Scaling analysis of bio-molecular dynamics derived from elastic incoherent neutron scattering experiments.

Numerous neutron scattering studies of bio-molecular dynamics employ a qualitative analysis of elastic scattering data and atomic mean square displacements. We provide a new quantitative approach showing that the intensity at zero energy exchange can be a rich source of information of bio-structural fluctuations on a pico- to nano-second time scale. Elastic intensity scans performed either as a function of the temperature (back-scattering) and∕or by varying the instrumental resolution (time of flight spectroscopy) yield the activation parameters of molecular motions and the approximate structural correlation function in the time domain. The two methods are unified by a scaling function, which depends on the ratio of correlation time and instrumental resolution time. The elastic scattering concept is illustrated with a dynamic characterization of alanine-dipeptide, protein hydration water, and water-coupled protein motions of lysozyme, per-deuterated c-phycocyanin (CPC) and hydrated myoglobin. The complete elastic scattering function versus temperature, momentum exchange, and instrumental resolution is analyzed instead of focusing on a single cross-over temperature of mean square displacements at the apparent onset temperature of an-harmonic motions. Our method predicts the protein dynamical transition (PDT) at Td from the collective (α) structural relaxation rates of the solvation shell as input. By contrast, the secondary (ß) relaxation enhances the amplitude of fast local motions in the vicinity of the glass temperature Tg. The PDT is specified by step function in the elastic intensity leading from elastic to viscoelastic dynamic behavior at a transition temperature Td.

Dynamical transition of protein-hydration water.

Thin layers of water on biomolecular and other nanostructured surfaces can be supercooled to temperatures not accessible with bulk water. Chen et al. [Proc. Natl. Acad. Sci. U.S.A. 103, 9012 (2006)]10.1073/pnas.0602474103 suggested that anomalies near 220 K observed by quasielastic neutron scattering can be explained by a hidden critical point of bulk water. Based on more sensitive measurements of water on perdeuterated phycocyanin, using the new neutron backscattering spectrometer SPHERES, and an improved data analysis, we present results that show no sign of such a fragile-to-strong transition. The inflection of the elastic intensity at 220 K has a dynamic origin that is compatible with a calorimetric glass transition at 170 K. The temperature dependence of the relaxation times is highly sensitive to data evaluation; it can be brought into perfect agreement with the results of other techniques, without any anomaly.

Dynamics of well-folded and natively disordered proteins in solution: a time-of-flight neutron scattering study.

Casein proteins belong to the class of natively disordered proteins. The existence of disordered biologically active proteins questions the assumption that a well-folded structure is required for function. A hypothesis generally put forward is that the unstructured nature of these proteins results from the functional need of a higher flexibility. This interplay between structure and dynamics was investigated in a series of time-of-flight neutron scattering experiments, performed on casein proteins, as well as on three well-folded proteins with distinct secondary structures, namely, myoglobin (alpha), lysozyme (alpha/beta) and concanavalin A (beta). To illustrate the subtraction of the solvent contribution from the scattering spectra, we used the dynamic susceptibility spectra emphasizing the high frequency part of the spectrum, where the solvent dominates. The quality of the procedure is checked by comparing the corrected spectra to those of the dry and hydrated protein with negligible solvent contamination. Results of spectra analysis reveal differences in motional amplitudes of well-folded proteins, where beta-sheet structures appear to be more rigid than a cluster of alpha-helices. The disordered caseins display the largest conformational displacements. Moreover their global diffusion rates deviate from the expected dependence, suggesting further large-scale conformational motions.

Effect of calcium concentration on the structure of casein micelles in thin films.

The structure of thin casein films prepared with spin-coating is investigated as a function of the calcium concentration. Grazing incidence small-angle x-ray scattering and atomic force microscopy are used to probe the micelle structure. For comparison, the corresponding casein solutions are investigated with dynamic light-scattering experiments. In the thin films with added calcium three types of casein structures, aggregates, micelles, and mini-micelles, are observed in coexistence with atomic force microscopy and grazing incidence small-angle x-ray scattering. With increasing calcium concentration, the size of the aggregates strongly increases, while the size of micelles slightly decreases and the size of the mini-micelles increases. This effect is explained in the framework of the particle-stabilizing properties of the hairy layer of kappa-casein surrounding the casein micelles.

Thin casein films as prepared by spin-coating: influence of film thickness and of pH.

Casein films were successfully prepared with the spin-coating technique of aqueous casein solutions on base-treated glass surfaces. The film structure is investigated in real space with optical microscopy and atomic force microscopy and for the first time in reciprocal space with grazing incidence small-angle X-ray scattering (GISAXS). The size of the substructures detected in the film increases with pH from 170 nm (pH 5.1) up to 490 nm (pH 9.4). Dynamic light scattering experiments reveal that the average diameters of casein micelles in solution exhibit the same quantitative increase. This result suggests that the substructures detected in the bulklike films with GISAXS reflect intact casein micelles. However, with thin homogeneous casein films, the micelle size diminishes with decreasing film thickness. This indicates that the moderate pressures introduced by spin-coating force the micelles to rearrange into a more compact structure.

Pressure-induced dissociation of casein micelles: size distribution and effect of temperature.

Pressure-induced dissociation of a turbid solution of casein micelles was studied in situ in static and dynamic light scattering experiments. We show that at high pressure casein micelles decompose into small fragments comparable in size to casein monomers. At intermediate pressure we observe particles measuring 15 to 20 nm in diameter. The stability against pressure dissociation increased with temperature, suggesting enhanced hydrophobic contacts. The pressure transition curves are biphasic, compatible with a temperature (but not pressure)-dependent conformational equilibrium of two micelle species. Our thermodynamic model predicts an increase in structural entropy with temperature.

High pressure near infrared study of the mutated light-harvesting complex LH2.

The pressure sensitivities of the near infrared spectra of the light-harvesting (LH2) complex and a mutant complex with a simplified BChl-B850 binding pocket were compared. In the mutant an abrupt change in the spectral properties occurred at 250 MPa, which was not observed with the native sample. Increased disorder due to collapse of the chromophore pocket is suggested.

Pressure-induced dissociation of casein micelles: size distribution and effect of temperature

Pressure-induced dissociation of a turbid solution of casein micelles was studied in situ in static and dynamic light scattering experiments. We show that at high pressure casein micelles decompose into small fragments comparable in size to casein monomers. At intermediate pressure we observe particles measuring 15 to 20 nm in diameter. The stability against pressure dissociation increased with temperature, suggesting enhanced hydrophobic contacts. The pressure transition curves are biphasic, compatible with a temperature (but not pressure)-dependent conformational equilibrium of two micelle species. Our thermodynamic model predicts an increase in structural entropy with temperature.

High pressure near infrared study of the mutated light-harvesting complex LH2

The pressure sensitivities of the near infrared spectra of the light-harvesting (LH2) complex and a mutant complex with a simplified BChl-B850 binding pocket were compared. In the mutant an abrupt change in the spectral properties occurred at 250 MPa, which was not observed with the native sample. Increased disorder due to collapse of the chromophore pocket is suggested.

Heme-solvent coupling: a Mössbauer study of myoglobin in sucrose.

The Mössbauer effect of 57Fe-enriched samples was used to investigate the coupling of 80% sucrose/water, a protein-stabilizing solvent, to vibrational and diffusive modes of the heme iron of CO-myoglobin. For comparison we also determined the Mössbauer spectra of K4 57Fe (CN)6 (potassium ferrocyanide, PFC), where the iron is fully exposed in the same solvent. The temperature dependence of the Mössbauer parameters derived for the two samples proved to be remarkably similar, indicative of a strong coupling of the main heme displacements to the viscoelastic relaxation of the solvent. We show that CO escape out of the heme pocket couples to the same type of fluctuations, whereas intramolecular bond formation involves solvent-decoupled heme deformation modes that are less prominent in the Mössbauer spectrum. With respect to other solvents, however, sucrose shows a reduced viscosity effect on heme displacements and the kinetics of ligand binding due to preferential hydration of the protein. This result confirms thermodynamic predictions of the stabilizing action of sucrose by a dynamic method.

Solvent composition and viscosity effects on the kinetics of CO binding to horse myoglobin.

Ligand binding to myoglobin in aqueous solution involves two kinetic components, one extramolecular and one intramolecular, which have been interpreted in terms of two sequential kinetic barriers. In mixed solvents and sub-zero temperatures, the outer barrier increases and the inner barrier splits into several components, giving rise to fast intramolecular recombination. The nature of these barriers and their relation to structural relaxation are examined using the effect of solvent composition and viscosity on the kinetics of CO binding to horse myoglobin in 60% ethylene glycol/water, 75% and 90% glycerol/water, 80% and 92% sucrose/water solutions. Measurements of the corresponding solvent structural relaxation rates by frequency resolved calorimetry allow us to discriminate between solvent composition and viscosity-related effects. The outer kinetic barrier controlling ligand entry and release depends on the viscosity consistent with Kramers-Stokes law of activated escape in the presence of friction. At high cosolvent concentration, we observe deviations from Stokes law, implying a smaller microviscosity at the protein-solvent interface as compared to the bulk. The inner barrier and its coupling to structural relaxation appears to be independent of viscosity but changes with solvent composition. As a possible explanation, we discuss the role of distal water molecules in the formation of the effective inner barrier. At low temperatures, this barrier has a distributed height, depending only slightly on the nature of the cosolvent and temperature at low cosolvent concentrations. In contrast, myoglobin embedded in a sucrose glass (92% sucrose/water) exhibits a temperature-dependent and bimodal enthalpy distribution. This result demonstrates that the exchange between protonation states of His64, A0 left and right arrow A1, can take place in the glass and at temperatures as low as 80 K.

Water-coupled low-frequency modes of myoglobin and lysozyme observed by inelastic neutron scattering.

Conformational changes of proteins often involve the relative motion of rigid structural domains. Normal mode analysis and molecular dynamics simulations of small globular proteins predict delocalized vibrations with frequencies below 20 cm(-1), which may be overdamped in solution due to solvent friction. In search of these modes, we have studied deuterium-exchanged myoglobin and lysozyme using inelastic neutron scattering in the low-frequency range at full and low hydration to modify the degree of damping. At room temperature, the hydrated samples exhibit a more pronounced quasielastic spectrum due to diffusive motions than the dehydrated samples. The analysis of the corresponding lineshapes suggests that water modifies mainly the amplitude, but not the characteristic time of fast protein motions. At low temperatures, in contrast, the dehydrated samples exhibit larger motional amplitudes than the hydrated ones. The excess scattering, culminating at 16 cm(-1), is suggested to reflect water-coupled librations of polar side chains that are depressed in the hydrated system by strong intermolecular hydrogen bonding. Both myoglobin and lysozyme exhibit ultra-low-frequency modes below 10 cm(-1) in the dry state, possibly related to the breathing modes predicted by harmonic analysis.

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 mainchain 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.

The transition from inhomogeneous to homogeneous kinetics in CO binding to myoglobin.

Heme proteins react inhomogeneously with ligands at cryogenic temperatures and homogeneously at room temperature. We have identified and characterized a transition from inhomogeneous to homogeneous behavior at intermediate temperatures in the time dependence of CO binding to horse myoglobin. The turnover is attributed to a functionally important tertiary protein relaxation process during which the barrier increases dynamically. This is verified by a combination of theory and multipulse measurements. A likely biological significance of this effect is in the autocatalysis of the ligand release process.

Structural relaxation and nonexponential kinetics of CO-binding to horse myoglobin. Multiple flash photolysis experiments.

The geminate recombination kinetics of CO-myoglobin strongly deviates from single exponential behavior in contrast to what is expected for unimolecular reactions (1). At low temperatures, this result was attributed to slowly exchanging conformational states which differ substantially in barrier height for ligand binding. Above 160 K the kinetics apparently slow down with temperature increase. Agmon and Hopfield (2) explain this result in terms of structural relaxation perpendicular to the reaction coordinate, which enhances the activation energy. In their model, structural relaxation homogenizes the kinetic response. Recently, Steinbach et al. (3) proposed a relaxation model which conserves the kinetic inhomogeneity. Below we test these conjectures by single and multiple excitation experiments. This method allows for discrimination between parallel (inhomogeneous) and sequential (homogeneous) kinetic schemes. The kinetic anomaly above 160 K is shown to result from a homogeneous, structurally relaxed intermediate. However a second anomaly is found above 210 K concerning the inhomogeneous phase which may indicate either a shift in activation energy or entropy.

Solvent damping of internal processes in myoglobin studied by specific heat spectroscopy and flash photolysis.

We address the question of dynamic coupling between protein and solvent by comparing the enthalpy relaxation of the solvent (75% v/v glycerol-water) to internal ligand binding in myoglobin. When the solvent relaxation is slow compared to intramolecular events we observe decoupling of protein motions from the solvent. In the opposite limit there is a significant contribution of the solvent to internal friction. The solvent enhances the apparent activation energy of transitions in myoglobin. This result is discussed in terms of a generalized Kramer's law involving a dynamic friction coefficient.

Temperature dependence of the low frequency dynamics of myoglobin. Measurement of the vibrational frequency distribution by inelastic neutron scattering.

Inelastic neutron scattering spectra of myoglobin hydrated to 0.33 g water (D2O)/g protein have been measured in the low frequency range (1-150 cm-1) at various temperatures between 100 and 350 K. The spectra at low temperatures show a well-resolved maximum in the incoherent dynamic structure factor Sinc(q, omega) at approximately 25 cm-1 and no elastic broadening. This maximum becomes gradually less distinct above 180 K due to the increasing amplitude of quasielastic scattering which extends out to 30 cm-1. The vibrational frequency distribution derived independently at 100 and 180 K are very similar, suggesting harmonic behavior at these temperatures. This result has been used to separate the vibrational motion from the quasielastic motion at temperatures above 180 K. The form of the density of states of myoglobin is discussed in relation to that of other amorphous systems, to theoretical calculations of low frequency modes in proteins, and to previous observations by electron-spin relaxation of fractal-like spectral properties of proteins. The onset of quasielastic scattering above 180 K is indicative of a dynamic transition of the system and correlates with an anomalous increase in the atomic mean-squared displacements observed by Mössbauer spectroscopy (Parak, F., E. W. Knapp, and D. Kucheida. 1982. J. Mol. Biol. 161: 177-194.) and inelastic neutron scattering (Doster, W., S. Cusack, and W. Petry, 1989. Nature [Lond.]. 337: 754-756.) Similar behavior is observed for a hydrated powder of lysozyme suggesting that the low frequency dynamics of globular proteins have common features.

Percolation model of ionic channel dynamics.

The nonexponential closed-time distributions observed for ionic channels have been explained recently by quasi-one-dimensional models of structural diffusion (Millhauser, G. L., E. E. Salpeter, and R. E. Oswald. 1988. Proc. Natl. Acad. Sci. USA. 85: 1503-1507; Condat, C. A., and J. Jäckle. 1989. Biophys. J. 55: 915-925; Levitt, D. G. 1989. Biophys. J. 55: 489-498). We generalize this treatment by allowing for more complex trajectories using percolation theory. We assume that the gating transition depends on marginally connected conformational states leading to the observed spread in time scales.