Solvent Motions Research Articles

Protein folding is slaved to solvent motions.

Proteins, the workhorses of living systems, are constructed from chains of amino acids, which are synthesized in the cell based on the instructions of the genetic code and then folded into working proteins. The time for folding varies from microseconds to hours. What controls the folding rate is hotly debated. We postulate here that folding has the same temperature dependence as the alpha-fluctuations in the bulk solvent but is much slower. We call this behavior slaving. Slaving has been observed in folded proteins: Large-scale protein motions follow the solvent fluctuations with rate coefficient k(alpha) but can be slower by a large factor. Slowing occurs because large-scale motions proceed in many small steps, each determined by k(alpha). If conformational motions of folded proteins are slaved, so a fortiori must be the motions during folding. The unfolded protein makes a Brownian walk in the conformational space to the folded structure, with each step controlled by k(alpha). Because the number of conformational substates in the unfolded protein is extremely large, the folding rate coefficient, k(f), is much smaller than k(alpha). The slaving model implies that the activation enthalpy of folding is dominated by the solvent, whereas the number of steps n(f) = k(alpha)/k(f) is controlled by the number of accessible substates in the unfolded protein and the solvent. Proteins, however, undergo not only alpha- but also beta-fluctuations. These additional fluctuations are local protein motions that are essentially independent of the bulk solvent fluctuations and may be relevant at late stages of folding.

Projections of Quantum Observables onto Classical Degrees of Freedom in Mixed Quantum-Classical Simulations: Understanding Linear Response Failure for the Photoexcited Hydrated Electron

We present a general analytic method for understanding how specific motions of a classical bath influence the dynamics of quantum-mechanical observables in mixed quantum-classical molecular dynamics simulations. We apply our method and develop expressions for the special case of quantum solvation, allowing us to examine how specific classical solvent motions couple to the equilibrium energy fluctuations and nonequilibrium energy relaxation of a quantum-mechanical solute. As a first application of our formalism, we investigate the motions of classical water underlying the equilibrium and nonequilibrium excited-state solvent response functions of the hydrated electron; the results allow us to explain why the linear response approximation fails for this system.

Excited-State Charge Transfer at a Conical Intersection: Effects of an Environment

The influence of a polar and polarizable environment on charge transfer processes at a conical intersection (CI) can be described by a diabatic free energy model yielding coupled surfaces as a function of both molecular coordinates and a solvent coordinate. We extend and apply this model for the S1-S0 CI in protonated Schiff bases, representing a model for retinal isomerization (Faraday Discuss. 2004, 127, 395, 2004). A dielectric continuum description of the solvent is combined with a minimal, two-electron-two-orbital electronic structure model according to Bonacić-Koutecký, Koutecký, and Michl (Angew. Chem. 1987, 26, 170), which characterizes the charge translocation effects at the CI. The model predicts that the nonequilibrium solvent state resulting from the S0-->S1 Franck-Condon transition can entail the disappearance of the CI, such that solvent motion is necessary to reach the CI seam. The concerted evolution of the intramolecular coordinates and the solvent coordinate is illustrated by an excited-state minimum energy path.

Protein and solvent dynamics as studied by QENS and dielectric spectroscopy

We have investigated the dynamics of a protein (hemoglobin) in three different solvents by broadband dielectric spectroscopy and quasi-elastic neutron scattering (QENS). The solvents used were water, glycerol and methanol. From the dielectric measurements we were able to extract four relaxation processes, where the fastest process is due to solvent dynamics, and the three slower processes arise from protein motions of a different nature, and hence, visible on different time and temperature scales. The results from the mean square displacement (MSD) obtained by quasi-elastic neutron scattering indicate that the fast and local protein motions are strongly related (slaved) by the fastest and most local solvent motions in the case of water and glycerol. In contrast, for methanol we found the low temperature dynamics are dominated by the CH3 group rotation, which does not promote any protein dynamics.

Quantitative theory of structural relaxation in supercooled liquids and folded proteins

This article provides a brief, up-to-date review of the theory of activated relaxations in supercooled condensed systems, of Wolynes and coworkers. Supercooled liquids and frozen glasses are truly frustrated systems whose microscopic dynamics consist of cooperative motions, high in the energy spectrum of structural states, and well above the defect states of an ordered solid. There is a temperature below which activated processes dominate dynamics and thus a free energy landscape emerges, many of whose microscopic attributes can be computed. In addition to signature phenomena in supercooled liquids, we apply this microscopic picture to the phenomenon of slaving of large scale conformational changes of a folded protein, imbedded in a glass-forming solvent, to the solvent motions. The size of the basin encompassing the corresponding conformational substates will be deduced, based on kinetic measurements alone. Implications of the theory for interpreting computer simulations of glass-forming systems are discussed.

A macroion electrokinetics algorithm

A numerical algorithm is presented for the standard model of macroion electrokinetics and certain generalizations of it. The macroion consists of a cylindrical section with identical, hemispheroidal endcaps, each piece having arbitrary length. The system of one macroion and adjoining salt solution is subjected to an arbitrary sequence of pulsed electrical fields and pulsed translational and rotational velocities. Numerical solutions are obtained for the time dependent electrostatic and mobile ion concentration fields and the solvent velocity. From these fields the dielectric response, force, and torque are calculated. Generalizations of the standard model include the diffusive motion of macroion surface charges, partial slip of solvent motion at the macroion surface, and a simple model for the reactive exchange of surface charge with solution ions. The primary illustrative application is to recent measurements of electric birefringence versus applied field frequency for poly-(tetrafluorothylene) colloidal particles, but a few results are presented for the dielectric response of DNA fragments and of spherical colloidal particles. The source code and additional details are provided as supplementary documentation.

Towards Accurate Ab Initio QM/MM Calculations of Free-Energy Profiles of Enzymatic Reactions

Reliable studies of enzymatic reactions by combined quantum mechanical/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a large amount of computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. This work presents major progress toward the evaluation of ab initio QM/MM free-energy surfaces and activation free energies of reactions in enzymes and in solutions. This is done by exploiting our previous idea of using the empirical valence bond (EVB) method as a reference potential and then using the linear response approximation (LRA) approach to evaluate the free energies of transfer from the EVB to the QM/MM surfaces in the reactant and product state. However, the new crucial step involves the use of a constraint at the transition state that fixes the system at a given value of the reaction coordinate and allows us to use the LRA at the transition state. The advance offered by the present approach is particularly significant because it evaluates the free energy associated with both the substrate and the solvent motions. This evaluation appeared to be a relatively simple task once one uses a classical reference potential. The main problem has been using the reference potential for the evaluation of the free-energy contributions associated with the solute motions where the difference between the reference EVB potential and the QM/MM potential can be large. The present refinement finally allows us to overcome the problems with the solute fluctuations and therefore to obtain, for the first time, a free-energy barrier that reflects the solute entropy properly. Thus, we present a way to evaluate the complete QM/MM activation free energy with an equal footing treatment of the solute and the solvent. This provides a general consistent and effective strategy for evaluating the QM/MM activation free energies in proteins and in solution. Our advance allows one to explore consistently various mechanistic and catalytic proposals while using ab initio (ai) QM/MM approaches.

Recombination of photodissociated iodine: A time-resolved x-ray-diffraction study

A time-resolved x-ray-diffraction experiment is presented that aims to study the recombination of laser-dissociated iodine molecules dissolved in CCl4. This process is monitored over an extended time interval from pico- to microseconds. The variations of atom-atom distances are probed with a milliangstrom resolution. A recent theory of time-resolved x-ray diffraction is used to analyze the experimental data; it employs the correlation function approach of statistical mechanics. The most striking outcome of this study is the experimental determination of time-dependent I-I atom-atom distribution functions. The structure of the CCl4 solvent changes simultaneously; the solvent thus appears as a reaction partner rather than an inert medium hosting it. Thermal expansion of the system is nonuniform in time, an effect due to the presence of the acoustic horizon. One concludes that a time-resolved x-ray diffraction permits real-time visualization of solvent and solute motions during a chemical reaction.

Excited‐State Triple Proton Transfer of 7‐Hydroxyquinoline along a Hydrogen‐Bonded Alcohol Chain: Vibrationally Assisted Proton Tunneling

Proton relay in cyclic 7-hydroxyquinoline–(alcohol)2 complexes (see picture) has been explored in nonpolar solvents. The asymmetric triple proton transfer has an unusually large, temperature-independent, and viscosity-dependent kinetic isotope effect. Heavy-atom motions (wavy arrow) of solvent and bridging molecules allow proton tunneling by assisting the complex to reach the optimal precursor configuration. Supporting information for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2002/2006/z503209_s.pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Role of Protein Dynamics in Reaction Rate Enhancement by Enzymes

An integrated view of protein structure, dynamics, and function is emerging, where proteins are considered as dynamically active assemblies and internal motions are closely linked to function such as enzyme catalysis. Further, the motion of solvent bound to external regions of protein impacts internal motions and, therefore, protein function. Recently, we discovered a network of protein vibrations in enzyme cyclophilin A, coupled to its catalytic activity of peptidyl-prolyl cis-trans isomerization. Detailed studies suggest that this network, extending from surface regions to active site, is a conserved part of enzyme structure and has a role in promoting catalysis. In this report, theoretical investigations of concerted conformational fluctuations occurring on microsecond and longer time scales within the discovered network are presented. Using a new technique, kinetic energy was added to protein vibrational modes corresponding to conformational fluctuations in the network. The results reveal that protein dynamics promotes catalysis by altering transition state barrier crossing behavior of reaction trajectories. An increase in transmission coefficient and number of productive trajectories with increasing amounts of kinetic energy in vibrational modes is observed. Variations in active site enzyme-substrate interactions near transition state are found to be correlated with barrier recrossings. Simulations also showed that energy transferred from first solvation shell to surface residues impacts catalysis through network fluctuations. The detailed characterization of network presented here indicates that protein dynamics plays a role in rate enhancement by enzymes. Therefore, coupled networks in enzymes have wide implications in understanding allostericity and cooperative effects, as well as protein engineering and drug design.

Ultrafast Solvation of N‐Methyl‐6‐quinolone Probes Local IR Spectrum

A molecular dipole field (see picture) is created by femtosecond excitation of the title compound, and the response of the environment is observed by stimulated emission spectroscopy of the dye. Strong frequency modulation in the dynamic Stokes shift reflects coherent solvent motion. The IR spectrum of the solvent is related quantitatively to the experiment by dielectric continuum theory. Supporting information for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2002/2005/z501397_s.pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Ac-Electrogravimetry study of an all solid state potassium selective electrode with polypyrrole as the solid internal contact

The performances of all solid state potassium selective electrodes with polypyrrole film as solid internal contact were evaluated. Potentiometric measurements revealed near Nernstian responses close to values already given in the literature for classic ISEs. In addition, ac-electrogravimetry was used in order to study the ions and solvent motions at the membrane/electrolyte interface. We have found that potassium ions enter the selective membrane firstly but solvent molecules and anions are also participating in the phenomenon.

Mosaic Energy Landscapes of Liquids and the Control of Protein Conformational Dynamics by Glass-Forming Solvents

Using recent advances in the Random First-Order Transition (RFOT) Theory of glass-forming liquids, we explain how the molecular motions of a glass-forming solvent distort the protein's boundary and slave some of the protein's conformational motions. Both the length and time scales of the solvent imposed constraints are provided by the RFOT theory. Comparison of the protein relaxation rate to that of the solvent provides an explicit lower bound on the size of the conformational space explored by the protein relaxation. Experimental measurements of slaving of myoglobin motions indicate that a major fraction of functionally important motions have significant entropic barriers.

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.

Kinetic Pathways of β-Hairpin (Un)folding in Explicit Solvent

We examine the dynamical (un)folding pathways of the C-terminal β-hairpin of protein G-B1 at room temperature in explicit solvent, by employing transition path sampling algorithms. The path ensembles contain information on the folding kinetics, including solvent motion. We determine the transition state ensembles for the two main transitions: 1), the hydrophobic collapse; and 2), the backbone hydrogen bond formation. In both cases the transition state ensembles are characterized by a layer ( 1) or a strip ( 2) of water molecules in between the two hairpin strands, supporting the hypothesis of the solvent as lubricant in the folding process. The transition state ensembles do not correspond with saddle points in the equilibrium free-energy landscapes. The kinetic pathways are thus not completely determined by the free-energy landscape. This phenomenon can occur if the order parameters obey different timescales. Using the transition interface sampling technique, we calculate the rate constants for (un)folding and find them in reasonable agreement with experiments, thus supporting the validation of using all-atom force fields to study protein folding.

Polar Solvation Dynamics in Zn(II)-Substituted Cytochrome c: Diffusive Sampling of the Energy Landscape in the Hydrophobic Core and Solvent-Contact Layer

We employed picosecond time-resolved fluorescence spectroscopy to characterize polar diffusive protein and solvent dynamics in Zn(II)-substituted cytochrome c. The solvent-response function, obtained from the dynamic Stokes shift of the Zn(II) porphyrin's fluorescence 0-0 transition energy over the 100-ps to 12-ns time scale, exhibits a double-exponential decay (250 ps and 1.45 ns time constants). The addition of glycerol to the external solvent medium slows only the slower of the two exponential components; in the presence of 50% (v/v) glycerol, the second time constant was lengthened to 2.2 ns. The magnitude of the decay accounts for 85% of the reorganization energy and leaves room for only a minor inertial component on the sub-ps time scale. The results show that two types of polypeptide motions are sensed by the intrinsic Zn(II) porphyrin. The slower of the motions arises from polypeptide motions in the interfacial, solvent-contact portion of the protein. The faster, solvent-independent part of the response arises from motions of the polypeptide in the hydrophobic core of the protein. The two classes of motion are apparently not strongly coupled, nor is the dynamic Stokes shift coupled to the nonpolar reorganization that accompanies the excited-state photodissociation of the Zn(II) porphyrin's protein-derived axial ligands. The finding that the inertial response is limited to a small fraction of the total reorganization energy suggests that the hydrophobic core of the protein is largely incapable of the free-rotor or librational character of polypeptide and solvent motions that is observed near the solvent interface.

Electrons in finite-sized water cavities: hydration dynamics observed in real time.

We directly observed the hydration dynamics of an excess electron in the finite-sized water clusters of (H2O)n- with n = 15, 20, 25, 30, and 35. We initiated the solvent motion by exciting the hydrated electron in the cluster. By resolving the binding energy of the excess electron in real time with femtosecond resolution, we captured the ultrafast dynamics of the electron in the presolvated ("wet") and hydrated states and obtained, as a function of cluster size, the subsequent relaxation times. The solvation time (300 femtoseconds) after the internal conversion [140 femtoseconds for (H2O)35-] was similar to that of bulk water, indicating the dominant role of the local water structure in the dynamics of hydration. In contrast, the relaxation in other nuclear coordinates was on a much longer time scale (2 to 10 picoseconds) and depended critically on cluster size.

Solvation dynamics of room-temperature ionic liquids: evidence for collective solvent motion on sub-picosecond timescales

Little is known about the microscopic mechanism of solvation dynamics in room-temperature ionic liquids, but experimental studies have found that the solvent response has both sub-picosecond and nanosecond timescale components. We present the results of molecular dynamics calculations of the time-resolved fluorescence response of a chromophore in an ionic liquid, and analyze the solute–solvent interactions responsible for the observed signal. We find evidence for collective cation–anion motion on sub-picosecond timescales, contradicting earlier work suggesting the sub-picosecond response is purely anionic. We present an alternative hypothesis to explain our results and the widely disparate timescales for solvation response.

Elucidating the initial dynamics of electron photodetachment from atoms in liquids using variably-time-delayed resonant multiphoton ionization.

We study the photodetachment of electrons from sodium anions in room temperature liquid tetrahydrofuran (THF) using a new type of three-pulse pump-probe spectroscopy. Our experiments use two variably-time-delayed pulses for excitation in what is essentially a resonant 1+1 two-photon ionization: By varying the arrival time of the second excitation pulse, we can directly observe how solvent motions stabilize and trap the excited electron prior to electron detachment. Moreover, by varying the arrival times of the ionization (excitation) and probe pulses, we also can determine the fate of the photoionized electrons and the distance they are ejected from their parent Na atoms. We find that as solvent reorganization proceeds, the second excitation pulse becomes less effective at achieving photoionization, and that the solvent motions that stabilize the excited electron following the first excitation pulse occur over a time of approximately 450 fs. We also find that there is no spectroscopic evidence for significant solvent relaxation after detachment of the electron is complete. In combination with the results of previous experiments and molecular dynamics simulations, the data provide new insight into the role of the solvent in solution-phase electron detachment and charge-transfer-to-solvent reactions.

Theoretical simulations of dynamics of excess electron attachment to acetonitrile clusters

Dynamics of the attachment of an excess electron to acetonitrile clusters has been studied using mixed quantum-classical method, in which the electron motion were quantum-mechanically propagated in the ground electronic state and the acetonitrile solvent motions were treated classically. A one-electron pseudo-potential model was employed for electron–acetonitrile interaction, while an empirical site–site model was used for acetonitrile–acetonitrile interaction. Initial geometric configurations were obtained from the standard molecular dynamics simulation at a constant temperature. An excess electron, initially in a diffuse weakly bound surface state, is solvated via the solvent reorientation within several picoseconds. It has been found that the attachment of an electron to the acetonitrile cluster involves the formation of an internal localization state except for small clusters with low temperatures, for which metastable surface states were observed during the simulation time. The electron binding energies calculated from the simulations were also compared to recent experimental results; however, we found that our model significantly overestimates the electron binding energies.