Conformational transitions of glycine induced by vibrational excitation of the O-H stretch

Vibrational energy flow and conformational transitions following excitation of the OH stretching mode of the most stable conformer of glycine are studied by classical trajectories. "On the fly" simulations with the PM3 semiempirical electronic structure method for the potential surface are used. Initial conditions are selected to correspond to the ν=1 excitation of the OH stretch. The main findings are: (1) An an equilibrium-like ratio is established between the populations of the 3 lowest-lying conformers after about 10 picoseconds. (2) There is a high probability throughout the 150 ps of the simulations for finding the molecule in geometries far from the equilibrium structures of the lowest-energy conformers. (3) Energy from the initial excited OH (ν=1) stretch flows preferentially to 5 other vibrational modes, including the bending motion of the H atom. (4) RRK theory yields conformational transition rates that deviate substantially from the classical trajectory results. Possible implication of these results for vibrational energy flow and conformational transitions in small biological molecules are discussed.     

Conformational and electronic properties of a microperoxidase in aqueous solution: a computational study.

A theoretical study of the conformational properties of a small heme peptide in aqueous solution is carried out by classical, long-timescale molecular dynamics simulations. The electronic properties of this species, that is, the relative energies of its excited electronic states and the redox potential, are reproduced and related to the conformational behavior using the perturbed matrix method and basic statistical mechanics. Our results show an interesting coupling between the conformational transitions and the electronic properties. These investigations, beyond the biophysically relevant results addressing the long-standing question of the actual role of the enzyme structure on the enzyme activity, are also of some methodological interest since they offer a further computational perspective for including the electronic degrees of freedom into the modeling of rather complex molecular systems.     

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.     

Different chemical dynamics for different conformers of biological molecules: photoionization of glycine

Single-photon ionization dynamics of two conformers of glycine is studied by classical trajectory simulations using the semiempirical PM3 potential surface in "on the fly" calculations. Initial conditions for the trajectories are weighted according to the Wigner distribution function computed for the initial vibrational ground state. Vertical ionization in the spirit of the classical Franck-Condon principle is assumed. The dynamics of the two conformers are compared during the first 10 ps. The comparison shows very different dynamical behavior for the two conformers. In particular, the chemical fragmentation pathways differ in part. Also, one of the conformers gives much higher rates of conformational transitions, while the other conformer gives larger chemical fragmentation yields. The example shows significantly different chemical dynamics for two conformers close in energy and separated by a low barrier.     

Dominant folding pathways of a peptide chain from ab initio quantum-mechanical simulations

Using the dominant reaction pathways method, we perform an ab initio quantum-mechanical simulation of a conformational transition of a peptide chain. The method we propose makes it possible to investigate the out-of-equilibrium dynamics of these systems, without resorting to an empirical representation of the molecular force field. It also allows to study rare transitions involving rearrangements in the electronic structure. By comparing the results of the ab initio simulation with those obtained by employing a standard force field, we discuss its capability to describe the nonequilibrium dynamics of conformational transitions.     

The role of the torsional potential in relaxation dynamics: a molecular dynamics study of polyethylene

The role of the torsional potential in bulk polymer chain dynamics is investigated via molecular dynamics simulation using polyethylene as a model system. A number of three-fold barrier values, both greater and less than the standard one, were invoked. The one-fold potential that determines the gauche vs trans energy difference was also varied. For each of the selected torsional potentials, the MD volumetric glass transition temperature, T_g, was located. It was found that T_g is quite sensitive to the three-fold barrier magnitude, moving from below 100 K to nearly 400 K as the barrier goes from zero to twice the standard value. However T_g was found to be quite insensitive to the gauche trans energy difference. Details of the conformational dynamics were studied for the case of a zero torsional potential. This included the rate and location of conformational transitions, the decay of the torsional angle autocorrelation function (ACF) and the cooperativity of conformational transitions, all as a function of temperature. The temperature dependence of the conformational transition rate remains Arrhenius at all temperatures. The relaxation time characterizing the torsional angle ACF decay exhibits WLF temperature behavior. The conformational transitions are randomly distributed over the bonds at high temperature, but near T_g they become spatially heterogeneous and localized. The transitions show next-neighbor correlation as well as self-correlated forward-backward transitions. All of these features are similar to those found in previous simulations under the standard torsional potential.     

Evaporation of Lennard-Jones clusters

Extensive molecular dynamics simulations have been done to study the evaporation of a 13-atom Lennard-Jones cluster. The survival probability and the evaporative lifetime are calculated as a function of the cluster total energy from a classical trajectory analysis. The results are interpreted in terms of the RRK theory of unimolecular dissociation. The calculation of the binding energy of the evaporated species from the evaporation rate and the average kinetic energy release is discussed.     

A possible effect of quantum characteristics of vibrational dynamics on the conformational dynamics in polymers

Dielectric losses in poly(vinyl acetate) and poly(ethyleneterephthalate) polar polymers are measured in wide ranges of frequencies and temperatures. The temperature dependences of the frequency of activation transitions of two types, small-scale and conformational, are derived. For conformational transitions, it is revealed that the temperature dependence of their frequency exhibits nonlinear behavior (in Arrhenius coordinates); it determines the temperature dependence of barriers to transitions and the defreezing temperature of conformational dynamics (∼300 K for poly(vinyl acetate) and ∼370 K for poly(ethyleneterephthalate)). This temperature is found to be close to the temperatures of the quantum defreezing of the molecular dynamics of poly(vinyl acetate) and poly(ethyleneterephthalate) (∼300 and 400 K) according to IR spectroscopy data. It is assumed that a decrease in the barrier to the conformational transitions that provide defreezing of the conformational dynamics is caused by a decrease that occurs in the rigidity of polymer molecules owing to quantum defreezing of the vibrational molecular dynamics of the polymers.     

Extending molecular dynamics time scales with milestoning: example of complex kinetics in a solvated peptide

A recently introduced computational algorithm to extend time scales of atomically detailed simulations is illustrated. The algorithm, milestoning, is based on partitioning the dynamics to a sequence of trajectories between "milestones" and constructing a non-Markovian model for the motion along a reaction coordinate. The kinetics of a conformational transition in a blocked alanine is computed and shown to be accurate, more efficient than straightforward molecular dynamics by a factor of about 9, and nonexponential. A general scaling argument predicts a linear speedup with the number of milestones for diffusive processes and an exponential speedup for transitions over barriers. The algorithm is also trivial to parallelize. As a side result, milestoning also produces the free energy profile along the reaction coordinate and is able to describe nonequilibrium motions along one (or a few) degrees of freedom.     

Ant colony optimization for predicting RNA folding pathways

RNA folding dynamics plays important roles in various functions of RNAs. To date, coarse-grained modeling has been successfully employed to simulate RNA folding dynamics on the energy landscape composed of secondary structures. In such a modeling, the energy barrier height between metastable structures is a key parameter that crucially affects the simulation results. Although a number of approaches ranging from the exact method to heuristic ones are available to predict the barrier heights, developing an efficient heuristic for this purpose is still an algorithmic challenge.We developed a novel RNA folding pathway prediction method, ACOfoldpath, based on Ant Colony Optimization (ACO). ACO is a widely used powerful combinatorial optimization algorithm inspired from the food-seeking behavior of ants. In ACOfoldpath, to accelerate the folding pathway prediction, we reduce the search space by utilizing originally devised structure generation rules. To evaluate the performance of the proposed method, we benchmarked ACOfoldpath on the known nineteen conformational RNA switches. As a result, ACOfoldpath successfully predicted folding pathways better than or comparable to the previous heuristics. The results of RNA folding dynamics simulations and pseudoknotted pathway predictions are also presented.     

Single molecule conformational dynamics of adenylate kinase: energy landscape, structural correlations, and transition state ensembles

We developed a coarse grained two-well model to study the single molecule protein conformational dynamics in microscopic detail at the residue level, overcoming the often encountered computational bottleneck. In particular, we explored the underlying conformational energy landscape of adenylate kinase, a crucial protein for signal transduction in the cell, and identified two major kinetic pathways for the conformational switch between open and closed states through either the intermediate state or the transient state. Based on the parameters fitted to the room-temperature experimental data, we predicted open and closed kinetic rates at the whole temperature ranges from 10 to 50 degrees C, which agree well with the experimental turnover numbers. After uncovering the underlying mechanism for conformational dynamics and exploring the structural correlations, we found the crucial dynamical interplay between the nucleoside monophosphate binding domain (NMP) and the ATP-binding domain (LID) in controlling the conformational switch. The key residues and contacts responsible for the conformational transitions are identified by following the time evolution of the two-dimensional spatial contact maps and characterizing the transition state as well as intermediate structure ensembles through phi value analysis. Our model provides a general framework to study the conformational dynamics of biomolecules and can be applied to many other systems.     

Conformational evolution of ubiquitin ions in electrospray mass spectrometry: molecular dynamics simulations at gradually increasing temperatures

Evidence from cross section data indicates that ubiquitin +13 ions lose their secondary and tertiary structure in mass spectrometric experiments. These transitions from the folded state into the near linear final structure occur at the experimental temperatures on time scales that are far too long for conventional molecular dynamics simulations. In this study, an approach to mass spectrometric unfolding processes is developed and a detailed application to an ubiquitin +13 ion system is presented. The approach involves a sequence of molecular dynamics simulations at gradually increasing temperatures leading to identification of major intermediate states, and the unfolding pathway. The unfolding rate at any temperature can then be calculated by a Rice-Ramsperger-Kassel (RRK) approach. For ubiquitin +13, three interesting intermediate states were found and the final near linear geometry was computed. The several relevant energy barriers calculated for the process are in the range of 7 to 15 kcal mol(-1). The unfolding time scale at 300 K was computed to be 2 ms. Cross section calculations using a hard sphere scattering model were carried out for the final structure and found to be in good accord with the results of electrospray experiments supporting the theoretical model used. The approach employed here should be applicable to any other solvent-free protein system.     

Sparsity‐weighted outlier FLOODing (OFLOOD) method: Efficient rare event sampling method using sparsity of distribution

As an extension of the Outlier FLOODing (OFLOOD) method [Harada et al., J. Comput. Chem. 2015, 36, 763], the sparsity of the outliers defined by a hierarchical clustering algorithm, FlexDice, was considered to achieve an efficient conformational search as sparsity‐weighted “OFLOOD.” In OFLOOD, FlexDice detects areas of sparse distribution as outliers. The outliers are regarded as candidates that have high potential to promote conformational transitions and are employed as initial structures for conformational resampling by restarting molecular dynamics simulations. When detecting outliers, FlexDice defines a rank in the hierarchy for each outlier, which relates to sparsity in the distribution. In this study, we define a lower rank (first ranked), a medium rank (second ranked), and the highest rank (third ranked) outliers, respectively. For instance, the first‐ranked outliers are located in a given conformational space away from the clusters (highly sparse distribution), whereas those with the third‐ranked outliers are nearby the clusters (a moderately sparse distribution). To achieve the conformational search efficiently, resampling from the outliers with a given rank is performed. As demonstrations, this method was applied to several model systems: Alanine dipeptide, Met‐enkephalin, Trp‐cage, T4 lysozyme, and glutamine binding protein. In each demonstration, the present method successfully reproduced transitions among metastable states. In particular, the first‐ranked OFLOOD highly accelerated the exploration of conformational space by expanding the edges. In contrast, the third‐ranked OFLOOD reproduced local transitions among neighboring metastable states intensively. For quantitatively evaluations of sampled snapshots, free energy calculations were performed with a combination of umbrella samplings, providing rigorous landscapes of the biomolecules. © 2015 Wiley Periodicals, Inc.     

Parametric models to compute tryptophan fluorescence wavelengths from classical protein simulations

Fluorescence spectroscopy is an important method to study protein conformational dynamics and solvation structures. Tryptophan (Trp) residues are the most important and practical intrinsic probes for protein fluorescence due to the variability of their fluorescence wavelengths: Trp residues emit in wavelengths ranging from 308 to 360 nm depending on the local molecular environment. Fluorescence involves electronic transitions, thus its computational modeling is a challenging task. We show that it is possible to predict the wavelength of emission of a Trp residue from classical molecular dynamics simulations by computing the solvent‐accessible surface area or the electrostatic interaction between the indole group and the rest of the system. Linear parametric models are obtained to predict the maximum emission wavelengths with standard errors of the order 5 nm. In a set of 19 proteins with emission wavelengths ranging from 308 to 352 nm, the best model predicts the maximum wavelength of emission with a standard error of 4.89 nm and a quadratic Pearson correlation coefficient of 0.81. These models can be used for the interpretation of fluorescence spectra of proteins with multiple Trp residues, or for which local Trp environmental variability exists and can be probed by classical molecular dynamics simulations. © 2018 Wiley Periodicals, Inc.     

Hybrid quantum/classical path integral approach for simulation of hydrogen transfer reactions in enzymes

A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.     

How do rotameric conformations influence the time-resolved fluorescence of tryptophan in proteins? A perspective based on molecular modeling and quantum chemistry

We discuss the dynamics of tryptophan rotamers in the context of the non-exponential fluorescence decay in proteins. The central question is: how does the ground-state conformational heterogeneity influence the time evolution of tryptophan fluorescence? This problem is examined here from the theoretical perspective. Three methods at different levels of theory, and with different scopes and computational requirements are reviewed. The Dead-end elimination method is limited to side-chain dynamics and provides an efficient way to detect the stable tryptophan rotamers in a protein. Its application to the study of heterogeneous emission characteristics is illustrated. Molecular dynamics is aimed at the full phase space of the macromolecule in solution, but must rely on classical force fields and laws of evolution. We examine to what extent the molecular mechanics paradigm yields sufficiently accurate thermodynamic results, and what are the possible kinetic implications. Finally Quantum Chemistry is the only theoretical method that allows a direct assessment of the excited states. It is necessarily restricted to small molecular systems, and thus must be used in a hybrid combination with classical methods and electrostatic models. So far understanding of the emitting state has greatly progressed as a result of these calculations, but the actual treatment of the photophysical decay processes at the quantum level has not yet really started.     

Protein folding pathways extracted by OFLOOD: Outlier FLOODing method

The Outlier FLOODing method (OFLOOD) is proposed as an efficient conformational sampling method to extract biologically rare events such as protein folding. In OFLOOD, sparse distributions (outliers in the conformational space) were regarded as relevant states for the transitions. Then, the transitions were enhanced through conformational resampling from the outliers. This evidence indicates that the conformational resampling of the sparse distributions might increase chances for promoting the transitions from the outliers to other meta‐stable states, which resembles a conformational flooding from the outliers to the neighboring clusters. OFLOOD consists of (i) detections of outliers from conformational distributions and (ii) conformational resampling from the outliers by molecular dynamics (MD) simulations. Cycles of (i) and (ii) are simply repeated. As demonstrations, OFLOOD was applied to folding of Chignolin and HP35. In both cases, OFLOOD automatically extracted folding pathways from unfolded structures with ns‐order computational costs, although µs‐order canonical MD failed to extract them. © 2014 Wiley Periodicals, Inc.     

Simulation of conformational transitions by the restricted perturbation-targeted molecular dynamics method

A method for the simulation of conformational transitions is presented. The method, based on targeted molecular dynamics (TMD), limits the conformational change at each molecular dynamics step to a fixed size, that minimizes the root mean square deviation from the target. The method is more efficient than standard TMD and yields lower energy pathways, but, like the TMD method, requires only a single molecular dynamics simulation. Test calculations and comparisons with standard TMD calculations for the alanine dipeptide with the analytic continuum electrostatics implicit solvent model are presented.     

Protein structure predictions by parallel simulated annealing molecular dynamics using genetic crossover

We propose a conformational search method to find a global minimum energy structure for protein systems. The simulated annealing is a powerful method for local conformational search. On the other hand, the genetic crossover can search the global conformational space. Our method incorporates these attractive features of the simulated annealing and genetic crossover. In the previous works, we have been using the Monte Carlo algorithm for simulated annealing. In the present work, we use the molecular dynamics algorithm instead. To examine the effectiveness of our method, we compared our results with those of the normal simulated annealing molecular dynamics simulations by using an α-helical miniprotein. We used genetic two-point crossover here. The conformations, which have lower energy than those obtained from the conventional simulated annealing, were obtained.