conducted a set of 45 MD simulations at nine different temperatures with each trajectory simulated to 100.0 and 200.0 ns. An excellent agreement between the REMD and the extended MD simulation results was observed for T>300 K, showing that REMD can accurately reproduce long-time MD results with high efficiency. The autocorrelation times of the calculated helicity demonstrate that REMD can significantly enhance the sampling efficiency by 14.3+/-6.4, 35.1+/-0.2, and 71.5+/-20.4 times at, respectively, approximately 360, approximately 300, and approximately 275 K in comparison to the regular MD. Convergence was less satisfactory at low temperatures (T<300 K) and a slow oscillatory behavior suggests that longer simulation time was needed to reach equilibrium. Other technical issues, including choice of exchange frequency, were also examined.     

Expanding molecular dynamics simulations to the NMR time scale. I. Studies of conformational interconversions of 1, 1-difluoro-4, 4-dimethylcycloheptane using MM3-MD

A molecular dynamics (MD) simulation of 35,000 picoseconds (ps) has been carried out to study the conformational interconversions of 1,1-difluoro-4,4-dimethylcycloheptane at room temperature using the MM3 force field. The exchange between axial and equatorial fluorine atoms was the only conformational interconversion that occurred, and it took place via the process of pseudorotation. Ring inversions (twist–chair < twist–boat < twist–chair) were not observed. The axial-equatorial exchange of the two fluorine atoms took place five times during the MD trajectory of 35,000 ps. The two CH₃ groups occupied symmetrical positions (exchangeable by a C₂-like rotations, where C₂-like means it would be C₂ if the fluorines were not present) in the MM3 structures, and during most of the time of the MD trajectory. The methyls occasionally moved off the C₂-like axis in the simulated process, mostly because the C₂-like axis was momentarily moved so that it did not pass through the ring atom to which the two CH₃ groups are bonded. A C₂-like symmetry of the twist-chair conformation was maintained approximately during most of the MD simulation. The conformational geometry with the highest energy obtained during the axial-equatorial exchange process was found and used to locate the transition state. The energy barrier for this axial-equatorial exchange was calculated to be 4.7 kcal/mol, and it compares with the value (5.0 kcal/mol) determined by dynamic nuclear magnetic resonance (NMR). © 1994 by John Wiley & Sons, Inc.     

Conformational pathways of saturated six-membered rings. A static and dynamical density functional study

The conformation of the six-membered ring of pyranosyl sugars has pronounced effects on the physical and chemical properties of carbohydrates. We present a method to determine key features of the potential energy surfaces, such as transition states associated with the inversion pathways of the model compounds cyclohexane, tetrahydropyran, p-dioxane, m-dioxane, s-trioxane, and 2-oxanol. Finally, we make the first determination of the pathways for inversion of penta-O-methyl-alpha-D-glucopyranose and penta-O-methyl-beta-D-glucopyranose. For both anomers, a transition state with five coplanar atoms with appreciable (O)E character was found. The method is based on constrained Car-Parrinello ab initio molecular dynamics, as implemented in the projector augmented-wave (PAW) method. The constraints are derived from the normal modes of six-membered rings and are described in terms of the canonical conformations (1)C(4) chair, (1,4)B boat, and (O)S(2) skew-boat. The PAW derived trajectories are in agreement with previous suggestions in the literature that pseudorotation is an important feature of such conformational interconversions. The dynamic nature as well as the internal coordinate-based constraints provide a method which can reliably accommodate pseudorotation. To determine semiquantitative energies, we recalculate key conformations using standard quantum mechanical calculations while keeping the ring dihedral angles frozen at their values found in the dynamics. In all cases where experimental barriers are known, our results are in excellent agreement.     

Conformational behavior of 3-borabicyclo[3.3.1]nonanes: 1. Study of molecular dynamics in 3-methoxy-7α-phenyl-1,5-dimethyl-3-borabicyclo[3.3.1]nonane

3-Methoxy-7α-phenyl-1,5-dimethyl-3-borabicyclo[3.3.1]nonane 5 in solution at room temperature exists in the double chair conformation, as shown by NMR studies. Increasing the temperature leads to an increase in the population of the chair–boat conformation. At decreased temperature hindered rotation around the B---O bond is observed for 5. Dissolving 5 in deuteropyridine leads to the reversible formation of complex 6, which exists in the chair–boat conformation. The chair–boat conformation is also the most stable one for chelate compound 7 with a tetracoordinated boron atom.     

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.     

Conformationally controlled intramolecular charge transfer complexes

Trans-1-acceptor-2-donor-substituted cyclohexanes (1), as well as their 4- (or 5-)methyl-substituted homologues (2), have been prepared and are shown to form intramolecular charge-transfer (donor-acceptor) complexes. These weak complexes are turned on and off by the chair-chair interconversion of the cyclohexane ring. The CT absorptions have been measured and the equilibrium constants for the ring reversal have been determined by UV/vis spectroscopy at 298 K, as well as by NMR spectroscopy at two temperatures: at 183 K, by direct comparison of signals due to the two chair conformations, and at 300 K, by comparison of calculated and measured widths of the alpha-proton signals. The Gibbs free energies assigned to the donor-acceptor interactions range between 0 and -1 kcal mol(-1). A crystal structure of one of the complexes (1b) confirms the intramolecular donor-acceptor alignment and interaction. The regioisomers of the methyl-substituted complexes were characterized by NOE interaction between the methyl and an alpha-proton cis to it.     

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.     

Structure and conformational properties of 1,3,3-trimethyl-1,3-azasilinane: gas electron diffraction, dynamic NMR, and theoretical study

Structure and the conformational properties of 1,3,3-trimethyl-1,3-azasilinane have been studied. According to gas electron diffraction (GED), the molecule exists in a slightly distorted chair conformation with the N-Me group in equatorial position. High-level quantum chemical calculations excellently reproduce the experimental geometry. Employing variable temperature (1)H and (13)C NMR spectroscopy down to 103 K, the conformational equilibrium could be frozen and the barrier to ring inversion determined.     

Computational protocols for prediction of solute NMR relative chemical shifts. a case study of L-tryptophan in aqueous solution

In this study, we have applied two different spanning protocols for obtaining the molecular conformations of L-tryptophan in aqueous solution, namely a molecular dynamics simulation and a molecular mechanics conformational search with subsequent geometry re-optimization of the stable conformers using a quantum mechanically based method. These spanning protocols represent standard ways of obtaining a set of conformations on which NMR calculations may be performed. The results stemming from the solute-solvent configurations extracted from the MD simulation at 300 K are found to be inferior to the results stemming from the conformations extracted from the MM conformational search in terms of replicating an experimental reference as well as in achieving the correct sequence of the NMR relative chemical shifts of L-tryptophan in aqueous solution. We find this to be due to missing conformations visited during the molecular dynamics run as well as inaccuracies in geometrical parameters generated from the classical molecular dynamics simulations.     

Molecular Dynamics of Pectin Extension

Summary: A pectin 10mer under constant pulling speed and constant force was studied using the atomistic simulations. Molecular dynamics (MD) with the Amber99 and Amber-Glycam04 forcefields were performed. The main result of the present Amber-based MD simulations is that the two plateaux of the experimental force- extension dependence for pectin can be explained by transitions between three conformational states of pectin monomer ring (first from a chair (⁴C₁) to boat conformation and second from boat to an inverted chair (¹C₄) conformation). A multi-state dynamical model of single biopolymer extension under external force was elaborated and applied to extension of polymers with three-state monomers relevant to pectin.     

A method for conformational sampling of loops in proteins based on adiabatic decoupling and temperature or force scaling

A method for conformational Boltzmann sampling of loops in proteins in aqueous solution is presented that is based on adiabatic decoupling molecular dynamics (MD) simulation with temperature or force scaling. To illustrate the enhanced sampling, the loop from residues 33 to 43 in the bovine protein ribonuclease A is adiabatically decoupled from the rest of the protein and the solvent with a mass scaling factor s(m) =1000 and the sampling is enhanced with a scaling of the temperature using s(T) =2 or of the force using s(V) =0.667. Over 5 ns of simulation the secondary structure of the protein remains unaltered while a combined dihedral-angle conformational cluster analysis shows an increase of conformations outside the first most populated cluster of loop conformations for adiabatic decoupling MD with temperature scaling using s(T) =2 or force scaling using s(V) =0.667 compared to the standard MD simulation. The atom-positional root-mean-square fluctuations of the C(α) atoms of the loop show an increase in the movement of the loop as well, indicating that adiabatic decoupling MD with upscaling of the temperature or downscaling of the force is a promising method for conformational Boltzmann sampling.     

Nuclear magnetic resonance spectra of psychotherapeutic agents. V*—conformational analysis of 1,3,4,5-tetrahydro-2H-1,5-benzodiazepin-2-ones

The conformational analysis of biologically active lofendazam (7-chloro-5-phenyl-1,3,4,5-tetrahydro-2H-1,5-benzodiazepin-2-one) is carried out by means of lanthanide shift reagent assisted ¹H NMR spectroscopy: the lanthanide induced shift computer simulation suggests that in deuteriochloroform the heterocyclic ring of lofendazam assumes a cycloheptene-like chair conformation, where 1-N moves away from trigonal stereochemistry to a very flattened pyramidal structure. At room temperature the conformational equilibrium is markedly shifted (85%) towards the conformer showing pseudoaxial H-1 and 5-Ph. The remarkable influence of steric requirements in controlling conformation, and the importance of 3- and/or 4-methyl groups in hindering the ring inversion at room temperature, have been verified by conformational analysis of suitable analogous 1,3,4,5-tetraydro-2H-1,5-benzodiazepin-2-ones.     

Investigations into conformational transitions and solvation structure of a 7-piperidino-5,9-methanobenzo[8] annulene in water

Solvation shell structure of a 7-piperidino-5,9-methanobenzo[8] annulene (PMA) in water has been investigated in ambient conditions using both molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) calculations. From the MD calculations, we find that this molecule exists in three major conformational states out of which two are in twist-boat forms and one in chair form. Due to the limited time scale accessible in CPMD simulations, we have studied all the three conformational states separately using CPMD. The molecular geometry, electronic charge distribution and solvation structure for all three forms are investigated. The stability order of the chair and twist-boat conformations in water solvent has been reversed when compared to the gaseous phase results and in the case of polar aprotic solvents (J. Org. Chem., 1999, 61, 5979). From the radial distribution function, we find that the solvent density around the chair form is significantly lower, which has to be directly related to the smaller solvent accessible area for this conformation and this is in complete agreement with earlier reports. Among the findings are that the solvation shell structure around the nitrogen atom in the chair form of PMA is considerably different from the open conformational forms or the twist-boat forms. The dipole moment for the closed form is found to be significantly larger when compared to the twist-boat forms.     

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.     

Convergence and sampling efficiency in replica exchange simulations of peptide folding in explicit solvent

Replica exchange methods (REMs) are increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. However, despite having been shown to be very effective on model systems, the application of REM in complex systems such as for the simulation of protein and peptide folding in explicit solvent has not been objectively tested in detail. Here we present a comparison of conventional MD and temperature replica exchange MD (T-REMD) simulations of a beta-heptapeptide in explicit solvent. This system has previously been shown to undergo reversible folding on the time scales accessible to MD simulation and thus allows a direct one-to-one comparison of efficiency. The primary properties compared are the free energy of folding and the relative populations of different conformers as a function of temperature. It is found that to achieve a similar degree of precision T-REMD simulations starting from a random set of initial configurations were approximately an order of magnitude more computationally efficient than a single 800 ns conventional MD simulation for this system at the lowest temperature investigated (275 K). However, whereas it was found that T-REMD simulations are more than four times more efficient than multiple independent MD simulations at one temperature (300 K) the actual increase in conformation sampling was only twofold. The overall gain in efficiency using REMD resulted primarily from the ordering of different conformational states over temperature, as opposed to a large increase of conformational sampling. It is also shown that in this system exchanges are accepted primarily based on (random) fluctuations within the solvent and are not strongly correlated with the instantaneous peptide conformation raising questions in regard to the efficiency of T-REMD in larger systems.     

Stereochemistry of sesquiterpenes of the germacrane type

An analysis has been made of the conformations of the 10-membered ring in the known sesquiterpene E,E-germacranes and a relationship has been established between the realization of one of the four conformers and the positions and orientations of substituents in the 10-membered ring. A relationship is presented between the conformational states of the germacrolides and the structures of their bicyclic derivatives — guaianes and eudesmanes.Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 497–506, July–August, 1997.     

Spatial structure of 5-phenyl-5-oxo-2,4,6-triisopropyl-1,3,5-dioxa phosphorinane

Conclusions By means of x-ray structure analysis, it has been shown that the stereoisomer of 5-phenyl-5-oxo-2,4,6-triisopropyl-1,3,5-dioxaphosphorinane with mp 215°C has the chair conformation with all equatorial substituents of the ring atoms and axial substituents of the phosphoryl group. The conformations of the isopropyl groups are retarded relative to the ring bonds. The benzene ring at the P atom is perpendicular to the plane of the heterocycle.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No.3, pp. 599–603, March, 1982.     

The Conformation of Cycloartenol Investigated by NMR and Molecular Mechanics

Cycloartenol ( 4 ), a natural plant sterol, was shown to be an effective membrane reinforcer; this was attributed to its conformation. We now present a conformational analysis of 4 by molecular modeling and NMR. Molecular modeling suggests that two conformations I and II coexist, differing mainly at the level of ring C, and of nearly equal energy, I and II each having ring A and B in a chair and half-chair conformation, respectively, with ring C 1,3-diplanar in I (solid-state structure as determined by X-ray crystallography) and in chair conformation in II . A complete assignment of the ¹H- and ¹³C-NMR spectra of 4 and the entire coupling network in rings A and B is determined by various modern NMR techniques. The conformation of rings A and B thus determined is in agreement with conformations I and II . Low-temperature NMR experiments show a fast equilibrium between two conformations, presumably I and II . It is concluded, therefore, that the cyclopropane ring of 4 produces a flexibility at the level of ring C which may be important for the membrane properties.