Temperature-dependent X-ray diffraction as a probe of protein structural dynamics

Hydration effect on low-frequency protein dynamics observed in simulated neutron scattering spectra

Hydration effects on protein dynamics were investigated by comparing the frequency dependence of the calculated neutron scattering spectra between full and minimal hydration states at temperatures between 100 and 300 K. The protein boson peak is observed in the frequency range 1–4 meV at 100 K in both states. The peak frequency in the minimal hydration state shifts to lower than that in the full hydration state. Protein motions with a frequency higher than 4 meV were shown to undergo almost harmonic motion in both states at all temperatures simulated, whereas those with a frequency lower than 1 meV dominate the total fluctuations above 220 K and contribute to the origin of the glass-like transition. At 300 K, the boson peak becomes buried in the quasielastic contributions in the full hydration state but is still observed in the minimal hydration state. The boson peak is observed when protein dynamics are trapped within a local minimum of its energy surface. Protein motions, which contribute to the boson peak, are distributed throughout the whole protein. The fine structure of the dynamics structure factor is expected to be detected by the experiment if a high resolution instrument (<∼20 μeV) is developed in the near future.

Biophysical study of thermal denaturation of apo-calmodulin: dynamics of native and unfolded states

Apo-calmodulin, a small, mainly alpha, soluble protein is a calcium-dependent protein activator. This article presents a study of internal dynamics of native and thermal unfolded apo-calmodulin, using quasi-elastic neutron scattering. This technique can probe protein internal dynamics in the picosecond timescale and in the nanometer length-scale. It appears that a dynamical transition is associated with thermal denaturation of apo-calmodulin. This dynamical transition goes together with a decrease of the confinement of hydrogen atoms, a decrease of immobile protons proportion and an increase of dynamical heterogeneity. The comparison of native and unfolded states dynamics suggests that the dynamics of protein atoms is more influenced by their distance to the backbone than by their solvent exposure.

Sampling of the native conformational ensemble of myoglobin via structures in different crystalline environments

Proteins sample multiple conformational substates in their native environment, but the process of crystallization selects the conformers that allow for close packing. The population of conformers can be shifted by varying the environment through a range of crystallization conditions, often resulting in different space groups and changes in the packing arrangements. Three high resolution structures of myoglobin (Mb) in different crystal space groups are presented, including one in a new space group P6(1)22 and two structures in space groups P2(1)2(1)2(1) and P6. We compare coordinates and anisotropic displacement parameters (ADPs) from these three structures plus an existing structure in space group P2(1). While the overall changes are small, there is substantial variation in several external regions with varying patterns of crystal contacts across the space group packing arrangements. The structural ensemble containing four different crystal forms displays greater conformational variance (Calpha rmsd of 0.54-0.79 A) in comparison to a collection of four Mb structures with different ligands and mutations in the same crystal form (Calpha rmsd values of 0.28-0.37 A). The high resolution of the data enables comparison of both the magnitudes and directions of ADPs, which are found to be suppressed by crystal contacts. A composite dynamic profile of Mb structural variation from the four structures was compared with an independent structural ensemble developed from NMR refinement. Despite the limitations and biases of each method, the ADPs of the crystallographic ensemble closely match the positional variance from the solution NMR ensemble with linear correlation of 0.8. This suggests that crystal packing selects conformers representative of the solution ensemble, and several different crystal forms give a more complete view of the plasticity of a protein structure.

Mechanistic elements of protein cold denaturation

Globular proteins undergo structural transitions to denatured states when sufficient thermodynamic state or chemical perturbations are introduced to their native environment. Cold denaturation is a somewhat counterintuitive phenomenon whereby proteins lose their compact folded structure as a result of a temperature drop. The currently accepted explanation for cold denaturation is based on an associated favorable change in the contact free energy between water and nonpolar groups at colder temperatures which would weaken the hydrophobic interaction and is thought to eventually allow polymer entropy to disrupt protein tertiary structure. In this paper we explore how this environmental perturbation leads to changes in the protein hydration and local motions in apomyoglobin. We do this by analyzing changes in protein hydration and protein motion from molecular dynamics simulation trajectories initially at 310 K, followed by a temperature drop to 278 K. We observe an increase in the number of solvent contacts around the protein and, in particular, distinctly around nonpolar atoms. Further analysis shows that the fluctuations of some protein atoms increase with decreasing temperature. This is accompanied by an observed increase in the isothermal compressibility of the protein, indicating an increase in the protein interior interstitial space. Closer inspection reveals that atoms with increased compressibility and larger-than-expected fluctuations are localized within the protein core regions. These results provide insight into a description of the mechanism of cold denaturation. That is, the lower temperature leads to solvent-induced packing defects at the protein surface, and this more favorable water-protein interaction in turn destabilizes the overall protein structure.

Site-specific modification and PEGylation of pharmaceutical proteins mediated by transglutaminase

Transglutaminase (TGase, E.C. 2.3.2.13) catalyzes acyl transfer reactions between the gamma-carboxamide groups of protein-bound glutamine (Gln) residues, which serve as acyl donors, and primary amines, resulting in the formation of new gamma-amides of glutamic acid and ammonia. By using an amino-derivative of poly(ethylene glycol) (PEG-NH(2)) as substrate for the enzymatic reaction with TGase it is possible to covalently bind the PEG polymer to proteins of pharmaceutical interest. In our laboratory, we have conducted experiments aimed to modify proteins of known structure using TGase and, surprisingly, we were able to obtain site-specific modification or PEGylation of protein-bound Gln residue(s) in the protein substrates. For example, in apomyoglobin (apoMb, myoglobin devoid of heme) only Gln91 was modified and in human growth hormone only Gln40 and Gln141, despite these proteins having many more Gln residues. Moreover, we noticed that these proteins suffered highly selective limited proteolysis phenomena at the same chain regions being attacked by TGase. We have analysed also the results of other published experiments of TGase-mediated modification or PEGylation of several proteins in terms of protein structure and dynamics, among them alpha-lactalbumin and interleukin-2, as well as disordered proteins. A noteworthy correlation was observed between chain regions of high temperature factor (B-factor) determined crystallographically and sites of TGase attack and limited proteolysis, thus emphasizing the role of chain mobility or local unfolding in dictating site-specific enzymatic modification. We propose that enhanced chain flexibility favors limited enzymatic reactions on polypeptide substrates by TGases and proteases, as well as by other enzymes involved in a number of site-specific post-translational modifications of proteins, such as phosphorylation and glycosylation. Therefore, it is possible to predict the site(s) of TGase-mediated modification and PEGylation of a therapeutic protein on the basis of its structure and dynamics and, consequently, the likely effects of modifications on the functional properties of the protein.

Asymmetric band profile of the Soret band of deoxymyoglobin is caused by electronic and vibronic perturbations of the heme group rather than by a doming deformation

We measured the Soret band of deoxymyoglobin (deoxyMb), myoglobin cyanide (MbCN), and aquo-metmyoglobin (all from horse heart) with absorption and circular dichroism (CD) spectroscopies. A clear non-coincidence was observed between the absorption and CD profiles of deoxyMb and MbCN, with the CD profiles red- and blueshifted with respect to the absorption band position, respectively. On the contrary, the CD and absorption profiles of aquametMb were nearly identical. The observed noncoincidence indicates a splitting of the excited B state due to heme-protein interactions. CD and absorption profiles of deoxyMb and MbCN were self-consistently analyzed by employing a perturbation approach for weak vibronic coupling as well as the relative intensities and depolarization ratios of seven bands in the respective resonance Raman spectra measured with B-band excitation. The respective B(y) component was found to dominate the observed Cotton effect of both myoglobin derivatives. The different signs of the noncoincidences between CD and absorption bands observed for deoxyMb and MbCN are due to different signs of the respective matrix elements of A(1g) electronic interstate coupling, which reflects an imbalance of Gouterman's 50:50 states. The splitting of the B band reflects contributions from electronic and vibronic perturbations of B(1g) symmetry. The results of our analysis suggest that the broad and asymmetric absorption band of deoxyMb results from this band splitting rather than from its dependence on heme doming. Thus, we are able to explain recent findings that the temperature dependences of CO rebinding to myoglobin and the Soret band profile are uncorrelated[Ormos et al., Proc. Natl. Acad. Sci U.S.A. 95, 6762 (1998)].

Influence of water clustering on the dynamics of hydration water at the surface of a lysozyme

Dynamics of hydration water at the surface of a lysozyme molecule is studied by computer simulations at various hydration levels in relation with water clustering and percolation transition. Increase of the translational mobility of water molecules at the surface of a rigid lysozyme molecule upon hydration is governed by the water-water interactions. Lysozyme dynamics strongly affect translational motions of water and this dynamic coupling is maximal at hydration levels, corresponding to the formation of a spanning water network. Anomalous diffusion of hydration water does not depend on hydration level up to monolayer coverage and reflects spatial disorder. Rotational dynamics of water molecules show stretched exponential decay at low hydrations. With increasing hydration, we observe appearance of weakly bound water molecules with bulklike rotational dynamics, whose fraction achieves 20-25% at the percolation threshold.

Picosecond fluctuating protein energy landscape mapped by pressure temperature molecular dynamics simulation

Microscopic statistical pressure fluctuations can, in principle, lead to corresponding fluctuations in the shape of a protein energy landscape. To examine this, nanosecond molecular dynamics simulations of lysozyme are performed covering a range of temperatures and pressures. The well known dynamical transition with temperature is found to be pressure-independent, indicating that the effective energy barriers separating conformational substates are not significantly influenced by pressure. In contrast, vibrations within substates stiffen with pressure, due to increased curvature of the local harmonic potential in which the atoms vibrate. The application of pressure is also shown to selectively increase the damping of the anharmonic, low-frequency collective modes in the protein, leaving the more local modes relatively unaffected. The critical damping frequency, i.e., the frequency at which energy is most efficiently dissipated, increases linearly with pressure. The results suggest that an invariant description of protein energy landscapes should be subsumed by a fluctuating picture and that this may have repercussions in, for example, mechanisms of energy dissipation accompanying functional, structural, and chemical relaxation.

Origin of the dynamic transition upon pressurization of crystalline proteins

We study the role of hydration water in the dynamic transition of low-hydrated proteins upon pressurization found recently (Meinhold, L.; Smith, J. C. Phys. Rev. E 2005, 72, 061908). Clustering and percolation of water in the hydration shells of protein molecules in crystalline Staphylococcal nuclease are analyzed at various pressures. The number of water molecules in the hydration shell increases and the hydrogen-bonded network of hydration water spans with increasing pressure. The dynamic transition of protein occurs when the spanning water network exists with the probability of about 50% and hydration water shows large density fluctuations. Formation of a spanning water network upon pressurization promotes protein dynamics as in the case of the dynamic transition with increasing hydration. Properties of hydration water in various thermodynamic states and their influence on biological function are discussed.

Molecular crowding inhibits intramolecular breathing motions in proteins

In aqueous solution some proteins undergo large-scale movements of secondary structures, subunits or domains, referred to as protein "breathing", that define a native-state ensemble of structures. These fluctuations are sensitive to the nature and concentration of solutes and other proteins and are thereby expected to be different in the crowded interior of a cell than in dilute solution. Here we use a combination of wide angle X-ray scattering (WAXS) and computational modeling to derive a quantitative measure of the spatial scale of conformational fluctuations in a protein solution. Concentration-dependent changes in the observed scattering intensities are consistent with a model of structural fluctuations in which secondary structures undergo rigid-body motions relative to one another. This motion increases with decreasing protein concentration or increasing temperature. Analysis of a set of five structurally and functionally diverse proteins reveals a diversity of kinetic behaviors. Proteins with multiple disulfide bonds exhibit little or no increase in breathing in dilute solutions. The spatial extent of structural fluctuations appears highly dependent on both protein structure and concentration and is universally suppressed at very high protein concentrations.

Adaptation to high temperatures through macromolecular dynamics by neutron scattering

Work on the relationship between hyperthermophile protein dynamics, stability and activity is reviewed. Neutron spectroscopy has been applied to measure and compare the macromolecular dynamics of various hyperthermophilic and mesophilic proteins, under different conditions. First, molecular dynamics have been analyzed for the hyperthermophile malate dehydrogenase from Methanococcus jannaschii and a mesophilic homologue, the lactate dehydrogenase from Oryctolagus cunniculus (rabbit) muscle. The neutron scattering approach has provided independent measurements of the global flexibility and structural resilience of each protein, and it has been demonstrated that macromolecular dynamics represents one of the molecular mechanisms of thermoadaptation. The resilience was found to be higher for the hyperthermophilic protein, thus ensuring similar flexibilities in both enzymes at their optimal activity temperature. Second, the neutron method has been developed to quantify the average macromolecular flexibility and resilience within the natural crowded environment of the cell, and mean macromolecular motions have been measured in vivo in psychrophile, mesophile, thermophile and hyperthermophile bacteria. The macromolecular resilience in bacteria was found to increase with adaptation to high temperatures, whereas flexibility was maintained within narrow limits, independent of physiological temperature for all cells in their active state. Third, macromolecular motions have been measured in free and immobilized dihydrofolate reductase from Escherichia coli. The immobilized mesophilic enzyme has increased stability and decreased activity, so that its properties are changed to resemble those of a thermophilic enzyme. Quasi-elastic neutron scattering measurements have also been performed to probe the protein motions. Compared to the free enzyme, the average height of the activation free energy barrier to local motions was found to be increased by 0.54 kcal.mol(-1) in the immobilized dihydrofolate reductase, a value that is of the same order as expected from the theoretical rate equation.

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.

Comparative normal mode analysis of LFA-1 integrin I-domains

The conformational dynamics of the Inserted domain (I-domain) from the lymphocyte function-associated antigen-1 (LFA-1) was investigated by normal mode analysis of multiple structures of the low, intermediate, and high affinity states. LFA-1 is an integrin expressed on leukocytes and is of critical importance in adhesion reactions, like antigen-specific responses, homing, and diapedesis. The main ligand binding site of LFA-1 is the I-domain, which recognizes intercellular adhesion molecules (ICAMs), members of the immunoglobulin superfamily. From experimental crystal structures, a large-scale conformational change of, among others, the alpha7 helix of the I-domain has been observed leading to the proposal that these structural changes are linked to the conformational regulation of LFA-1. The results from the present calculations show that structural changes of the alpha7 helix consistent with those observed in the crystal structures are significantly sampled by the low frequency modes. This was found to be particularly true for the low affinity state of the I-domain, indicating that low frequency motions favor the conformational transition implicated in activation. However, beyond the simple downward shift of the helix implied by the crystal structures, the calculations further show that there is a noticeable swinging-out motion of the helix. The consequences of this motion are discussed in the context of integrin activation and inhibition. Moreover, significant changes in the atomic-level dynamics and in long-range correlated motions of the I-domain were found to occur upon binding of the natural ligand ICAM. These changes were more local upon binding of an allosteric inhibitor. The present study opens the question of how changes in dynamics may contribute to the long-range transmission of signal upon ICAM binding by the LFA-1 I-domain.

Mosaic energy landscapes of liquids and the control of protein conformational dynamics by glass-forming solvents

Using recent advances in the Random First-Order Transition (RFOT) Theory of glass-forming liquids, we explain how the molecular motions of a glass-forming solvent distort the protein's boundary and slave some of the protein's conformational motions. Both the length and time scales of the solvent imposed constraints are provided by the RFOT theory. Comparison of the protein relaxation rate to that of the solvent provides an explicit lower bound on the size of the conformational space explored by the protein relaxation. Experimental measurements of slaving of myoglobin motions indicate that a major fraction of functionally important motions have significant entropic barriers.

Detecting similarities among distant homologous proteins by comparison of domain flexibilities

Aim of this work is to assess the informativeness of protein dynamics in the detection of similarities among distant homologous proteins. To this end, an approach to perform large-scale comparisons of protein domain flexibilities is proposed. CONCOORD is confirmed as a reliable method for fast conformational sampling. The root mean square fluctuation of alpha carbon positions in the essential dynamics subspace is employed as a measure of local flexibility and a synthetic index of similarity is presented. The dynamics of a large collection of protein domains from ASTRAL/SCOP40 is analyzed and the possibility to identify relationships, at both the family and the superfamily levels, on the basis of the dynamical features is discussed. The obtained picture is in agreement with the SCOP classification, and furthermore suggests the presence of a distinguishable familiar trend in the flexibility profiles. The results support the complementarity of the dynamical and the structural information, suggesting that information from dynamics analysis can arise from functional similarities, often partially hidden by a static comparison. On the basis of this first test, flexibility annotation can be expected to help in automatically detecting functional similarities otherwise unrecoverable.

Dynamics of electron transfer in photosystem II

Photosystem II, being a constituent of light driven photosynthetic apparatus, is a highly organized pigment-protein-lipid complex. The arrangement of PSII active redox cofactors insures efficiency of electron transfer within it. Donation of electrons extracted from water by the oxygen evolving complex to plastoquinones requires an additional activation energy. In this paper we present theoretical discussion of the anharmonic fluctuations of the protein-lipid matrix of PSII and an experimental evidence showing that the fluctuations are responsible for coupling of its donor and acceptor side. We argue that the fast collective motions liberated at temperatures higher that 200 K are crucial for the two final steps of the water splitting cycle and that one can distinguish three different dynamic regimes of PSII action which are controlled by the timescales of forward electron transfer, which vary with temperature. The three regimes of the dynamical behavior are related to different spatial domains of PSII.

Protein structural variation in computational models and crystallographic data

Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational flexibility. Normal modes from four simple elastic network model potentials and from the CHARMM force field are calculated for a data set of 83 diverse, ultrahigh-resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, all-atom potentials have a clear edge at prediction of directionality, and the CHARMM potential has the highest prediction quality. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity.

High apparent dielectric constant inside a protein reflects structural reorganization coupled to the ionization of an internal Asp

The dielectric properties of proteins are poorly understood and difficult to describe quantitatively. This limits the accuracy of methods for structure-based calculation of electrostatic energies and pK(a) values. The pK(a) values of many internal groups report apparent protein dielectric constants of 10 or higher. These values are substantially higher than the dielectric constants of 2-4 measured experimentally with dry proteins. The structural origins of these high apparent dielectric constants are not well understood. Here we report on structural and equilibrium thermodynamic studies of the effects of pH on the V66D variant of staphylococcal nuclease. In a crystal structure of this protein the neutral side chain of Asp-66 is buried in the hydrophobic core of the protein and hydrated by internal water molecules. Asp-66 titrates with a pK(a) value near 9. A decrease in the far UV-CD signal was observed, concomitant with ionization of this aspartic acid, and consistent with the loss of 1.5 turns of alpha-helix. These data suggest that the protein dielectric constant needed to reproduce the pK(a) value of Asp-66 with continuum electrostatics calculations is high because the dielectric constant has to capture, implicitly, the energetic consequences of the structural reorganization that are not treated explicitly in continuum calculations with static structures.

Loop formation in unfolded polypeptide chains on the picoseconds to microseconds time scale

Intrachain loop formation allows unfolded polypeptide chains to search for favorable interactions during protein folding. We applied triplet-triplet energy transfer between a xanthone moiety and naphthylalanine to directly measure loop formation in various unfolded polypeptide chains with loop regions consisting of polyserine, poly(glycine-serine) or polyproline. By combination of femtosecond and nanosecond laserflash experiments loop formation could be studied over many orders of magnitude in time from picoseconds to microseconds. The results reveal processes on different time scales indicating motions on different hierarchical levels of the free energy surface. A minor (<15%) very fast reaction with a time constant of approximately 3 ps indicates equilibrium conformations with donor and acceptor in contact at the time of the laserflash. Complex kinetics of loop formation were observed on the 50- to 500-ps time scale, which indicate motions within a local well on the energy landscape. Conformations within this well can form loops by undergoing local motions without having to cross major barriers. Exponential kinetics observed on the 10- to 100-ns time scale are caused by diffusional processes involving large-scale motions that allow the polypeptide chain to explore the complete conformational space. These results indicate that the free energy landscape for unfolded polypeptide chains and native proteins have similar properties. The presence of local energy minima reduces the conformational space and accelerates the conformational search for energetically favorable local intrachain contacts.

Hyperquenching for protein cryocrystallography

When samples having volumes characteristic of protein crystals are plunge cooled in liquid nitrogen or propane, most cooling occurs in the cold gas layer above the liquid. By removing this cold gas layer, cooling rates for small samples and modest plunge velocities are increased to 1.5 × 10(4) K s(-1), with increases of a factor of 100 over current best practice possible with 10 μm samples. Glycerol concentrations required to eliminate water crystallization in protein-free aqueous mixtures drop from ∼28% w/v to as low as 6% w/v. These results will allow many crystals to go from crystallization tray to liquid cryogen to X-ray beam without cryoprotectants. By reducing or eliminating the need for cryoprotectants in growth solutions, they may also simplify the search for crystallization conditions and for optimal screens. The results presented here resolve many puzzles, such as why plunge cooling in liquid nitrogen or propane has, until now, not yielded significantly better diffraction quality than gas-stream cooling.

Protein fluctuations and breakdown of time-scale separation in rate theories

A long-time fluctuation correlation function with a power-law form has been observed in recent single-molecule experiments by the Xie group. By analyzing the dynamics of an elastic network model (ENM) under white noise, we show that the observed long-time memory kernel can be explained by the discrepancy between the experimentally measured coordinate (or the coordinate directly coupled to protein function) and the minimum energy path of the system. Consequently, the dynamics of the measured collective coordinate has contributions from degrees of freedoms with a broad distribution of time scales. Our study also implies that the widely used ENM Hamiltonian should be viewed as a coarse-grained model of a protein over a rugged energy landscape. Large effective drag coefficients are needed to describe protein dynamics with the ENM's.

Investigation of spectral diffusion in ribonuclease by photolabeling of intrinsic aromatic amino acids

Spectral diffusion dynamics in ribonuclease A was observed via the broadening of photochemical holes burned into the absorption spectrum of intrinsic tyrosine residues. Unlike previous results based on hole burning of chromophores in the pockets of heme proteins, where spectral diffusion develops according to a power law in time, the dynamics in ribonuclease follow a logarithmic law. The results suggest that the experiment preferentially labels the tyrosines located on the surface of the protein where the two-level system dynamics of the glass host matrix exert a strong influence.

Structural and dynamical examination of the low-temperature glass transition in serum albumin

The nuclear magnetic transverse decay and the proton second moment of bovine serum albumin samples dry and hydrated with different water isotope compositions show that at temperatures around 170 K, there is a dramatic change in the dynamics of the water associated with the protein interface. By comparison, observation of the protein protons when hydrated with deuterium oxide provides no evidence for significant dynamical changes near 170 K. The proton second moment of the hydrated protein shows that the protein structure becomes more open with increasing hydration from the lyophilized condition and that the side chains extend from the protein surface into the solvent in the hydrated but not the dry cases. The proton second moment of serum albumin hydrated with H(2)O increases dramatically with decreasing temperature near 170 K, demonstrating that the water forms a rigid solid around the protein which effectively fills the surface irregularities created by the protein fold. Solvation with dimethyl sulfoxide yields small effects compared with water.

Evolutionary conservation of protein backbone flexibility

Internal protein dynamics is essential for biological function. During evolution, protein divergence is functionally constrained: properties more relevant for function vary more slowly than less important properties. Thus, if protein dynamics is relevant for function, it should be evolutionary conserved. In contrast with the well-studied evolution of protein structure, the evolutionary divergence of protein dynamics has not been addressed systematically before, apart from a few case studies. X-Ray diffraction analysis gives information not only on protein structure but also on B-factors, which characterize the flexibility that results from protein dynamics. Here we study the evolutionary divergence of protein backbone dynamics by comparing the C(alpha) flexibility (B-factor) profiles for a large dataset of homologous proteins classified into families and superfamilies. We show that C(alpha) flexibility profiles diverge slowly, so that they are conserved at family and superfamily levels, even for pairs of proteins with nonsignificant sequence similarity. We also analyze and discuss the correlations among the divergences of flexibility, sequence, and structure.

Modeling protein thermodynamics and fluctuations at the mesoscale

We use an extended Go model, in unfrustrated and frustrated variants, to study the energy landscape and the fluctuations of a model protein. The model exhibits two transitions, folding and dynamical transitions, when changing the temperature. The inherent structures corresponding to the minima of the landscape are analyzed and we show how their energy density can be obtained from simulations around the folding temperature. The scaling of this energy density is found to reflect the folding transition. Moreover, this approach allows us to build a reduced thermodynamics in the inherent structure landscape. Equilibrium studies, from full molecular dynamics (MD) simulations and from the reduced thermodynamics, detect the features of a dynamical transition at low temperature and we analyze the location and time scale of the fluctuations of the protein, showing the need of some frustration in the model to get realistic results. The frustrated model also shows the presence of a kinetic trap which strongly affects the dynamics of folding.

Spinach on the ceiling: a theoretical chemist's return to biology

I was born in Vienna and came to the United States as a refugee in October 1938. This experience played an important role in my view of the world and my approach to science: It contributed to my realization that it was safe to stop working in fields that I felt I understood and to focus on different areas of research by asking questions that would teach me and others something new. I describe my experiences that led me from chemistry and physics back to my first love, biology, and outline some of the contributions I have made as part of my ongoing learning experience.

Prediction of protein B-factor profiles

The polypeptide backbones and side chains of proteins are constantly moving due to thermal motion and the kinetic energy of the atoms. The B-factors of protein crystal structures reflect the fluctuation of atoms about their average positions and provide important information about protein dynamics. Computational approaches to predict thermal motion are useful for analyzing the dynamic properties of proteins with unknown structures. In this article, we utilize a novel support vector regression (SVR) approach to predict the B-factor distribution (B-factor profile) of a protein from its sequence. We explore schemes for encoding sequences and various settings for the parameters used in SVR. Based on a large dataset of high-resolution proteins, our method predicts the B-factor distribution with a Pearson correlation coefficient (CC) of 0.53. In addition, our method predicts the B-factor profile with a CC of at least 0.56 for more than half of the proteins. Our method also performs well for classifying residues (rigid vs. flexible). For almost all predicted B-factor thresholds, prediction accuracies (percent of correctly predicted residues) are greater than 70%. These results exceed the best results of other sequence-based prediction methods.

Local flexibility in molecular function paradigm

It is generally accepted that the functional activity of biological macromolecules requires tightly packed three-dimensional structures. Recent theoretical and experimental evidence indicates, however, the importance of molecular flexibility for the proper functioning of some proteins. We examined high resolution structures of proteins in various functional categories with respect to the secondary structure assessment. The latter was considered as a characteristic of the inherent flexibility of a polypeptide chain. We found that the proteins in functionally competent conformational states might be comprised of 20-70% flexible residues. For instance, proteins involved in gene regulation, e.g. transcription factors, are on average largely disordered molecules with over 60% of amino acids residing in "coiled" configurations. In contrast, oxygen transporters constitute a class of relatively rigid molecules with only 30% of residues being locally flexible. Phylogenic comparison of a large number of protein families with respect to the propagation of secondary structure illuminates the growing role of the local flexibility in organisms of greater complexity. Furthermore the local flexibility in protein molecules appears to be dependent on the molecular confinement and is essentially larger in extracellular proteins.

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.

Temperature-dependent structural and functional features of a hyperthermostable enzyme using elastic neutron scattering

The dynamic behavior of an endoglucanase from the hyperthermophilic microorganism Pyrococcus furiosus was investigated using elastic neutron scattering. The temperature dependence of the atomic motions was correlated with conformational and functional characteristics of the enzyme. The onset of biological function at temperatures higher than approximately 25 degrees C (the hyperthermostable enzyme is essentially inactive at room temperature) was associated with a dynamical transition in the anharmonic motions domain. This transition from the nonactive to the enzymatically active conformation involved structurally similar conformational substates in the energy landscape. From the mean-square displacement of the protein atoms, the molecular flexibility and the effective force constants were calculated at different temperature zones. The results showed that the activity increases at higher temperatures where the intramolecular bonds are weakened and the overall rigidity of the protein is decreased. Further temperature increase resulted in significantly increased atomic fluctuations featuring heat denaturation of the protein.

Reduced and oxidized cytochrome c4 exhibit differences in dynamics

The temperature-dependent dynamics of the fully reduced and fully oxidized forms of Pseudomonas stutzeri cytochrome c4 have been studied by Mössbauer spectroscopy. Prior to the dynamic analysis, an efficient labelling strategy has been developed for the expression of highly enriched (57)Fe recombinant cytochrome c4. Subsequently, the protein has been purified to apparent homogeneity. Mössbauer measurements were recorded in the temperature range 77-240 K for both protein forms. A detailed analysis of the high quality spectra is presented. Based on the information obtained from Mössbauer spectroscopy, similarities and differences between cytochrome c4, cytochrome c and HiPIP are discussed. The obtained results reveal that (a) cytochrome c4 exists in pure low spin electronic configuration in both oxidation states in the temperature range 77-240 K, (b) the heme pocket is more relaxed in cytochrome c4 than in cytochrome c, (c) the reduced cytochrome c4 is the most flexible at low temperatures, and (d) protein specific dynamics are most distinct in the oxidized protein.

Thermodynamic and dynamic factors involved in the stability of native protein structure in amorphous solids in relation to levels of hydration

The internal, dynamical fluctuations of protein molecules exhibit many of the features typical of polymeric and bulk small molecule glass forming systems. The response of a protein's internal molecular mobility to temperature changes is similar to that of other amorphous systems, in that different types of motions freeze out at different temperatures, suggesting they exhibit the alpha-beta-modes of motion typical of polymeric glass formers. These modes of motion are attributed to the dynamic regimes that afford proteins the flexibility for function but that also develop into the large-scale collective motions that lead to unfolding. The protein dynamical transition, T(d), which has the same meaning as the T(g) value of other amorphous systems, is attributed to the temperature where protein activity is lost and the unfolding process is inhibited. This review describes how modulation of T(d) by hydration and lyoprotectants can determine the stability of protein molecules that have been processed as bulk, amorphous materials. It also examines the thermodynamic, dynamic, and molecular factors involved in stabilizing folded proteins, and the effects typical pharmaceutical processes can have on native protein structure in going from the solution state to the solid state.

Coupling between lysozyme and glycerol dynamics: Microscopic insights from molecular-dynamics simulations

We explore possible molecular mechanisms behind the coupling of protein and solvent dynamics using atomistic molecular-dynamics simulations. For this purpose, we analyze the model protein lysozyme in glycerol, a well-known protein-preserving agent. We find that the dynamics of the hydrogen bond network between the solvent molecules in the first shell and the surface residues of the protein controls the structural relaxation (dynamics) of the whole protein. Specifically, we find a power-law relationship between the relaxation time of the aforementioned hydrogen bond network and the structural relaxation time of the protein obtained from the incoherent intermediate scattering function. We demonstrate that the relationship between the dynamics of the hydrogen bonds and the dynamics of the protein appears also in the dynamic transition temperature of the protein. A study of the dynamics of glycerol as a function of the distance from the surface of the protein indicates that the viscosity seen by the protein is not the one of the bulk solvent. The presence of the protein suppresses the dynamics of the surrounding solvent. This implies that the protein sees an effective viscosity higher than the one of the bulk solvent. We also found significant differences in the dynamics of surface and core residues of the protein. The former is found to follow the dynamics of the solvent more closely than the latter. These results allowed us to propose a molecular mechanism for the coupling of the solvent-protein dynamics.

On the importance of atomic fluctuations, protein flexibility, and solvent in ion permeation

Proteins, including ion channels, often are described in terms of some average structure and pictured as rigid entities immersed in a featureless solvent continuum. This simplified view, which provides for a convenient representation of the protein's overall structure, incurs the risk of deemphasizing important features underlying protein function, such as thermal fluctuations in the atom positions and the discreteness of the solvent molecules. These factors become particularly important in the case of ion movement through narrow pores, where the magnitude of the thermal fluctuations may be comparable to the ion pore atom separations, such that the strength of the ion channel interactions may vary dramatically as a function of the instantaneous configuration of the ion and the surrounding protein and pore water. Descriptions of ion permeation through narrow pores, which employ static protein structures and a macroscopic continuum dielectric solvent, thus face fundamental difficulties. We illustrate this using simple model calculations based on the gramicidin A and KcsA potassium channels, which show that thermal atomic fluctuations lead to energy profiles that vary by tens of kcal/mol. Consequently, within the framework of a rigid pore model, ion-channel energetics is extremely sensitive to the choice of experimental structure and how the space-dependent dielectric constant is assigned. Given these observations, the significance of any description based on a rigid structure appears limited. Creating a conducting channel model from one single structure requires substantial and arbitrary engineering of the model parameters, making it difficult for such approaches to contribute to our understanding of ion permeation at a microscopic level.

Protein–water displacement distributions

The statistical properties of fast protein-water motions are analyzed by dynamic neutron scattering experiments. Using isotopic exchange, one probes either protein or water hydrogen displacements. A moment analysis of the scattering function in the time domain yields model-independent information such as time-resolved mean square displacements and the Gauss-deviation. From the moments, one can reconstruct the displacement distribution. Hydration water displays two dynamical components, related to librational motions and anomalous diffusion along the protein surface. Rotational transitions of side chains, in particular of methyl groups, persist in the dehydrated and in the solvent-vitrified protein structure. The interaction with water induces further continuous protein motions on a small scale. Water acts as a plasticizer of displacements, which couple to functional processes such as open-closed transitions and ligand exchange.

Structure of the Rotor Ring of F-Type Na+-ATPase from Ilyobacter tartaricus

In the crystal structure of the membrane-embedded rotor ring of the sodium ion-translocating adenosine 5'-triphosphate (ATP) synthase of Ilyobacter tartaricus at 2.4 angstrom resolution, 11 c subunits are assembled into an hourglass-shaped cylinder with 11-fold symmetry. Sodium ions are bound in a locked conformation close to the outer surface of the cylinder near the middle of the membrane. The structure supports an ion-translocation mechanism in the intact ATP synthase in which the binding site converts from the locked conformation into one that opens toward subunit a as the rotor ring moves through the subunit a/c interface.

Picosecond thermometer in the amide I band of myoglobin

The amide I and II bands in myoglobin show a heterogeneous temperature dependence, with bands at 6.17 and 6.43 microm which are more intense at low temperatures. The amide I band temperature dependence is on the long wavelength edge of the band, while the short wavelength side has almost no temperature dependence. We compare concepts of anharmonic solid-state crystal physics and chemical physics for the origins of these bands. We suggest that the long wavelength side is composed of those amino acids which hydrogen bond to the hydration shell of the protein, and that temperature dependent bands can be used to determine the time it takes vibrational energy to flow into the hydration shell. We determine that vibrational energy flow to the hydration shell from the amide I takes approximately 20 ps to occur.

Downhill kinetics of biomolecular interface binding: globally connected scenario

We study the kinetics of the biomolecular binding process at the interface using energy landscape theory. The global kinetic connectivity case is considered for a downhill funneled energy landscape. By solving the kinetic master equation, the kinetic time for binding is obtained and shown to have a U-shape curve-dependence on the temperature. The kinetic minimum of the binding time monotonically decreases when the ratio of the underlying energy gap between native state and average non-native states versus the roughness or the fluctuations of the landscape increases. At intermediate temperatures, fluctuations measured by the higher moments of the binding time lead to non-Poissonian, non-exponential kinetics. At both high and very low temperatures, the kinetics is nearly Poissonian and exponential.

Methyl group dynamics as a probe of the protein dynamical transition

Hydrated proteins undergo a dynamical transition around 200 K from glasslike to liquidlike motion. Molecular dynamics simulations have been used to study the temperature dependence of the dynamics of ribonuclease A in the hydrated crystal, a model dehydrated powder, and aqueous solution. Changes in the dynamics accompanying the transition throughout the protein have been quantified in terms of the mean-squared fluctuations (MSFs) of methyl hydrogen atoms on the 100 ps time scale. In solution at 300 K the MSFs span a broad distribution, consistent with NMR relaxation measurements. The MSF distribution in the hydrated crystal at 300 K is qualitatively similar to the solution result, except for a slight shift to lower values, and dehydration results in a dramatic shift of the MSFs to lower values. As the temperature is lowered, the whole distribution of methyl group fluctuations in the hydrated crystal shifts to lower values. Most of the methyl groups in the hydrated protein display a nonlinear temperature dependence with a dynamical transition at approximately 200 K, but most methyl groups do not undergo a transition in the dehydrated protein. We conclude that the dynamical transition occurs throughout most of the protein and that solvent is required for the transition.