The influence of solvent composition on global dynamics of human butyrylcholinesterase powders: a neutron-scattering study

A major result of incoherent elastic neutron-scattering experiments on protein powders is the strong dependence of the intramolecular dynamics on the sample environment. We performed a series of incoherent elastic neutron-scattering experiments on lyophilized human butyrylcholinesterase (HuBChE) powders under different conditions (solvent composition and hydration degree) in the temperature range from 20 to 285 K to elucidate the effect of the environment on the enzyme atomic mean-square displacements. Comparing D(2)O- with H(2)O-hydrated samples, we were able to investigate protein as well as hydration water molecular dynamics. HuBChE lyophilized from three distinct buffers showed completely different atomic mean-square displacements at temperatures above approximately 200 K: a salt-free sample and a sample containing Tris-HCl showed identical small-amplitude motions. A third sample, containing sodium phosphate, displayed highly reduced mean-square displacements at ambient temperature with respect to the other two samples. Below 200 K, all samples displayed similar mean-square displacements. We draw the conclusion that the reduction of intramolecular protein mean-square displacements on an Angstrom-nanosecond scale by the solvent depends not only on the presence of salt ions but also on their type.     

Picosecond timescale rigid-helix and side-chain motions in deoxymyoglobin

The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two typesof rigid-body motions are considered: one in which the helices are rigid units and one in which the side-chains are rigid units. Using a quaternionbased algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid-body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean-square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen: rigid-helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the helix,: atom (backbone and side-chain) mean square displacements and only 1.1% of total kinetic energy. Only very low-frequency motions contribute to the rigid-helix dynamics; the rigid-body analysis allows characteristic rigid-helix vibrations to be identified and described. Treating the side-chains as rigid bodies is foundto be an excellent approximation to both their diffusive and vibrationalmean-square displacements: 96% of side-chain atom mean-square displacements originate from rigid side-Chain motions. However, the errors in theside-chain atomic positional fits are not always small. An analysis is madeof factors contributing to the positional error for different types of side-chain. © Wiley-Liss, Inc.     

Comparison of normal mode analyses on a small globular protein in dihedral angle space and Cartesian coordinate space

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm(-1) contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm(-1), but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis.     

Protein dynamics and stability: the distribution of atomic fluctuations in thermophilic and mesophilic dihydrofolate reductase derived using elastic incoherent neutron scattering

The temperature dependence of the dynamics of mesophilic and thermophilic dihydrofolate reductase is examined using elastic incoherent neutron scattering. It is demonstrated that the distribution of atomic displacement amplitudes can be derived from the elastic scattering data by assuming a (Weibull) functional form that resembles distributions seen in molecular dynamics simulations. The thermophilic enzyme has a significantly broader distribution than its mesophilic counterpart. Furthermore, although the rate of increase with temperature of the atomic mean-square displacements extracted from the dynamic structure factor is found to be comparable for both enzymes, the amplitudes are found to be slightly larger for the thermophilic enzyme. Therefore, these results imply that the thermophilic enzyme is the more flexible of the two.     

Dynamical coupling of intrinsically disordered proteins and their hydration water: comparison with folded soluble and membrane proteins

Hydration water is vital for various macromolecular biological activities, such as specific ligand recognition, enzyme activity, response to receptor binding, and energy transduction. Without hydration water, proteins would not fold correctly and would lack the conformational flexibility that animates their three-dimensional structures. Motions in globular, soluble proteins are thought to be governed to a certain extent by hydration-water dynamics, yet it is not known whether this relationship holds true for other protein classes in general and whether, in turn, the structural nature of a protein also influences water motions. Here, we provide insight into the coupling between hydration-water dynamics and atomic motions in intrinsically disordered proteins (IDP), a largely unexplored class of proteins that, in contrast to folded proteins, lack a well-defined three-dimensional structure. We investigated the human IDP tau, which is involved in the pathogenic processes accompanying Alzheimer disease. Combining neutron scattering and protein perdeuteration, we found similar atomic mean-square displacements over a large temperature range for the tau protein and its hydration water, indicating intimate coupling between them. This is in contrast to the behavior of folded proteins of similar molecular weight, such as the globular, soluble maltose-binding protein and the membrane protein bacteriorhodopsin, which display moderate to weak coupling, respectively. The extracted mean square displacements also reveal a greater motional flexibility of IDP compared with globular, folded proteins and more restricted water motions on the IDP surface. The results provide evidence that protein and hydration-water motions mutually affect and shape each other, and that there is a gradient of coupling across different protein classes that may play a functional role in macromolecular activity in a cellular context.     

Deriving protein dynamical properties from weighted protein contact number

It has recently been shown that in proteins the atomic mean-square displacement (or B-factor) can be related to the number of the neighboring atoms (or protein contact number), and that this relationship allows one to compute the B-factor profiles directly from protein contact number. This method, referred to as the protein contact model, is appealing, since it requires neither trajectory integration nor matrix diagonalization. As a result, the protein contact model can be applied to very large proteins and can be implemented as a high-throughput computational tool to compute atomic fluctuations in proteins. Here, we show that this relationship can be further refined to that between the atomic mean-square displacement and the weighted protein contact-number, the weight being the square of the reciprocal distance between the contacting pair. In addition, we show that this relationship can be utilized to compute the cross-correlation of atomic motion (the B-factor is essentially the auto-correlation of atomic motion). For a nonhomologous dataset comprising 972 high-resolution X-ray protein structures (resolution <2.0 A and sequence identity <25%), the mean correlation coefficient between the X-ray and computed B-factors based on the weighted protein contact-number model is 0.61, which is better than those of the original contact-number model (0.51) and other methods. We also show that the computed correlation maps based on the weighted contact-number model are globally similar to those computed through normal model analysis for some selected cases. Our results underscore the relationship between protein dynamics and protein packing. We believe that our method will be useful in the study of the protein structure-dynamics relationship.     

Protein flexibility from the dynamical transition: a force constant analysis

A standard analysis of the scattered neutron incoherent elastic intensity measured with very good energy resolution yields elastic scans, i.e., mean-square displacements of atomic motions (in a pico to nanosecond time scale) in a sample as a function of temperature. This provides a quick way for characterizing the dynamical behavior of biological macromolecules, such behavior being correlated with biological function and activity. Elastic scans of proteins exhibit a dynamical transition at approximately 200 K, marking a cross-over in molecular fluctuations between harmonic and nonharmonic dynamical regimes. This paper presents an approach allowing analysis of the elastic scan in terms of force constants and related parameters, such as the free energy barrier DeltaG at the transition. We find that the increased protein flexibility beyond the dynamical transition is associated with DeltaG approximately equals RT and effective force constants of the order of 0.1-3 N/m. The analysis provides a set of parameters for characterizing molecular resilience and exploring relations among dynamics, function, and activity in proteins.     

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.     

Allostery without conformational change

A general model is presented whereby lignand-induced changes in protein dynamics could produce allosteric communication between distinct binding sites, even in the absence of a macromolecular conformational change. Theoretical analysis, based on the statistical thermodynamics of ligand binding, shows that cooperative interaction free energies amounting to several kJ · mol^-1 may be generated by this means. The effect arises out of the possible changes in frequencies and amplitudes of macromolecular thermal fluctuations in response to ligand attachment, and can involve all forms of dynamic behaviour, ranging from highly correlated, low-frequency normal mode vibrations to random local anharmonic motions of individual atoms or groups. Dynamic allostery of this form is primarily an entropy effect, and we derive approximate expressions which might allow the magnitude of the interaction in real systems to be calculated directly from experimental observations such as changes in normal mode frequencies and mean-square atomic displacements. Long-range influence of kinetic processes at different sites might also be mediated by a similar mechanism. We suggest that proteins and other biological macromolecules may have evolved to take functional advantage not only of mean conformational states but also of the inevitable thermal fluctuations about the mean.     

Direct Correlation between Molecular Dynamics and Enzymatic Stability: A Comparative Neutron Scattering Study of Native Human Butyrylcholinesterase and its “Aged” Soman Conjugate

An incoherent elastic neutron scattering study of the molecular dynamics of native human butyrylcholinesterase and its “aged” soman-inhibited conjugate revealed a significant change in molecular flexibility on an angstrom-nanosecond scale as a function of temperature. The results were related to the stability of each state as established previously by differential scanning calorimetry. A striking relationship was found between the denaturation behavior and the molecular flexibility of the native and inhibited enzymes as a function of temperature. This was reflected in a quantitative correlation between the atomic mean-square displacements on an angstrom-nanosecond scale determined by neutron spectroscopy and the calorimetric specific heat. By the application of a simple two-state model that describes the transition from a folded to a denatured state, the denaturation temperatures of the native and the inhibited enzyme were correctly extracted from the atomic mean-square displacements. Furthermore, the transition entropy and enthalpy extracted from the model fit of the neutron data were, within the experimental accuracy, compatible with the values determined by differential scanning calorimetry.     

Correlations of atomic movements in lysozyme crystals.

Diffuse scattering data have been collected on two crystal forms of lysozyme, tetragonal and triclinic, using synchrotron radiation. The observed diffraction patterns were simulated using an exact theory for simple model crystals which relates the diffuse scattering intensity distribution to the amplitudes and correlations of atomic movements. Although the mean square displacements in the tetragonal form are twice that in the triclinic crystal, the predominant component of atomic movement in both crystals is accounted for by short-range coupled motions where displacement correlations decay exponentially as a function of atomic separation, with a relaxation distance of approximately 6 A. Lattice coupled movements with a correlation distance approximately 50 A account for only about 5-10% of the total atomic mean square displacements in the protein crystals. The results contradict various presumptions that the disorder in protein crystals can be modeled predominantly by elastic vibrations or rigid body movements.     

Structural dynamics of liganded myoglobin.

X-ray crystallography can reveal the magnitudes and principal directions of the mean-square displacements of every atom in a protein. This structural information is complementary to the temporal information obtainable by spectroscopic techniques such as nuclear magnetic resonance. Determination of the temperature dependence of the mean-square displacements makes it possible to separate large conformational motions from simple thermal vibrations. The contribution of crystal lattice disorder to the overall apparent displacement can be estimated by Mössbauer spectroscopy. This technique has been applied to high resolution x-ray diffraction data from sperm whale myoglobin in its Met iron and oxy cobalt forms. Both crystal structures display regions of large conformational motions, particularly at the chain termini and in the region of the proximal histidine. Overall, the mean-square displacement increases with increasing distance from the center of gravity of the molecule. Some regions of the heme pocket in oxy cobalt myoglobin are more rigid than the corresponding regions in Met myoglobin.     

Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model

Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple subunits, however, generally requires large computational costs; therefore, development of an efficient algorithm is required. We developed a fast fitting program, “gmfit”, which employs a Gaussian mixture model (GMM) to represent approximated shapes of the 3D density map and the atomic models. A GMM is a distribution function composed by adding together several 3D Gaussian density functions. Because our model analytically provides an integral of a product of two distribution functions, it enables us to quickly calculate the fitness of the density map and the atomic models. Using the integral, two types of potential energy function are introduced: the attraction potential energy between a 3D density map and each subunit, and the repulsion potential energy between subunits. The restraint energy for symmetry is also employed to build symmetrical origomeric complexes. To find the optimal configuration of subunits, we randomly generated initial configurations of subunit models, and performed a steepest-descent method using forces and torques of the three potential energies. Comparison between an original density map and its GMM showed that the required number of Gaussian distribution functions for a given accuracy depended on both resolution and molecular size. We then performed test fitting calculations for simulated low-resolution density maps of atomic models of homodimer, trimer, and hexamer, using different search parameters. The results indicated that our method was able to rebuild atomic models of a complex even for maps of 30 Å resolution if sufficient numbers (eight or more) of Gaussian distribution functions were employed for each subunit, and the symmetric restraints were assigned for complexes with more than three subunits. As a more realistic test, we tried to build an atomic model of the GroEL/ES complex by fitting 21-subunit atomic models into the 3D density map obtained by cryoelectron microscopy using the C7 symmetric restraints. A model with low root mean-square deviations (14.7 Å) was obtained as the lowest-energy model, showing that our fitting method was reasonably accurate. Inclusion of other restraints from biological and biochemical experiments could further enhance the accuracy.     

Mean-squared atomic displacements in hydrated lysozyme,native and denatured

We use elastic neutron scattering to demonstrate that a sharp increase in the mean-squared atomic displacements, commonly observed in hydrated proteins above 200 K and often referred to as the dynamical transition, is present in the hydrated state of both native and denatured lysozyme. A direct comparison of the native and denatured protein thus confirms that the presence of the transition in the mean-squared atomic displacements is not specific to biologically functional molecules.     

Differences in internal dynamics of actin under different structural states detected by neutron scattering

F-actin, a helical polymer formed by polymerization of the monomers (G-actin), plays crucial roles in various aspects of cell motility. Flexibility of F-actin has been suggested to be important for such a variety of functions. Understanding the flexibility of F-actin requires characterization of a hierarchy of dynamical properties, from internal dynamics of the actin monomers through domain motions within the monomers and relative motions between the monomers within F-actin to large-scale motions of F-actin as a whole. As a first step toward this ultimate purpose, we carried out elastic incoherent neutron scattering experiments on powders of F-actin and G-actin hydrated with D₂O and characterized the internal dynamics of F-actin and G-actin. Well established techniques and analysis enabled the extraction of mean-square displacements and their temperature dependence in F-actin and in G-actin. An effective force constant analysis with a model consisting of three energy states showed that two dynamical transitions occur at ∼150 K and ∼245 K, the former of which corresponds to the onset of anharmonic motions and the latter of which couples with the transition of hydration water. It is shown that behavior of the mean-square displacements is different between G-actin and F-actin, such that G-actin is “softer” than F-actin. The differences in the internal dynamics are detected for the first time between the different structural states (the monomeric state and the polymerized state). The different behavior observed is ascribed to the differences in dynamical heterogeneity between F-actin and G-actin. Based on structural data, the assignment of the differences observed in the two samples to dynamics of specific loop regions involved in the polymerization of G-actin into F-actin is proposed.     

Construction and validation of an atomic model for bacterial TSPO from electron microscopy density,evolutionary constraints,and biochemical and biophysical data

The 18 kDa protein TSPO is a highly conserved transmembrane protein found in bacteria, yeast, animals and plants. TSPO is involved in a wide range of physiological functions, among which the transport of several molecules. The atomic structure of monomeric ligand-bound mouse TSPO in detergent has been published recently. A previously published low-resolution structure of Rhodobacter sphaeroides TSPO, obtained from tubular crystals with lipids and observed in cryo-electron microscopy, revealed an oligomeric structure without any ligand. We analyze this electron microscopy density in view of available biochemical and biophysical data, building a matching atomic model for the monomer and then the entire crystal. We compare its intra- and inter-molecular contacts with those predicted by amino acid covariation in TSPO proteins from evolutionary sequence analysis. The arrangement of the five transmembrane helices in a monomer of our model is different from that observed for the mouse TSPO. We analyze possible ligand binding sites for protoporphyrin, for the high-affinity ligand PK 11195, and for cholesterol in TSPO monomers and/or oligomers, and we discuss possible functional implications.     

Molecular dynamics simulation study of a pulmonary surfactant film interacting with a carbonaceous nanoparticle

This article reports an all-atom molecular dynamics simulation to study a model pulmonary surfactant film interacting with a carbonaceous nanoparticle. The pulmonary surfactant is modeled as a dipalmitoylphosphatidylcholine monolayer with a peptide consisting of the first 25 residues from surfactant protein B. The nanoparticle model with a chemical formula C₁₈₈H₅₃ was generated using a computational code for combustion conditions. The nanoparticle has a carbon cage structure reminiscent of the buckyballs with open ends. A series of molecular-scale structural and dynamical properties of the surfactant film in the absence and presence of nanoparticle are analyzed, including radial distribution functions, mean-square displacements of lipids and nanoparticle, chain tilt angle, and the surfactant protein B peptide helix tilt angle. The results show that the nanoparticle affects the structure and packing of the lipids and peptide in the film, and it appears that the nanoparticle and peptide repel each other. The ability of the nanoparticle to translocate the surfactant film is one of the most important predictions of this study. The potential of mean force for dragging the particle through the film provides such information. The reported potential of mean force suggests that the nanoparticle can easily penetrate the monolayer but further translocation to the water phase is energetically prohibitive. The implication is that nanoparticles can interact with the lung surfactant, as supported by recent experimental data by Bakshi et al.     

Projection Methods for the Analysis of Complex Motions in Macromolecules

Abstract

In studies of macromolecular dynamics it is often desirable to analyze complex motions in terms of a small number of coordinates. Only for simple types of motion, e.g., rigid-body motions, these coordinates can be easily constructed from the Cartesian atomic coordinates. This article presents an approach that is applicable to infinitesimal or approximately infinitesimal motions, e.g., Cartesian velocities, normal modes, or atomic fluctuations. The basic idea is to characterize the subspace of interesting motions by a set of (possibly linearly dependent) vectors describing elementary displacements, and then project the dynamics onto this subspace. Often the elementary displacements can be found by physical intuition. The restriction to small displacements facilitates the study of complicated coupled motions and permits the construction of collective-motion subspaces that do not correspond to any set of generalized coordinates.

As an example for this technique, we analyze the low-frequency normal modes of proteins up to ≈ 20 THz (600 cm^?1) in order to see what kinds of motions occupy which frequency range. This kind of analysis is useful for the interpretation of spectroscopic measurements on proteins, e.g., inelastic neutron scattering experiments.     

Protein sequence and structure relationship ARMA spectral analysis: application to membrane proteins.

If it is assumed that the primary sequence determines the three-dimensional folded structure of a protein, then the regular folding patterns, such as alpha-helix, beta-sheet, and other ordered patterns in the three-dimensional structure must correspond to the periodic distribution of the physical properties of the amino acids along the primary sequence. An AutoRegressive Moving Average (ARMA) model method of spectral analysis is applied to analyze protein sequences represented by the hydrophobicity of their amino acids. The results for several membrane proteins of known structures indicate that the periodic distribution of hydrophobicity of the primary sequence is closely related to the regular folding patterns in a protein's three-dimensional structure. We also applied the method to the transmembrane regions of acetylcholine receptor alpha subunit and Shaker potassium channel for which no atomic resolution structure is available. This work is an extension of our analysis of globular proteins by a similar method.