Glassy behavior of a protein

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

The energy landscape approach has played a fundamental role in advancing our understanding of protein folding. Here, we quantify protein folding energy landscapes by exploring the underlying density of states. We identify three quantities essential for characterizing landscape topography: the stabilizing energy gap between the native and nonnative ensembles δE, the energetic roughness ΔE, and the scale of landscape measured by the entropy S. We show that the dimensionless ratio between the gap, roughness, and entropy of the system Λ=δE/(ΔE√(2S)) accurately predicts the thermodynamics, as well as the kinetics of folding. Large Λ implies that the energy gap (or landscape slope towards the native state) is dominant, leading to more funneled landscapes. We investigate the role of topological and energetic roughness for proteins of different sizes and for proteins of the same size, but with different structural topologies. The landscape topography ratio Λ is shown to be monotonically correlated with the thermodynamic stability against trapping, as characterized by the ratio of folding temperature versus trapping temperature. Furthermore, Λ also monotonically correlates with the folding kinetic rates. These results provide the quantitative bridge between the landscape topography and experimental folding measurements.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Wild type, mutant protein unfolding and phase transition detected by single-nanopore recording

Understanding protein folding remains a challenge. A difficulty is to investigate experimentally all the conformations in the energy landscape. Only single molecule methods, fluorescence and force spectroscopy, allow observing individual molecules along their folding pathway. Here we observe that single-nanopore recording can be used as a new single molecule method to explore the unfolding transition and to examine the conformational space of native or variant proteins. We show that we can distinguish unfolded states from partially folded ones with the aerolysin pore. The unfolding transition curves of the destabilized variant are shifted toward the lower values of the denaturant agent compared to the wild type protein. The dynamics of the partially unfolded wild type protein follows a first-order transition. The denaturation curve obtained with the aerolysin pore is similar to that obtained with the α-hemolysin pore. The nanopore geometry or net charge does not influence the folding transition but changes the dynamics.

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".

Proteins and Glasses

The structure, the energy landscape, and the dynamics of proteins and glasses are similar. Both types of systems display characteristic nonexponential time dependencies of relaxation phenomena. Experiments suggest that both, proteins and glasses, are heterogeneous and that this fact causes the observed time dependence. This result is discussed in terms of the rough energy landscape characteristic of complex systems.

Configurational subdiffusion of peptides: a network study

Molecular dynamics (MD) simulation of linear peptides reveals configurational subdiffusion at equilibrium extending from 10⁻¹² to 10⁻⁸ s. Rouse chain and continuous-time random walk models of the subdiffusion are critically discussed. Network approaches to analyzing MD simulations are shown to reproduce the time dependence of the subdiffusive mean squared displacement, which is found to arise from the fractal-like geometry of the accessible volume in the configuration space. Convergence properties of the simulation pertaining to the subdiffusive dynamics are characterized and the effect on the subdiffusive properties of representing the solvent explicitly or implicitly is compared. Non-Markovianity and other factors limiting the range of applicability of the network models are examined.

Softening of the packing density of horseradish peroxidase by a H-donor bound near the heme pocket

We use pressure tuning of spectral holes to estimate the compressibility of protein molecules by optical means. We found that the compressibility of mesoporphyrin-substituted horseradish peroxidase increases by a factor of three when it incorporates small aromatic H-donor molecules that bind in the vicinity of its heme pocket. Such a dramatic softening of its packing density corresponds to a jump from a compressibility range characteristic for the solid state into that characteristic for liquids.

Logarithmic decay in single-particle relaxation of hydrated lysozyme powder

We present the self-dynamics of protein amino acids of hydrated lysozyme powder around the physiological temperature by means of molecular dynamics simulations. The self-intermediate scattering functions of the amino acid residue center of mass display a logarithmic decay over 3 decades of time, from 2 ps to 2 ns, followed by an exponential alpha relaxation. This kind of slow dynamics resembles the relaxation scenario within the beta-relaxation time range predicted by mode coupling theory in the vicinity of higher-order singularities. These results suggest a strong analogy between the single-particle dynamics of the protein and the dynamics of colloidal, polymeric, and molecular glass-forming liquids.

Frontiers in biotransport: water transport and hydration

Biotransport, by its nature, is concerned with the motions of molecules in biological systems while water remains as the most important and the most commonly studied molecule across all disciplines. In this review, we focus on biopreservation and thermal therapies from the perspective of water, exploring how its molecular motions, properties, kinetic, and thermodynamic transitions govern biotransport phenomena and enable preservation or controlled destruction of biological systems.

Coupled relaxations at the protein-water interface in the picosecond time scale

The spectral behaviour of a protein and its hydration water has been investigated through neutron scattering. The availability of both hydrogenated and perdeuterated samples of maltose-binding protein (MBP) allowed us to directly measure with great accuracy the signal from the protein and the hydration water alone. Both the spectra of the MBP and its hydration water show two distinct relaxations, a behaviour that is reminiscent of glassy systems. The two components have been described using a phenomenological model that includes two Cole-Davidson functions. In MBP and its hydration water, the two relaxations take place with similar average characteristic times of approximately 10 and 0.2 ps. The common time scales of these relaxations suggest that they may be a preferential route to couple the dynamics of the water hydrogen-bond network around the protein surface with that of protein fluctuations.

Frontiers in Biotransport: Water Transport and Hydration

Biotransport, by its nature, is concerned with the motions of molecules in biological systems while water remains as the most important and the most commonly studied molecule across all disciplines. In this review, we focus on biopreservation and thermal therapies from the perspective of water, exploring how its molecular motions, properties, kinetic, and thermodynamic transitions govern biotransport phenomena and enable preservation or controlled destruction of biological systems.

From shell to cell: neutron scattering studies of biological water dynamics and coupling to activity

An integrated picture of hydration shell dynamics and of its coupling to functional macromolecular motions is proposed from studies on a soluble protein, on a membrane protein in its natural lipid environment, and on the intracellular environment in bacteria and red blood cells. Water dynamics in multimolar salt solutions was also examined, in the context of the very slow water component previously discovered in the cytoplasm of extreme halophilic archaea. The data were obtained from neutron scattering by using deuterium labelling to focus on the dynamics of different parts of the complex systems examined.

Observation of a low-temperature, dynamically driven structural transition in a polypeptide by solid-state NMR spectroscopy

At reduced temperatures, proteins and other biomolecules are generally found to exhibit dynamic as well as structural transitions. This includes a so-called protein glass transition that is universally observed in systems cooled between 200 and 230 K, and which is generally attributed to interactions between hydrating solvent molecules and protein side chains. However, there is also experimental and theoretical evidence for a low-temperature transition in the intrinsic dynamics of the protein itself, absent any solvent. Here, we use low-temperature solid-state NMR to examine site-specific fluctuations in atomic structure and dynamics in the absence of solvents. In particular, we employ magic angle spinning NMR to examine a structural phase transition associated with dynamic processes in a solvent-free polypeptide, N-f-MLF-OH, lattice at temperatures as low as 90 K. This transition is characterized by the appearance of an extra set of lines in 1D (15)N spectra as well as additional cross peaks in 2D (13)C-(13)C and (13)C-(15)N spectra. Interestingly, the gradual, temperature-dependent appearance of the new spectral component is not accompanied by the line broadening typical of dynamic transitions. A direct comparison between the spectra of N-f-MLF-OH and the analog N-f-MLF-OMe, which does not display this transition, indicates a correlation of the structural transition to the temperature dependent motion of the aromatic phenylalanine side chain. Several quantitative solid state NMR experiments were employed to provide site-specific measurements of structural and motional features of the observed transition.

Switch from conventional to distributed kinetics in the bacteriorhodopsin photocycle

Below 195 K, the bacteriorhodopsin photocycle could not be adequately described with exponential kinetics [Dioumaev, A. K., and Lanyi, J. K. (2007) Proc. Natl. Acad. Sci. U.S.A. 104, 9621-9626] but required distributed kinetics, previously found in hemoglobin and myoglobin at temperatures below the vitrification point of the surrounding solvent. The aim of this study is to determine which factors cause the switch from this low-temperature regime to the conventional kinetics observed at ambient temperature. The photocycle was monitored by time-resolved FTIR between 180 and 280 K, using the D96N mutant. Depending on the temperature, decay and temporal redistribution of two or three intermediates (L, M, and N) were observed. Above approximately 245 K, an abrupt change in the kinetic behavior of the photocycle takes place. It does not affect the intermediates present but greatly accelerates their decay. Below approximately 240 K, a kinetic pattern with partial decay that cannot be explained by conventional kinetics, but suggesting distributed kinetics, was dominant, while above approximately 250 K, there were no significant deviations from exponential behavior. The approximately 245 K critical point is >/=10 K below the freezing point of interbilayer water, and we were unable to correlate it with any FTIR-detectable transition of the lipids. Therefore, we attribute the change from distributed to conventional kinetics to a thermodynamic phase transition in the protein. Most probably, it is related to the freezing and thawing of internal fluctuations of the protein, known as the dynamic phase transition, although in bacteriorhodopsin the latter is usually believed to take place at least 15 K below the observed critical temperature of approximately 245 K.

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.

Single-molecule nonequilibrium periodic Mg2+-concentration jump experiments reveal details of the early folding pathways of a large RNA

The evolution of RNA conformation with Mg(2+) concentration ([Mg(2+)]) is typically determined from equilibrium titration measurements or nonequilibrium single [Mg(2+)]-jump measurements. We study the folding of single RNA molecules in response to a series of periodic [Mg(2+)] jumps. The 260-residue catalytic domain of RNase P RNA from Bacillus stearothermophilus is immobilized in a microfluidic flow chamber, and the RNA conformational changes are probed by fluorescence resonance energy transfer (FRET). The kinetics of population redistribution after a [Mg(2+)] jump and the observed connectivity of FRET states reveal details of the folding pathway that complement and transcend information from equilibrium or single-jump measurements. FRET trajectories for jumps from [Mg(2+)] = 0.01 to 0.1 mM exhibit two-state behavior whereas jumps from 0.01 mM to 0.4 mM exhibit two-state unfolding but multistate folding behavior. RNA molecules in the low and high FRET states before the [Mg(2+)] increase are observed to undergo dynamics in two distinct regions of the free energy landscape separated by a high barrier. We describe the RNA structural changes involved in crossing this barrier as a "hidden" degree of freedom because the changes do not alter the detected FRET value but do alter the observed dynamics. The associated memory prevents the populations from achieving their equilibrium values at the end of the 5- to 10-sec [Mg(2+)] interval, thereby creating a nonequilibrium steady-state condition. The capability of interrogating nonequilibrium steady-state RNA conformations and the adjustable period of [Mg(2+)]-jump cycles makes it possible to probe regions of the free energy landscape that are infrequently sampled in equilibrium or single-jump measurements.

Dynamics of hydration water in deuterated purple membranes explored by neutron scattering

The function and dynamics of proteins depend on their direct environment, and much evidence has pointed to a strong coupling between water and protein motions. Recently however, neutron scattering measurements on deuterated and natural-abundance purple membrane (PM), hydrated in H2O and D2O, respectively, revealed that membrane and water motions on the ns-ps time scale are not directly coupled below 260 K (Wood et al. in Proc Natl Acad Sci USA 104:18049-18054, 2007). In the initial study, samples with a high level of hydration were measured. Here, we have measured the dynamics of PM and water separately, at a low-hydration level corresponding to the first layer of hydration water only. As in the case of the higher hydration samples previously studied, the dynamics of PM and water display different temperature dependencies, with a transition in the hydration water at 200 K not triggering a transition in the membrane at the same temperature. Furthermore, neutron diffraction experiments were carried out to monitor the lamellar spacing of a flash-cooled deuterated PM stack hydrated in H2O as a function of temperature. At 200 K, a sudden decrease in lamellar spacing indicated the onset of long-range translational water diffusion in the second hydration layer as has already been observed on flash-cooled natural-abundance PM stacks hydrated in D2O (Weik et al. in J Mol Biol 275:632-634, 2005), excluding thus a notable isotope effect. Our results reinforce the notion that membrane-protein dynamics may be less strongly coupled to hydration water motions than the dynamics of soluble proteins.

Anomalous lineshapes and aging effects in two-dimensional correlation spectroscopy

Multitime correlation functions provide useful probes for the ensembles of trajectories underlying the stochastic dynamics of complex systems. These can be obtained by measuring their optical response to sequences of ultrashort optical pulse. Using the continuous time random walk model for spectral diffusion, we analyze the signatures of anomalous relaxation in two-dimensional four wave mixing signals. Different models which share the same two point joint probability distribution show markedly different lineshapes and may be distinguished. Aging random walks corresponding to waiting time distributions with diverging first moment show dependence of 2D lineshapes on initial observation time, which persist for long times.

Coupling of protein and hydration-water dynamics in biological membranes

The dynamical coupling between proteins and their hydration water is important for the understanding of macromolecular function in a cellular context. In the case of membrane proteins, the environment is heterogeneous, composed of lipids and hydration water, and the dynamical coupling might be more complex than in the case of the extensively studied soluble proteins. Here, we examine the dynamical coupling between a biological membrane, the purple membrane (PM), and its hydration water by a combination of elastic incoherent neutron scattering, specific deuteration, and molecular dynamics simulations. Examining completely deuterated PM, hydrated in H(2)O, allowed the direct experimental exploration of water dynamics. The study of natural abundance PM in D(2)O focused on membrane dynamics. The temperature-dependence of atomic mean-square displacements shows inflections at 120 K and 260 K for the membrane and at 200 K and 260 K for the hydration water. Because transition temperatures are different for PM and hydration water, we conclude that ps-ns hydration water dynamics are not directly coupled to membrane motions on the same time scale at temperatures <260 K. Molecular-dynamics simulations of hydrated PM in the temperature range from 100 to 296 K revealed an onset of hydration-water translational diffusion at approximately 200 K, but no transition in the PM at the same temperature. Our results suggest that, in contrast to soluble proteins, the dynamics of the membrane protein is not controlled by that of hydration water at temperatures <260 K. Lipid dynamics may have a stronger impact on membrane protein dynamics than hydration water.

Solid State Chemistry of Proteins: I. Glass Transition Behavior in Freeze Dried Disaccharide Formulations of Human Growth Hormone (HGH)

Although freeze dried formulations are commonly characterized using differential scanning calorimetry (DSC), a protein-rich system behaves as a "strong glass", and the glass transition temperature, T(g), cannot be directly determined by DSC. A strong glass means a small heat capacity change at T(g), triangle upC(p), and a very broad glass transition region, or a large triangle upT(g). However, direct experimental evidence for a small triangle upC(p) and a large triangle upT(g) have been lacking. Here, we utilize extrapolation of thermal analysis data in protein:disaccharide mixtures to evaluate T(g), triangle upT(g), and triangle upC(p) for "pure" human growth hormone (hGH) from low to moderate residual water. We find that triangle upT(g) is indeed large and triangle upC(p) is very small. Also, the T(g) for pure hGH decreases from a value of about 136 degrees C when dry to around 25 degrees C at 12% water. This glass transition is not the onset of mobility within the protein molecule but rather signals onset of whole molecule rotation and translation. We also observe complex pre-T(g) thermal events in the DSC data, which are interpreted as consequences of relaxation events, largely due to the disaccharide, and are characteristic of freeze dried systems having a broad distribution of relaxing substates.

Coarse-grained biomolecular simulation with REACH: realistic extension algorithm via covariance Hessian

Coarse-graining of protein interactions provides a means of simulating large biological systems. Here, a coarse-graining method, REACH, is introduced, in which the force constants of a residue-scale elastic network model are calculated from the variance-covariance matrix obtained from atomistic molecular dynamics (MD) simulation. In test calculations, the C(alpha)-atoms variance-covariance matrices are calculated from the ensembles of 1-ns atomistic MD trajectories in monomeric and dimeric myoglobin, and used to derive coarse-grained force constants for the local and nonbonded interactions. Construction of analytical model functions of the distance-dependence of the interresidue force constants allows rapid calculation of the REACH normal modes. The model force constants from monomeric and dimeric myoglobin are found to be similar in magnitude to each other. The MD intra- and intermolecular mean-square fluctuations and the vibrational density of states are well reproduced by the residue-scale REACH normal modes without requiring rescaling of the force constant parameters. The temperature-dependence of the myoglobin REACH force constants reveals that the dynamical transition in protein internal fluctuations arises principally from softening of the elasticity in the nonlocal interactions. The REACH method is found to be a reliable way of determining spatiotemporal protein motion without the need for expensive computations of long atomistic MD simulations.

Role of the solvent in the dynamical transitions of proteins: The case of the lysozyme-water system

We study the dynamics of hydration water in the protein lysozyme in the temperature range 180 K<T<360 K using Fourier-transform-infrared and nuclear magnetic resonance (NMR) spectroscopies. By analyzing the thermal evolution of spectra of the OH-stretching vibration modes and the NMR self-diffusion (DS) and spin-lattice relaxation time (T1), we demonstrate the existence of two dynamical transitions in the protein hydration water. Below the first transition, at about 220 K, the hydration water displays an unambiguous fragile-to-strong dynamic crossover, resulting in the loss of the protein conformational flexibility. Above the second transition, at about 346 K, where the protein unfolds, the dynamics of the hydration water appears to be dominated by the non-hydrogen-bonded fraction of water molecules.

Coupling between lysozyme and trehalose dynamics: microscopic insights from molecular-dynamics simulations

We have carried out molecular-dynamics simulations on fully flexible all-atom models of the protein lysozyme immersed in trehalose, an effective biopreservative, with the purpose of exploring the nature and extent of the dynamical coupling between them. Our study shows a strong coupling over a wide range of temperatures. We found that the onset of anharmonic behavior was dictated by changes in the dynamics and relaxation processes in the trehalose glass. The physical origin of protein-trehalose coupling was traced to the hydrogen bonds formed at the interface between the protein and the solvent. Moreover, protein-solvent hydrogen bonding was found to control the structural relaxation of the protein. The dynamics of the protein was found to be heterogeneous; the motions of surface and core atoms had different dependencies on temperature and, in addition, the surface atoms were more sensitive to the dynamics of the solvent than the core atoms. From the solvent perspective we found that the dynamics near the protein surface showed an unexpected enhanced mobility compared to the bulk. These results shed some light on the microscopic origins of the dynamical coupling in protein-solvent systems.

Temperature-dependent protein dynamics: a simulation-based probabilistic diffusion-vibration Langevin description

An enduring challenge in the understanding of internal protein motions is the effective separation and characterization of diffusive and vibrational dynamical components. To address this problem, here nanosecond molecular dynamics trajectories of myoglobin in aqueous solution, performed over a range of temperatures between 120 and 300 K, are subjected to principal component analysis, and the coordinate autocorrelation functions of the resulting principal modes are interpreted using a model combining damped Langevin vibration within potential wells and barrier-crossing diffusion between them. Both the vibrational frequency and the fraction of the mean-square fluctuation arising from vibrational motion undergo transitions with temperature at about 180 K. In contrast, the vibrational friction remains linear with temperature. The diffusional component of the mean-square fluctuation increases dramatically at the dynamical transition. The heights of the energy barriers between the potential wells are estimated, and the associated diffusion constants are calculated using Kramers' rate theory. Model functions of the frequency dependence of the frictional and diffusional quantities are obtained. The dynamic structure factor from the full molecular dynamics trajectory is well reproduced by the model. Overall, the results indicate that a global description of nanosecond temperature-dependent diffusion and vibrational internal protein dynamics can be obtained by applying the results of the present diffusion-vibration model to the vibrational motions obtained from a normal-mode analysis.

Langevin model of the temperature and hydration dependence of protein vibrational dynamics

The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.

Enhancement of the fluorescence of the blue fluorescent proteins by high pressure or low temperature

Green fluorescent proteins bearing the Y66H mutation exhibit strongly blue-shifted fluorescence excitation and emission spectra. However, these blue fluorescent proteins (BFPs) have lower quantum yields of fluorescence (Phi(f) approximately 0.20), which is believed to stem from the increased conformational freedom of the smaller chromophore. We demonstrate that suppression of chromophore mobility by increasing hydrostatic pressure or by decreasing temperature can enhance the fluorescence quantum yield of these proteins without significantly affecting their absorption properties or the shape of the fluorescence spectra. Analysis of the fluorescence lifetimes in the picosecond and nanosecond regimes reveals that the enhancement of the fluorescence quantum yield is due to the inhibition of fast quenching processes. Temperature-dependent fluorescence measurements reveal two barriers ( approximately 19 and 3 kJ/mol, respectively) for the transition into nonfluorescing states. These steps are probably linked with dissociation of the hydrogen bond between the chromophore and His148 or an intervening water molecule and to the barrier for chromophore twisting in the excited state, respectively. The chromophore's hydrogen-bond equilibrium at room temperature is dominated by entropic effects, while below approximately 200 K the balance is enthalpy-driven.

Bacteriorhodopsin photocycle at cryogenic temperatures reveals distributed barriers of conformational substates

The time course of thermal reactions after illumination of 100% humidified bacteriorhodopsin films was followed with FTIR spectroscopy between 125 and 195 K. We monitored the conversion of the initial photoproduct, K, to the next, L intermediate, and a shunt reaction of the L state directly back to the initial BR state. Both reactions can be described by either multiexponential kinetics, which would lead to apparent end-state mixtures that contain increasing amounts of the product, i.e., L or BR, with increasing temperature, or distributed kinetics. Conventional kinetic schemes that could account for the partial conversion require reversible reactions, branching, or parallel cycles. These possibilities were tested by producing K or L and monitoring their interconversion at a single temperature and by shifting the temperature upward or downward after an initial incubation and after their redistribution. The results are inconsistent with any conventional scheme. Instead, we attribute the partial conversions to the other alternative, distributed kinetics, observed previously in myoglobin, which arise from an ensemble of frozen conformational substates at the cryogenic temperatures. In this case, the time course of the reactions reflects the progressive depletion of distinct microscopic substates in the order of their increasing activation barriers, with a distribution width for K to L reaction of approximately 7 kJ/mol.

Coupling Between Chemical Reactivity and Structural Relaxation in Pharmaceutical Glasses

PURPOSE

To test the hypothesis that the molecular motions associated with chemical degradation in glassy amorphous systems are governed by the molecular motions associated with structural relaxation. The extent to which a chemical process is linked to the motions associated with structural relaxation will depend on the nature of the chemical process and molecular motion requirements (e.g., translation of a complete molecule, rotational diffusion of a chemical functional group). In this study the chemical degradation and molecular mobility were measured in model systems to assess the degree of coupling between chemical reactivity and structural relaxation. The model systems included pure amorphous cephalosporin drugs, and amorphous molecular mixtures containing a chemically labile drug and an additive expected to moderate molecular mobility.

METHODS

Amorphous drugs and mixtures with additives were prepared by lyophilization from aqueous solution. The physical properties of the model systems were characterized using optical microscopy and differential scanning calorimetry. The chemical degradation of the drugs alone and in mixtures with additives was measured using high-performance liquid chromatography (HPLC). Molecular mobility was measured using isothermal microcalorimetry to measure enthalpy changes associated with structural relaxation below T (g).

RESULTS

A weak correlation between the rates of degradation and structural relaxation times in pure amorphous cephalosporins suggests that reactivity in these systems is coupled to molecular motions in the glassy state. However, when sucrose was added to one of the cephalosporin drugs stability improved even though this addition reduced T (g) and the relaxation time constant, tau(D)(beta), suggesting that there was no correlation between reactivity and structural relaxation in the cephalosporin mixtures. In contrast, the rate of ethacrynate sodium dimer formation in mixtures was more strongly coupled to the relaxation time constant, tau(D)(beta).

CONCLUSIONS

These studies suggest that the extent to which chemical degradation is coupled to structural relaxation in glasses motions is determined by how closely the motions of the rate controlling step in chemical degradation are associated with structural relaxation. Moderate coupling between the rate of dimer formation for ethacrynate sodium in mixtures with sucrose, trehalose and PVP and structural relaxation constants suggests that chemical changes that require more significant molecular motion, and includes at least some translational diffusion, are more strongly coupled to the molecular motions associated with structural relaxation. The observation that sucrose stabilizes cefoxitin sodium even though it lowers T (g) and reduces the relaxation time constant, tau(D)(beta) is perhaps a result of the importance of other kinds of molecular motions in determining the chemical reactivity in glasses.

Controlling the protein dynamical transition with sugar-based bioprotectant matrices: a neutron scattering study

Through elastic neutron scattering we measured the mean-square displacements of the hydrogen atoms of lysozyme embedded in a glucose-water glassy matrix as a function of the temperature and at various water contents. The elastic intensity of all the samples has been interpreted in terms of the double-well model in the whole temperature range. The dry sample shows an onset of anharmonicity at approximately 100 K, which can be attributed to the activation of methyl group reorientations. Such a protein intrinsic dynamics is decoupled from the external environment on the whole investigated temperature range. In the hydrated samples an additional and larger anharmonic contribution is provided by the protein dynamical transition, which appears at a higher temperature Td. As hydration increases the coupling between the protein internal dynamics and the surrounding matrix relaxations becomes more effective. The behavior of Td that, as a function of the water content, diminishes by approximately 60 K, supports the picture of the protein dynamics as driven by solvent relaxations. A possible connection between the protein dynamical response versus T and the thermal stability in glucose-water bioprotectant matrices is proposed.

Observation of fragile-to-strong dynamic crossover in protein hydration water

At low temperatures, proteins exist in a glassy state, a state that has no conformational flexibility and shows no biological functions. In a hydrated protein, at temperatures greater-- similar 220 K, this flexibility is restored, and the protein is able to sample more conformational substates, thus becoming biologically functional. This "dynamical" transition of protein is believed to be triggered by its strong coupling with the hydration water, which also shows a similar dynamic transition. Here we demonstrate experimentally that this sudden switch in dynamic behavior of the hydration water on lysozyme occurs precisely at 220 K and can be described as a fragile-to-strong dynamic crossover. At the fragile-to-strong dynamic crossover, the structure of hydration water makes a transition from predominantly high-density (more fluid state) to low-density (less fluid state) forms derived from the existence of the second critical point at an elevated pressure.

Glasslike structure of globular proteins and the boson peak

Vibrational spectra of proteins and topologically disordered solids display a common anomaly at low frequencies, known as boson peak. We show that such feature in globular proteins can be deciphered in terms of an energy landscape picture, as it is for glassy systems. Exploiting the tools of Euclidean random matrix theory, we clarify the physical origin of such anomaly in terms of a mechanical instability of the system. As a natural explanation, we argue that such instability is relevant for proteins in order for their molecular functions to be optimally rooted in their structures.

Thermodynamic Confinement and α-Helix Persistence Length in Poly(γ-benzyl-l-glutamate)-b-poly(dimethyl siloxane)-b-poly(γ-benzyl-l-glutamate) Triblock Copolymers

The structure and the associated dynamics of a series of poly(gamma-benzyl-L-glutamate)-b-poly(dimethyl siloxane)-b-poly(gamma-benzyl-L-glutamate) (PBLG-b-PDMS-b-PBLG) triblock copolymers were investigated using small- and wide-angle X-ray scattering, NMR, transmission electron microscopy, and dielectric spectroscopy, respectively. The structural analysis revealed phase separation in the case of the longer blocks with defected alpha-helical segments embedded within the block copolymer nanodomains. The alpha-helical persistence length was found to depend on the degree of segregation; thermodynamic confinement and chain stretching results in the partial annihilation of helical defects.

Effects of counterion valency on the damping of phonons propagating along the axial direction of liquid-crystalline DNA

The phonon propagation and damping along the axial direction of films of aligned 40 wt % calf-thymus DNA rods are studied by inelastic x-ray scattering (IXS). The IXS spectra are analyzed with the generalized three effective eigenmode theory, from which we extract the dynamic structure factor S(Q,E) as a function of transferred energy E=variant Planck's over 2piomega, and the magnitude of the transferred wave vector Q. S(Q,E) of a DNA sample typically consists of three peaks, one central Rayleigh scattering peak, and two symmetric Stokes and anti-Stokes Brillouin side peaks. By analyzing the Brillouin peaks, the phonon excitation energy and damping can be extracted at different Q values from about 4 to 30 nm(-1). A high-frequency sound speed is obtained from the initial slope of the linear portion of the dispersion relation below Q=4 nm(-1). The high-frequency sound speed obtained in this Q range is 3100 ms, which is about twice faster than the ultrasound speed of 1800 ms, measured by Brillouin light scattering at Q approximately 0.01 nm(-1) at the similar hydration level. Our observations provide further evidence of the strong coupling between the internal dynamics of a DNA molecule and the dynamics of the solvent. The effect on damping and propagation of phonons along the axial direction of DNA rods due to divalent and trivalent counterions has been studied. It is found that the added multivalent counterions introduce stronger phonon damping. The phonons at the range between approximately 12.5 and approximately 22.5 nm(-1) are overdamped by the added counterions according to our model analyses. The intermediate scattering function is extracted and it shows a clear two-step relaxation with the fast relaxation time ranging from 0.1 to 4 ps.

Energy landscape and dynamics of biomolecules extended abstract

Proteins are not isolated homogeneous systems. Each protein can exist in a very large number of conformations (conformational substates) that are characterized by an energy landscape. The main conformational motions, similar to the α and β fluctuations in glasses, are linked to fluctuations in the bulk solvent and the hydration shell.