Structure of ferricytochrome c' from Rhodospirillum molischianum at 1.67 A resolution

The structure of ferricytochrome c' from Rhodospirillum molischianum has been crystallographically refined to 1.67 A resolution using a combination of reciprocal space and restrained least-squares refinement methods. The final crystallographic R-factor for 30,533 reflections measured with I greater than sigma (I) between infinity and 1.67 A is 0.188. The final model incorporates 1944 unique protein atoms (of a total of 1972) together with 194 bound solvent molecules. The structure has been analysed with respect to its detailed conformational properties, secondary structural features, temperature factor behavior, bound solvent sites, and heme geometry. The asymmetric unit of the cytochrome c' crystal contains a dimer composed of chemically identical 128-residue polypeptide chains. Although the refined structure shows the monomers to be very similar, examination of the differences that do occur allows an evaluation of how different lattice contacts affect protein conformation and solvent binding. In particular, comparison of solvent binding sites in the two subunits allows identification of a common set that are not altered by lattice interactions. The preservation of these solvent interactions in different lattice environments suggests that they play a structural role in protein stabilization in solution. The refined structure additionally reveals some new features that relate to the ligand binding properties and unusual mixed-spin state character of cytochrome c'. Finally, comparison of the heme binding geometry in cytochrome c' and other structurally unrelated c-type cytochromes shows that two alternative, but sterically favorable, conformational variants occur among the seven examples examined.     

Domain association in immunoglobulin molecules. The packing of variable domains

We have analyzed the structure of the interface between VL and VH domains in three immunoglobulin fragments: Fab KOL, Fab NEW and Fab MCPC 603. About 1800 A2 of protein surface is buried between the domains. Approximately three quarters of this interface is formed by the packing of the VL and VH beta-sheets in the conserved "framework" and one quarter from contacts between the hypervariable regions. The beta-sheets that form the interface have edge strands that are strongly twisted (coiled) by beta-bulges. As a result, the edge strands fold back over their own beta-sheet at two diagonally opposite corners. When the VL and VH domains pack together, residues from these edge strands form the central part of the interface and give what we call a three-layer packing; i.e. there is a third layer composed of side-chains inserted between the two backbone side-chain layers that are usually in contact. This three-layer packing is different from previously described beta-sheet packings. The 12 residues that form the central part of the three observed VL-VH packings are absolutely or very strongly conserved in all immunoglobulin sequences. This strongly suggests that the structure described here is a general model for the association of VL and VH domains and that the three-layer packing plays a central role in forming the antibody combining site.     

An analysis of incorrectly folded protein models. Implications for structure predictions

Proteins with homologous amino acid sequences have similar folds and it has been assumed that an unknown three-dimensional structure can be obtained from a known homologous structure by substituting new side-chains into the polypeptide chain backbone, followed by relatively small adjustment of the model. To examine this approach of structure prediction and, more generally, to isolate the characteristics of native proteins, we constructed two incorrectly folded protein models. Sea-worm hemerythrin and the variable domain of mouse immunoglobulin K-chain, two proteins with no sequence homology, were chosen for study; the former is composed of a bundle of four alpha-helices and the latter consists of two 4-stranded beta-sheets. Using an automatic computer procedure, hemerythrin side-chains were substituted into the immunoglobulin domain and vice versa. The structures were energy-minimized with the program CHARMM and the resulting structures compared with the correctly folded forms. It was found that the incorrect side-chains can be incorporated readily into both types of structures (alpha-helices, beta-sheets) with only small structural adjustments. After constrained energy-minimization, which led to an average atomic co-ordinate shift of no more than 0.7 to 0.9 A, the incorrectly folded models arrived at potential energy values comparable to those of the correct structures. Detailed analysis of the energy results shows that the incorrect structures have less stabilizing electrostatic, van der Waals' and hydrogen-bonding interactions. The difference is particularly pronounced when the electrostatic and van der Waals' energy terms are calculated by modified equations that include an approximate representation of solvent effects. The incorrectly folded structures also have a significantly larger solvent-accessible surface and a greater fraction of non-polar side-chain atoms exposed to solvent. Examination of their interior shows that the packing of side-chains at the secondary structure interfaces, although corresponding to sterically allowed conformations, deviates from the characteristics found in normal proteins. The analysis of incorrectly folded structures has made it clear that the absence of bad non-bonded contacts, though necessary, is not sufficient to demonstrate the validity of model-built structures and that modeling of homologous structures has to be accompanied by a thorough quantitative evaluation of the results. Further, certain features that characterize native proteins are made evident by their absence in misfolded models.     

Protein folding: evaluation of some simple rules for the assembly of helices into tertiary structures with myoglobin as an example

A computer program designed to fold a peptide chain consisting solely of helical segments and connecting links of known length is described and evaluated. This study is a detailed extension of certain aspects of the earlier work of Ptitsyn &; Rashin (1975). Possible interaction sites on the helices are sequence dependent and are calculated as described by Richmond &; Richards (1978) using probable changes in solvent contact area as a guide. The helices are then paired according to the list of potential sites, with each helix being paired at least once. The lists of pairings are then examined geometrically, each site having a defined dihedral helix axis angle, a specified inter-helix axis distance, and defined rotations, when required, about each helix axis. Two simplified filters are used: (1) lengths of connecting links must be equal to or greater than the end-to-end distances of the helices; and (2) non-paired helices must not collide. With myoglobin as a test example and only six of the eight helices being considered, a conformation space consisting of more than 3 × 10⁸ structures was surveyed. The two filters reduced the acceptable structure list to 121. Slight readjustment of the parameters in the filters would have reduced this to 20 structures. Of these 20, one closely resembles the actual distribution of helices in myoglobin. The possible utility and pitfalls of this approach as part of an overall protein folding program are discussed.     

Complementary specificity of restriction endonucleases of Diplococcus pneumoniae with respect to DNA methylation.

An algorithm is presented to identify peptide chain turns from X-ray-elucidated co-ordinate data. Chain turns are those regions in a globular protein where the backbone is folded back upon itself. The concept of a turn is important both because turns constitute recognizable structural units in proteins and because turns are situated at the solvent-accessible surface of the molecule.Current algorithms for turn identification are highly operational in character, often finding false turns and omitting actual ones. The algorithm presented here uses only the C-alpha co-ordinates for every residue in the protein. No other information of any kind is required, and notions about hydrogen bonding at these loci are irrelevant to the geometric nature of the argument. In this sense, the algorithm provides an objective criterion for the recognition of turns as strictly structural components in proteins.The algorithm is used to find the turns in a test set of proteins. Results of this application are in excellent agreement with visual turn identification from physical models.     

Acidic pH-induced conformational changes in amyloidogenic mutant transthyretin

Several proteins, including transthyretin (TTR), can generate in tissues extracellular insoluble aggregates, in the form of fibrils, that are associated with pathological states known as amyloidoses. To date, more than 80 different TTR point mutations have been associated with hereditary amyloidosis in humans. In vitro, the formation of amyloid fibrils by human TTR is known to be triggered by acidic pH. We show here that, in vitro, the natural amyloidogenic I84S and the non-natural I84A TTR mutant forms exhibit a propensity to produce fibrils in an acidic medium significantly higher than that of wild-type TTR. The two mutant forms have been crystallized at both neutral and acidic pH. Their neutral pH crystal structures are very similar to that of wild-type TTR, consistent with previous evidence indicating that only minor structural changes are induced by amyloidogenic mutations. On the contrary, their crystal structures at moderately low pH (4.6) show significant conformational differences as compared to their neutral pH structures. Remarkably, such changes are not induced in wild-type TTR crystallized at low pH. The most relevant consist of the unwinding of the TTR short alpha-helix and of the change in conformation of the loop connecting the alpha-helix to beta-strand F. Only one monomer of the crystallographic dimer is affected, causing a disruption of the tetrameric symmetry. This asymmetry and a possible destabilization of the tetrameric quaternary structure of TTR may be responsible for the amyloidogenic potential of the two TTR mutant forms at low pH.     

Characterization of crystals of a cytochrome oxidase (nitrite reductase) from Pseudomonas aeruginosa by x-ray diffraction and electron microscopy

Cytochrome oxidase from Pseudomonas aeruginosa has been crystallized from 2 m-ammonium sulfate. The crystals occur principally as thin diamond-shaped plates of space group P2₁2₁2 with unit cell dimensions of 92 Å × 115 Å × 76 Å. Determination of the density of glutaraldehyde-fixed, water-equilibrated crystals (1.167 g/cm³), coupled with the unit cell volume (804,000 ų), indicates that there is one subunit (~63,000 Mr) per asymmetric unit. X-ray diffraction data which were limited to 12 Å resolution due to small crystal size were obtained for the hk0 and 0kl zones using precession photography. Amplitude and phase data for the hk0, 0kl, and h0l zones were obtained from computer-based Fourier analysis of appropriate micrographs recorded from negatively stained microplates and thin sections of larger crystals using minimal beam electron microscopy. For crystals embedded in the presence of tannic acid it was possible to achieve 20 Å resolution which is comparable to the resolution achieved with negative staining of thin crystalline arrays. In addition, unstained electron diffraction on glutaraldehyde-fixed, glucose-stabilized plates was recorded to a resolution of 9 Å. The three-dimensional packing of the cytochrome oxidase dimer in the unit cell has been deduced from computer reconstructed images of the three principal projections along the crystallographic axes. The cytochrome oxidase dimer is located in the unit cell with the dimer axis coincident with a crystallographic 2-fold axis; thus within the resolution of the present data in projection (9 Å) the two subunits are identical, in agreement with biochemical evidence. The crystals have been prepared with the enzyme in the fully oxidized state and upon reduction a progressive cracking of the crystals is observed, possibly due to a conformational change dependent on the oxidation state of the heme iron.     

Structure of calmodulin refined at 2.2 A resolution

The crystal structure of mammalian calmodulin has been refined at 2.2 A (1 A = 0.1 nm) resolution using a restrained least-squares method. The final crystallographic R-factor, based on 6685 reflections in the range 2.2 A less than or equal to d less than or equal to 5.0 A with intensities exceeding 2.5 sigma, is 0.175. Bond lengths and bond angles in the molecule have root-mean-square deviations from ideal values of 0.016 A and 1.7 degrees, respectively. The refined model includes residues 5 to 147, four Ca2+ and 69 water molecules per molecule of calmodulin. The electron density for residues 1 to 4 and 148 is poorly defined, and they are not included in the model. The molecule is shaped somewhat like a dumbbell, with an overall length of 65 A; the two lobes are connected by a seven-turn alpha-helix. Prominent secondary structural features include seven alpha-helices, four Ca2+-binding loops, and two short, double-stranded antiparallel beta-sheets between pairs of adjacent Ca2+-binding loops. The four Ca2+-binding domains in calmodulin have a typical EF hand conformation (helix-loop-helix) and are similar to those described in other Ca2+-binding proteins. The X-ray structure determination of calmodulin shows a large hydrophobic cleft in each half of the molecule. These hydrophobic regions probably represent the sites of interaction with many of the pharmacological agents known to bind to calmodulin.     

Structure of ubiquitin refined at 1.8 A resolution

The crystal structure of human erythrocytic ubiquitin has been refined at 1.8 A resolution using a restrained least-squares procedure. The crystallographic R-factor for the final model is 0.176. Bond lengths and bond angles in the molecule have root-mean-square deviations from ideal values of 0.016 A and 1.5 degrees, respectively. A total of 58 water molecules per molecule of ubiquitin are included in the final model. The last four residues in the molecule appear to have partial occupancy or large thermal motion. The overall structure of ubiquitin is extremely compact and tightly hydrogen-bonded; approximately 87% of the polypeptide chain is involved in hydrogen-bonded secondary structure. Prominent secondary structural features include three and one-half turns of alpha-helix, a short piece of 3(10)-helix, a mixed beta-sheet that contains five strands, and seven reverse turns. There is a marked hydrophobic core formed between the beta-sheet and alpha-helix. The molecule features a number of unusual secondary structural features, including a parallel G1 beta-bulge, two reverse Asx turns, and a symmetrical hydrogen-bonding region that involves the two helices and two of the reverse turns.     

Structure of papain refined at 1.65 A resolution

Papain is a sulfhydryl protease from the latex of the papaya fruit. Its molecules consist of one polypeptide chain with 212 amino acid residues. The chain is folded into two domains with the active site in a groove between the domains. We have refined the crystal structure of papain, in which the sulfhydryl group was oxidized, by a restrained least-squares procedure at 1.65 A to an R-factor of 16.1%. The estimated accuracy in the atomic co-ordinates is 0.1 A, except for disordered atoms. All phi/psi angles for non-glycine residues are found within the outer limit boundary of a Ramachandran plot and this provides another check on the quality of the model. In the alpha-helical parts of the structure, the C = O bonds are directed more away from the helix axis than in a classical alpha-helix, leading to somewhat longer hydrogen bonds, 2.98 A, compared to 2.89 A. The hydrogen-bonding parameters and conformational angles in the anti-parallel beta-sheet structure show a large diversity. Hydrogen bonds in the core of the sheet are generally shorter than those at the more twisted ends. The average value is 2.91 A. The hydrogen bond distance Ni+3-Oi in turns is relatively long and the geometry is far from linear. Hydrogen bond formation, therefore, is perhaps not an essential prerequisite for turn formation. Although the crystallization medium is 62% (w/w) methanol in water, only 29 out of 224 solvent molecules can be regarded with any certainty as methanol molecules. The water molecules play an important role in maintaining structural stability. This is specially true for internal water. Twenty-one water molecules are located in contact areas between adjacent papain molecules. It seems as if the enzyme is trapped in a grid of water molecules with only a limited number of direct interactions between the protein molecules. The residues in the active site cleft belong to the most static parts of the structure. In general, disorder in atomic positions increases when going from the interior of the protein molecule to its surface. This behavior was quantified and it was found that the point of minimum disorder is near the molecular centroid.     

Crystallographic evidence for water-assisted photo-induced peptide cleavage in the stony coral fluorescent protein Kaede

A coral fluorescent protein from Trachyphyllia geoffroyi, Kaede, possesses a tripeptide of His62-Tyr63-Gly64, which forms a chromophore with green fluorescence. This chromophore's fluorescence turns red following UV light irradiation. We have previously shown that such photoconversion is achieved by a formal beta-elimination reaction, which results in a cleavage of the peptide bond found between the amide nitrogen and the alpha-carbon at His62. However, the stereochemical arrangement of the chromophore and the precise structural basis for this reaction mechanism previously remained unknown. Here, we report the crystal structures of the green and red form of Kaede at 1.4 A and 1.6 A resolutions, respectively. Our structures depict the cleaved peptide bond in the red form. The chromophore conformations both in the green and red forms are similar, except a well-defined water molecule in the proximity of the His62 imidazole ring in the green form. We propose a molecular mechanism for green-to-red photoconversion, which is assisted by the water molecule.     

Structural evidence for ligand-induced sequential conformational changes in glyceraldehyde 3-phosphate dehydrogenase

Glyceraldehyde 3-phosphate dehydrogenase is a tetramer of four chemically identical subunits which requires the cofactor nicotinamide adenine dinucleotide (NAD) for activity. The structure of the holo-enzyme from Bacillus stearothermophilus has recently been refined using X-ray data to 2.4 A resolution. This has facilitated the structure determination of both the apo-enzyme and the enzyme with one molecule of NAD bound to the tetramer. These structures have been refined at 4 A resolution using the constrained-restrained parameter structure factor least-squares refinement program CORELS. When combined with individual atomic temperature factors from the holo-enzyme, these refined models give crystallographic R factors of 30.2% and 30.4%, respectively, for data to 3 A resolution. The apo-enzyme has 222 molecular symmetry, and the subunit structure is related to that of the holo-enzyme by an approximate rigid-body rotation of the coenzyme binding domain by 4.3 degrees with respect to the catalytic domains, which form the core of the tetramer. The effect of this rotation is to shield the coenzyme and active site from solvent in the holo-enzyme. In addition to the rigid-body rotation, there is a rearrangement of several residues involved in NAD binding. The structure of the 1 NAD enzyme is asymmetric. The subunit which contains the bound NAD adopts a conformation very similar to that of a holo-enzyme subunit, while the other three unliganded subunits are very similar to the apo-enzyme conformation. This result provides unambiguous evidence for ligand-induced sequential conformational changes in B. stearothermophilus glyceraldehyde 3-phosphate dehydrogenase.     

Structure of porin refined at 1.8 A resolution.

The crystal structure of porin from Rhodobacter capsulatus has been refined using the simulated annealing method. The final model consists of all 301 amino acid residues well obeying standard geometry, three calcium ions, 274 solvent molecules, three detergent molecules and one unknown ligand modeled as a detergent molecule. The final crystallographic R-factor is 18.6% based on 42,851 independent reflections in the resolution range 10 to 1.8 A. The model is described in detail.     

Structure of beef liver catalase

The three-dimensional structure of beef liver catalase has been determined to 2.5 å resolution by a combination of isomorphous and molecular replacement techniques. Heavy-atom positions were found using vector search and difference Fourier methods. The tetrameric catalase molecule has 222 symmetry with one of its dyads coincident with a crystallographic 2-fold axis. The known polypeptide sequence has been unambiguously fitted to the electron density map. The heme is well buried in a hydrophobic pocket, 20 Å below the surface of the molecule, and accessible through a hydrophobic channel. Residues that line the heme pocket belong to two different subunits. Tyr357 is the proximal heme ligand and the catalytically important residues on the distal side are residues His74 and Asnl47. The tertiary structure consists of four domains: an extended non-globular amino-terminal arm, which stabilizes the quaternary structure; an anti-parallel, eight-stranded β-barrel providing the residues on the distal side of the heme; a rather random “wrapping domain” around the subunit exterior including the proximal heme ligand; and a final λ-helical structure resembling the E, F, G and H helices of the globins.     

Structural basis for glutamate racemase inhibition

d-Glutamic acid is a required biosynthetic building block for peptidoglycan, and the enzyme glutamate racemase (GluR) catalyzes the inter-conversion of D and L-glutamate enantiomers. Therefore, GluR is considered as an attractive target for the design of new antibacterial drugs. Here, we report the crystal structures of GluR from Streptococcus pyogenes in both inhibitor-free and inhibitor-bound forms. The inhibitor free GluR crystallized in two different forms, which diffracted to 2.25 Å and 2.5 Å resolution, while the inhibitor-bound crystal diffracted to 2.5 Å resolution. GluR is composed of two domains of α/β protein that are related by pseudo-2-fold symmetry and the active site is located at the domain interface. The inhibitor, γ-2-naphthylmethyl-d-glutamate, which was reported earlier as a novel potent competitive inhibitor, makes several hydrogen bonds with protein atoms, and the naphthyl moiety is located in the hydrophobic pocket. The inhibitor binding induces a disorder in one of the loops near the active site. In both crystal forms, GluR exists as a dimer and the interactions seen at the dimer interface are almost identical. This agrees well with the results from gel filtration and dynamic light-scattering studies.     

Structure of cyclodextrin glycosyltransferase refined at 2.0 A resolution.

The previously reported structural model of cyclodextrin glycosyltransferase (EC 2.4.1.19) from Bacillus circulans has been improved. For this purpose the known sequence was built into an electron density map established by multiple isomorphous replacement and subsequent solvent-flattening at 2.5 A resolution. The resulting model was refined at 2.0 A resolution using a simulated annealing refinement method. Based on 70,171 independent reflections in the range 7.0 to 2.0 A resolution, a final R-factor of 17.6% was obtained with a model obeying standard geometry within 0.013 A in bond lengths and 2.7 degrees in bond angles. The final model consists of all 684 amino acid residues, two calcium ions and 588 solvent molecules.     

Structure of prothrombin fragment 1 refined at 2.8 A resolution

The structure of prothrombin fragment 1, solved at 2.8 A resolution (1 A = 0.1 nm) by a combination of multiple and single isomorphous replacement methods utilizing solvent flattening, has been refined by restrained least-squares methods (R = 0.24), solvent not included, using fairly stringent restraints on the molecular geometry and individual thermal parameters. The inner kringle loop possesses significantly lower B-values than the outer loops even though the former also constitutes a surface of the folded kringle structure. This surface forms the Lys sub-site of the fibrin binding site of other kringles. The hydrogen bonding network and ion pair interactions of fragment 1 appear to maintain a compact folded structure among the various loops of the kringle structure. On the other hand, since there is only one hydrogen bond between the kringle and its preceding 30 residues, considerable flexibility is suggested for the Gla-domain consistent with its disorder in crystals. A chitobiose has been located at the Asn77 glycosylation site, but only a single N-acetyl-glucosamine is ordered at Asn101. The lysine binding site region of other kringles is not properly developed in fragment 1, accounting for its lack of Lys/fibrin affinity. Most of the conserved sequence among 11 different kringles is associated with either: (1) protecting the inner loop disulfides Cys87-127, Cys115-139 upon which the folding is based; or (2) a requirement of the lysine binding site. The remainder of the conservation is generally associated with the ten reverse turns of the folding; of these 40 residues, or about half the sequence, 14 are conserved among eight different turns. The intermolecular packing consists of infinite helical columns of fragment 1 molecules related by a crystallographic 4(3) screw axis, which are held together by van der Waals' interactions of aromatic clusters from different molecules related by a crystallographic 2-fold rotation axis.     

Bovine chymotrypsinogen A X-ray crystal structure analysis and refinement of a new crystal form at 1.8 A resolution

The X-ray structure of a new crystal form of chymotrypsinogen A grown from ethanol/water has been determined at 1.8 A resolution using Patterson search techniques. The crystals are of orthorhombic space group P212121 and contain two molecules in the asymmetric unit. Both independent molecules (referred to as A and B) have been crystallographically refined to a final R value of 0.173 with reflection data to 1.8 A resolution. Owing to different crystal contacts, both independent molecules show at various sites conformational differences, especially in segments 33-38, 142-153 and 215-222. If these three loops are omitted in a comparison, the root-mean-square (r.m.s.) deviation of the main-chain atoms of molecules A and B is 0.32 A. If segments 70-79, 143-152 and 215-221 are omitted, a comparison of either molecule A or molecule B with the chymotrypsinogen model of Freer et al. (1970) reveals an r.m.s. deviation of the alpha-carbon atoms of about 0.7 A. Compared with the active enzyme, four spatially adjacent peptide segments, in particular, are differently organized in the zymogen: the amino-terminal segment 11-19 runs in a rigid but strained conformation along the molecular surface due to the covalent linkage through Cys1; also segment 184-194 is in a rigid unique conformation due to several mutually stabilizing interactions with the amino-terminal segment; segment 216-222, which also lines the specificity pocket, adapts to different crystal contacts and exists in both chymotrypsinogen molecules in different, but defined conformations; in particular, disulfide bridge 191-220, which covalently links both latter segments, has opposite handedness in molecules A and B; finally, the autolysis loop 142 to 153 is organized in a variety of ways and in its terminal part is completely disordered. Thus, the allosteric activation domain (Huber & Bode, 1978) is organized in defined although different conformations in chymotrypsinogen molecules A and B, in contrast to trypsinogen, where all four homologous segments of the activation domain are disordered. This reflects the structural variability and deformability of the activation domain in serine proteinase proenzymes. If the aforementioned peptide segments are omitted, a comparison of our chymotrypsinogen models with gamma-chymotrypsin (Cohen et al., 1981) yields an r.m.s. deviation for alpha-carbon atoms of about 0.5 A. The residues of the "active site triad" are arranged similarly, but the oxyanion hole is lacking in chymotrypsinogen.(ABSTRACT TRUNCATED AT 400 WORDS)     

Structure of bacteriophage T4 lysozyme refined at 1.7 A resolution

The structure of the lysozyme from bacteriophage T4 has been refined at 1.7 A resolution to a crystallographic residual of 19.3%. The final model has bond lengths and bond angles that differ from "ideal" values by 0.019 A and 2.7 degrees, respectively. The crystals are grown from electron-dense phosphate solutions and the use of an appropriate solvent continuum substantially improved the agreement between the observed and calculated structure factors at low resolution. Apart from changes in the conformations of some side-chains, the refinement confirms the structure of the molecule as initially derived from a 2.4 A resolution electron density map. There are 118 well-ordered solvent molecules that are associated with the T4 lysozyme molecule in the crystal. Four of these are more-or-less buried. There is a clustering of water molecules within the active site cleft but, other than this, the solvent molecules are dispersed around the surface of the molecule and do not aggregate into ice-like structures or pentagonal or hexagonal clusters. The apparent motion of T4 lysozyme in the crystal can be interpreted in terms of significant interdomain motion corresponding to an opening and closing of the active site cleft. For the amino-terminal domain the motion can be described equally well (correlation coefficients approx. 0.87) as quasi-rigid-body motion either about a point or about an axis of rotation. The motion in the crystals of the carboxy-terminal domain is best described as rotation about an axis (correlation coefficient 0.80) although in this case the apparent motion seems to be influenced in part by crystal contacts and may be of questionable relevance to dynamics in solution.