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The structure, dynamics, and thermal stability of the structurally similar 14-mer RNA hairpins uCACGg and cUUCGg are studied by using replica-exchange molecular dynamics simulations. The two RNA hairpins exhibited similar structures at room temperature, but the UUCG loop was found to be more flexible than the CACG loop.

Adopting trialanine as a paradigm of a small peptide, a comprehensive comparison of six popular force fields is presented, including the recent versions of AMBER, CHARMM, GROMOS, and OPLS models. For all force fields under consideration a 20ns long MD simulation is performed to study in detail the structure and conformational dynamics of the solvated peptide.

The fluorescence and resonance Raman emission of molecular systems undergoing ultrafast nonadiabatic isomerization is discussed. The validity of the approximation is studied by employing a two-mode, two-state model of photoisomerization of retinal.

A technique for the photoisomerization of retinal rhodopsin using a vibronically coupled electronic two-state system is described.

The time-resolved femtosecond spectroscopy in conjunction with nonequilibrium molecular dynamics (MD) simulations was used to study the energy transport in a short helical peptide in chloroform solution. A simple harmonic model of heat transport adopted on the bases of results showed that the heat diffusivity decreased significantly at temperatures initially reached by high-energy excitation.

The [phis], [psi] backbone angle distribution of small homopolymeric model peptides are examined by a joint molecular dynamics (MD) simulation and heteronuclear NMR study. It is found that the alanine peptides [Ala.sub.n] exhibit the same conformational distribution.

The calculation of transient absorption spectra of cis-trans photoreactive system in the condensed phase is described theoretically. The formulation consists of a multidimensional model of nonadiabatic photoisomerization, a Redfield treatment of the environment within the secular approximation, and a doorway-window formulation to calculate transient pump-probe spectra.

A method for site-directed spin labeling of oligonucleotides with TPA and a precise 4-pulse electron double resonance (PELDOR) based nanometer distance ruler, in the range from 19 to 53 A for folded DNA/RNA in aqueous buffer solution, is presented.

The classical periodic orbits of an electron-transfer system are studied. Femtosecond time-resolved experiments on chemical and biophysical electron-transfer systems are conducted for this purpose and it is demonstrated that transient oscillations observed in electron-transfer femtosecond experiments may be explained in terms of a few classical trajectories.

The conformational structure and dynamics of trialanine in water are studied with the help of a molecular dynamics (MD) study. The MD study reveals that the conformational structures and dynamics show good overall agreement with experimental data.

Adopting extensive molecular dynamicssimulations of villin headpieceprotein (HP35) by Shaw and co-workers, a detailed theoretical analysisof the folding of HP35 is presented. The approach is based on therecently proposed most probable pathalgorithm whichidentifies the metastable states of the system, combined with dynamicalcoring of these states in order to obtain a consistent Markov statemodel. The method facilitates the construction of a dendrogram associatedwith the folding free-energy landscape of HP35, which reveals a hierarchicalfunnel structure and shows that the native state is rather a kinetictrap than a network hub. The energy landscape of HP35 consists ofthe entropic unfolded basin U, where the prestructuringof the protein takes place, the intermediate basin I, which is connected to Uvia the rate-limiting U→ Itransition state reflectingthe formation of helix-1, and the native basin N,containing a state close to the NMR structure and a native-like statethat exhibits enhanced fluctuations of helix-3. The model is in linewith recent experimental observations that the intermediate and nativestates differ mostly in their dynamics (locked vs unlocked states).Employing dihedral angle principal component analysis, subdiffusivemotion on a multidimensional free-energy surface is found. [ABSTRACT FROM AUTHOR]

Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled, nonequilibrium processes can be associated with a biased energy landscape, which accounts for finite sampling effects and external driving. When the data-driven Langevin equation (dLE) approach [ Phys . Rev . Lett . 2015 , 115 , 050602] is extended to the modeling of nonequilibrium processes, an efficient way to calculate multidimensional Langevin fields is outlined. The dLE is shown to correctly account for various nonequilibrium processes, including the enforced dissociation of sodium chloride in water, the pressure-jump induced nucleation of a liquid of hard spheres, and the conformational dynamics of a helical peptide sampled from nonstationary short trajectories.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

As standard unbiased molecular dynamics (MD) simulations become impractical for sampling rare events, "targeted MD" employs a moving distance constraint to enforce rare transitions along some reaction coordinate x. To calculate free energy profiles from these nonequilibrium simulations via Δ G( x) = W( x) - W diss ( x), apart from the (readily obtained) work W( x) performed on the system, the dissipated work W diss ( x) is also required. By employing a second-order cumulant expansion of Jarzynski's equality combined with an analysis within Langevin theory, the dissipated work can be expressed via a nonequilibrium friction coefficient Γ NEQ ( x) that may be calculated on-the-fly from constraint force fluctuations. Adopting the ion dissociation of NaCl in water as a test system, this friction correction is shown to result in accurate free energy profiles, even for a modest number of simulations and at high constraint velocities. As a bonus, the analysis of Γ NEQ ( x) may yield valuable insight into the microscopic mechanism of friction.

We present a systematic approach to reduce the dimensionality of a complex molecular system. Starting with a data set of molecular coordinates (obtained from experiment or simulation) and an associated set of metastable conformational states (obtained from clustering the data), a supervised machine learning model is trained to assign unknown molecular structures to the set of metastable states. In this way, the model learns to determine the features of the molecular coordinates that are most important to discriminate the states. Using a new algorithm that exploits this feature importance via an iterative exclusion principle, we identify the essential internal coordinates (such as specific interatomic distances or dihedral angles) of the system, which are shown to represent versatile reaction coordinates that account for the dynamics of the slow degrees of freedom and explain the mechanism of the underlying processes. Moreover, these coordinates give rise to a free energy landscape that may reveal previously hidden intermediate states of the system.

The molecular actions of proteins occur along reaction coordinates. Current computer methods have limited ability to explore them. We describe a fast protocol called MELD-path that (1) efficiently samples relevant conformational states via MELD, an accelerator of Molecular Dynamics (MD), (2) seeds multiple short MD trajectories from MELD states, and then (3) constructs Markov State Models (MSM) that give the routes and kinetics. We tested the method against extensive (multi μs) MD simulations of the right-handed- to left-handed-helix transition of a 9-mer peptide of AIB, the symmetry of which allows us to establish convergence. MELD-path finds all the metastable states, their correct relative populations, and the full ensemble of routes, not just a single assumed route. For this transition, we find a very broad route structure. MELD-path is highly parallelizable and efficient, yielding the full route map in a few days of computation. We believe MELD-path could be a general and rapid way to explore mechanistic processes in biomolecules on the computer.

While adequately chosen reaction coordinates are expected to reveal the mechanism of a dynamical process, it proves to be notoriously difficult to model the complex structural rearrangements of a macromolecule by a low-dimensional collective coordinate. Adopting the hinge-bending motion of T4 lysozyme (T4L) as a prominent example and performing a 50 μs long unbiased molecular dynamics (MD) simulation of T4L, a general strategy to identify reaction coordinates of protein functional dynamics is developed. As a systematic method to reduce the dimensionality of the dynamics, first various types of principal component analyses are employed, and it is shown that the applicability and outcome of the approach crucially depends on the type of input coordinates used. In a second step, prospective candidates for a reaction coordinate are tested by studying the molecule's response to external pulling along the coordinate, using targeted MD simulations. While trying to directly enforce the open-closed transition does not recover the two-state behavior of T4L, this transition is triggered by a locking mechanism, by which the side chain of Phe4 changes from a solvent-exposed to a hydrophobically buried state. The mechanism is found to stabilize the open and closed states of T4L and thereby causes their relatively long lifetime of ∼10 μs. In extension of the usual two-state picture, a four-state model of the functional motion of T4L is proposed, which describes a hierarchical coupling of the fast nanosecond opening-closing motion and the slow microsecond locking transition.

A density-based clustering method is proposed that is deterministic, computationally efficient, and self-consistent in its parameter choice. By calculating a geometric coordinate space density for every point of a given data set, a local free energy is defined. On the basis of these free energy estimates, the frames are lumped into local free energy minima, ultimately forming microstates separated by local free energy barriers. The algorithm is embedded into a complete workflow to robustly generate Markov state models from molecular dynamics trajectories. It consists of (i) preprocessing of the data via principal component analysis in order to reduce the dimensionality of the problem, (ii) proposed density-based clustering to generate microstates, and (iii) dynamical clustering via the most probable path algorithm to construct metastable states. To characterize the resulting state-resolved conformational distribution, dihedral angle content color plots are introduced which identify structural differences of protein states in a concise way. To illustrate the performance of the method, three well-established model problems are adopted: conformational transitions of hepta-alanine, folding of villin headpiece, and functional dynamics of bovine pancreatic trypsin inhibitor.

The binding of a ligand to a protein may induce long-range structural or dynamical changes in the biomacromolecule even at sites physically well separated from the binding pocket. A system for which such behavior has been widely discussed is the PDZ2 domain of human tyrosine phosphatase 1E. Here, we present results from equilibrium trajectories of the PDZ2 domain in the free and ligand-bound state, as well as nonequilibrium simulations of the relaxation of PDZ2 after removal of its peptide ligand. The study reveals changes in inter-residue contacts, backbone dihedral angles, and C(α) positions upon ligand release. Our findings show a long-range conformational response of the PDZ2 domain to ligand release in the form of a collective shift of the secondary structure elements α2, β2, β3, α1-β4, and the C terminal loop relative to the rest of the protein away from the N-terminus, and a shift of the loops β2-β3 and β1-β2 in the opposite direction. The shifts lead to conformational changes in the backbone, especially in the β2-β3 loop but also in the β5-α2 and the α2-β6 loop, and are accompanied by changes of inter-residue contacts mainly within the β2-β3 loop as well as between the α2 helix and other segments. The residues showing substantial changes of inter-residue contacts, backbone conformations, or C(α) positions are considered "key residues" for the long-range conformational response of PDZ2. By comparing these residues with various sets of residues highlighted by previous studies of PDZ2, we investigate the statistical correlation of the various approaches. Interestingly, we find a considerable correlation of our findings with several works considering structural changes but no significant correlations with approaches considering energy flow or networks based on inter-residue energies.

Computational studies of vibrational energy flow in biomolecules have to date mapped out transport pathways on a case-by-case basis. To provide a more general approach, we derive scaling rules for vibrational energy transport in a globular protein, which are identified from extensive nonequilibrium molecular dynamics simulations of vibrational energy flow in the villin headpiece subdomain HP36. We parametrize a master equation based on inter-residue, residue-solvent, and heater-residue energy-transfer rates, which closely reproduces the results of the all-atom simulations. From that fit, two scaling rules emerge, one for energy transport along the protein backbone which relies on a diffusion model and another for energy transport between tertiary contacts, which is based on a harmonic model. Requiring only the calculation of mean and variance of relatively few atomic distances, the approach holds the potential to predict the pathways and time scales of vibrational energy flow in large proteins.

We are interested inferring rate processes on networks. In particular, given a network's topology, the stationary populations on its nodes, and a few global dynamical observables, can we infer all the transition rates between nodes? We draw inferences using the principle of maximum caliber (maximum path entropy). We have previously derived results for discrete-time Markov processes. Here, we treat continuous-time processes, such as dynamics among metastable states of proteins. The present work leads to a particularly important analytical result: namely, that when the network is constrained only by a mean jump rate, the rate matrix is given by a square-root dependence of the rate, kab ∝ (πb/πa)(1/2), on πa and πb, the stationary-state populations at nodes a and b. This leads to a fast way to estimate all of the microscopic rates in the system. As an illustration, we show that the method accurately predicts the nonequilibrium transition rates in an in silico gene expression network and transition probabilities among the metastable states of a small peptide at equilibrium. We note also that the method makes sensible predictions for so-called extra-thermodynamic relationships, such as those of Bronsted, Hammond, and others.

Biomolecules exhibit structural dynamics on a number of time scales, including picosecond (ps) motions of a few atoms, nanosecond (ns) local conformational transitions, and microsecond (μs) global conformational rearrangements. Despite this substantial separation of time scales, fast and slow degrees of freedom appear to be coupled in a nonlinear manner; for example, there is theoretical and experimental evidence that fast structural fluctuations are required for slow functional motion to happen. To elucidate a microscopic mechanism of this multiscale behavior, Aib peptide is adopted as a simple model system. Combining extensive molecular dynamics simulations with principal component analysis techniques, a hierarchy of (at least) three tiers of the molecule's free energy landscape is discovered. They correspond to chiral left- to right-handed transitions of the entire peptide that happen on a μs time scale, conformational transitions of individual residues that take about 1 ns, and the opening and closing of structure-stabilizing hydrogen bonds that occur within tens of ps and are triggered by sub-ps structural fluctuations. Providing a simple mechanism of hierarchical dynamics, fast hydrogen bond dynamics is found to be a prerequisite for the ns local conformational transitions, which in turn are a prerequisite for the slow global conformational rearrangement of the peptide. As a consequence of the hierarchical coupling, the various processes exhibit a similar temperature behavior which may be interpreted as a dynamic transition.

A local perturbation of a protein may lead to functional changes at some distal site. An example is the PDZ2 domain of human tyrosine phosphatase 1E, which shows an allosteric transition upon binding to a peptide ligand. Recently Buchli et al. presented a time-resolved study of this transition by covalently linking an azobenzene photoswitch across the binding groove and using a femtosecond laser pulse that triggers the cis-trans photoisomerization of azobenzene. To aid the interpretation of these experiments, in this work seven microsecond runs of all-atom molecular dynamics simulations each for the wild-type PDZ2 in the ligand-bound and -free state, as well as the photoswitchable protein (PDZ2S) in the cis and trans states of the photoswitch, in explicit water were conducted. First the theoretical model is validated by recalculating the available NMR data from the simulations. By comparing the results for PDZ2 and PDZ2S, it is analyzed to what extent the photoswitch indeed mimics the free-bound transition. A detailed description of the conformational rearrangement following the cis-trans photoisomerization of PDZ2S reveals a series of photoinduced structural changes that propagate from the anchor residues of the photoswitch via intermediate secondary structure segments to the C-terminus of PDZ2S. The changes of the conformational distribution of the C-terminal region is considered as the distal response of the isolated allosteric protein.

Recent molecular dynamics simulations of biopolymers have shown that in many cases the global features of the free energy landscape can be characterized in terms of the metastable conformational states of the system. To identify these states, a conceptionally and computationally simple approach is proposed. It consists of (i) an initial preprocessing via principal component analysis to reduce the dimensionality of the data, followed by k-means clustering to generate up to 10(4) microstates, (ii) the most probable path algorithm to identify the metastable states of the system, and (iii) boundary corrections of these states via the introduction of cluster cores in order to obtain the correct dynamics. By adopting two well-studied model problems, hepta-alanine and the villin headpiece protein, the potential and the performance of the approach are demonstrated.

To describe the structure and dynamics of oligomers during peptide aggregation, a method is proposed that considers both the intramolecular and intermolecular structures of the multimolecule system and correctly accounts for its degeneracy. The approach is based on the "by-parts" strategy, which partitions a complex molecular system into parts, determines the metastable conformational states of each part, and describes the overall conformational state of the system in terms of a product basis of the states of the parts. Starting from a molecular dynamics simulation of n molecules, the method consists of three steps: (i) characterization of the intramolecular structure, that is, of the conformational states of a single molecule in the presence of the other molecules (e.g., β-strand or random coil); (ii) characterization of the intermolecular structure through the identification of all occurring aggregate states of the peptides (dimers, trimers, etc.); and (iii) construction of the overall conformational states of the system in terms of a product basis of the n "single-molecule" states and the aggregate states. Considering the Alzheimer β-amyloid peptide fragment Aβ16-22 as a first application, about 700 overall conformational states of the trimer (Aβ16-22)3 were constructed from all-atom molecular dynamics simulation in explicit water. Based on these states, a transition network reflecting the free energy landscape of the aggregation process can be constructed that facilitates the identification of the aggregation pathways.

Employing nonequilibrium molecular dynamics (MD) simulations and transient infrared (IR) spectroscopy, a joint theoretical/experimental study on a water-soluble photoswitchable octapeptide designed by Renner et al. [Biopolymers 2002, 63, 382] is presented. The simulations predict the cooling of the hot photoproducts on a time scale of 7 ps and complex conformational rearrangements ranging from a few picoseconds to several nanoseconds. The experiments yield a dominant fast relaxation time of 5 ps, which is identified as the cooling time of the peptide in water and also accounts for initial conformational changes of the system. Moreover, a weaker component of 300 ps is found, which reflects the overall conformational relaxation of the system. The virtues and the limitations of the joint MD/IR approach to describe biomolecular conformational rearrangements are discussed.

Pulsed electron double resonance (PELDOR) experiments on oligonucleotides provide a distance ruler that allows the measurement of nanometer distances accurately. The technique requires attachment of nitroxide spin labels to the nucleotides, which may possibly perturb its conformation. To study to what extent nitroxide spin labels may affect RNA structure, all-atom molecular dynamics simulations in explicit solvent are performed for six double-labeled RNA duplexes. A new parametrization of the force field for the nitroxide spin label is developed, which leads to intramolecular distances that are in good agreement with experimental results. Comparison of the results for spin-labeled and unlabeled RNA reveals that the conformational effect of the spin label depends significantly on whether the spin label is attached to the major or the minor groove of RNA. While major-groove spin labeling may to some extent affect the conformation of nearby base pairs, minor-groove spin labeling has the advantage of mostly preserving the RNA conformation.

Classical formulations are considered that allow for the calculation of time- and frequency-resolved pump-probe spectra of nonadiabatically coupled molecular systems. When the semiclassical Franck-Condon approximation in the theoretical framework of the doorway-window formalism is employed, various first- and second-order expressions for the classical doorway and window functions are derived. Moreover, a classical analogue of the electronic dipole transition operator is employed. When established models describing ultrafast photoinduced electron transfer are adopted, it is found that the first-order approximations give rise to spurious structures of the time-resolved signal, which indicate that these approximations fail to correctly account for the averaging effect caused by finite pulses. The higher-order approximations, on the other hand, are shown to give a fairly accurate description of the transient absorption spectrum. By comparing to exact quantum-mechanical calculations, the merits and shortcomings of the various approaches as well as the generally achievable accuracy of a classical modeling of optical spectra is discussed.

Classical molecular dynamics simulations of a 14-mer UUCG RNA hairpin are performed to study its conformational dynamics and corresponding NMR relaxation parameters. The direct calculation of the relaxation rates from the trajectory yields good agreement with experiment, indicating the validity of the theoretical model. Various ways to provide a link between theory and experiment are considered, including the "model-free approach" of Lipari and Szabo and Gaussian axial fluctuation model of Brüschweilwer. It is studied if the underlying assumptions of these approaches are satisfied in the case of a flexible RNA hairpin. Being consistent with the analysis of the NMR experiments, Lipari-Szabo fits of the first 100 or 1000 ps of the internal correlation functions lead to a nice agreement between calculated and experimental order parameters and internal correlation times. Finally, the relation between NMR order parameters and the underlying internal motion of the RNA hairpin is discussed in detail. A principal component analysis reveals that the principal motions of the molecule account only partially for the measured NMR order parameters, because the latter are insensitive to internal dynamics occurring on a nanosecond time scale due to molecular tumbling.