Glassy behavior of a protein

Glasslike dynamical behavior of the plastocyanin hydration water

The dynamical behavior of water around plastocyanin has been investigated in a wide temperature range by molecular dynamics simulation. The mean square displacements of water oxygen atoms show, at long times, a t(alpha) trend for all temperatures. Below 150 K, alpha is constant and equal to 1; at higher temperatures it drops to a value significantly smaller than 1, and thereafter decreases with increasing temperature. The occurrence of such an anomalous diffusion matches the onset of the dynamical transition observed in the protein. The intermediate scattering function of water is characterized, at high temperature, by a stretched exponential decay evolving, at low temperature, toward a two step relaxation behavior, which becomes more evident on increasing the exchanged wave vector q. Both the mean square displacements and the intermediate scattering functions show, beyond the ballistic regime, a plateau, which progressively extends for longer times as long as the temperature is lowered, such behavior reflecting trapping of water molecules within a cage formed by the nearest neighbors. At low temperature, a low frequency broad inelastic peak is observed in the dynamical structure factor of hydration water; such an excess of vibrational modes being reminiscent of the boson peak, characteristic of disordered, amorphous systems. All these features, which are typical of complex systems, can be traced back to the glassy character of the hydration water and suggest a dynamical coupling occurring at the macromolecule-solvent interface.

Solvent dependence of dynamic transitions in protein solutions

A transition as a function of increasing temperature from harmonic to anharmonic dynamics has been observed in globular proteins by using spectroscopic, scattering, and computer simulation techniques. We present here results of a dynamic neutron scattering analysis of the solvent dependence of the picosecond-time scale dynamic transition behavior of solutions of a simple single-subunit enzyme, xylanase. The protein is examined in powder form, in D(2)O, and in four two-component perdeuterated single-phase cryosolvents in which it is active and stable. The scattering profiles of the mixed solvent systems in the absence of protein are also determined. The general features of the dynamic transition behavior of the protein solutions follow those of the solvents. The dynamic transition in all of the mixed cryosolvent-protein systems is much more gradual than in pure D(2)O, consistent with a distribution of energy barriers. The differences between the dynamic behaviors of the various cryosolvent protein solutions themselves are remarkably small. The results are consistent with a picture in which the picosecond-time scale atomic dynamics respond strongly to melting of pure water solvent but are relatively invariant in cryosolvents of differing compositions and melting points.

Modeling the correlation functions of conformational motions in proteins

A first principles calculation of the correlation function for conformational motion (CM) in proteins is carried out within the framework of a microscopic model of a protein as a heterogeneous system. The fragments of the protein are assumed to be identical hard spheres undergoing the CM within their conformational potentials about some mean equilibrium positions assigned by the tertiary structure. The memory friction function (MFF) for the generalized Langevin equation describing the CM of the particle is obtained on the basis of the direct calculation which is feasible for the present model of the protein due to the existence of a natural large parameter, viz. the ratio of the minimal distance between the mean equilibrium positions of the particles (approximately 7A) to the amplitude of their CM (<1A). A relationship between the MFF and the correlation functions of the CM of the particles is derived which makes their calculation to be a self-consistent mathematical problem. The general analysis of the MFF is exemplified by a simple model case in which the mean equilibrium positions of the particles form a regular lattice so that the correlation functions for all particles are the same. In this case the MFF is shown to be an infinite series of the powers of the auto-correlation function whose coefficients are independent on temperature. The latter is a result of the abstraction of the interaction potential by that of hard spheres which actually corresponds to the high temperature limit. On the examples of cubic and triangular lattices the coefficients are shown to be non-negative values which increase with the increase of the packing density of the particles and quickly tend to zero with the increase of their index. Thus the MFF can be approximated by a polynomial of the correlation function and the resulting mathematical equation is analogous to the one from the dynamic theory of liquids. The correlation function of the CM is obtained by numerical solution of the equation. At realistic packing densities for proteins it exhibits transparent non-exponential decay and includes two relaxation processes: the first one on the intermediate timescale (tens of picoseconds) and the second on the long timescale (its characteristic time is about tens of nanoseconds at small values of the friction coefficient and increases by orders of the magnitude with the increase of the latter). Thus the present approach provides the microscopic basis for previous phenomenological models of cooperative dynamics in proteins.

Universal low-frequency vibrations of proteins from a simple interaction potential

A pairwise Born potential connecting the heavy atom sites within a prescribed cutoff, and the equation of motion method (EOM), reproduce the existence of a universal singularity in the low-frequency vibrational density of states of typical globular proteins. This is due to quasilocalization of acoustic waves and an analogy with a similar feature found in glasses is stressed. We explain the dependence of this anomaly with the effective dimensionality of the protein. The EOM method allows for the study of even the largest proteins with a simple personal computer.

Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems

Logarithmic oscillations superimposed on the temporal relaxation patterns of complex systems are considered from the standpoint of their hierarchical origin. We propose that a closer examination of experimental data should reveal logarithmic oscillations in systems that are characterized by a hierarchical structure of their dynamical degrees of freedom. On that footing, a new methodology of data analysis is proposed that may prove important for the dynamics of protein folding and of conformational fluctuations in proteins in which the relevant time scales of the dynamical evolution underlying the relaxation kinetics can be deduced from these oscillations.

Neutron scattering evidence of a boson peak in protein hydration water

Measurement of the low temperature neutron excess of scattering of H2O-hydrated plastocyanin relative to D2O-hydrated protein allowed us to reveal the presence of an inelastic peak at about 3.5 meV. This excess of vibrational modes, elsewhere termed "boson peak," is due to the dynamical behavior of the water molecules belonging to the H2O-hydration shell surrounding the protein. The relevance of the boson peak to the dynamical coupling between the solvent and the protein, and hence to the protein functionality is addressed.

Connection between the taxonomic substates and protonation of histidines 64 and 97 in carbonmonoxy myoglobin

Infrared spectra of heme-bound CO in sperm whale carbonmonoxy myoglobin and two mutants (H64L and H97F) were studied in the pH range from 4.2 to 9.5. Comparison of the native protein with the mutants shows that the observed pH effects can be traced to protonations of two histidine residues, H64 and H97, near the active site. Their imidazole sidechains experience simple, uncoupled Henderson-Hasselbalch type protonations, giving rise to four different protonation states. Because two of the protonation states are linked by a pH-independent equilibrium, the overall pH dependence of the spectra is described by a linear combination of three independent components. Global analysis, based on singular value decomposition and matrix least-squares algorithms enabled us to extract the pK values of the two histidines and the three basis spectra of the protonating species. The basis spectra were decomposed into the taxonomic substates A(0), A(1), and A(3), previously introduced in a heuristic way to analyze CO stretch spectra in heme proteins at fixed pH (see for instance, Biophys. J. 71:1563-1573). Moreover, an additional, weakly populated substate, called A(x), was identified. Protonation of H97 gives rise to a blue shift of the individual infrared lines by about 2 cm(-1), so that the A substates actually appear in pairs, such as A(0) and A(0)(+). The blue shift can be explained by reduced backbonding from the heme iron to the CO. Protonation of the distal histidine, H64, leads to a change of the infrared absorption from the A(1) or A(3) substate lines to A(0). This behavior can be explained by a conformational change upon protonation that moves the imidazole sidechain of H64 away from the CO into the high-dielectric solvent environment, which avoids the energetically unfavorable situation of an uncompensated electric charge in the apolar, low-dielectric protein interior. Our results suggest that protonation reactions serve as an important mechanism to create taxonomic substates in proteins.

The temperature dependence of internal molecular motions in hydrated and dry alpha-amylase: the role of hydration water in the dynamical transition of proteins

Internal molecular motions of proteins are strongly affected by environmental conditions, like temperature and hydration. As known from numerous studies, the dynamical behavior of hydrated proteins on the picosecond time scale is characterized by vibrational motions in the low-temperature regime and by an onset of stochastic large-amplitude fluctuations at a transition temperature of 180-230 K. The present study reports on the temperature dependence of internal molecular motions as measured with incoherent neutron scattering from the globular water-soluble protein alpha-amylase and from a protein-lipid complex of rhodopsin in disk membranes. Samples of alpha-amylase have been measured in a hydrated and dehydrated state. In contrast to the hydrated sample, which exhibits a pronounced dynamical transition near 200 K, the dehydrated alpha-amylase does not show an appreciable proportion of stochastic large-amplitude fluctuations and no dynamical transition in the measured temperature range of 140-300 K. The obtained results, which are compared to the dynamical behavior of protein-lipid complexes, are discussed with respect to the influence of hydration on the dynamical transition and in the framework of the glass transition.

Native protein fluctuations: the conformational-motion temperature and the inverse correlation of protein flexibility with protein stability

We study the fluctuations of native proteins by exact enumeration using the HP lattice model. The model fluctuations increase with temperature. We observe a low-temperature point, below which large fluctuations are frozen out. This prediction is consistent with the observation by Tilton et al. [R. F. Tilton, Jr., J. C. Dewan, and G. A. Petsko, Biochemistry 31, 2469 (1992)], that the thermal motions of ribonuclease A increase sharply above about 200 K. We also explore protein "flexibility" as defined by Debye-Waller-like factors and solvent accessibilities of core residues to hydrogen exchange. We find that proteins having greater stability tend to have fewer large fluctuations, and hence lower flexibilities. If flexibility is necessary for enzyme catalysis, this could explain why proteins from thermophilic organisms, which are exceptionally stable, may be catalytically inactive at normal temperatures.

The photoexcited triplet state as a probe of chromophore-protein interaction in myoglobin

The photoexcited metastable triplet state of Mg(2+)-mesoporphyrin IX (MgMPIX) or Mg(2+)-protoporphyrin IX (MgPPIX) located in the heme pocket of horse myoglobin (Mb) was investigated by optical and electron paramagnetic resonance (EPR) spectroscopy, and its properties were compared with the model complexes, MgMPIX, MgPPIX, and Mg2+ etioporphyrin I (MgETIOI), in noncoordinating and coordinating organic glasses. Zero-field splitting parameters, line shape, and Jahn-Teller distortion in the temperature range of 3.8-110 K are discussed in terms of porphyrin-protein interactions. The triplet line shapes for MgMPIXMb and MGPPIXMb show no temperature-dependent spectral line shape changes suggestive of Jahn-Teller dynamics, and it is concluded that the energy splitting is >> 150 cm-1, suggesting symmetry breaking from the anisotropy of intermal electric fields of the protein, and consistent with previous predictions (Geissinger et al. 1995. J. Phys. Chem. 99:16527-16529). Both MgMPIXMb and MgPPIXMb demonstrate electron spin polarization at low temperature, and from the polarization pattern it can be concluded that intersystem crossing occurs predominantly into in-plane spin sublevels of the triplet state. The splitting in the Q0.0 absorption band and the temperature dependence and splitting of the photoexcited triplet state of myoglobin in which the iron was replaced by Mg2+ are interpreted in terms of effects produced by electric field asymmetry in the heme pocket.

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

Real-time observation of conformational fluctuations in Zn-substituted myoglobin by time-resolved transient hole-burning spectroscopy

Equilibrium fluctuations of the protein conformation have been studied in myoglobin by a novel method of time-resolved transient hole-burning spectroscopy over a temperature range of 180-300 K and a time range of 10 ns to 10 ms. The temporal shift of the hole spectrum has been observed in a wide temperature region of 200-300 K. It has been found that the time behavior of the peak position of the hole is highly nonexponential and can be expressed by a stretched exponential function with a beta value of 0.22. As compared with the results for a dye solution sample, the time scale of the fluctuation of the protein conformation is much more weakly dependent on temperature. The time scale of the observed conformational dynamics shows a temperature dependence similar to that associated with the ligand escape process of myoglobin.

Electron transfer and protein dynamics in the photosynthetic reaction center

We have measured the kinetics of electron transfer (ET) from the primary quinone (Q(A)) to the special pair (P) of the reaction center (RC) complex from Rhodobacter sphaeroides as a function of temperature (5-300 K), illumination protocol (cooled in the dark and under illumination from 110, 160, 180, and 280 K), and warming rate (1.3 and 13 mK/s). The nonexponential kinetics are interpreted with a quantum-mechanical ET model (Fermi's golden rule and the spin-boson model), in which heterogeneity of the protein ensemble, relaxations, and fluctuations are cast into a single coordinate that relaxes monotonically and is sensitive to all types of relaxations caused by ET. Our analysis shows that the structural changes that occur in response to ET decrease the free energy gap between donor and acceptor states by 120 meV and decrease the electronic coupling between donor and acceptor states from 2.7 x 10(-4) cm(-1) to 1.8 x 10(-4) cm(-1). At cryogenic temperatures, conformational changes can be slowed or completely arrested, allowing us to monitor relaxations on the annealing time scale (approximately 10(3)-10(4) s) as well as the time scale of ET (approximately 100 ms). The relaxations occur within four broad tiers of conformational substates with average apparent Arrhenius activation enthalpies of 17, 50, 78, and 110 kJ/mol and preexponential factors of 10(13), 10(15), 10(21), and 10(25) s(-1), respectively. The parameterization provides a prediction of the time course of relaxations at all temperatures. At 300 K, relaxations are expected to occur from 1 ps to 1 ms, whereas at lower temperatures, even broader distributions of relaxation times are expected. The weak dependence of the ET rate on both temperature and protein conformation, together with the possibility of modeling heterogeneity and dynamics with a single conformational coordinate, make RC a useful model system for probing the dynamics of conformational changes in proteins.

Theory of protein folding: the energy landscape perspective

The energy landscape theory of protein folding is a statistical description of a protein's potential surface. It assumes that folding occurs through organizing an ensemble of structures rather than through only a few uniquely defined structural intermediates. It suggests that the most realistic model of a protein is a minimally frustrated heteropolymer with a rugged funnel-like landscape biased toward the native structure. This statistical description has been developed using tools from the statistical mechanics of disordered systems, polymers, and phase transitions of finite systems. We review here its analytical background and contrast the phenomena in homopolymers, random heteropolymers, and protein-like heteropolymers that are kinetically and thermodynamically capable of folding. The connection between these statistical concepts and the results of minimalist models used in computer simulations is discussed. The review concludes with a brief discussion of how the theory helps in the interpretation of results from fast folding experiments and in the practical task of protein structure prediction.

Picosecond molecular motions in bacteriorhodopsin from neutron scattering

The characteristics of internal molecular motions of bacteriorhodopsin in the purple membrane have been studied by quasielastic incoherent neutron scattering. Because of the quasihomogeneous distribution of hydrogen atoms in biological molecules, this technique enables one to study a wide variety of intramolecular motions, especially those occurring in the picosecond to nanosecond time scale. We performed measurements at different energy resolutions with samples at various hydration levels within a temperature range of 10-300 K. The analysis of the data revealed a dynamical transition at temperatures Td between 180 K and 220 K for all motions resolved at time scales ranging from 0.1 to a few hundred picoseconds. Whereas below Td the motions are purely vibrational, they are predominantly diffusive above Td, characterized by an enormously broad distribution of correlation times. The variation of the hydration level, on the other hand, mainly affects motions slower than a few picoseconds.

An EPR investigation on the structural heterogeneity in copper azurin and plastocyanin

The effects of cooling rate and of solvent properties on the active site heterogeneity of two copper proteins, azurin and plastocyanin, have been investigated at low temperature by electron paramagnetic resonance spectroscopy. The spectra of theses proteins have been analyzed, by an accurate computer simulation, in terms of a distribution of some relevant spin-Hamiltonian parameters. The results show that the structural heterogeneity of both proteins, quantified by the width of the distribution in the g and A tensors, is affected by both the freezing procedure and the solvent composition. In particular, the g distribution width is found to be reduced in the slow cooling regime; such a reduction appearing more significant when glycerol is added to the protein solutions. Despite of the similarity in the copper ion microenvironments of the two proteins, the effects are more pronounced in azurin. The results are discussed also in connection with the role played by the solvent and the rate of freezing in featuring the conformational substate landscape.

Biological cryo atomic force microscopy: a brief review

Despite many successes, atomic force microscopy (AFM) of biological specimens at room temperature is still severely limited by at least two factors: the softness and the thermal motion of flexible multi-domain/subunit molecules. Both problems can be overcome by imaging biological structures at cryogenic temperatures. Even though the instrumentation is considerably more complex and earlier attempts were largely unsuccessful, cryo-AFM has recently been demonstrated on a number of biological specimens, using an AFM operated in liquid nitrogen vapor under ambient pressure. In this brief review, both the method of instrumentation and the latest biological applications are discussed. Not only has the cryo-AFM attained high resolution on those specimens that could not be well imaged at room temperature, but it has also produced potentially important information on several specimens. These results firmly establish the cryo-AFM as a useful and versatile structural probe in biology with its own unique capabilities.

Ligand binding to heme proteins. VI. Interconversion of taxonomic substates in carbonmonoxymyoglobin

The kinetic properties of the three taxonomic A substates of sperm whale carbonmonoxy myoglobin in 75% glycerol/buffer are studied by flash photolysis with monitoring in the infrared stretch bands of bound CO at nu(A0) approximately 1967 cm-1, nu(A1) approximately 1947 cm-1, and nu(A3) approximately 1929 cm-1 between 60 and 300 K. Below 160 K the photodissociated CO rebinds from the heme pocket, no interconversion among the A substates is observed, and rebinding in each A substate is nonexponential in time and described by a different temperature-independent distribution of enthalpy barriers with a different preexponential. Measurements in the electronic bands, e.g., the Soret, contain contributions of all three A substates and can, therefore, be only approximately modeled with a single enthalpy distribution and a single preexponential. The bond formation step at the heme is fastest for the A0 substate, intermediate for the A1 substate, and slowest for A3. Rebinding between 200 and 300 K displays several processes, including geminate rebinding, rebinding after ligand escape to the solvent, and interconversion among the A substates. Different kinetics are measured in each of the A bands for times shorter than the characteristic time of fluctuations among the A substates. At longer times, fluctuational averaging yields the same kinetics in all three A substates. The interconversion rates between A1 and A3 are determined from the time when the scaled kinetic traces of the two substates merge. Fluctuations between A1 and A3 are much faster than those between A0 and either A1 or A3, so A1 and A3 appear as one kinetic species in the exchange with A0. The maximum-entropy method is used to extract the distribution of rate coefficients for the interconversion process A0 <--> A1 + A3 from the flash photolysis data. The temperature dependencies of the A substate interconversion processes are fitted with a non-Arrhenius expression similar to that used to describe relaxation processes in glasses. At 300 K the interconversion time for A0 <--> A1 + A3 is 10 microseconds, and extrapolation yields approximately 1 ns for A1 <--> A3. The pronounced kinetic differences imply different structural rearrangements. Crystallographic data support this conclusion: They show that formation of the A0 substate involves a major change of the protein structure; the distal histidine rotates about the C(alpha)-C(beta) bond, and its imidazole sidechain swings out of the heme pocket into the solvent, whereas it remains in the heme pocket in the A1 <--> A3 interconversion. The fast A1 <--> A3 exchange is inconsistent with structural models that involve differences in the protonation between A1 and A3.

Using buried water molecules to explore the energy landscape of proteins

Buried water molecules constitute a highly conserved, integral part of nearly all known protein structures. Such water molecules exchange with external solvent as a result of protein conformational fluctuations. We report here the results of water (17)O and (2)H magnetic relaxation dispersion measurements on wild-type and mutant bovine pancreatic trypsin inhibitor in aqueous solution at 4-80 degrees C. These data lead to the first determination of the exchange rate of a water molecule buried in a protein. The strong temperature dependence of this rate is ascribed to large-scale conformational fluctuations in an energy landscape with a statistical ruggedness of approximately 10 kJ mol(-1).