Structure and dynamics of the solvation of bovine pancreatic trypsin inhibitor in explicit water: a comparative study of the effects of solvent and protein polarizability

To isolate the effects of the inclusion of polarizability in the force field model on the structure and dynamics of the solvating water in differing electrostatic environments of proteins, we present the results of molecular dynamics simulations of the bovine pancreatic trypsin inhibitor (BPTI) in water with force fields that explicitly include polarization for both the protein and the water. We use three model potentials for water and two model potentials for the protein. Two of the water models and one of the protein models are polarizable. A total of six systems were simulated representing all combinations of these polarizable and nonpolarizable protein and water force fields. We find that all six systems behave in a similar manner in regions of the protein that are weakly electrostatic (either hydrophobic or weakly hydrophilic). However, in the vicinity of regions of the protein with relatively strong electrostatic fields (near positively or negatively charged residues), we observe that the water structure and dynamics are dependent on both the model of the protein and the model of the water. We find that a large part of the dynamical dependence can be described by small changes in the local environments of each region that limit the local density of non-hydrogen-bonded waters, precisely the water molecules that facilitate the dynamical relaxation of the water-water hydrogen bonds. We introduce a simple method for rescaling for this effect. When this is done, we are able to effectively isolate the influence of polarizability on the dynamics. We find that the solvating water's relaxation is most affected when both the protein and the water models are polarizable. However, when only one model (or neither) is polarizable, the relaxation is similar regardless of the models used.     

Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9

To elucidate enzyme catalysis through computer simulation, a prerequisite is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio quantum mechanical/molecular mechanical approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9 and its corresponding uncatalyzed reaction in aqueous solution, respectively. Our calculated activation free energy barrier for the enzyme catalyzed reaction is 22.5 kcal/mol, which agrees very well with the experimental value of 20.9 kcal/mol. The difference in potential of mean force between a corresponding prereaction state and the transition state for the solution reaction is computed to be 30.9 kcal/mol. Thus, our simulations indicate that the enzyme SET7/9 plays an essential catalytic role in significantly lowering the barrier for the methyl-transfer reaction step. For the reaction in solution, it is found that the hydrogen bond network near the reaction center undergoes a significant change, and there is a strong shift in electrostatic field from the prereaction state to the transition state, whereas for the enzyme reaction, such an effect is much smaller and the enzyme SET7/9 is found to provide a preorganized electrostatic environment to facilitate the methyl-transfer reaction. Meanwhile, we find that the transition state in the enzyme reaction is a little more dissociative than that in solution.     

How much do enzymes really gain by restraining their reacting fragments?

The steric effect, exerted by enzymes on their reacting substrates, has been considered as a major factor in enzyme catalysis. In particular, it has been proposed that enzymes catalyze their reactions by pushing their reacting fragments to a catalytic configuration which is sometimes called near attack configuration (NAC). This work uses computer simulation approaches to determine the relative importance of the steric contribution to enzyme catalysis. The steric proposal is expressed in terms of well defined thermodynamic cycles that compare the reaction in the enzyme to the corresponding reaction in water. The S(N)2 reaction of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10, which was used in previous studies to support the strain concept is chosen as a test case for this proposal. The empirical valence bond (EVB) method provides the reaction potential surfaces in our studies. The reliability and efficiency of this method make it possible to obtain stable results for the steric free energy. Two independent strategies are used to evaluate the actual magnitude of the steric effect. The first applies restraints on the substrate coordinates in water in a way that mimics the steric effect of the protein active site. These restraints are then released and the free energy associated with the release process provides the desired estimate of the steric effect. The second approach eliminates the electrostatic interactions between the substrate and the surrounding in the enzyme and in water, and compares the corresponding reaction profiles. The difference between the resulting profiles provides a direct estimate of the nonelectrostatic contribution to catalysis and the corresponding steric effect. It is found that the nonelectrostatic contribution is about -0.7 kcal/mol while the full "apparent steric contribution" is about -2.2 kcal/mol. The apparent steric effect includes about -1.5 kcal/mol electrostatic contribution. The total electrostatic contribution is found to account for almost all the observed catalytic effect ( approximately -6.1 kcal/mol of the -6.8 calculated total catalytic effect). Thus, it is concluded that the steric effect is not the major source of the catalytic power of haloalkane dehalogenase. Furthermore, it is found that the largest component of the apparent steric effect is associated with the solvent reorganization energy. This solvent-induced effect is quite different from the traditional picture of balance between the repulsive interaction of the reactive fragments and the steric force of the protein.     

Intermolecular electrostatic interactions and Brownian tumbling in protein solutions

It is often implicitly assumed that the long-range intermolecular electrostatic interactions in homogeneous protein solutions either are negligible for affecting protein Brownian tumbling or cause its deceleration without changing the shape of rotational auto-correlation function. This review presents a wide set of experimental data (NMR relaxation, dielectric spectroscopy and Brownian dynamics simulations) demonstrating that the interprotein electrostatic steering leads to a complication of the rotational correlation function. The key point of this effect is the rotational anisotropy caused by the interaction of the electric dipole moment of a protein with the external electric field produced by charges of neighboring proteins. Taking this effect into account in some cases might be of critical importance for the correct interpretation of various experimental data.     

How protein surfaces induce anomalous dynamics of hydration water

Water around biomolecules slows down with respect to pure water, and both rotation and translation exhibit anomalous time dependence in the hydration shell. The origin of such behavior remains elusive. We use molecular dynamics simulations of water dynamics around several designed protein models to establish the connection between the appearance of the anomalous dynamics and water-protein interactions. For the first time we quantify the separate effect of protein topological and energetic disorder on the hydration water dynamics. When a static protein structure is simulated, we show that both types of disorder contribute to slow down water diffusion, and that allowing for protein motion, increasing the spatial dimensionality of the interface, reduces the anomalous character of hydration water. The rotation of water is, instead, altered by the energetic disorder only; indeed, when electrostatic interactions between the protein and water are switched off, water reorients even faster than in the bulk. The dynamics of water is also related to the collective structure--à voir the hydrogen bond (H-bond) network--formed by the solvent enclosing the protein surface. We show that, as expected for a full hydrated protein, when the protein surface offers pinning sites (charged or polar sites), the superficial water-water H-bond network percolates throughout the whole surface, hindering the water diffusion, whereas it does not when the protein surface lacks electrostatic interactions with water and the water diffusion is enhanced.     

Millisecond dynamics in glutaredoxin during catalytic turnover is dependent on substrate binding and absent in the resting states

Conformational dynamics is important for enzyme function. Which motions of enzymes determine catalytic efficiency and whether the same motions are important for all enzymes, however, are not well understood. Here we address conformational dynamics in glutaredoxin during catalytic turnover with a combination of NMR magnetization transfer, R(2) relaxation dispersion, and ligand titration experiments. Glutaredoxins catalyze a glutathione exchange reaction, forming a stable glutathinoylated enzyme intermediate. The equilibrium between the reduced state and the glutathionylated state was biochemically tuned to exchange on the millisecond time scale. The conformational changes of the protein backbone during catalysis were followed by (15)N nuclear spin relaxation dispersion experiments. A conformational transition that is well described by a two-state process with an exchange rate corresponding to the glutathione exchange rate was observed for 23 residues. Binding of reduced glutathione resulted in competitive inhibition of the reduced enzyme having kinetics similar to that of the reaction. This observation couples the motions observed during catalysis directly to substrate binding. Backbone motions on the time scale of catalytic turnover were not observed for the enzyme in the resting states, implying that alternative conformers do not accumulate to significant concentrations. These results infer that the turnover rate in glutaredoxin is governed by formation of a productive enzyme-substrate encounter complex, and that catalysis proceeds by an induced fit mechanism rather than by conformer selection driven by intrinsic conformational dynamics.     

Water rotational relaxation and diffusion in hydrated lysozyme

This paper is concerned with the dynamics of water around a small globular protein. Dipolar second-rank relaxation time and diffusion properties of surface water were computed by extensive molecular dynamics simulations of lysozyme in water which lasted a total of 28 ns. Our results indicate that the rotational relaxation of water in the vicinity of lysozyme is 3-7 times slower than that in the bulk depending on how the hydration shell is defined in the calculation. We have also verified that the dynamics of water translational diffusion in the vicinity of lysozyme have retardations similar to rotational relaxation. This is a common assumption in nuclear magnetic relaxation dispersion (NMRD) studies to derive residence times. In contrast to bulk water dynamics, surface water is in a dispersive diffusion regime or subdiffusion. Very good agreement of dipolar second-rank relaxation time with NMRD estimates is obtained by using appropriate dimensions of the hydration shell. Although our computed second-rank dipolar retardations are independent of the water model, SPC/E describes more realistically the time scale of the water dynamics around lysozyme than does TIP3P.     

Solvation in supercritical water

Solvation in supercritical water under equilibrium and nonequilibrium conditions is studied via molecular dynamics simulations. The influence of solute charge distributions and solvent density on the solvation structures and dynamics is examined with a diatomic probe solute molecule. It is found that the solvation structure varies dramatically with the solute dipole moment, especially in low-density water, in accord with many previous studies on ion solvation. This electrostrictive effect has important consequences for solvation dynamics. In the case of a nonequilibrium solvent relaxation, if there are sufficiently many water molecules close to the solute at the outset of the relaxation, the solvent response measured as a dynamic Stokes shift is almost completely governed by inertial rotations of these water molecules. By contrast, in the opposite case of a low local solvent density near the solute, not only rotations but also translations of water molecules play an important role in solvent relaxation dynamics. The applicability of a linear response is found to be significantly restricted at low water densities.     

A comparison of Coulombic interaction methods in non-equilibrium studies of heat transfer in water

We investigate the impact of the treatment of electrostatic interactions on the heat conduction of liquid water. With this purpose, we report a series of non-equilibrium molecular dynamics computer simulations of the Modified Central Force Model of water. We consider both the Ewald summation approach, which includes the full range of the electrostatic interactions, and the Wolf method, which uses a cutoff to truncate the long range contributions. It is shown that the relaxation of the temperature profiles towards the stationary state solution and the equation of state of the liquid are not affected by the treatment of the electrostatic interactions. However, the truncation of the interactions results in lower internal energy fluxes as well as lower thermal conductivities. We also find that the anomalous increase of the thermal conductivity of water with temperature is reproduced by the different methods considered in this work, showing that this physical behavior is independent of the treatment of the long range electrostatic interactions.     

Water dynamics at protein interfaces: ultrafast optical Kerr effect study

The behavior of water molecules surrounding a protein can have an important bearing on its structure and function. Consequently, a great deal of attention has been focused on changes in the relaxation dynamics of water when it is located at the protein surface. Here we use the ultrafast optical Kerr effect to study the H-bond structure and dynamics of aqueous solutions of proteins. Measurements are made for three proteins as a function of concentration. We find that the water dynamics in the first solvation layer of the proteins are slowed by up to a factor of 8 in comparison to those in bulk water. The most marked slowdown was observed for the most hydrophilic protein studied, bovine serum albumin, whereas the most hydrophobic protein, trypsin, had a slightly smaller effect. The terahertz Raman spectra of these protein solutions resemble those of pure water up to 5 wt % of protein, above which a new feature appears at ~80 cm(-1), which is assigned to a bending of the protein amide chain.     

Reorientation dynamics of nanoconfined water: power-law decay, hydrogen-bond jumps, and test of a two-state model

The reorientation dynamics of water confined within nanoscale, hydrophilic silica pores are investigated using molecular dynamics simulations. The effect of surface hydrogen-bonding and electrostatic interactions are examined by comparing with both a silica pore with no charges (representing hydrophobic confinement) and bulk water. The OH reorientation in water is found to slow significantly in hydrophilic confinement compared to bulk water, and is well-described by a power-law decay extending beyond one nanosecond. In contrast, the dynamics of water in the hydrophobic pore are more modestly affected. A two-state model, commonly used to interpret confined liquid properties, is tested by analysis of the position-dependence of the water dynamics. While the two-state model provides a good fit of the orientational decay, our molecular-level analysis evidences that it relies on an over-simplified picture of water dynamics. In contrast with the two-state model assumptions, the interface dynamics is markedly heterogeneous, especially in the hydrophilic pore and there is no single interfacial state with a common dynamics.     

Origin of the absorption maxima of the photoactive yellow protein resolved via ab initio multiconfigurational methods

We discuss the role of the protein in controlling the absorption spectra of photoactive yellow protein (PYP), the archetype xanthopsin photoreceptor, using quantum mechanics/molecular mechanics (QM/MM) methods based on ab initio multireference perturbation theory, combined with molecular dynamics (MD) simulations. It is shown that in order to get results in agreement with the experimental data, it is necessary to use a model that allows for a proper relaxation of the whole system and treats the states involved in the electronic spectrum in a balanced way, avoiding biased results due to the effect of nonrepresentative electrostatic interactions on the chromophore.     

Protein-water electrostatics and principles of bioenergetics

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.     

Dynamics on the electronically excited state surface of the bioluminescent firefly luciferase-oxyluciferin system

Dynamics of the firefly luciferase-oxyluciferin complex in its electronic ground and excited states are studied using various theoretical approaches. By mimicking the physiological conditions with realistic models of the chromophore oxyluciferin, the enzyme luciferase, and solvating water molecules and by performing real time simulations with a molecular dynamics technique on the model surfaces, we reveal that the local chromophore-surrounding interaction patterns differ rather severely in the two states. Because of the presence of protein, the solvation dynamics of water around the chromophore is also peculiar and shows widely different time scales on the two terminal oxygen atoms. In addition, simulations of the emission with the quantum-mechanics/molecular-mechanics approach show a close relationship between the emission color variation and the environmental dynamics, mostly through electrostatic effects from the chromophore-surrounding interaction. We also discuss the importance of considering the time scales of the luminescence and the dynamics of the interaction.     

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.     

Hydrogen‐bonding interactions in the active site of a low molecular weight protein‐tyrosine phosphatase

Molecular dynamics simulation of the Michaelis complex, phospho‐enzyme intermediate, and the wild‐type and C12S mutant have been carried out to examine hydrogen‐bonding interactions in the active site of the bovine low molecular weight protein‐tyrosine phosphatase (BPTP). It was found that the S_γ atom of the nucleophilic residue Cys‐12 is ideally located at a position opposite from the phenylphosphate dianion for an inline nucleophilic substitution reaction. In addition, electrostatic and hydrogen‐bonding interactions from the backbone amide groups of the phosphate‐binding loop strongly stabilize the thiolate anion, making Cys‐12 ionized in the active site. In the phospho‐enzyme intermediate, three water molecules are found to form strong hydrogen bonds with the phosphate group. In addition, another water molecule can be identified to form bridging hydrogen bonds between the phosphate group and Asp‐129, which may act as the nucleophile in the subsequent phosphate hydrolysis reaction, with Asp‐129 serving as a general base. The structural difference at the active site between the wild‐type and C12S mutant has been examined. It was found that the alkoxide anion is significantly shifted toward one side of the phosphate binding loop, away from the optimal position enjoyed by the thiolate anion of the wild‐type enzyme in an S_N2 process. This, coupled with the high pK_a value of an alcoholic residue, makes the C12S mutant catalytically inactive. These molecular dynamics simulations provided details of hydrogen bonding interactions in the active site of BPTP, and a structural basis for further studies using combined quantum mechanical and molecular mechanical potential to model the entire dephosphorylation reaction by BPTP. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1192–1203, 2000     

Protein dynamics control of electron transfer in photosynthetic reaction centers from Rps. sulfoviridis

In the cycle of photosynthetic reaction centers, the initially oxidized special pair of bacteriochlorophyll molecules is subsequently reduced by an electron transferred over a chain of four hemes of the complex. Here, we examine the kinetics of electron transfer between the proximal heme c-559 of the chain and the oxidized special pair in the reaction center from Rps. sulfoviridis in the range of temperatures from 294 to 40 K. The experimental data were obtained for three redox states of the reaction center, in which one, two, or three nearest hemes of the chain are reduced prior to special pair oxidation. The experimental kinetic data are analyzed in terms of a Sumi-Marcus-type model developed in our previous paper,1 in which similar measurements were reported on the reaction centers from Rps. viridis. The model allows us to establish a connection between the observed nonexponential electron-transfer kinetics and the local structural relaxation dynamics of the reaction center protein on the microsecond time scale. The activation energy for relaxation dynamics of the protein medium has been found to be around 0.1 eV for all three redox states, which is in contrast to a value around 0.4-0.6 eV in Rps. viridis.1 The possible nature of the difference between the reaction centers from Rps. viridis and Rps. sulfoviridis, which are believed to be very similar, is discussed. The role of the protein glass transition at low temperatures and that of internal water molecules in the process are analyzed.     

What is the time scale for α-helix nucleation?

Helix formation is an elementary process in protein folding, influencing both the rate and mechanism of the global folding reaction. Yet, because helix formation is less cooperative than protein folding, the kinetics are often multiexponential, and the observed relaxation times are not straightforwardly related to the microscopic rates for helix nucleation and elongation. Recent ultrafast spectroscopic measurements on the peptide Ac-WAAAH(+)-NH(2) were best fit by two relaxation modes on the ～0.1-1 ns time scale, (1) apparently much faster than had previously been experimentally inferred for helix nucleation. Here, we use replica-exchange molecular dynamics simulations with an optimized all-atom protein force field (Amber ff03w) and an accurate water model (TIP4P/2005) to study the kinetics of helix formation in this peptide. We calculate temperature-dependent microscopic rate coefficients from the simulations by treating the dynamics between helical states as a Markov process using a recently developed formalism. The fluorescence relaxation curves obtained from simulated temperature jumps are in excellent agreement with the experimentally determined results. We find that the kinetics are multiphasic but can be approximated well by a double-exponential function. The major processes contributing to the relaxation are the shrinking of helical states at the C-terminal end and a faster re-equilibration among coil states. Despite the fast observed relaxation, the helix nucleation time is estimated from our model to be 20-70 ns at 300 K, with a dependence on temperature well described by Arrhenius kinetics.