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Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

The 2D-Raman-THz response in all possible time-orderings (Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman) of amorphous water ice is calculated in two ways: from atomistic molecular dynamics simulations and with the help of a Feynman diagram model, the latter of which power-expands the potential energy surface and the dipole and polarizability surfaces up to leading order. Comparing both results allows one to dissect the 2D-Raman-THz response into contributions from mechanical anharmonicity, as well as electrical dipole and polarizability anharmonicities. Mechanical anharmonicity dominates the 2D-Raman-THz response of the hydrogen-bond stretching and hydrogen-bond bending bands of water, and dipole anharmonicity dominates that of the librational band, while the contribution of polarizability anharmonicity is comparably weak. A distinct echo of the hydrogen-bond stretching band is observed for the THz-Raman-THz pulse sequence, again dominated by mechanical anharmonicity. A peculiar mechanism is discussed, which is based on the coupling between the many normal modes within the hydrogen-bond stretching band and which will inevitably generate such an echo for an amorphous structure. [ABSTRACT FROM AUTHOR]

2D-Raman-THz spectroscopy of liquid water, which has been presented recently [J. Savolainen et al., Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)], directly probes the intermolecular degrees of freedom of the hydrogen-bond network. However, being a relatively new technique, its information content is not fully explored to date. While the spectroscopic signal can be simulated based on molecular dynamics simulation in connection with a water force field, it is difficult to relate spectroscopic signatures to the underlying microscopic features of the force field. Here, a completely different approach is taken that starts from an as simple as possible model, i.e., a single vibrational mode with electrical and mechanical anharmonicity augmented with homogeneous and inhomogeneous broadening. An intuitive Feynman diagram picture is developed for all possible pulse sequences of hybrid 2D-Raman-THz spectroscopy. It is shown that the model can explain the experimental data essentially quantitatively with a very small set of parameters, and it is tentatively concluded that the experimental signal originates from the hydrogen-bond stretching vibration around 170 cm−1. Furthermore, the echo observed in the experimental data can be quantified by fitting the model. A dominant fraction of its linewidth is attributed to quasi-inhomogeneous broadening in the slow-modulation limit with a correlation time of 370 fs, reflecting the lifetime of the hydrogen-bond networks giving rise to the absorption band. [ABSTRACT FROM AUTHOR]

A polarizable water model is presented which has been calibrated against experimental THz and Raman spectra of bulk water. These low-frequency spectra directly probe the dynamics, and thereby intermolecular interactions, on time scales relevant to molecular motions. The model is based on the TL4P force field developed recently by Tavan and co-workers [J. Phys. Chem. B 117, 9486 (2013)], which has been designed to be transferable between different environments; in particular, to correctly describe the electrostatic properties of both the isolated water molecule in the gas-phase and the liquid water at ambient conditions. Following this design philosophy, TL4P was amended with charge transfer across hydrogen-bonded dimers as well as an anisotropic polarizability in order to correctly reproduce the THz and Raman spectra. The thermodynamic and structural properties of the new model are of equal quality as those of TL4P, and at the same time, an almost quantitative agreement with the spectroscopic data could be achieved. Since TL4P is a rigid model with a single polarizable site, it is computationally very efficient, while the numerical overhead for the addition of charge transfer and the anisotropic polarizability is minor. Overall, the model is expected to be well suited for, e.g., large scale simulations of 2D-Raman-THz spectra or biomolecular simulations. [ABSTRACT FROM AUTHOR]

We present experimental and simulated 2D IR spectra of some high-pressure forms of isotope-pure D2O ice and compare the results to those of ice Ih published previously [F. Perakis and P. Hamm, Phys. Chem. Chem. Phys. 14, 6250 (2012); L. Shi et al., ibid. 18, 3772 (2016)]. Ice II, ice V, and ice XIII have been chosen for this study, since this selection covers many aspects of the polymorphism of ice. That is, ice II is a hydrogen-ordered phase of ice, in contrast to ice Ih, while ice V and ice XIII are a hydrogen-disordered/ordered couple that shares essentially the same oxygen structure and hydrogenbonded network. For the transmission 2D IR spectroscopy, a novel method had to be developed for the preparation of ultrathin films (1-2 μm) of high-pressure ices with good optical quality. We also simulated 2D IR spectra based on molecular dynamics simulations connected to a vibrational exciton picture. These simulations agree with the experimental results in a semi-quantitative manner for ice II, while the same approach failed for ice V and ice XIII. From the perspective of 2D IR spectroscopy, ice II appears to be more inhomogeneously broadened than ice Ih, despite its hydrogen-order, which we attribute to the fact that ice II is structurally more complex with four distinguishable hydrogen bonds that mix due to exciton coupling. Ice V and ice XIII, on the other hand, behave as expected with the hydrogen-disordered case (ice V) being more inhomogenously broadened. Furthermore, in all hydrogen-ordered forms (ice II and ice XIII), cross peaks could be identified in the anisotropic 2D IR spectrum, whose signs reveal the relative direction of the corresponding excitonic states. [ABSTRACT FROM AUTHOR]

In a recent paper, the experimental 2D-Raman-THz response of liquid water at ambient conditions has been presented [J. Savolainen, S. Ahmed, and P. Hamm, Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)]. Here, all-atom molecular dynamics simulations are performed with the goal to reproduce the experimental results. To that end, the molecular response functions are calculated in a first step, and are then convoluted with the laser pulses in order to enable a direct comparison with the experimental results. The molecular dynamics simulation are performed with several different water models: TIP4P/2005, SWM4-NDP, and TL4P. As polarizability is essential to describe the 2D-Raman-THz response, the TIP4P/2005 water molecules are amended with either an isotropic or a anisotropic polarizability a posteriori after the molecular dynamics simulation. In contrast, SWM4-NDP and TL4P are intrinsically polarizable, and hence the 2D-Raman-THz response can be calculated in a self-consistent way, using the same force field as during the molecular dynamics simulation. It is found that the 2D-Raman-THz response depends extremely sensitively on details of the water model, and in particular on details of the description of polarizability. Despite the limited time resolution of the experiment, it could easily distinguish between various water models. Albeit not perfect, the overall best agreement with the experimental data is obtained for the TL4P water model. [ABSTRACT FROM AUTHOR]

While allostery is of paramount importance for protein regulation, the underlying dynamical process of ligand (un)binding at one site, resulting time evolution of the protein structure, and change of the binding affinity at a remote site are not well understood. Here the ligand-induced conformational transition in a widely studied model system of allostery, the PDZ2 domain, is investigated by transient infrared spectroscopy accompanied by molecular dynamics simulations. To this end, an azobenzene derived photoswitch is linked to a peptide ligand in a way that its binding affinity to the PDZ2 domain changes upon switching, thus initiating an allosteric transition in the PDZ2 domain protein. The subsequent response of the protein, covering four decades of time, ranging from ∼1 ns to ∼10 µs, can be rationalized by a remodeling of its rugged free-energy landscape, with very subtle shifts in the populations of a small number of structurally well-defined states. It is proposed that structurally and dynamically driven allostery, often discussed as limiting scenarios of allosteric communication, actually go hand-in-hand, allowing the protein to adapt its free-energy landscape to incoming signals. [ABSTRACT FROM AUTHOR]

Using classical molecular dynamics simulations, the 2D infrared (IR) spectroscopy of CN- solvated in D2O is investigated. Depending on the force field parametrizations, most of which are based on multipolar interactions for the CN- molecule, the frequency-frequency correlation function and observables computed from it differ. Most notably, models based on multipoles for CN- and TIP3P for water yield quantitatively correct results when compared with experiments. Furthermore, the recent finding that T1 times are sensitive to the van der Waals ranges on the CN- is confirmed in the present study. For the linear IR spectrum, the best model reproduces the full widths at half maximum almost quantitatively (13.0 cm-1 vs. 14.9 cm-1) if the rotational contribution to the linewidth is included. Without the rotational contribution, the lines are too narrow by about a factor of two, which agrees with Raman and IR experiments. The computed and experimental tilt angles (or nodal slopes) α as a function of the 2D IR waiting time compare favorably with the measured ones and the frequency fluctuation correlation function is invariably found to contain three time scales: a sub-ps, 1 ps, and one on the 10-ps time scale. These time scales are discussed in terms of the structural dynamics of the surrounding solvent and it is found that the longest time scale (≈10 ps) most likely corresponds to solvent exchange between the first and second solvation shell, in agreement with interpretations from nuclear magnetic resonance measurements. [ABSTRACT FROM AUTHOR]

Free-energy landscape theory is often used to describe complex molecular systems. Here, a microscopic description of water structure and dynamics based on configuration-space-networks and molecular dynamics simulations of the TIP4P/2005 model is applied to investigate the free-energy landscape of water. The latter is built on top of a large set of water microstates describing the kinetic stability of local hydrogen-bond arrangements up to the second solvation shell. In temperature space, the landscape displays three different regimes. At around ambient conditions, the free-energy surface is characterized by many short-lived basins of attraction which are structurally well-defined (inhomogeneous regime). At lower temperatures instead, the liquid rapidly becomes homogeneous. In this regime, the free energy is funneled-like, with fully coordinated water arrangements at the bottom of the funnel. Finally, a third regime develops below the temperature of maximal compressibility (Widom line) where the funnel becomes steeper with few interconversions between microstates other than the fully coordinated ones. Our results present a way to manage the complexity of water structure and dynamics, connecting microscopic properties to its ensemble behavior. [ABSTRACT FROM AUTHOR]

We discuss the hybrid 2D-Raman-THz spectroscopy of liquid water. This two-dimensional spectroscopy is designed to directly work in the low-frequency range of the intermolecular degrees of freedom. The information content of 2D-Raman-THz spectroscopy is similar to 2D-Raman or 2D-THz spectroscopy, but its experimental implementation should be easier. That is, 2D-Raman-THz spectroscopy is a 3rd-order nonlinear spectroscopy and as such completely avoids cascading of consecutive 3rd-order signals, which turned out to be a major difficulty in 5th-order 2D-Raman spectroscopy. On the other hand, it does not require any intense THz pump-pulse, the lack of which limits 2D-THz spectroscopy to the study of semiconductor quantum wells as the currently available pulse energies are too low for molecular systems. In close analogy to 2D-Raman spectroscopy, the 2D-Raman-THz response of liquid water is simulated from an all-atom molecular dynamics simulation, and the expected spectral features are discussed. [ABSTRACT FROM AUTHOR]

The mechanism of vibrational energy flow is studied in a regime where a diffusion equation is likely to break down, i.e., on length scales of a few chemical bonds and time scales of a few picoseconds. This situation occurs, for example, during photochemical reactions in protein environment. To that end, a toy model is introduced that on the one hand mimics the vibrational normal mode distribution of proteins, and on the other hand is small enough to numerically time propagate the system fully quantum mechanically. Comparing classical and quantum-mechanical results, the question is addressed to what extent the classical nature of the molecular dynamics simulations (which would be the only choice for the modeling of a real molecular system) affects the vibrational energy flow mechanism. Small differences are found which are due to the different ways classical and quantum mechanics distribute thermal energy over vibrational modes. In either case, a ballistic and a diffusive phase can be identified. For these small length and time scales, the latter is governed by intrasite vibrational energy redistribution, since vibrational energy does not necessarily thermalize completely within individual peptide units. Overall, the model suggests a picture that unifies many of the observations made recently in experiments. [ABSTRACT FROM AUTHOR]

Characterizing the dynamics of the OH stretch in isotopically substituted liquid water (HOD in D2O) in terms of three-point frequency fluctuation correlation functions and joint probability densities shows that dynamics during hydrogen bond rearrangements occur primarily along a coordinate which is perpendicular to the spectroscopic coordinate. Molecular dynamics simulations show that three-point correlation functions are sensitive to this motion, unlike two-point correlation functions, and can select sets of trajectories which linger in the area of the transition state. Three-dimensional-infrared correlation spectroscopy could potentially measure these dynamics, though motional narrowing significantly changes the shape of the resulting spectra. [ABSTRACT FROM AUTHOR]

Nonlinear time-resolved vibrational spectroscopy is used to compare spectral broadening of the amide I band of the small peptide trialanine with that of N-methylacetamide, a commonly used model system for the peptide bond. In contrast to N-methylacetamide, the amide I band of trialanine is significantly inhomogeneously broadened. Employing classical molecular-dynamics simulations combined with density-functional-theory calculations, the origin of the spectral inhomogeneity is investigated. While both systems exhibit similar hydrogen-bonding dynamics, it is found that the conformational dynamics of trialanine causes a significant additional spectral broadening. In particular, transitions between the poly(Gly)II and the α[SUBR] conformations are identified as the main source of the additional spectral inhomogeneity of trialanine. The experimental and computational results suggest that trialanine adopts essentially two conformations: poly(Gly)II (80%) and α[SUBR] (20%). The potential of the joint experimental and computational approach to explore conformational dynamics of peptides is discussed. [ABSTRACT FROM AUTHOR]

While the theory of protein folding is well developed, including concepts such as rugged energy landscape, folding funnel, etc., the same degree of understanding has not been reached for the description of the dynamics of allosteric transitions in proteins. This is not only due to the small size of the structural change upon ligand binding to an allosteric site, but also due to challenges in designing experiments that directly observe such an allosteric transition. On the basis of recent pump-probe-type experiments (Buchli et al. 2013 Proc. Natl Acad. Sci. USA 110, 11 725-11 730. (doi:10.1073/ pnas.1306323110)) and non-equilibrium molecular dynamics simulations (Buchenberg et al. 2017 Proc. Natl Acad. Sci. USA 114, E6804-E6811. (doi:10.1073/pnas.1707694114)) studying an photoswitchable PDZ2 domain as model for an allosteric transition, we outline in this perspective how such a description of allosteric communication might look. That is, calculating the dynamical content of both experiment and simulation (which agree remarkably well with each other),we find that allosteric communication shares some properties with downhill folding, except that it is an 'order-order' transition. Discussing themultiscale and hierarchical features of the dynamics, the validity of linear response theory as well as the meaning of 'allosteric pathways', we conclude that non-equilibrium experiments and simulations are a promising way to study dynamical aspects of allostery. [ABSTRACT FROM AUTHOR]

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology. [ABSTRACT FROM AUTHOR]

Abstract: pH jumps are a truly biomimetic technique to initiate non-equilibrium dynamics of biomolecules. In this work, the pH jump induced α-helix folding of poly-l-glutamic acid is investigated upon proton release from o-nitrobenzaldehyde. The aim of this work is twofold: On the one hand, design criteria of pH jump experiments are discussed, on the other hand, the folding mechanism of poly-l-glutamic acid is clarified by probing the IR response of the amide I band. Its folding kinetics is studied in dependence of the starting pD, the size of the pD jump and the length of the helix. While no dependence on the first two parameters could be detected, the folding time varies from 0.6μs to 1.8μs for helix lengths of 20 residue to 440 residue, respectively. It converges to a long-length limit at about 50 residue, a result which is attributed to a nucleation–propagation mechanism. [Copyright &y& Elsevier]

We investigate energy transport through an α-aminoisobutyric acid-based 310-helix dissolved in chloroform in a combined experimental-theoretical approach. Vibrational energy is locally deposited at the N terminus of the helix by ultrafast internal conversion of a covalently attached, electronically excited, azobenzene moiety. Heat flow through the helix is detected with subpicosecond time resolution by employing vibrational probes as local thermometers at various distances from the heat source. The experiment is supplemented by detailed nonequilibrium molecular dynamics (MD) simulations of the process, revealing good qualitative agreement with experiment: Both theory and experiment exhibit an almost instantaneous temperature jump of the reporter units next to the heater which is attributed to the direct impact of the isomerizing azobenzene moiety. After this impact event, helix and azobenzene moiety appear to be thermally decoupled. The energy deposited in the helix thermalizes on a subpicosecond timescale and propagates along the helix in a diffusive-like process, accompanied by a significant loss into the solvent. However, in terms of quantitative numbers, theory and experiment differ. In particular, the MD simulation seems to overestimate the heat diffusion constant (2 Ų ps-1 from the experiment) by a factor of five. [ABSTRACT FROM AUTHOR]

Using time-resolved IR spectroscopy, we monitored the kinetics of folding and unfolding processes of a photoswitchable 16-residue alanine-based α-helical peptide on a timescale from few picoseconds to almost 40 μs and over a large temperature range (279–318 K). The folding and unfolding processes were triggered by an ultrafast laser pulse that isomerized the cross linker within a few picoseconds. The main folding and unfolding times (700 ns and 150 ns, respectively, at room temperature) are in line with previous T-jump experiments obtained from similar peptides. However, both processes show complex, strongly temperature-dependent spectral kinetics that deviate clearly from a single-exponential behavior. Whereas in the unfolding experiment the ensemble starts from a well defined folded state, the starting ensemble in the folding experiment is more heterogeneous, which leads to distinctly different kinetics of the experiments, because they are sensitive to different regions of the energy surface. A qualitative agreement with the experimental data-set can be obtained by a model where the unfolded states act as a hub connected to several separated ‘misfolded’ states with a distribution of rates. We conclude that a rather large spread of rates (k1 : kn ≈9) is needed to explain the experimentally observed stretched exponential response with stretching factor β = 0.8 at 279 K. [ABSTRACT FROM AUTHOR]

In a previous paper [P. Hamm and J. Savolainen, J. Chem. Phys. 136, 094516 (2012)], we have studied the 2D-Raman-THz response of liquid water, based on an all-atom molecular dynamics simulation. In the pulse sequence we investigated a near-infraredlaser pulse excites a vibrational coherence through a Raman process that switches it into another coherence by a THz pulse after some time, and finally read out by the emission of a THz field.In the present note, we explore the inverted time-ordered pulse sequence, in which the first coherence is generated by a direct THz excitation, while the switching of coherences is achieved by a Raman interaction. Since the dependence of the polarizibility on the nuclear coordinates is more nonlinear compared to that of the dipole moment, this pulse sequence reveals more of the couplings and correlations between the various degrees of freedom of water. Compared to 2D-Raman spectroscopy and the original pulse sequence, this pulse sequence reveals the clearest signature of a photon echo. [ABSTRACT FROM AUTHOR]

A local perturbation of a proteinmay lead to functional changesat some distal site. An example is the PDZ2 domain of human tyrosinephosphatase 1E, which shows an allosteric transition upon bindingto a peptide ligand. Recently Buchli et al. presented a time-resolvedstudy of this transition by covalently linking an azobenzene photoswitchacross the binding groove and using a femtosecond laser pulse thattriggers the cis–trans photoisomerization of azobenzene. Toaid the interpretation of these experiments, in this work seven microsecondruns of all-atom molecular dynamics simulations each for the wild-typePDZ2 in the ligand-bound and -free state, as well as the photoswitchableprotein (PDZ2S) in the cis and trans states of the photoswitch, inexplicit water were conducted. First the theoretical model is validatedby recalculating the available NMR data from the simulations. By comparingthe results for PDZ2 and PDZ2S, it is analyzed to what extent thephotoswitch indeed mimics the free-bound transition. A detailed descriptionof the conformational rearrangement following the cis–transphotoisomerization of PDZ2S reveals a series of photoinduced structuralchanges that propagate from the anchor residues of the photoswitchvia intermediate secondary structure segments to the C-terminus ofPDZ2S. The changes of the conformational distribution of the C-terminalregion is considered as the distal response of the isolated allostericprotein. [ABSTRACT FROM AUTHOR]

Amyloid aggregates are highly ordered fibrillar assembliesof polypeptidesinvolved in a number of neurodegenerative diseases. Very little isknown on the pathways of self-assembly of peptides into the finalamyloid fibrils, which is due in part to the difficulty of triggeringthe aggregation process in a controlled manner. Here we present thedesign and validation of a cross-linked hexapeptide that reversiblyaggregates and dissociates under ultraviolet light irradiation control.First molecular dynamics simulations were carried out to identify,among hundreds of possible sequences, those with the highest propensityto form ordered (β-sheet) oligomers in the trans state of theazobenzene cross-linker, and at the same time with the highest solubilityin the cis state. In the simulations, the peptides were observed tospontaneously form ordered oligomers with cross-β contacts whenthe cross-linker was in the trans state, whereas in the cis statethey self-assemble into amorphous aggregates. For the most promisingsequence emerging from the simulations (Ac-Cys-His-Gly-Gln-Cys-Lys-NH2cross-linked at the two cysteine residues), the photoisomerizationof the azobenzene group was shown to induce reversible aggregationby time-resolved light scattering and fluorescence measurements. Theamyloid-like fibrillar topology was confirmed by electron microscopy.Potential applications of minimally designed peptides with photoswitchableamyloidogenic propensity are briefly discussed. [ABSTRACT FROM AUTHOR]

In a combined experimental–theoretical study, we investigated the transport of vibrational energy from the surrounding solvent into the interior of a heme protein, the sperm whale myoglobin double mutant L29W-S108L, and its dependence on temperature from 20 to 70 K. The hindered libration of a CO molecule that is not covalently bound to any part of the protein but is trapped in one of its binding pockets (the Xe4 pocket) was used as the local thermometer. Energy was deposited into the solvent by IR excitation. Experimentally, the energy transfer rate increased from (30 ps)−1at 20 K to (8 ps)−1at 70 K. This temperature trend is opposite to what is expected, assuming that the mechanism of heat transport is similar to that in glasses. In order to elucidate the mechanism and its temperature dependence, nonequilibrium molecular dynamics (MD) simulations were performed, which, however, predicted an essentially temperature-independent rate of vibrational energy flow. We tentatively conclude that the MD potentials overestimate the coupling between the protein and the CO molecule, which appears to be the rate-limiting step in the real system at low temperatures. Assuming that this coupling is anharmonic in nature, the observed temperature trend can readily be explained. [ABSTRACT FROM AUTHOR]

A series of photoswitchable, α-helical peptides were studied using two-dimensional infrared spectroscopy (2D-IR). Single-isotope labeling with 13C18O at various positions in the sequence was employed to spectrally isolate particular backbone positions. We show that a single 13C18O label can give rise to two bands along the diagonal of the 2D-IR spectrum, one of which is from an amide group that is hydrogen-bonded internally, or to a solvent molecule, and the other from a non-hydrogen-bonded amide group. The photoswitch enabled examination of both the folded and unfolded state of the helix. For most sites, unfolding of the peptide caused a shift of intensity from the hydrogen-bonded peak to the non-hydrogen-bonded peak. The relative intensity of the two diagonal peaks gives an indication of the fraction of molecules hydrogen-bonded at a certain location along the sequence. As this fraction varies quite substantially along the helix, we conclude that the helix is not uniformly folded. Furthermore, the shift in hydrogen bonding is much smaller than the change of helicity measured by CD spectroscopy, indicating that non-native hydrogen-bonded or mis-folded loops are formed in the unfolded ensemble. [ABSTRACT FROM AUTHOR]