Computer simulation to investigate the FRET application in DNA hybridization systems

Molecular dynamics (MD) and quantum mechanics (QM) were used to investigate fluorescence resonance energy transfer (FRET) between coumarin and ethidium in two Mergny's DNA hybridization systems. By combining the transition dipoles calculated by the quantum semi-empirical method and the conformations of the FRET probes collected by MD, FRET efficiencies were derived from the F?rster equation at five temperatures from 273 K to 313 K. The plotted efficiencies were compared with Mergny's experiments, and showed good agreement. The simulated orientation factor and isotropically averaged orientation factor were compared, and the results demonstrated that the assumption of isotropic orientations is invalid when FRET probes are close to each other. The first order kinetic assumptions were also used to calculate the transfer efficiencies, and the results show that this D-A FRET process approximates the first order kinetic reactions.     

Hybrid molecular dynamics-quantum mechanics simulations of solute spectral properties in the condensed phase: evaluation of simulation parameters

We have explored the impact of a number of basic simulation parameters on the results of a recently developed hybrid molecular dynamics-quantum mechanics (MD-QM) method (Mercer et al., J Phys Chem B 1999, 103, 7720). The method utilizes MD simulations to explore the ground-state configuration space of the system and QM evaluation of those structures to yield the time-dependent electronic transition energy, which is transformed into the optical line-broadening function using the second-order cumulant expansion. Both linear and nonlinear optical spectra can then be generated for comparison to experiment. The dependence of the resulting spectra on the length of the MD trajectory, the QM sampling rate, and the QM model chemistry have all been examined. In particular, for the system of oxazine-4 in methanol studied here, at least 20 ps of MD trajectory are needed for qualitative convergence of linear spectral properties, and >100 ps is needed for quantitative convergence. Surprisingly, little difference is found between the 3-21G and 6-31G(d) basis sets, and the CIS and TD-B3LYP methods yield remarkably similar spectra. The semiempirical INDO/s method yields the most accurate results, reproducing the experimental Stokes shift to within 5% and the FWHM to within 20%. Nonlinear 3-pulse photon echo peak shift (3PEPS) decays have also been simulated. Decays are generally poorly reproduced, though the initial peak shift which depends on the overall coupling of motions to the solute transition energy is within 15% of experiment for all model chemistries other than those using the STO-3G basis.     

Calculations of the exciton coupling elements between the DNA bases using the transition density cube method

Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases.     

Probability distributions of molecular observables computed from Markov models

Molecular dynamics (MD) simulations can be used to estimate transition rates between conformational substates of the simulated molecule. Such an estimation is associated with statistical uncertainty, which depends on the number of observed transitions. In turn, it induces uncertainties in any property computed from the simulation, such as free energy differences or the time scales involved in the system's kinetics. Assessing these uncertainties is essential for testing the reliability of a given observation and also to plan further simulations in such a way that the most serious uncertainties will be reduced with minimal effort. Here, a rigorous statistical method is proposed to approximate the complete statistical distribution of any observable of an MD simulation provided that one can identify conformational substates such that the transition process between them may be modeled with a memoryless jump process, i.e., Markov or Master equation dynamics. The method is based on sampling the statistical distribution of Markov transition matrices that is induced by the observed transition events. It allows physically meaningful constraints to be included, such as sampling only matrices that fulfill detailed balance, or matrices that produce a predefined equilibrium distribution of states. The method is illustrated on mus MD simulations of a hexapeptide for which the distributions and uncertainties of the free energy differences between conformations, the transition matrix elements, and the transition matrix eigenvalues are estimated. It is found that both constraints, detailed balance and predefined equilibrium distribution, can significantly reduce the uncertainty of some observables.     

IR spectra of N-methylacetamide in water predicted by combined quantum mechanical/molecular mechanical molecular dynamics simulations

We applied the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulation method in assessing IR spectra of N-methylacetamide and its deuterated form in aqueous solutions. The model peptide is treated at the Austin Model 1 (AM1) level and the induced dipole effects by the solvent are incorporated in fluctuating solute dipole moments, which are calculated using partial charges from Mulliken population analyses without resorting to any available high-level ab initio dipole moment data. Fourier transform of the solute dipole autocorrelation function produces in silico IR spectra, in which the relative peak intensities and bandwidths of major amide bands are quantitatively compatible with experimental results only when both geometric and electronic polarizations of the peptide by the solvent are dealt with at the same quantum-mechanical level. We cast light on the importance of addressing dynamic charge fluctuations of the solute in calculating IR spectra by comparing classical and QM/MM MD simulation results. We propose the adjustable scaling factors for each amide mode to be directly compared with experimental data.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

Adiabatic states derived from a spin-coupled diabatic transformation: semiclassical trajectory study of photodissociation of HBr and the construction of potential curves for LiBr+

The development of spin-coupled diabatic representations for theoretical semiclassical treatments of photodissociation dynamics is an important practical goal, and some of the assumptions required to carry this out may be validated by applications to simple systems. With this objective, we report here a study of the photodissociation dynamics of the prototypical HBr system using semiclassical trajectory methods. The valence (spin-free) potential energy curves and the permanent and transition dipole moments were computed using high-level ab initio methods and were transformed to a spin-coupled diabatic representation. The spin-orbit coupling used in the transformation was taken as that of atomic bromine at all internuclear distances. Adiabatic potential energy curves, nonadiabatic couplings and transition dipole moments were then obtained from the diabatic ones and were used in all the dynamics calculations. Nonadiabatic photodissociation probabilities were computed using three semiclassical trajectory methods, namely, coherent switching with decay of mixing (CSDM), fewest switches with time uncertainty (FSTU), and its recently developed variant with stochastic decoherence (FTSU/SD), each combined with semiclassical sampling of the initial vibrational state. The calculated branching fraction to the higher fine-structure level of the bromine atom is in good agreement with experiment and with more complete theoretical treatments. The present study, by comparing our new calculations to wave packet calculations with distance-dependent ab initio spin-orbit coupling, validates the semiclassical trajectory methods, the semiclassical initial state sample scheme, and the use of a distance-independent spin-orbit coupling for future applications to polyatomic photodissociation. Finally, using LiBr(+) as a model system, it is shown that accurate spin-coupled potential curves can also be constructed for odd-electron systems using the same strategy as for HBr.     

Selective sampling of transition paths

In this short paper, we introduce an approximate method for the quick estimate of rate constants based on a simple sampling method of reactive transition paths over high energy barriers. It makes use of the previously introduced accelerated molecular dynamics (MD) simulation method to generate initial points for trajectory shooting. The accelerated MD simulations, although with the loss of real dynamics, lead to a quick calculation of thermodynamic properties and at the same time produce an ensemble of configurations with an enhanced sampling over the phase space that is more "reactive." The forward/backward trajectory shooting as that used in the transition path sampling method is then initiated from the configurations obtained from accelerated MD simulations to generate transition paths on the original unbiased potential. This method selectively enhances sampling of successful trajectories and at the same time accelerates significantly the calculation of rate constants.     

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.     

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

Fluorescence spectra of organic dyes in solution: a time dependent multilevel approach

Classical all-atom molecular dynamics (MD) simulations and quantum mechanical (QM) time-dependent density functional theory (TD-DFT) calculations are employed to study the conformational and photophysical properties of the first emitter excited state of tetramethyl-rhodamine iso-thiocyanate fluorophore in aqueous solution. For this purpose, a specific and accurate force field has been parameterised from QM data to model the fluorophore's first bright excited state. During the MD simulations, the consequences of the π→π* electronic transition on the structure and microsolvation sphere of the dye has been analysed in some detail and compared to the ground state behaviour. Thereafter, fluorescence has been calculated at the TD-DFT level on configurations sampled from the simulated MD trajectories, allowing us to include time dependent solvent effects in the computed emission spectrum. The latter, when compared with the absorption spectrum, reproduces well the experimental Stokes shift, further validating the proposed multilevel computational procedure.     

Geometry optimization based on linear response free energy with quantum mechanical/molecular mechanical method: applications to Menshutkin-type and Claisen rearrangement reactions in aqueous solution

The authors present a method based on a linear response theory that allows one to optimize the geometries of quantum mechanical/molecular mechanical (QM/MM) systems on the free energy surfaces. Two different forms of linear response free energy functionals are introduced, and electronic wave functions of the QM region, as well as the responses of electrostatic and Lennard-Jones potentials between QM and MM regions, are self-consistently determined. The covariant matrix relating the QM charge distribution to the MM response is evaluated by molecular dynamics (MD) simulation of the MM system. The free energy gradients with respect to the QM atomic coordinates are also calculated using the MD trajectory results. They apply the present method to calculate the free energy profiles of Menshutkin-type reaction of NH3 with CH3Cl and Claisen rearrangement of allyl vinyl ether in aqueous solution. For the Menshutkin reaction, the free energy profile calculated with the modified linear response free energy functional is in good agreement with that by the free energy perturbation calculations. They examine the nonequilibrium solvation effect on the transmission coefficient and the kinetic isotope effect for the Claisen rearrangement.     

Comparison of radii sets,entropy, QM methods,and sampling on MM‐PBSA,MM‐GBSA,and QM/MM‐GBSA ligand binding energies of F. tularensis enoyl‐ACP reductase (FabI)

To validate a method for predicting the binding affinities of FabI inhibitors, three implicit solvent methods, MM‐PBSA, MM‐GBSA, and QM/MM‐GBSA were carefully compared using 16 benzimidazole inhibitors in complex with Francisella tularensis FabI. The data suggests that the prediction results are sensitive to radii sets, GB methods, QM Hamiltonians, sampling protocols, and simulation length, if only one simulation trajectory is used for each ligand. In this case, QM/MM‐GBSA using 6 ns MD simulation trajectories together with GB^neck2, PM3, and the mbondi2 radii set, generate the closest agreement with experimental values (r² = 0.88). However, if the three implicit solvent methods are averaged from six 1 ns MD simulations for each ligand (called “multiple independent sampling”), the prediction results are relatively insensitive to all the tested parameters. Moreover, MM/GBSA together with GB^HCT and mbondi, using 600 frames extracted evenly from six 0.25 ns MD simulations, can also provide accurate prediction to experimental values (r² = 0.84). Therefore, the multiple independent sampling method can be more efficient than a single, long simulation method. Since future scaffold expansions may significantly change the benzimidazole's physiochemical properties (charges, etc.) and possibly binding modes, which may affect the sensitivities of various parameters, the relatively insensitive “multiple independent sampling method” may avoid the need of an entirely new validation study. Moreover, due to large fluctuating entropy values, (QM/)MM‐P(G)BSA were limited to inhibitors’ relative affinity prediction, but not the absolute affinity. The developed protocol will support an ongoing benzimidazole lead optimization program. © 2015 Wiley Periodicals, Inc.     

Generation of initial trajectories for transition path sampling of chemical reactions with ab initio molecular dynamics

Transition path sampling is an innovative method for focusing a molecular dynamics simulation on a reactive event. Although transition path sampling methods can generate an ensemble of reactive trajectories, an initial reactive trajectory must be generated by some other means. In this paper, the authors have evaluated three methods for generating initial reactive trajectories for transition path sampling with ab initio molecular dynamics. The authors have tested each of these methods on a set of chemical reactions involving the breaking and making of covalent bonds: the 1,2-hydrogen elimination in the borane-ammonia adduct, a tautomerization, and the Claisen rearrangement. The first method is to initiate trajectories from the potential energy transition state, which was effective for all reactions in the test set. Assigning atomic velocities found using normal mode analysis greatly improved the success of this method. The second method uses a high temperature molecular dynamics simulation and then iteratively reduces the total energy of the simulation until a low temperature reactive trajectory is found. This was effective in generating a low temperature trajectory from an initial trajectory run at 3000 K of the tautomerization reaction, although it failed for the other two. The third uses an orbital based bias potential to find a reactive trajectory and uses this trajectory to initiate an unbiased trajectory. The authors found that a highest occupied molecular orbital-lowest unoccupied molecular orbital bias could be used to find a reactive trajectory for the Claisen rearrangement, although it failed for the other two reactions. These techniques will help make it practical to use transition path sampling to study chemical reaction mechanisms that involve bond breaking and forming.     

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.     

The coupling constant polarizability and hyperpolarizabilty of 1J(NH) in N-methylacetamide, and its application for the multipole spin-spin coupling constant polarizability/reaction field approach to solvation

We present a benchmark study of a combined multipole spin-spin coupling constant (SSCC) polarizability/reaction field (MJP/RF) approach to the calculation of both specific and bulk solvation effects on SSCCs of solvated molecules. The MJP/RF scheme is defined by an expansion of the SSCCs of the solvated molecule in terms of coupling constant dipole and quadrupole polarizabilities and hyperpolarizabilities derived from single molecule ab initio calculations. The solvent electric field and electric field gradient are calculated based on data derived from molecular dynamics (MD) simulations thereby accounting for solute-solvent dynamical effects. The MJP/RF method is benchmarked against polarizable QM/MM calculations for the one-bond N-H coupling constant in N-methylacetamide. The best agreement between the MJP/RF and QM/MM approaches is found by truncating the electric field expansion in the MJP/RF approach at the linear electric field level. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the ab initio calculations of the coupling constant (hyper-)polarizabilities and find that they are affected by the basis set in a way similar to the coupling constants themselves.     

离子液体的量化计算及分子动力学模拟研究进展

离子液体是由有机阳离子和无机/有机阴离子构成的盐类,一般在室温或接近于室温下呈液态,因此常被称为室温离子液体(RTIL).依据不同的划分标准,离子液体有多种分类方式:根据年代的不同可将离子液体分为第一代、第二代及第三代离子液体,例如:烷基咪唑和烷基吡啶的金属卤化物盐等[1];根据阳离子的不同可将离子液体分为季鏻