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Photoproteins such as bacteriorhodopsin (bR) and rhodopsin (Rho) need to effectively dissipate photoinduced excess energy to prevent themselves from damage. Another well-studied seven transmembrane (TM) helices protein is the β2adrenergic receptor (β2AR), a G protein-coupled receptor for which energy dissipation paths have been linked with allosteric communication. To study the vibrational energy transport in the active and inactive states of these proteins, a master equation approach [J. Chem. Phys.2020, 152, 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure. Despite their overall structural similarity, the three 7TM proteins reveal quite different strategies to redistribute excess energy. While bR quickly removes the energy using the TM7 helix as a “lightning rod”, Rho exhibits a rather poor energy dissipation, which might eventually require the hydrolysis of the Schiff base between the protein and the retinal chromophore to prevent overheating. Heating the ligand adrenaline of β2AR, the resulting energy transport network of the protein is found to change significantly upon switching from the active state to the inactive state. While the energy flow may highlight aspects of the inter-residue couplings of β2AR, it seems not particularly suited to explain allosteric phenomena.

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.

We explore the capability of the non-natural amino acid azidohomoalanine (AHA) as an IR label to sense relatively small structural changes in proteins with the help of 2D IR difference spectroscopy. To that end, we AHA-labeled an allosteric protein (the PDZ2 domain from human tyrosine-phosphatase 1E) and furthermore covalently linked it to an azobenzene-derived photoswitch as to mimic its conformational transition upon ligand binding. To determine the strengths and limitations of the AHA label, in total six mutants have been investigated with the label at sites with varying properties. Only one mutant revealed a measurable 2D IR difference signal. In contrast to the commonly observed frequency shifts that report on the degree of solvation, in this case we observe an intensitychange. To understand this spectral response, we performed classical MD simulations, evaluating local contacts of the AHA labels to water molecules and protein side chains and calculating the vibrational frequency on the basis of an electrostatic model. Although these simulations revealed in part significant and complex changes of the number of intraprotein and water contacts upon trans–cisphotoisomerization, they could not provide a clear explanation of why this one label would stick out. Subsequent quantum-chemistry calculations suggest that the response is the result of an electronic interaction involving charge transfer of the azido group with sulfonate groups from the photoswitch. To the best of our knowledge, such an effect has not been described before.

Markov state models represent a popular means to interpret biomolecular processes in terms of memoryless transitions between metastable conformational states. To gain insight into the underlying mechanism, it is instructive to determine all relevant pathways between initial and final states of the process. Currently available methods, such as Markov chain Monte Carlo and transition path theory, are convenient for identifying the most frequented pathways. They are less suited to account for the typically huge amount of pathways with low probability which, though, may dominate the cumulative flux of the reaction. On the basis of a systematic construction of all possible pathways, the here proposed method MSMPathfinder is able to characterize the multitude of unique pathways (say, up to 1010) in a complex system and to quantitatively calculate their correct weights and associated waiting times with predefined accuracy. Adopting the chiral transitions of a peptide helix and the folding of the villin headpiece as model problems, mechanisms and associated waiting times of these processes are discussed using a kinetic network representation. The analysis reveals that the waiting time distribution may yield only little insight into the diversity of pathways, because the measured folding times do typically not reflect the most probable path lengths but rather the cumulative effect of many different pathways.

To facilitate the observation of biomolecular energy transport in real time and with single-residue resolution, recent experiments by Baumann et al. (Angew. Chem. Int. Ed.2019, 58, 2899, DOI: 10.1002/anie.201812995) have used unnatural amino acids β-(1-azulenyl)alanine (Azu) and azidohomoalanine (Aha) to site-specifically inject and probe vibrational energy in proteins. To aid the interpretation of such experiments, non-equilibrium molecular dynamics simulations of the anisotropic energy flow in proteins TrpZip2 and PDZ3 domains are presented. On this account, an efficient simulation protocol is established that accurately mimics the excitation and probing steps of Azu and Aha. The simulations quantitatively reproduce the experimentally found cooling times of the solvated proteins at room temperature and predict that the cooling slows by a factor 2 below the glass temperature of water. In PDZ3, vibrational energy is shown to travel from the initially excited peptide ligand via a complex network of inter-residue contacts and backbone transport to distal regions of the protein. The supposed connection of these energy transport pathways with pathways of allosteric communication is discussed.

An azobenzene-derived photoswitch has been covalently cross-linked to two sites of the S-peptide in the RNase S complex in a manner that the α-helical content of the S-peptide reduces upon cis-to-transisomerization of the photoswitch. Three complementary experimental techniques have been employed, isothermal titration calorimetry, circular dichroism spectroscopy and intrinsic tyrosine fluorescence quenching, to determine the binding affinity of the S-peptide to the S-protein in the two states of the photoswitch. Five mutants with the photoswitch attached to different sites of the S-peptide have been explored, with the goal to maximize the change in binding affinity upon photoswitching, and to identify the mechanisms that determine the binding affinity. With regard to the first goal, one mutant has been identified, which binds with reasonable affinity in the one state of the photoswitch, while specific binding is completely switched off in the other state. With regard to the second goal, accompanying molecular dynamics simulations combined with a quantitative structure activity relationship revealed that the α-helicity of the S-peptide in the binding pocket correlates surprisingly well with measured dissociation constants. Moreover, the simulations show that both configurations of all S-peptides exhibit quite well-defined structures, even in apparently disordered states.

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 ΔG(x) = W(x) – Wdiss(x), apart from the (readily obtained) work W(x) performed on the system, the dissipated work Wdiss(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 ΓNEQ(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 ΓNEQ(x) may yield valuable insight into the microscopic mechanism of friction.

The noncanonical amino acid azidohomoalanine (Aha) is known to be an environment-sensitive infrared probe for the site-specific investigation of protein structure and dynamics. Here, the capability of that label is explored to detect protein–ligand interactions by incorporating it in the vicinity of the binding groove of a PDZ2 domain. Circular dichroism and isothermal titration calorimetry measurements reveal that the perturbation of the protein system by mutation is negligible, with minimal influence on protein stability and binding affinity. Two-dimensional infrared spectra exhibit small (1–3 cm–1) but clearly measurable red shifts of the Aha vibrational frequency upon binding of two different peptide ligands, while accompanying molecular dynamics simulations suggest that these red shifts are induced by polar contacts with side chains of the peptide ligands. Hence, Aha is a versatile and minimally invasive vibrational label that is not only able to report on large structural changes during, e.g., protein folding, but also on very subtle changes of the electrostatic environment upon ligand binding.

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.

To sample rare events, dissipation-corrected targeted molecular dynamics (dcTMD) applies a constant velocity constraint along a one-dimensional reaction coordinate s, which drives an atomistic system from an initial state into a target state. Employing a cumulant approximation of Jarzynski’s identity, the free energy ΔG(s) is calculated from the mean external work and dissipated work of the process. By calculating the friction coefficient Γ(s) from the dissipated work, in a second step, the equilibrium dynamics of the process can be studied by propagating a Langevin equation. While so far dcTMD has been mostly applied to study the unbinding of protein–ligand complexes, here its applicability to rare conformational transitions within a protein and the prediction of their kinetics are investigated. As this typically requires the introduction of multiple collective variables {xj} = x, a theoretical framework is outlined to calculate the associated free energy ΔG(x) and friction Γ(x) from dcTMD simulations along coordinate s. Adopting the α–β transition of alanine dipeptide as well as the open–closed transition of T4 lysozyme as representative examples, the virtues and shortcomings of dcTMD to predict protein conformational transitions and the related kinetics are studied.

Markov state models represent a popular means to interpret molecular dynamics trajectories in terms of memoryless transitions between metastable conformational states. To provide a mechanistic understanding of the considered biomolecular process, these states should reflect structurally distinct conformations and ensure a time scale separation between fast intrastate and slow interstate dynamics. Adopting the folding of villin headpiece (HP35) as a well-established model problem, here we discuss the selection of suitable input coordinates or “features”, such as backbone dihedral angles and interresidue distances. We show that dihedral angles account accurately for the structure of the native energy basin of HP35, while the unfolded region of the free energy landscape and the folding process are best described by tertiary contacts of the protein. To construct a contact-based model, we consider various ways to define and select contact distances and introduce a low-pass filtering of the feature trajectory as well as a correlation-based characterization of states. Relying on input data that faithfully account for the mechanistic origin of the studied process, the states of the resulting Markov model are clearly discriminated by the features, describe consistently the hierarchical structure of the free energy landscape, and─as a consequence─correctly reproduce the slow time scales of the process.

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 pathalgorithm 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 Cαpositions 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-β3and β1-β2in the opposite direction. The shifts lead to conformational changes in the backbone, especially in the β2-β3loop but also in the β5-α2and the α2-β6loop, and are accompanied by changes of inter-residue contacts mainly within the β2-β3loop as well as between the α2helix and other segments. The residues showing substantial changes of inter-residue contacts, backbone conformations, or Cαpositions 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.

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 πaand πb, the stationary-state populations at nodes aand 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 silicogene 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.

The friction coefficient of fluids may become a function of the velocity at increased external driving. This non-Newtonian behavior is of general theoretical interest and of great practical importance, for example, for the design of lubricants. Although the effect has been observed in large-scale atomistic simulations of bulk liquids, its theoretical formulation and microscopic origin are not well understood. Here, we use dissipation-corrected targeted molecular dynamics, which pulls apart two tagged liquid molecules in the presence of surrounding molecules, and analyze this nonequilibrium process via a generalized Langevin equation. The approach is based on a second-order cumulant expansion of Jarzynski’s identity, which is shown to be valid for fluids and therefore allows for an exact computation of the friction profile as well of the underlying memory kernel. We show that velocity-dependent friction in fluids results from an intricate interplay of near-order structural effects and the non-Markovian behavior of the friction memory kernel. For complex fluids such as the model lubricant C40H82, the memory kernel exhibits a stretched-exponential long-time decay, which reflects the multitude of timescales of the system.

To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component analysis (TICA), which aim to maximize the variance and the time scale of the first components, respectively. A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances. As typically only a small subset of those coordinates is involved in a specific biomolecular process, it is important to discard the remaining uncorrelated motions or weakly correlated noise coordinates. This is because they may exhibit large amplitudes or long time scales and therefore will be erroneously considered important by PCA and TICA, respectively. To discriminate collective motions underlying functional dynamics from uncorrelated motions, the correlation matrix of the input coordinates is block-diagonalized by a clustering method. This strategy avoids possible bias due to presumed functional observables and conformational states or variation principles that maximize variance or time scales. Considering several linear and nonlinear correlation measures and various clustering algorithms, it is shown that the combination of linear correlation and the Leiden community detection algorithm yields excellent results for all considered model systems. These include the functional motion of T4 lysozyme to demonstrate the successful identification of collective motion, as well as the folding of the villin headpiece to highlight the physical interpretation of the correlated motions in terms of a functional mechanism.

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 104microstates, (ii) the most probable pathalgorithm 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 nmolecules, the method consists of three steps: (i) characterization of the intramolecularstructure, 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 intermolecularstructure through the identification of all occurring aggregate states of the peptides (dimers, trimers, etc.); and (iii) construction of the overallconformational 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 Aβ16–22as a first application, about 700 overall conformational states of the trimer (Aβ16–22)3were 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.

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.

Employing nonequilibrium molecular dynamics simulations, a comprehensive computational study of the photoinduced conformational dynamics of a photoswitchable bicyclic azobenzene octapeptide is presented. The calculation of time-dependent probability distributions along various global and local reaction coordinates reveals that the conformational rearrangement of the peptide is rather complex and occurs on at least four timescales: 1) After photoexcitation, the azobenzene unit of the molecule undergoes nonadiabatic photoisomerization within 0.2ps. 2) On the picosecond timescale, the cooling (13ps) and the stretching (14ps) of the photoexcited peptide is observed. 3) Most reaction coordinates exhibit a 50–100ps component reflecting a fast conformational rearrangement. 4) The 500–1000ps component observed in the simulation accounts for the slow diffusion-controlled conformational equilibration of the system. The simulation of the photoinduced molecular processes is in remarkable agreement with time-resolved optical and infrared experiments, although the calculated cooling as well as the initial conformational rearrangements of the peptide appear to be somewhat too slow. Based on an ab initio parameterized vibrational Hamiltonian, the time-dependent amide I frequency shift is calculated. Both intramolecular and solvent-induced contributions to the frequency shift were found to change by ≲2cm−1, in reasonable agreement with experiment. The potential of transient infrared spectra to characterize the conformational dynamics of peptides is discussed in some detail.

Molecular dynamics simulations of the binding of the heterochiral tripeptide KkN to the transactivation responsive (TAR) RNA of HIV-1 is presented, using an all-atom force field with explicit water. To obtain starting structures for the TAR-KkN complex, semirigid docking calculations were performed that employ an NMR structure of free TAR RNA. The molecular dynamics simulations show that the starting structures in which KkN binds to the major groove of TAR (as it is the case for the Tat-TAR complex of HIV-1) are unstable. On the other hand, the minor-groove starting structures are found to lead to several binding modes, which are stabilized by a complex interplay of stacking, hydrogen bonding, and electrostatic interactions. Although the ligand does not occupy the binding position of Tat protein, it is shown to hinder the interhelical motion of free TAR RNA. The latter is presumably necessary to achieve the conformational change of TAR RNA to bind Tat protein. Considering the time evolution of the trajectories, the binding process is found to be ligand-induced and cooperative. That is, the conformational rearrangement only occurs in the presence of the ligand and the concerted motion of the ligand and a large part of the RNA binding site is necessary to achieve the final low-energy binding state.

Durch Kombination von klassischen und quantenmechanischen Theorien lassen sich Quantenphänomene mittlerweile auch in komplexen Systemen wie Flüssigkeiten, Nanostrukturen und Biomolekülen beschreiben. Die theoretische Spektroskopie ist das Bindeglied zwischen Molekülphysik und Reaktionsdynamik. Fortschritte in der Methodenentwicklung machen den routinemäßigen Einsatz in Analytik und Strukturchemie absehbar. Die Dichtefunktionaltheorie hat sich zu einem wichtigen Bestandteil der chemischen Forschung entwickelt. Die Suche nach Lösungen für fundamentale Probleme bleibt aber schwierig. Durch Kombination von klassischen und quantenmechanischen Theorien lassen sich Quantenphänomene mittlerweile auch in komplexen Systemen wie Flüssigkeiten, Nanostrukturen und Biomolekülen beschreiben. Die theoretische Spektroskopie ist das Bindeglied zwischen Molekülphysik und Reaktionsdynamik. Fortschritte in der Methodenentwicklung machen den routinemäßigen Einsatz in Analytik und Strukturchemie absehbar. Die Dichtefunktionaltheorie hat sich zu einem wichtigen Bestandteil der chemischen Forschung entwickelt. Die Suche nach Lösungen für fundamentale Probleme bleibt aber schwierig.

A computational scheme to calculate the femtosecond time-resolved photoelectron spectrum of polyatomic molecules is outlined. The method exploits (i) the fact that the calculation of the ionization yield at a particular photoelectron energy is formally equivalent to the calculation of the total transient absorption into a single excited electronic state, and (ii) a recently proposed convolution scheme (S. Hahn and G. Stock, Chem. Phys. Lett., 1998, 296, 137), which allows for an efficient calculation of the transient absorption. Obtaining the complete photoelectron spectrum from a single transient-absorption calculation, the approach circumvents the cumbersome discretization of the electron continuum. To demonstrate its capability, the method is applied to a four-mode vibronic-coupling model of pyrazine, which includes the three lowest singlet states (S₀, S₁, S₂) as well as the two lowest cation states (I₀, I₁) of pyrazine. Explicit simulations of femtosecond ionization experiments are presented for this model and compared to recent experiments. It is demonstrated that the time-resolved photoelectron spectrum directly monitors the ultrafast S₂→S₁ internal conversion process in pyrazine.