Viscosity scaling and protein dynamics

The rates of molecular motions in the interior of some proteins were found to scale with an inverse power of the external solvent viscosity. The data were explained by a flexible protein structure whose dynamics is partially controlled by the solvent. Reaction dynamics in the presence of structural fluctuations with finite lifetimes lead to a dynamic friction coefficient defined by a generalized Langevin equation and a fluctuation-dissipation theorem. A model for the dynamic friction is derived assuming that the fluctuation spectrum at the reaction site involves two components: solvent-independent diffusion of local structural defects in the protein matrix and global fluctuations coupled to the solvent. The theory is applied to the viscosity dependence of molecular oxygen-binding rates in sperm whale myoglobin.     

The protein glass transition as measured by dielectric spectroscopy and differential scanning calorimetry

The glass transition and its related dynamics of myoglobin in water and in a water–glycerol mixture have been investigated by dielectric spectroscopy and differential scanning calorimetry (DSC). For all samples, the DSC measurements display a glass transition that extends over a large temperature range. Both the temperature of the transition and its broadness decrease rapidly with increasing amount of solvent in the system. The dielectric measurements show several dynamical processes, due to both protein and solvent relaxations, and in the case of pure water as solvent the main protein process (which most likely is due to conformational changes of the protein structure) exhibits a dynamic glass transition (i.e. reaches a relaxation time of 100 s) at about the same temperature as the calorimetric glass transition temperature T_g is found. This glass transition is most likely caused by the dynamic crossover and the associated vanishing of the α-relaxation of the main water relaxation, although it does not contribute to the calorimetric T_g. This is in contrast to myoglobin in water–glycerol, where the main solvent relaxation makes the strongest contribution to the calorimetric glass transition. For all samples it is clear that several proteins processes are involved in the calorimetric glass transition and the broadness of the transition depends on how much these different relaxations are separated in time.     

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.     

Dielectric spectroscopy study of myoglobin in glycerol-water mixtures

Due to the interest in protein dynamics, there are numerous dielectric relaxation studies of proteins in water and in glass-forming aqueous solvents such as glycerol-water mixtures. In the regime of low frequencies, the inevitable dc-conductivity of such systems limits the resolution of dynamics that are slow compared with the solvent relaxation. Solutions of myoglobin in glycerol/water mixtures of various compositions are measured by dielectric spectroscopy in the frequency range from 10 mHz to 10 MHz. The resolution of low frequency modes is improved by two approaches: electrical ‘cleaning’ and the analysis of the derivative of the real component of permittivity, which shows no direct signature of dc-conductivity. Effects of internal interfacial polarization are also addressed by measuring the same solvents in confinement as well as mixed with glass beads. We find two processes, the structural relaxation of the solvent and the slower rotational mode of the protein, with no indication at even lower frequencies of a dielectric signature of fluctuations associated with protein dynamics.     

Hydration,slaving and protein function

Protein dynamics is crucial for protein function. Proteins in living systems are not isolated, but operate in networks and in a carefully regulated environment. Understanding the external control of protein dynamics is consequently important. Hydration and solvent viscosity are among the salient properties of the environment. Dehydrated proteins and proteins in a rigid environment do not function properly. It is consequently important to understand the effect of hydration and solvent viscosity in detail. We discuss experiments that separate the two effects. These experiments have predominantly been performed with wild-type horse and sperm whale myoglobin, using the binding of carbon monoxide over a broad range of temperatures as a tool. The experiments demonstrate that data taken only in the physiological temperature range are not sufficient to understand the effect of hydration and solvent on protein relaxation and function. While the actual data come from myoglobin, it is expected that the results apply to most or all globular proteins.     

Myoglobin and cytochrome b5: a nuclear magnetic resonance study of a highly dynamic protein complex

The transient complex of bovine myoglobin and cytochrome b(5) has been investigated using a combination of NMR chemical shift mapping, (15)N relaxation data, and protein docking simulations. Chemical shift perturbations observed for cytochrome b(5) amide resonances upon complex formation with either metmyoglobin (Fe(III)) or carbon monoxide-bound myoglobin (Fe(II)) are more than 10-fold smaller than in other transient redox protein complexes. From (15)N relaxation experiments, an increase in the overall correlation time of cytochrome b(5) in the presence of myoglobin is observed, confirming that complex formation is occurring. The chemical shift perturbations of proton and nitrogen amide nuclei as well as heme protons of cytochrome b(5) titrate with increasing myoglobin concentrations, also demonstrating the formation of a weak complex with a K(a) in the inverse millimolar range. The perturbed residues map over a wide surface area of cytochrome b(5), with patches of residues located around the exposed heme 6-propionate as well as at the back of the protein. The nature of the affected residues is mostly negatively charged contrary to perturbed residues in other transient complexes, which are mainly hydrophobic or polar. Protein docking simulations using the NMR data as constraints show several docking geometries both close to and far away from the exposed heme propionates of myoglobin. Overall, the data support the emerging view that this complex consists of a dynamic ensemble of orientations in which each protein constantly diffuses over the surface of the other. The characteristic NMR features may serve as a structural tool for the identification of such dynamic complexes.     

From metmyoglobin to deoxy myoglobin: relaxations of an intermediate state

Metmyoglobin has been reduced at low temperature (below 100 K) using x-rays or by excitation of tris(2,2′,bipyridine)ruthenium(II) chloride with visible light. Upon reduction, an intermediate state is formed where the structure of the protein is very similar to that of metmyoglobin with the water molecule still bound to the heme iron, but the iron is II low spin. The nature of the intermediate state has been investigated with optical spectroscopy. The Q_o and Q_v bands of the intermediate state are split, suggesting that the protoporphyrin is distorted. The intermediate state undergoes a relaxation observed by a shifting of the Soret band at temperatures above 80 K. Above 140 K, the protein begins to relax to the deoxy conformation. The relaxation kinetics of the protein have been monitored optically as a function of time and temperature from minutes to several hours and from 150 K to 190 K. By measuring the entire visible spectrum, we are able to distinguish between electron transfer processes and the protein relaxation from the intermediate state to deoxy myoglobin. The relaxation has been measured in both horse myoglobin and sperm whale myoglobin with the relaxation occurring on faster time scales in horse myoglobin. Both the reduction kinetics and the relaxation show non-exponential behavior. The reduction kinetics can be fit well to a stretched exponential. The structural relaxation from the intermediate state to the deoxy conformation shows a more complex, dynamical behavior and the reaction is most likely affected by the relaxation of the protein within the intermediate state. Received: 30 June 1997 / Accepted: 6 November 1997     

Langevin modes of macromolecules: applications to crambin and DNA hexamers

Langevin modes describe the behavior of atoms moving on a harmonic potential surface subject to viscous damping described by a classical Langevin equation. We present applications to the protein crambin and to the DNA duplex d(CpGpCpGpCpG)2 and its complex with ethidium. Our friction matrix is weighted according to surface area exposed to solvent, and results are reported for various values of the solvent viscosity and models for hydrodynamic interactions. Even for relatively small solvent friction (eta = 0.3 cp) a substantial number of modes are overdamped, and time correlation functions decay smoothly without the oscillations characteristic of gas-phase calculations. Perturbation theory starting from the gas-phase modes is accurate for many low-frequency modes (which are overdamped in the presence of solvent), but fails badly for higher modes. For correlation functions of interest to fluorescence depolarization or nmr relaxation, the plateau values are insensitive to solvent viscosity, but the relaxation times are not. The advantages and limitations of this analysis of macromolecular motions are discussed.     

Coupling of protein and environment fluctuations

We review the concepts of protein dynamics developed over the last 35years and extend applications of the unified model of protein dynamics to heat flow and spatial fluctuations in hydrated myoglobin (Mb) powders. Differential scanning calorimetry (DSC) and incoherent neutron scattering (INS) data on hydration Mb powders are explained by the temperature-dependence of the hydration-shell β(h) process measured by dielectric relaxation spectroscopy (DRS). The unified model explains the temperature dependence of DSC and INS data as a kinetic effect due to a fixed experimental time window and a broad distribution of hydration-shell β(h) fluctuation rates. We review the slaving of large scale protein motions to the bulk solvent α process, and the metastability of Mb molecules in glass forming bulk solvent at low temperatures. This article is part of a Special Issue entitled: "Protein Dynamics: Experimental and Computational Approaches".     

Infrared spectroscopic studies of solvent-induced conformational changes in globular proteins.

Infrared absorption spectroscopy has been used to study the effect of organic solvents on the conformation of myoglobin, apomyoglobin, hemoglobin, lysozyme and ribonuclease. Beta structure can easily be induced by specific solvent effects. Films prepared from a 50% (v/v) mixture of alcohol, acetone, pyridine, tetrahydrofuran or dimethylsulfoxide/water mixtures show a high proportion of beta structure. The degree of induction of beta structure depends on the hydrocarbon content of the alcohol in the order methanol greater than ethanol greater than butanol. No beta structure was observed in films prepared from aqueous octanol solutions. Lyophilization tends to decrease secondary structure. The conformation of the proteins depends on the particular solvent system and the solvent composition. Solution studies of myoglobin in pure dimethylsulfoxide show that the conformation is a mixture of random and beta forms while in dimethylsulfoxide/2H2O mixtures the conformation is a mixture of alpha-helical and beta forms.     

The position 68(E11) side chain in myoglobin regulates ligand capture, bond formation with heme iron, and internal movement into the xenon cavities

After photodissociation, ligand rebinding to myoglobin exhibits complex kinetic patterns associated with multiple first-order geminate recombination processes occurring within the protein and a simpler bimolecular phase representing second-order ligand rebinding from the solvent. A smooth transition from cryogenic-like to solution phase properties can be obtained by using a combination of sol-gel encapsulation, addition of glycerol as a bathing medium, and temperature tuning (-15 --> 65 degrees C). This approach was applied to a series of double mutants, myoglobin CO (H64L/V68X, where X = Ala, Val, Leu, Asn, and Phe), which were designed to examine the contributions of the position 68(E11) side chain to the appearance and disappearance of internal rebinding phases in the absence of steric and polar interactions with the distal histidine. Based on the effects of viscosity, temperature, and the stereochemistry of the E11 side chain, the three major phases, B --> A, C --> A, and D --> A, can be assigned, respectively, to ligand rebinding from the following: (i) the distal heme pocket, (ii) the xenon cavities prior to large amplitude side chain conformational relaxation, and (iii) the xenon cavities after significant conformational relaxation of the position 68(E11) side chain. The relative amplitudes of the B --> A and C --> A phases depend markedly on the size and shape of the E11 side chain, which regulates sterically both ligand return to the heme iron atom and ligand migration to the xenon cavities. The internal xenon cavities provide a transient docking site that allows side chain relaxations and the entry of water into the vacated distal pocket, which in turn slows ligand recombination markedly.     

A proton magnetic relaxation study of ferric myoglobin and haemoglobin in water/ethanediol solutions.

Structural alterations of the haem vicinity of the high-spin derivatives of bovine ferric myoglobin (metmyoglobin) and human haemoglobin and the changes of the interaction with inositol hexaphosphate induced by ethanediol were monitored by solvent-proton magnetic relaxation. On addition of ethanediol up to 60% the fluoromet derivatives exhibit a gradual increase in the accessibility of the haem for the molecules from the solvent. In aquomethaemoglobin solutions with more than 25% ethanediol there is no unique explanation of proton magnetic relaxation. Ethanediol enhances the binding of inositol hexaphosphate to methaemoglobin, but the structural consequences of this binding on the haem-pockets seem to be diminished. The mechanisms of the observed structural and functional alterations of myoglobin as well as haemoglobin tetramer are discussed here.     

Geminate rebinding in trehalose-glass embedded myoglobins reveals residue-specific control of intramolecular trajectories.

It is becoming increasingly apparent that hydrophobic cavities (also referred to as xenon cavities) within proteins have significant functional implications. The potential functional role of these cavities in modulating the internal dynamics of carbon monoxide in myoglobin (Mb) is explored in the present study by using glassy matrices derived from trehalose to limit protein dynamics and to eliminate ligand exchange between the solvent and the protein. By varying the temperature (-15 to 65 degrees C) and humidity for samples of carbonmonoxy myoglobin embedded in trehalose-glass, it is possible to observe a hierarchy of distinct geminate recombination phases that extend from nanosecond to almost seconds that can be directly associated with rebinding from specific hydrophobic cavities. The use of mutant forms of Mb reveals the role of key residues in modulating ligand access between these cavities and the distal hemepocket.     

Interaction between external medium and haem pocket in myoglobin probed by low-temperature optical spectroscopy

The visible absorption spectra of carbonmonoxymyoglobin in the temperature range 300 to 20 K are reported and compared with the analogous spectra of carbonomonoxyhaemoglobin. The temperature dependence of the zeroth, first and second moment of the observed bands is analysed to obtain information on the local dynamics in the proximity of the haem. Contrary to haemoglobin, the first moment of the observed bands in myoglobin is markedly affected by the solvent composition and its value saturates at temperatures at which the solvent undergoes the glass transition. These data indicate that solvent properties influence the haem pocket stereodynamics in myoglobin; moreover, the different behaviour between myoglobin and haemoglobin suggests that the process should involve the surfaces that are buried in the haemoglobin tetramer and exposed to the solvent in myoglobin, and/or the different protein compressibility.     

Effect of solvent viscosity on the heme-pocket dynamics of photolyzed (carbonmonoxy)hemoglobin

The heme-pocket dynamics subsequent to carbon monoxide photolysis from human hemoglobin have been monitored as a function of glycerol-water solvent composition with time-resolved resonance Raman spectroscopy. Prompt (geminate) ligand recombination rates and the transient heme-pocket geometry established within 10 ns after photolysis appear to be largely independent of solvent composition. The rate of relaxation of the transient geometry to an equilibrium deoxy configuration is, however, quite sensitive to solvent composition. These observations suggest that the former processes result from local, internal motions of the protein, while the relaxation dynamics of the proximal heme pocket are predicated upon more global protein motions that are dependent upon solvent viscosity.     

Ligand binding to heme proteins: connection between dynamics and function

Ligand binding to heme proteins is studied by using flash photolysis over wide ranges in time (100 ns-1 ks) and temperature (10-320 K). Below about 200 K in 75% glycerol/water solvent, ligand rebinding occurs from the heme pocket and is nonexponential in time. The kinetics is explained by a distribution, g(H), of the enthalpic barrier of height H between the pocket and the bound state. Above 170 K rebinding slows markedly. Previously we interpreted the slowing as a "matrix process" resulting from the ligand entering the protein matrix before rebinding. Experiments on band III, an inhomogeneously broadened charge-transfer band near 760 nm (approximately 13,000 cm-1) in the photolyzed state (Mb*) of (carbonmonoxy)myoglobin (MbCO), force us to reinterpret the data. Kinetic hole-burning measurements on band III in Mb* establish a relation between the position of a homogeneous component of band III and the barrier H. Since band III is red-shifted by 116 cm-1 in Mb* compared with Mb, the relation implies that the barrier in relaxed Mb is 12 kJ/mol higher than in Mb*. The slowing of the rebinding kinetics above 170 K hence is caused by the relaxation Mb*----Mb, as suggested by Agmon and Hopfield [(1983) J. Chem. Phys. 79, 2042-2053]. This conclusion is supported by a fit to the rebinding data between 160 and 290 K which indicates that the entire distribution g(H) shifts. Above about 200 K, equilibrium fluctuations among conformational substates open pathways for the ligands through the protein matrix and also narrow the rate distribution. The protein relaxations and fluctuations are nonexponential in time and non-Arrhenius in temperature, suggesting a collective nature for these protein motions. The relaxation Mb*----Mb is essentially independent of the solvent viscosity, implying that this motion involves internal parts of the protein. The protein fluctuations responsible for the opening of the pathways, however, depend strongly on the solvent viscosity, suggesting that a large part of the protein participates. While the detailed studies concern MbCO, similar data have been obtained for MbO2 and CO binding to the beta chains of human hemoglobin and hemoglobin Zürich. The results show that protein dynamics is essential for protein function and that the association coefficient for binding from the solvent at physiological temperatures in all these heme proteins is governed by the barrier at the heme.     

Differential halothane binding and effects on serum albumin and myoglobin.

To understand further the weak molecular interactions between inhaled anesthetics and proteins, we studied the character and dynamic consequences of halothane binding to bovine serum albumin (BSA) and myoglobin using photoaffinity labeling and hydrogen-tritium exchange (HX). We find that halothane binds saturably and with submillimolar affinity to BSA, but either nonspecifically or with considerably lower affinity to myoglobin. Titration of halothane binding with guanidine hydrochloride suggested more protection of binding sites from solvent in BSA as compared with myoglobin. Protection factors for slowly exchanging albumin hydrogens are increased in a concentration-dependent manner by up to 27-fold with 10 mM halothane, whereas more rapidly exchanging groups of albumin hydrogens have either unaltered or decreased protection factors. Protection factors for slowly exchanging hydrogens in myoglobin are decreased by halothane, suggesting destabilization through binding to an intermediate or completely unfolded conformer. These results demonstrate the conformation dependence of halothane binding and clear dynamic consequences that correlate with the character of binding in these model proteins. Preferential binding and stabilization of different conformational states may underlie anesthetic-induced protein dysfunction, as well as provide an explanation for heterogeneity of action.     

Solvent-induced organization: A physical model of folding myoglobin

The essential features of the in vitro refolding of myoglobin are expressed in a solvable physical model. Alpha helices are taken as the fundamental collective coordinates of the system, while the refolding is assumed to be mainly driven by solvent-induced hydrophobic forces. A quantitative model of these forces is developed and compared with experimental and theoretical results. The model is then tested by being employed in a simulation scheme designed to mimic solvent effects. Realistic dynamic trajectories of myoglobin are shown as it folds from an extended conformation to a close approximation of the native state. Various suggestive features of the process are discussed. The tenets of the model are further tested by folding the single-chain plant protein leghemoglobin. © 1994 Wiley-Liss, Inc.     

Vibrational frequency shifts as a probe of hydrogen bonds: thermal expansion and glass transition of myoglobin in mixed solvents

The contribution of hydrogen bonds to protein-solvent interactions and their impact on structural flexibility and dynamics of myoglobin are discussed. The shift of vibrational peak frequencies with the temperature of myoglobin in sucrose/water and glycerol/water solutions is used to probe the expansion of the hydrogen bond network. We observe a characteristic change in the temperature slope of the O–H stretching frequency at the glass transition which correlates with the discontinuity of the thermal expansion coefficient. The temperature-difference spectra of the amide bands show the same tendency, indicating that stronger hydrogen bonding in the bulk affects the main-chain solvent interactions in parallel. However, the hydrogen bond strength decreases relative to the bulk solvent with increasing cosolvent concentration near the protein surface, which suggests preferential hydration. Weaker and/or fewer hydrogen bonds are observed at low degrees of hydration. The central O–H stretching frequency of protein hydration water is red-shifted by 40 cm^–1 relative to the bulk. The shift increases towards lower temperatures, consistent with contraction and increasing strength of the protein-water bonds. The temperature slope shows a discontinuity near 180 K. The contraction of the network has reached a critical limit which leads to frozen-in structures. This effect may represent the molecular mechanism underlying the dynamic transition observed for the mean square displacements of the protein atoms and the heme iron of myoglobin. Received: 10 July 1996 / Accepted: 10 April 1997     

Structure of myoglobin-ethyl isocyanide. Histidine as a swinging door for ligand entry

The structure of myoglobin(Fe II)-ethyl isocyanide has been solved at 1.68 A resolution by X-ray crystallography. The isocyano group of the ligand is distorted from the linear conformation observed in solution and in model compounds. Local changes in the protein conformation are also seen. The side-chain of Arg-CD3 moves out into the solvent, and the side-chain of His-E7 swings up and away from the ligand. Both of these side-chains show disorder indicative of dynamic behavior. These outward movements of His-E7 and Arg-CD3 side-chains clear a path from the solvent to the heme iron, suggesting a mechanism for ligand entry.