Dynamical transition of myoglobin in a crystal: comparative studies of X-ray crystallography and Mössbauer spectroscopy

The crystallographic normal mode refinements of myoglobin at a wide range of temperature from 40 K to 300 K were carried out to study the temperature dependence of the internal atomic fluctuations. The refinement method decomposes the mean square displacement from the average position, (deltar2), into the contributions from the internal degrees of freedom and those from the external degrees of freedom. The internal displacements show linear temperature dependence as (deltar2)=alphaT+beta, throughout the temperature range measured here, and exhibit no obvious change in the slope alpha at the dynamical transition temperature (Tc=ca. 180 K). The slope alpha is practically the same as the value predicted theoretically by normal mode analysis. Such linear dependence is considered to be due to the following reason. The crystallographic Debye-Waller factor represents the static distribution caused by convolution of temperature-dependent normal mode motions and a temperature-independent set of the conformational substates. In contrast, M?ssbauer absorption spectroscopy shows a clear increase in the gradient alpha at Tc. This difference from X-ray diffraction originates from the incoherent nature of the M?ssbauer effect together with its high-energy resolution, which yields the self-correlation, and the temporal behavior of individual Fe atoms in the myoglobin crystal.     

Dynamics of wild-type HiPIPs: a Cys77Ser mutant and a partially unfolded HiPIP

The temperature dependence of the mean square displacement of the (57)Fe nuclei due to motion faster than 100 ns are measured by temperature-dependent M?ssbauer spectroscopy for oxidized and reduced HiPIPs from Ectothiorhodospira halophila, Chromatium vinosum WT and a Cys77Ser mutant. The behaviour is interpretable in the frame of the general model of protein dynamics distinguishing two temperature intervals. The character of harmonic and quasi-diffusional modes in HiPIPs is discussed. Dynamic information obtained from M?ssbauer spectroscopy and Fe K-edge EXAFS are compared. Structure dynamics of the iron-sulfur cluster in the partially unfolded reduced HiPIP from C. vinosum was investigated by M?ssbauer spectroscopy and EXAFS, indicating an intact metal centre and a protein backbone with a largely collapsed secondary structure. The role of the cofactor during protein folding is discussed. Differences in the dynamics between the native protein and the molten globule are found at physiological temperatures only. The structure and dynamic behaviour of the [Fe(4)S(4)]Cys(3)Ser cluster in the Cys77Ser mutant of the HiPIP from C. vinosum are analysed. The temperature dependence of electron relaxation in oxidized HiPIPs is investigated by M?ssbauer spectroscopy and analysed theoretically, considering spin-spin and spin-lattice relaxation. The latter consists of contributions from direct phonon bottleneck and Orbach mechanisms. The data agree with former pulsed EPR results. Orbach relaxation is interpreted as due to transitions between electronic isomers of oxidized HiPIPs. With this interpretation, the energetic difference between both isomers equals the energy gap estimated from the temperature dependence of the Orbach relaxation.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data.

A dynamic structure refinement method for X-ray crystallography, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the low-frequency normal modes whose amplitudes and eigenvectors are experimentally optimized in the process of the crystallographic refinement. In this model, the atomic fluctuations are treated as anisotropic and concerted. The normal modes of the external motion (TLS model) are also introduced to cover the factors other than the internal fluctuations, such as the lattice disorder and diffusion. A program for the normal mode refinement (NM-REF) has been developed. The method has first been tested against simulated diffraction data for human lysozyme calculated by a Monte Carlo simulation. Applications of the method have demonstrated that the normal mode refinement has: (1) improved the fitting to the diffraction data, even with fewer adjustable parameters; (2) distinguished internal fluctuations from external ones; (3) determined anisotropic thermal factors; and (4) identified concerted fluctuations in the protein molecule.     

Protein dynamics: Mössbauer spectroscopy on deoxymyoglobin crystals

Mössbauer absorption experiments on ⁵⁷Fe of deoxygenated myoglobin crystals and on K₄⁵⁷Fe(CN)₆ dissolved in the water of metmyoglobin crystals were performed over a large temperature range. At low temperatures the mean square displacements, 〈x²〉, of the iron indicate solid-like behaviour of the whole system, whereas at higher temperatures protein-specific modes of motion contribute to 〈x²>. The protein dynamics are correlated with the mobility of the water within the protein crystals. A Brownian oscillator is used to model the protein-specific modes of motion measured at the ⁵⁷Fe nucleus. Three modes are necessary for understanding the Mössbauer spectrum. Two of them correspond to an extremely overdamped Brownian oscillator. The third mode can be understood as quasi-free diffusion. Whereas the protein molecule is frozen in conformational substates in the low temperature regime, it reaches transition states with a finite probability in the high temperature regime. The surface water mediates a possible trigger mechanism that switches on protein dynamics within a narrow temperature interval. Results from Mössbauer spectroscopy and from X-ray structure analysis are compared.     

Mössbauer Effect in Hemoglobin and Some Iron-Containing Biological Compounds

The M?ssbauer effect in Fe(57) has been used to study the molecules, hemoglobin, O(2)-hemoglobin, CO(2)-hemoglobin, and CO-hemoglobin (within red cells) and the molecules, hemin and hematin (in the crystalline state). Quadrupole splittings and isomeric shifts observed in the M?ssbauer spectra of these molecules are tabulated. The temperature dependence of the quadrupole splitting and relative recoil-free fraction for hemoglobin with different ligands has been investigated. An estimate of the Debye-Waller factor in O(2)-hemoglobin at 5 degrees K is 0.83. An asymmetry in the quadrupole splitting observed in hemoglobin is attributed to a directional dependence of the recoil-free fraction which establishes the sign of the electric field gradient in the molecule and indicates that the lowest lying d orbital of the Fe atoms is |xy>. This asymmetry indicates that the iron atoms in hemoglobin are vibrating farther perpendicular to the heme planes than parallel to them, and, in fact, the ratio of the mean square displacements perpendicular and parallel to the heme planes in hemoglobin is approximately 5.5 at 5 degrees K. The temperature dependence of the quadrupole splitting in hemoglobin has been used to estimate a splitting between the lowest lying iron atom d orbitals of approximately 420 cm(-1).     

Nitrogenase. VIII. M?ssbauer and EPR spectroscopy. The MoFe protein component from Azotobacter vinelandii OP.

We have studied the molybdenum-iron protein (MoFe protein, also known as component I) from Azobacter vinelandi using M?ssbauer spectroscopy and electron paramagnetic resonance on samples enriched with 57Fe. These spectra can be interpreted in terms of two EPR active centers, each of which is reducible by one electron. A total of four different chemical environments of Fe can be discerned. One of them is a cluster of Fe atoms with a net electronic spin of 3/2, one of them is high-spin ferrous iron and the remaining two are iron in a reduced state (probably in clusters). The results are as follows: Chemical analysis yields 11.5 Fe atoms and 12.5 labile sulfur atoms per molybdenum atom; the molecule contains two Mo atoms per 300 000 daltons. The EPR spectrum of the MoFe protein exhibits g values at 4.32, 3.65 and 2.01, associated with the ground state doublet of a S = 3/2 spin system. The spin Hamiltonian H = D(S2/z minus 5/4 + lambda(S2/x minus S2/y)) + gbeta/o S-H fits the experimental data for go = 2.00 and lambda = 0.055. Quantitative analysis of the temperature dependence of the EPR spectrum yields D/k = 7.5 degrees K and 0.91 spins/molybdenum atom, which suggests that the MoFe protein has two EPR active centers. Quantitative evaluation of M?ssbauer spectra shows that approximately 8 iron atoms give rise to one quadrupole doublet; at lower temperatures magnetic spectra, associated with the groud electronic doublet, are observed; at least two magnetically inequivalent sites can be distinguished. Taken together the data suggest that each EPR center contains 4 iron atoms. The EPR and M?ssbauer data can only be reconciled if these iron atoms reside in a spin-coupled (S = 3/2) cluster. Under nitrogen fixing conditions the magnetic M?ssbauer spectra disappeared concurrently with the EPR signal and quadrupole doublets are obserced at all temperatures. The data suggest that each EPR active center is reduced by one electron. The M?ssbauer investigation reveals three other spectral components characteristic of iron nuclei in an environment of integer or zero electronic spin, i.e. they reside in complexes which are "EPR-silent". One of the components (3-4 iron atoms) has M?ssbauer parameters characteristic of the high-spin ferrous iron as in reduced ruberdoxin. However, measurements in strong fields indicate a diamagnetic environment. Another component, representing 9-11 iron atoms, seems to be diamagnetic also. It is suggested that these atoms are incorporated in spin-coupled clusters.     

Structural responses to cavity-creating mutations in an integral membrane protein

X-ray crystallography has been used to investigate the extent of structural changes in mutants of the purple bacterial reaction center that assemble without a particular ubiquinone or bacteriopheophytin cofactor. In the case of the bacteriopheophytin-exclusion mutant, in which Ala M149 was replaced by Trp (AM149W), the quality of protein crystals was improved over that seen in previous work by minimizing illumination, time, and temperature during the purification protocol and carrying out crystal growth at 4 degrees C after overnight incubation at 18 degrees C. The X-ray crystal structure of the AM149W mutant, determined to a resolution of 2.2 A, showed very little change in protein structure despite the absence of the bacteriopheophytin cofactor. Changes in the electron density map in the region of the cofactor binding site could be accounted for by changes in the conformation of the phytol side chains of adjacent cofactors and the presence of a buried water molecule. Residues lining the vacated binding pocket did not show any significant changes in conformation or increases in disorder as assessed through crystallographic atomic displacement parameters (B-factors). The X-ray crystal structure of a reaction center lacking the primary acceptor ubiquinone through mutation of Ala M248 to Trp (AM248W) was also determined, to a resolution of 2.8 A. Again, despite the absence of an internal cofactor only very minor changes in protein structure were observed. This is in contrast to a previous report on a reaction center lacking this ubiquinone through mutation of Ala M260 to Trp (AM260W) where more extensive changes in structure were apparent. All three mutant reaction centers showed a decrease in thermal stability when housed in the native membrane, but this decrease was smaller for the AM260W mutant than the AM248W complex, possibly due to beneficial effects of the observed changes in protein structure. The lack of major changes in protein structure despite the absence of large internal cofactors is discussed in terms of protein rigidity, the protective influence of the adaptable membrane environment, and the role of small molecules and ions as packing material in the internal cavities created by this type of mutation.     

The X-ray absorption spectroscopy Debye-Waller factors of an iron compound and of met-myoglobin as a function of temperature

Protein dynamics can be characterized by the mean square displacements of the individual atoms of a molecule. This concept is extended to X-ray absorption spectroscopy (XAS) of proteins where the physical information in the Debye-Waller factor is in general neglected. In a first step, a procedure for the investigation of the temperature dependence of XAS spectra has been developed for a small iron compound. Subsequently, experiments have been performed on met-myoglobin. It is shown that the mean square displacements of XAS are smaller than those obtained by M?ssbauer spectroscopy and far smaller than crystallographic mean square displacements. This behavior is explained by the different sensitivity of the methods. XAS measures a relative mean square displacement between the absorbing and backscattering atoms only. A comparison with mean square displacements calculated from normal modes shows that static displacements contribute significantly. It becomes obvious that the atoms of the active center show a high correlation of their motions.     

A water network within a protein: temperature-dependent water ligation in H64V-metmyoglobin and relaxation to deoxymyoglobin

The sperm whale myoglobin mutant H64V, where the distal histidine is mutated to valine, is known to be five coordinated in the ferric state at room temperature and physiological pH. A change of the ligation in this H64V-Mbmet has been observed by optical absorption spectroscopy as a function of temperature from 20 K to 300 K. Above the dynamical transition at about 180 K one observes the temperature-dependent equilibrium between five- and six-ligated heme. Below the dynamical transition the equilibrium is frozen-in at about 50% of six-coordinate molecules. The water ligation of the iron occurs at temperatures where protein-specific motions are present, as monitored by M?ssbauer spectroscopy. The X-ray structures of H64V-Mbmet at 300 K and 110 K are reported with a resolution of 1.5 A and 1.3 A, respectively. The measurements at high resolutions are possible owing to crystallization in the space group P2(1), whereas all mutant myoglobins studies up to now have been carried out with crystals in the space group P6. The overall structure at both temperatures is very close to the native myoglobin. The binding of water at the sixth coordination site at lower temperatures is possible owing to a stabilizing water network extending from the protein surface to the active centre. The reduction of the H64V-Mbmet by electrons obtained by X-ray irradiation of the water-glycerol solvent at 85 K produces an intermediate low-spin state of the water-ligated molecules where Fe(II) retains the six-fold coordination. M?ssbauer spectroscopy shows that the relaxation of the metastable low-spin state to high-spin H64V-Mbdeoxy with dissociation of the Fe(II)-H(2)O bond starts at about 115 K and is completed at about 170 K. Differences in the dynamics properties of the native and mutant myoglobin and the connection to the dynamical transition around 180 K are discussed.     

Full-matrix least-squares refinement of lysozymes and analysis of anisotropic thermal motion

Crystal structures of turkey egg lysozyme (TEL) and human lysozyme (HL) were refined by full-matrix least-squares method using anisotropic temperature factors. The refinement converged at the conventional R-values of 0.104 (TEL) and 0.115 (HL) for reflections with F_o > 0 to the resolution of 1.12 Å and 1.15 Å, respectively. The estimated r.m.s. coordinate errors for protein atoms were 0.031 Å (TEL) and 0.034 Å (HL). The introduction of anisotropic temperature factors markedly reduced the R-value but did not significantly affect the main chain coordinates. The degree of anisotropy of atomic thermal motion has strong positive correlation with the square of distance from the molecular centroid. The ratio of the radial component of thermal ellipsoid to the r.m.s. magnitude of three principal components has negative correlation with the distance from the molecular centroid, suggesting the domination of libration rather than breathing motion. The TLS model was applied to elucidate the characteristics of the rigid-body motion. The TLS tensors were determined by the least-squares fit to observed temperature factors. The profile of the magnitude of reproduced temperature factors by the TLS method well fitted to that of observed B_eqv. However, considerable disagreement was observed in the shape and orientation of thermal ellipsoid for atoms with large temperature factors, indicating the large contribution of local motion. The upper estimate of the external motion, 67% (TEL) and 61% (HL) of B_eqv, was deduced from the plot of the magnitude of TLS tensors determined for main chain atoms which were grouped into shells according to the distance from the center of libration. In the external motion, the translational portion is predominant and the contribution of libration and screw motion is relatively small. The internal motion, estimated by subtracting the upper estimate of the external motion from the observed temperature factor, is very similar between TEL and HL in spite of the difference in 54 of 130 amino acid residues and in crystal packing, being suggested to reflect the intrinsic internal motion of chicken-type lysozymes. Proteins 30:232–243, 1998. © 1998 Wiley-Liss, Inc.     

The structure of 2Zn pig insulin crystals at 1.5 A resolution

The paper describes the arrangement of the atoms within rhombohedral crystals of 2Zn pig insulin as seen in electron density maps calculated from X-ray data extending to 1.5 A (1 A = 10(-10) m = 10(-1) nm) at room temperature and refined to R = 0.153. The unit cell contains 2 zinc ions, 6 insulin molecules and about 3 x 283 water molecules. The atoms in the protein molecules appear well defined, 7 of the 102 side chains in the asymmetric unit have been assigned alternative disordered positions. The electron density over the water molecules has been interpreted in terms of 349 sites, 217 weighted 1.0, 126 weighted 0.5, 5 at 0.33 and 1 at 0.25 giving ca. 282 molecules. The positions and contacts of all the residues belonging to the two A and B chains of the asymmetric unit are shown first and then details of their arrangement in the two insulin molecules, 1 and 2, which are different. The formation from these molecules of a compact dimer and the further aggregation of three dimers to form a hexamer around two zinc ions, follows. It appears that in the packing of the hexamers in the crystal there are conflicting influences; too-close contacts between histidine B5 residues in neighbouring hexamers are probably responsible for movements of atoms at the beginning of the A chain of one of the two molecules of the dimer that initiate movements in other parts, particularly near the end of the B chain. At every stage of the building of the protein structure, residues to chains of definite conformation, molecules, dimers, hexamers and crystals, we can trace the effect of the packing of like groups to like, aliphatic groups together, aromatic groups together, hydrogen-bonded structures, positive and negative ions. Between the protein molecules, the water is distributed in cavities and channels that are continuous throughout the crystals. More than half the water molecules appear directly hydrogen bonded to protein atoms. These are generally in contact with other water molecules in chains and rings of increasing disorder, corresponding with their movement through the crystals. Within the established crystal structure we survey next the distribution of hydrogen bonds within the protein molecules and between water and protein and water and water; all but eight of the active atoms in the protein form at least one hydrogen bond.(ABSTRACT TRUNCATED AT 400 WORDS)     

High-resolution spot-scan electron microscopy of microcrystals of an alpha-helical coiled-coil protein

We describe the electron microscopy of a crystalline assembly of an alpha-helical coiled-coil protein extracted from the ootheca of the praying mantis. Electron diffraction patterns of unstained crystals show crystal lattice sampling of the coiled-coil molecular transform to a resolution beyond 1.5 A. Using a "spot-scan" method of electron imaging, micrographs of unstained crystals have been obtained that visibly diffract laser light from crystal spacings as small as 4.3 A. A projection map was calculated to 4 A using electron diffraction amplitudes and phases from computer-processed images. The projection map clearly shows modulations in density arising from the 5.1 A alpha-helical repeat, the first time this type of modulation has been revealed by electron microscopy. The crystals have p2 plane group symmetry with a = 92.4 A, b = 150.7 A, y = 92.4 degrees. Examination of tilted specimens shows that c is approximately 18 A, indicating that the unit cell is only one molecule thick. A preliminary interpretation shows tightly packed molecules some 400 A long lying with their long axes in the plane of the projection. The molecules have a coiled-coil configuration for most of their length. The possible modes of packing of the molecules in three dimensions are discussed.     

A few low-frequency normal modes predominantly contribute to conformational responses of hen egg white lysozyme in the tetragonal crystal to variations of molecular packing controlled by environmental humidity

The structures of proteins in crystals are fixed by molecular interactions with neighboring molecules, except in non-contacting flexible regions. Thus, it is difficult to imagine what conformational changes occur in solution. However, if molecular interactions can be changed by manipulating molecular packing in crystals, it may be possible to visualize conformational responses of proteins at atomic resolution by diffraction experiments. For this purpose, it is suitable to control the molecular packing in protein crystals by changing the volume of solvent channels through variation of the environmental relative humidity. Here, we studied conformational responses of hen egg white lysozyme (HEWL) in the tetragonal crystal by X-ray diffraction experiments using a humidity-control apparatus, which provided air flow of 20-98%rh at 298 K. First, we monitored the lattice parameters and crystalline order during dehydration and rehydration of HEWL crystal between 61 and 94%rh at 300 K. Then two crystal structures at a resolution of 2.1 ? using diffraction data obtained at 84.2 and 71.9%rh were determined to discuss the conformational responses of HEWL against the external perturbation induced by changes in molecular packing. The structure at 71.9%rh displayed a closure movement that was likely induced by the molecular contacts formed during dehydration and could be approximated by ten low-frequency normal modes for the crystal structure obtained at 84.2%rh. In addition, we observed reorganization of hydration structures at the molecular interfaces between symmetry neighbors. These findings suggest that humidity-controlled X-ray crystallography is an effective tool to investigate the responses of inherent intramolecular motions of proteins to external perturbations.     

Magnetic studies of the four-iron high-potential, non-heme protein from Chromatium vinosum.

Extensive EPR studies on high-potential, iron-sulfur protein from Chromatium vinosum indicate that the singular spectrum of this four-iron, non-heme protein consists of a superposition of three distinct signals; namely, two principal signals of equal weight, one reflecting axial and the other rhombic symmetry, and a third nearly isotropic minority component. In addition, magnetic susceptibility experiments on two oxidation states of the protein from 4.2 to approx. 260 degrees K indicate antiferromagnetic exchange coupling between iron atoms. Possible origins of the complex EPR signals are discussed, and a preferred model that is consistent with EPR, magnetic susceptibility, NMR, X-ray, and M?ssbauer data is presented.     

Accessibility to internal cavities and ligand binding sites monitored by protein crystallographic thermal factors

Protein structures are flexible both in solution and in the solid state. X-ray crystallographically determined thermal factors monitor the flexibility of protein atoms. A method utilizing such factors is proposed to delineate protein regions through which a ligand can exchange between binding site and bulk solvent. It is based on the assumption that thermally excited protein regions are excellent candidates for opening a ligand channel. Computationally simple and inexpensive, the method analyzes directions from which thermal factors can propagate within the protein, resulting in thermal motion paths (TMPs). Applications to engineered T4 lysozymes, where an artificial internal cavity can host hydrophobic molecules, and to sperm whale myoglobins, where the active site is completely buried, yielded results in agreement with other independent structural observations and with previous hypotheses. Further new features could also be suggested. The proposed TMP analysis could aid molecular dynamics simulation studies as well as time-resolved and site-directed mutagenesis experimental studies, especially given its modest computational expense and its direct roots in experimental results based on thermal factors determined in high-resolution crystallographic studies. Proteins 31:201–213,1998. © 1998 Wiley-Liss, Inc.     

M?ssbauer spectroscopic studies of deproteinised, sub-fractionated and reconstituted ferritins: the relationship between haemosiderin and ferritin

In a previous study of human haemosiderin and ferritin by a combination of M?ssbauer spectroscopy and electron microscopy, it was observed that the M?ssbauer spectra of haemosiderin showed a very different temperature dependence to those of ferritin. These differences were related to the superparamagnetic behaviour of small particles of a magnetic material and suggested that the magnetic anisotropy constant of the haemosiderin was considerably larger than that of the ferritin. In the present work, samples of ferritin have been examined by M?ssbauer spectroscopy following partial deproteinisation, subfractionation, and reconstitution with and without phosphate, in order to investigate whether these procedures lead to changes in the magnetic anisotropy constant of the iron-containing cores. There is no evidence from the present data that changes in the protein shell, in the size of the iron-containing cores of ferritin, or in the phosphate content lead to any significant changes in the magnetic anisotropy constant, as obtained from the temperature dependence of the M?ssbauer spectra. These results indicate that the different magnetic anisotropy constant observed in the case of human haemosiderin resulting from transfusional iron overload must arise from other significant differences in the composition or structure of the iron-containing cores.     

A combinatorial approach to crystallization of PX-BAR unit of the human Sorting Nexin 9

Sorting nexins (SNXs) form a family of proteins known to interact with endosomal vesicles and to regulate various steps of vesicle transport. Sorting Nexin 9 (SNX9) is involved in the interface of endocytic, actin polymerizing, and signal transduction events in the cell. Here we report crystallization of the SNX9 PX-BAR domain protein. Initially we used an ordinary protein construct design, and protein crystallization approaches resulted in obtaining granular crystal-like precipitation. SDS-PAGE and MS analysis of the crystal-like precipitation followed by protein construct optimization and using of macro seeding technique resulted in X-ray quality diffracting crystals. The crystals belonged to P2(1)2(1)2(1) space group (a=65.6 A, b=117.5 A, c=145.8 A) with two protein molecules per asymmetric unit. A complete SAD data set from Se-Methionine derived crystal (3.2 A) has been collected to solve the structure.     

Dynamics of hemoglobin investigated by M?ssbauer spectroscopy

M?ssbauer Spectra of Fe enriched horse hemoglobin and sperm whale myoglobin were measured in the temperature range from 80 K to 260 K. An analysis of the temperature dependence of the recoiless fraction (the Lamb-M?ssbauer factor) shows it to be sensitive to conformational fluctuations which affect the mean square displacement of the iron. We have found that the protein conformation has a dramatic effect on these measurements. For hemoglobin greater conformational fluctuations at lower temperatures are observed for carbonmonoxyhemoglobin in the liganded conformation than for deoxyhemoglobin in the unliganded conformation. On the other hand, the Lamb-M?ssbauer factor is insensitive to the binding of ligands to myoglobin and shows conformational fluctuations similar to deoxyhemoglobin even in the liganded state. It is also shown that a reversible complex with the distal histidine is formed in frozen deoxyhemoglobin solution above 200 K where the Lamb-M?ssbauer factor shows the excitation of new modes of conformational fluctuations. This complex is not formed with carbonmonoxyhemoglobin which already has a sixth ligand and with deoxymyoglobin which appears to undergo much more limited conformational fluctuations. A possible relationship between the formation of the distal histidine complex and the cooperative ligand binding reaction is suggested by results with partially liganded hemoglobin which indicate increased formation of the distal histidine complex.     

Fluctuations and correlations in crystalline protein dynamics: a simulation analysis of staphylococcal nuclease

Understanding collective motions in protein crystals is likely to furnish insight into functional protein dynamics and will improve models for refinement against diffraction data. Here, four 10 ns molecular dynamics simulations of crystalline Staphylococcal nuclease are reported and analyzed in terms of fluctuations and correlations in atomic motion. The simulation-derived fluctuations strongly correlate with, but are slightly higher than, the values derived from the experimental B-factors. Approximately 70% of the atomic fluctuations are due to internal protein motion. For 65% of the protein atoms the internal fluctuations converge on the nanosecond timescale. Convergence is much slower for the elements of the interatomic displacement correlation matrix--of these, >80% converge within 1 ns for interatomic distances less, approximately <6 A, but only 10% for separations approximately =12 A. Those collective motions that converged on the nanosecond timescale involve mostly correlations within the beta-barrel or between alpha-helices of the protein. The R-factor with the experimental x-ray diffuse scattering for the crystal, which is determined by the displacement variance-covariance matrix, decreases to 8% after 10 ns simulation. Both the number of converged correlation matrix elements and the R-factor depend logarithmically on time, consistent with a model in which the number of energy minima sampled depends exponentially on the maximum energy barrier crossed. The logarithmic dependence is also extrapolated to predict a convergence time for the whole variance-covariance matrix of approximately 1 micros.