Viscosity dependence of protein dynamics

The influence of solvent viscosity on protein dynamics was investigated with molecular dynamics simulations of factor Xa in two solvents differing only in viscosity, by a factor of 10. We obtained this viscosity change by changing the masses of the solvent atoms by a factor of 100. Equilibrium properties of the protein, that is, the average structure, its fluctuations, and the secondary structure, show no significant dependence on the solvent viscosity. The dynamic properties of the protein, that is, the atom-positional correlation times and torsional angle transitions, however, depend on the solvent viscosity. The protein appears to be much more mobile in the solvent of lower viscosity. It feels the influence of the solvent not only on the surface but even in its core. With increasing solvent viscosity, the positional relaxation times of atoms in the protein core increase as much as those of atoms on the protein surface, and the relative increase in the core is even larger than on the surface.     

Viscous cosolvent effect on the ultrasonic absorption of bovine serum albumin.

Protein-ligand binding and enzyme activity have been shown to be regulated by solvent viscosity, induced by the addition of viscous cosolvents. This was indirectly interpreted as an effect on protein dynamics. However, viscous cosolvents might affect dynamic, e.g., viscosity, as well as thermodynamic properties of the solution, e.g., activity of solution components. This work was undertaken to examine the effect of viscous cosolvent on the structural dynamics of proteins and its correlation with dynamic and thermodynamic solution properties. For this purpose we studied the effect of viscous cosolvent on the specific ultrasonic absorption, delta mu, of bovine serum albumin, at pH = 7.0 and at 21 degrees C, and frequency range of 3-4 MHz. Ultrasonic absorption (UA) directly probes protein dynamics related to energy dissipation processes. It was found that the addition of sucrose, glycerol, or ethylene glycol increased the BSA delta mu. This increase correlates well with the solvent viscosity, but not with the cosolvent mass concentration, activity of the solvent components, dielectric constant, or the hydration of charged groups. On the grounds of these results and previously reported findings, as well as theoretical considerations, we propose the following mechanism for the solvent viscosity effect on the protein structural fluctuations, reflected in the UA: increased solvent viscosity alters the frequency spectrum of the polypeptide chain movements; attenuating the fast (small amplitude) movements, and enhancing the slow (large amplitude) ones. This modulates the interaction strength between the polypeptide and water species that "lubricates" the chain's movements, leading to larger protein-volume fluctuation and higher ultrasonic absorption. This study demonstrates that solvent viscosity is a regulator of protein structural fluctuations.     

Solvent effects on protein motion and protein effects on solvent motion. Dynamics of the active site region of lysozyme

The stochastic boundary molecular dynamics methodology is applied to the active site of the enzyme lysozyme. A comparison is made of in vacuo dynamics results from the stochastic boundary method and a full conventional molecular dynamics simulation of lysozyme. Excellent agreement between the two approaches is obtained. The influence of solvent on the residues in the active site region is explored and it is shown that both the structure and dynamics are affected. Of particular importance for the structure of the protein is the solvation of polar residues and the stabilization of like-charged ion pairs. The magnitude of the fluctuations is only slightly altered by the solvent; the overall increase in the root-mean-square fluctuations, relative to the vacuum run, is 11%. The solvent effect on dynamical properties is found not to be simply related to the solvent viscosity. Both the solvent exposure and dynamic aspects of protein-solvent interactions, including the relative time scales of the motions, are shown to play a role. The effects of the protein on solvent dynamics and structure are also observed to be significant. The solvent molecules around atoms in charged, polar and apolar side-chains show markedly different diffusion coefficients as well as exhibiting different solvation structures. One key example is the water around apolar groups, which is much less mobile than bulk water, or water solvating polar groups.     

Solvent mobility and the protein 'glass' transition

Proteins and other biomolecules undergo a dynamic transition near 200 K to a glass-like solid state with small atomic fluctuations. This dynamic transition can inhibit biological function. To provide a deeper understanding of the relative importance of solvent mobility and the intrinsic protein energy surface in the transition, a novel molecular dynamics simulation procedure with the protein and solvent at different temperatures has been used. Solvent mobility is shown to be the dominant factor in determining the atomic fluctuations above 180 K, although intrinsic protein effects become important at lower temperatures. The simulations thus complement experimental studies by demonstrating the essential role of solvent in controlling functionally important protein fluctuations.     

Solvent Friction Changes the Folding Pathway of the Tryptophan Zipper TZ2

Because the rate of a diffusional process such as protein folding is controlled by friction encountered along the reaction pathway, the speed of folding is readily tunable through adjustment of solvent viscosity. The precise relationship between solvent viscosity and the rate of diffusion is complex and even conformation-dependent, however, because both solvent friction and protein internal friction contribute to the total reaction friction. The heterogeneity of the reaction friction along the folding pathway may have subtle consequences. For proteins that fold on a multidimensional free-energy surface, an increase in solvent friction may drive a qualitative change in folding trajectory. Our time-resolved experiments on the rapidly and heterogeneously folding β-hairpin TZ2 show a shift in the folding pathway as viscosity increases, even though the energetics of folding is unaltered. We also observe a nonlinear or saturating behavior of the folding relaxation time with rising solvent viscosity, potentially an experimental signature of the shifting pathway for unfolding. Our results show that manipulations of solvent viscosity in folding experiments and simulations may have subtle and unexpected consequences on the folding dynamics being studied.     

Hydrogen-deuterium exchange mass spectrometry for investigation of backbone dynamics of oxidized and reduced cytochrome P450cam

Backbone dynamics of the camphor monoxygenase cytochrome P450(cam) (CYP101) as a function of oxidation/ligation state of the heme iron were investigated via hydrogen/deuterium exchange (H/D exchange) as monitored by mass spectrometry. Main chain amide NH hydrogens can exchange readily with solvent and the rate of this exchange depends upon, among other things, dynamic fluctuations in local structural elements. A fluxional region of the polypeptide will exchange more quickly with solvent than one that is more constrained. In most regions of the enzyme, exchange rates were similar between oxidized high-spin camphor-bound and reduced camphor- and CO-bound CYP101 (CYP-S and CYP-S-CO, respectively). However, in regions of the protein that have previously been implicated in substrate access by structural and molecular dynamics investigations, the reduced enzyme shows significantly slower exchange rates than the oxidized CYP-S. This observation corresponds to increased flexibility of the oxidized enzyme relative to the reduced form. Structural features previously found to be perturbed in CYP-S-CO upon binding of the biologically relevant effector and reductant putidaredoxin (Pdx) as determined by nuclear magnetic resonance are also more protected from exchange in the reduced state. To our knowledge, this study represents the first experimental investigation of backbone dynamics within the P450 family using this methodology.     

Glycerol effects on protein flexibility: a tryptophan phosphorescence study.

In exploring the dynamic properties of protein structure, numerous studies have focussed on the dependence of structural fluctuations on solvent viscosity, but the emerging picture is still not well defined. Exploiting the sensitivity of the phosphorescence lifetime of tryptophan to the viscosity of its environment we have used the delayed emission as an intrinsic probe of protein flexibility and investigated the effects of glycerol as a viscogenic cosolvent. The phosphorescence lifetime of alcohol dehydrogenase, alkaline phosphatase, apoazurin and RNase T1, as a function of glycerol concentration was studied at various temperatures. Flexibility data, which refer to rather rigid sites of the globular structures, point out that, for some concentration ranges glycerol, effects on the rate of structural fluctuations of alcohol dehydrogenase and RNase T1 do not obey Kramers' a power law on solvent viscosity and emphasize that cosolvent-induced structural changes can be important, even for inner cores of the macromolecule. When the data is analyzed in terms of Kramers' model, for the temperature range 0-30 degrees C one derives frictional coefficients that are relatively large (0.6-0.7) for RNase T1, where the probe is in a flexible region near the surface of the macromolecule and much smaller, less than 0.2, for the rigid sites of the other proteins. For the latter sites the frictional coefficient rises sharply between 40 and 60 degrees C, and its value correlates weakly with molecular parameters such as the depth of burial or the rigidity of a particular site. For RNase T1, coupling to solvent viscosity increases at subzero temperatures, with the coefficient becoming as large as 1 at -20 degrees C.(ABSTRACT TRUNCATED AT 250 WORDS)     

Dynamical properties of fasciculin-2.

Fasciculin-2 (FAS2) is a potent protein inhibitor of the hydrolytic enzyme acetylcholinesterase. A 2-ns isobaric-isothermal ensemble molecular dynamics simulation of this toxin was performed to examine the dynamic structural properties which may play a role in this inhibition. Conformational fluctuations of the FAS2 protein were examined by a variety of techniques to identify flexible residues and determine their characteristic motion. The tips of the toxin "finger" loops and the turn connecting loops I and II were found to fluctuate, while the rest of the protein remained fairly rigid throughout the simulation. Finally, the structural fluctuations were compared to NMR data of fluctuations on a similar timescale in a related three-finger toxin. The molecular dynamics results were in good qualitative agreement with the experimental measurements. Proteins 1999;36:447-453.     

A comparison of structural and dynamic properties of different simulation methods applied to SH3.

The dynamic and static properties of molecular dynamics simulations using various methods for treating solvent were compared. The SH3 protein domain was chosen as a test case because of its small size and high surface-to-volume ratio. The simulations were analyzed in structural terms by examining crystal packing, distribution of polar residues, and conservation of secondary structure. In addition, the "essential dynamics" method was applied to compare each of the molecular dynamics trajectories with a full solvent simulation. This method proved to be a powerful tool for the comparison of large concerted atomic motions in SH3. It identified methods of simulation that yielded significantly different dynamic properties compared to the full solvent simulation. Simulating SH3 using the stochastic dynamics algorithm with a vacuum (reduced charge) force field produced properties close to those of the full solvent simulation. The application of a recently described solvation term did not improve the dynamic properties. The large concerted atomic motions in the full solvent simulation as revealed by the essential dynamics method were analyzed for possible biological implications. Two loops, which have been shown to be involved in ligand binding, were seen to move in concert to open and close the ligand-binding site.     

Structural compliance: A new metric for protein flexibility

Proteins are the active players in performing essential molecular activities throughout biology, and their dynamics has been broadly demonstrated to relate to their mechanisms. The intrinsic fluctuations have often been used to represent their dynamics and then compared to the experimental B-factors. However, proteins do not move in a vacuum and their motions are modulated by solvent that can impose forces on the structure. In this paper, we introduce a new structural concept, which has been called the structural compliance, for the evaluation of the global and local deformability of the protein structure in response to intramolecular and solvent forces. Based on the application of pairwise pulling forces to a protein elastic network, this structural quantity has been computed and sometimes is even found to yield an improved correlation with the experimental B-factors, meaning that it may serve as a better metric for protein flexibility. The inverse of structural compliance, namely the structural stiffness, has also been defined, which shows a clear anticorrelation with the experimental data. Although the present applications are made to proteins, this approach can also be applied to other biomolecular structures such as RNA. This present study considers only elastic network models, but the approach could be applied further to conventional atomic molecular dynamics. Compliance is found to have a slightly better agreement with the experimental B-factors, perhaps reflecting its bias toward the effects of local perturbations, in contrast to mean square fluctuations. The code for calculating protein compliance and stiffness is freely accessible at https://jerniganlab.github.io/Software/PACKMAN/Tutorials/compliance .     

Molecular dynamics effects on protein electrostatics

Electrostatic calculations have been carried out on a number of structural conformers of tuna cytochrome c. Conformers were generated using molecular dynamics simulations with a range of solvent simulating, macroscopic dielectric formalisms, and one solvent model that explicitly included solvent water molecules. Structures generated using the lowest dielectric models were relatively tight, with side chains collapsed on the surface, while those from the higher dielectric models had more internal and external fluidity, with surface side chains exploring a fuller range of conformational space. The average structure generated with the explicitly solvated model corresponded most closely with the crystal structure. Individual pK values, overall titration curves, and electrostatic potential surfaces were calculated for average structures and structures along each simulation. Differences between structural conformers within each simulation give rise to substantial changes in calculated local electrostatic interactions, resulting in pK value fluctuations for individual sites in the protein that vary by 0.3-2.0 pK units from the calculated time average. These variations are due to the thermal side chain reorientations that produce fluctuations in charge site separations. Properties like overall titration curves and pH dependent stability are not as sensitive to side chain fluctuations within a simulation, but there are substantial effects between simulations due to marked differences in average side chain behavior. These findings underscore the importance of proper dielectric formalism in molecular dynamics simulations when used to generate alternate solution structures from a crystal structure, and suggest that conformers significantly removed from the average structure have altered electrostatic properties that may prove important in episodic protein properties such as catalysis.     

Operator recognition by the phage 434 cI repressor: MD simulations of free and bound 50-bp DNA reveal important differences between the OR1 and OR2 sites

Using molecular dynamics simulations in explicit solvent, we investigated the behavior of a 50-bp DNA sequence containing the 434 bacteriophage operators OR1 and OR2 separated by an 8-bp spacer. Two simulations of 1 ns each were carried out, with DNA alone and with DNA complexed to dimers of the R1-69 DNA binding domain of the phage 434 cI repressor protein at the OR1 and OR2 sites. Strong correlations among average structural parameters are observed between our simulations and available experimental data for the bound OR1/OR2 subsites. In the free state, some differences appear between the three relevant fragments (OR1, the spacer, and OR2). Unbound OR1 exhibits a large, shallow major groove into which the base atoms protrude and is also bent toward the major groove. This structure is maintained because structural fluctuations are weak. Unbound OR2 resembles canonical B-DNA although the structural parameters show greater fluctuations, essentially due to a malleable step (the innermost CpA/TpG), absent in OR1. Complexation with the proteins slightly alters the base positions but strongly modifies the sugar and backbone motions. The most crucial repressor effects are changes in the flexibility of the OR1/OR2 sites. Structural fluctuations are enhanced for OR1, conferring a favorable energetic contribution to the OR1 binding, whereas they are reduced for OR2. Therefore, both structural and dynamic properties of DNA suggest OR1 is the most attractive site for the repressor, which may explain the different binding association constants observed for the OR1 and OR2 sites. Finally, we also investigated the impact of the protein on the DNA backbone dynamics and find that direct or indirect interactions facilitate the DNA structural variations required for achieving complementarity with the protein.     

The effect of the solvent viscosity on the migration of small molecules through the structure of myoglobin.

The migration rate of small molecules through the structure of proteins can be monitored by quenching the light emitted from an excited optical probe located within the protein. In the present study we examined the influence of the solvent viscosity on the migration rate of the quencher anthraquinone sulfonate through myoglobin towards an excited Zn protoporphyrin molecule at the binding site of the protein. The solvent viscosity was increased by adding dextrans of different molecular weight but forming isoviscous solutions. The results demonstrate that the migration rate in the protein decreases with increasing solvent viscosity. This suggests that the fluctuations on the protein structure, which make the above migration possible, are affected by the solvent macroviscosity.     

Effect of protein dynamics upon reactions that occur in the heme pocket of horseradish peroxidase

Free base and Pd porphyrin derivatives of horseradish peroxidase show long-lived excited states that are quenched by the presence of the peroxidase inhibitor, benzhydroxamic acid. The relaxation times of the excited-state luminescence and the rates of the quenching reaction for these derivatives of peroxidase were monitored as a function of pH, temperature, and viscosity with the view of examining how protein dynamics affect the quenching reaction. As solvent viscosity increases, the rate decreases, but at the limit of very high viscosity (i.e., high glycerol or sugar glass) the quenching still occurs. A model is presented that is consistent with the known structure of the enzyme-inhibitor complex. It is considered that the inhibitor is held at an established position but that solvent-dependent and independent motions allow a limited diffusion of the two reactants. Since there is a steep dependence upon distance and orientation, the diffusion toward the favorable position for reaction enhances the reaction rate. The solvent viscosity dependent and independent effects were separated and analyzed. The importance of internal reaction dynamics is demonstrated in the observation that rigidity of solvent imposed by incorporating the protein into glass at room temperature allows the reaction to occur, while the reaction is inhibited at low temperature. The results emphasize that protein dynamics plays a role in determining reaction rates.     

Molecular dynamics simulations and oxidation rates of methionine residues of granulocyte colony-stimulating factor at different pH values

To understand the connection between the conformation of a protein molecule and the oxidation of its methionine residues, we measured the rates of oxidation of methionine residues by H(2)O(2) in granulocyte colony-stimulating factor (G-CSF) as a function of pH and also studied the structural properties of this protein as a function of pH via molecular dynamics simulations. We found that each of the four methionine groups in G-CSF have significant and different rates of oxidation as a function of pH. Moreover, Met(1), in the unstructured N-terminal region, has a rate of oxidation as low as half that of free methionine. The structural properties of G-CSF as a function of pH are evaluated in terms of properties such as hydrogen bonding, deviations from X-ray structure, helical/helical packing, and the atomic covariance fluctuation matrix of alpha-carbons. We found that dynamics (structural fluctuations) are essential in explaining oxidation and that a static picture, such as that resulting from X-ray data, fails in this regard. Moreover, the simulation results also indicate that the solvent-accessible area, traditionally used to measure solvent accessibility of a protein site, of the sulfur atom of methionine residues does not correlate well with the rate of oxidation. Instead, we identified a structural property, average two-shell water coordination number, that correlates well with measured oxidation rates.     

The nature of folded states of globular proteins.

We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.     

Protein dynamics in solution and in a crystalline environment: a molecular dynamics study

The effect of a solvent and a crystalline environment on the dynamics of proteins is investigated by the method of computer simulation. Three 25-ps molecular dynamics simulations at 300 K of the bovine pancreatic trypsin inhibitor (BPTI), consisting of 454 heavy atoms, are compared: one of BPTI in vacuo, one of BPTI in a box with 2647 spherical nonpolar solvent atoms, and one of BPTI surrounded by fixed crystal image atoms. Both average and time-dependent molecular properties are examined to determine the effect of the environment on the behavior of the protein. The dynamics of BPTI in solution or in the crystal environment are found to be very similar to that found in the vacuum calculation. The primary difference in the average properties is that the equilibrium structure in the presence of solvent or the crystal field is significantly closer to the X-ray structure than is the vacuum result; concomitantly, the more realistic environment leads to a number density closer to experiment. The presence of solvent has a negligible effect on the overall magnitude of the positional or dihedral angle fluctuations in the interior of the protein; however, there are changes in the decay times of the fluctuations of interior atoms. For surface residues, both the magnitude and the time course of the motions are significantly altered by the solvent. There tends to be an increase in the displacements of long side chains and the flexible parts of the main chain that protrude into the solvent. Further, these motions tend to have a more diffusive character with longer relaxation times than in vacuo. The crystal environment has a specific effect on a number of side chains which are held in relatively fixed positions through hydrogen-bond and electric interactions with the neighboring protein atoms. Most of the effects of the solution environment seem to be sufficiently nonspecific that it may be possible to model them by applying a mean field and stochastic dynamic methods.     

Internal friction controls the speed of protein folding from a compact configuration

Several studies have found millisecond protein folding reactions to be controlled by the viscosity of the solvent: Reducing the viscosity allows folding to accelerate. In the limit of very low solvent viscosity, however, one expects a different behavior. Internal interactions, occurring within the solvent-excluded interior of a compact molecule, should impose a solvent-independent upper limit to folding speed once the bulk diffusional motions become sufficiently rapid. Why has this not been observed? We have studied the effect of solvent viscosity on the folding of cytochrome c from a highly compact, late-stage intermediate configuration. Although the folding rate accelerates as the viscosity declines, it tends toward a finite limiting value approximately 10(5) s(-1) as the viscosity tends toward zero. This limiting rate is independent of the cosolutes used to adjust solvent friction. Therefore, interactions within the interior of a compact denatured polypeptide can limit the folding rate, but the limiting time scale is very fast. It is only observable when the solvent-controlled stages of folding are exceedingly rapid or else absent. Interestingly, we find a very strong temperature dependence in these "internal friction"-controlled dynamics, indicating a large energy scale for the interactions that govern reconfiguration within compact, near-native states of a protein.     

A molecular dynamics analysis of protein structural elements

The relation between protein secondary structure and internal motions was examined by using molecular dynamics to calculate positional fluctuations of individual helix, beta-sheet, and loop structural elements in free and substrate-bound hen egg-white lysozyme. The time development of the fluctuations revealed a general correspondence between structure and dynamics; the fluctuations of the helices and beta-sheets converged within the 101 psec period of the simulation and were lower than average in magnitude, while the fluctuations of the loop regions were not converged and were mostly larger than average in magnitude. Notable exceptions to this pattern occurred in the substrate-bound simulation. A loop region (residues 101-107) of the active site cleft had significantly reduced motion due to interactions with the substrate. Moreover, part of a loop and a 3(10) helix (residues of 67-88) not in contact with the substrate showed a marked increase in fluctuations. That these differences in dynamics of free and substrate-bound lysozyme did not result simply from sampling errors was established by an analysis of the variations in the fluctuations of the two halves of the 101 psec simulation of free lysozyme. Concerted transitions of four to five mainchain phi and psi angles between dihedral wells were shown to be responsible for large coordinate shifts in the loops. These transitions displaced six or fewer residues and took place either abruptly, in 1 psec or less, or with a diffusive character over 5-10 psec. Displacements of rigid secondary structures involved longer timescale motions in bound lysozyme; a 0.5 A rms change in the position of a helix occurred over the 55 psec simulation period. This helix reorientation within the protein appears to be a response to substrate binding. There was little correlation between the solvent accessible surface area and the dynamics of the different structural elements.     

Effect of glycerol–water binary mixtures on the structure and dynamics of protein solutions

We have performed 20?ns of fully atomistic molecular dynamics simulations of Hen Egg-White Lysozyme in 0, 10, 20, 30, and 100% by weight of glycerol in water to better understand the microscopic physics behind the bioprotection offered by glycerol to naturally occuring biological systems. The solvent exposure of protein surface residues changes when glycerol is introduced. The dynamic behavior of the protein, as quantified by the incoherent intermediate scattering function, shows a nonmonotonic dependence on glycerol content. The fluctuations of the protein residues with respect to each other were found to be similar in all water-containing solvents, but different from the pure glycerol case. The increase in the number of protein–glycerol hydrogen bonds in glycerol–water binary mixtures explains the slowing down of protein dynamics as the glycerol content increases. We also explored the dynamic behavior of the hydration layer. We show that the short length scale dynamics of this layer are insensitive to glycerol concentration. However, the long length scale behavior shows a significant dependence on glycerol content. We also provide insights into the behavior of bound and mobile water molecules.