Hydrodynamic properties of nitrogenase--the MoFe protein from Azotobacter vinelandii studied by dynamic light scattering and hydrodynamic modelling

Loop formation and translational diffusion of intrinsically disordered proteins

The conformational flexibility and dynamics of unfolded peptide chains is of major interest in the context of protein folding and protein functioning. The rate with which amino acids at different positions along the peptide chain meet sets an upper speed limit for protein folding. By using single-molecule photo-induced energy transfer spectroscopy, we have systematically measured end-to-end and end-to-internal site contact formation rates for several intrinsically disordered protein fragments (IDPs) (11 to 41 amino acids) and have also determined their hydrodynamic radius using dual-focus fluorescence correlation spectroscopy. For interpreting the measured values, we have developed a Brownian dynamics model (based on bead-rod chain dynamics in a thermal bath including hydrodynamic interactions) which quantitatively reproduces all measured data surprisingly well while requiring only two fit parameters. The model provides a complete picture of the peptides' dynamics and allows us to translate the experimental rates and radii into molecular properties of the peptides: We find a persistence length of l_{P}=5.2±1.9Å, a hydrodynamic radius of a=3.5±0.7Å per amino acid, and that excluded volume effects play an important role in the dynamics of IDPs.

Distinguishing Between Monomeric scFv and Diabody in Solution Using Light and Small Angle X-ray Scattering

Depending on the linker length between the VH and the VL domain, single-chain Fv (scFv) antibody fragments form monomers, dimers (diabodies) or higher oligomers. We aimed at generating a diabody of the anti-MET antibody 3H3 to use it as crystallization chaperone to promote crystallization of the MET ectodomain through the introduction of a pre-formed twofold axis of symmetry. Size exclusion chromatography, however, suggested the protein to be monomeric. Hence, we used scattering techniques applied to solutions to further investigate its oligomerization state. The small angle X-ray scattering (SAXS) curve measured for our protein nicely fits to the scattering curve calculated from the known crystal structure of a diabody. In addition, concentration-dependent photon correlation spectroscopy (PCS) measurements revealed a hydrodynamic radius of 3.4 nm at infinite dilution and a negative interaction parameter kD, indicating attractive interactions that are beneficial for crystallization. Both SAXS and PCS measurements clearly suggest our antibody fragment to be a diabody in solution. Chemical cross-linking with glutaraldehyde and cell motility assays confirmed this conclusion.

Label-Free Measurements of Tenofovir Diffusion Coefficients in a Microbicide Gel Using Raman Spectroscopy

Confocal Raman spectroscopy was implemented in a new label-free technique to quantify molecular diffusion coefficients within gels. A leading anti-HIV drug, tenofovir, was analyzed in a clinical microbicide gel. The gel was tested undiluted, and in 10%-50% wt/wt dilutions with vaginal fluid simulant to capture the range of conditions likely occurring in vivo. The concentration distributions of tenofovir in gel over time and space were measured and input to a mathematical diffusion model to deduce diffusion coefficients. These were 3.16 ± 0.11 × 10^-6 cm²/s in undiluted gel, and increased by 11%-46% depending on the extent of dilution. Results were interpreted with respect to traditional release rate measurements in devices such as Franz cells. This comparison highlighted an advantage of our assay in that it characterizes the diffusive barrier within the gel material itself; in contrast, release rate in the traditional assay is affected by external conditions, such as drug partitioning at the gel/liquid sink interface. This new assay is relevant to diffusion in polymeric hydrogels over pharmacologically relevant length scales, for example, those characteristic of topical drug delivery. Resulting transport parameters are salient measures of drug delivery potential, and serve as inputs to computational models of drug delivery performance.

Mutations in hpyAVIBM, C⁵ cytosine DNA methyltransferase from Helicobacter pylori result in relaxed specificity

The genome of Helicobacter pylori is rich in restriction-modification (RM) systems. Approximately 4% of the genome codes for components of RM systems. hpyAVIBM, which codes for a phase-variable C(5) cytosine methyltransferase (MTase) from H. pylori, lacks a cognate restriction enzyme. Over-expression of M.HpyAVIB in Escherichia coli enhances the rate of mutations. However, when the catalytically inactive F9N or C82W mutants of M.HpyAVIB were expressed in E. coli, mutations were not observed. The M.HpyAVIB gene itself was mutated to give rise to different variants of the MTase. M.HpyAVIB variants were purified and differences in kinetic properties and specificity were observed. Intriguingly, purified MTase variants showed relaxed substrate specificity. Homologues of hpyAVIBM homologues amplified and sequenced from different clinical isolates showed similar variations in sequence. Thus, hpyAVIBM presents an interesting example of allelic variations in H. pylori where changes in the nucleotide sequence result in proteins with new properties.

Prediction of hydrodynamic and other solution properties of rigid proteins from atomic- and residue-level models

Here we extend the ability to predict hydrodynamic coefficients and other solution properties of rigid macromolecular structures from atomic-level structures, implemented in the computer program HYDROPRO, to models with lower, residue-level resolution. Whereas in the former case there is one bead per nonhydrogen atom, the latter contains one bead per amino acid (or nucleotide) residue, thus allowing calculations when atomic resolution is not available or coarse-grained models are preferred. We parameterized the effective hydrodynamic radius of the elements in the atomic- and residue-level models using a very large set of experimental data for translational and rotational coefficients (intrinsic viscosity and radius of gyration) for >50 proteins. We also extended the calculations to very large proteins and macromolecular complexes, such as the whole 70S ribosome. We show that with proper parameterization, the two levels of resolution yield similar and rather good agreement with experimental data. The new version of HYDROPRO, in addition to considering various computational and modeling schemes, is far more efficient computationally and can be handled with the use of a graphical interface.

Hydrodynamic effects in proteins

Experimental and numerical results pertaining to flow-induced effects in proteins are reviewed. Special emphasis is placed on shear-induced unfolding and on the role of solvent mediated hydrodynamic interactions in the conformational transitions in proteins.

Clathrin triskelia show evidence of molecular flexibility

The clathrin triskelion, which is a three-legged pinwheel-shaped heteropolymer, is a major component in the protein coats of certain post-Golgi and endocytic vesicles. At low pH, or at physiological pH in the presence of assembly proteins, triskelia will self-assemble to form a closed clathrin cage, or "basket". Recent static light scattering and dynamic light scattering studies of triskelia in solution showed that an individual triskelion has an intrinsic pucker similar to, but differing from, that inferred from a high resolution cryoEM structure of a triskelion in a clathrin basket. We extend the earlier solution studies by performing small-angle neutron scattering (SANS) experiments on isolated triskelia, allowing us to examine a higher q range than that probed by static light scattering. Results of the SANS measurements are consistent with the light scattering measurements, but show a shoulder in the scattering function at intermediate q values (0.016 A(-1)), just beyond the Guinier regime. This feature can be accounted for by Brownian dynamics simulations based on flexible bead-spring models of a triskelion, which generate time-averaged scattering functions. Calculated scattering profiles are in good agreement with the experimental SANS profiles when the persistence length of the assumed semiflexible triskelion is close to that previously estimated from the analysis of electron micrographs.

Proteins in a shear flow

The conformational dynamics of a single protein molecule in a shear flow is investigated using Brownian dynamics simulations. A structure-based coarse grained model of a protein is used. We consider two proteins, ubiquitin and integrin, and find that at moderate shear rates they unfold through a sequence of metastable states-a pattern which is distinct from a smooth unraveling found in homopolymers. Full unfolding occurs only at very large shear rates. Furthermore, the hydrodynamic interactions between the amino acids are shown to hinder the shear flow unfolding. The characteristics of the unfolding process depend on whether a protein is anchored or not, and if it is, on the choice of an anchoring point.

An efficient computational method for predicting rotational diffusion tensors of globular proteins using an ellipsoid representation

We propose a new computational method for predicting rotational diffusion properties of proteins in solution. The method is based on the idea of representing protein surface as an ellipsoid shell. In contrast to other existing approaches this method uses principal component analysis of protein surface coordinates, which results in a substantial increase in the computational efficiency of the method. Direct comparison with the experimental data as well as with the recent computational approach (Garcia de la Torre; et al. J. Magn. Reson. 2000, B147, 138-146), based on representation of protein surface as a set of small spherical friction elements, shows that the method proposed here reproduces experimental data with at least the same level of accuracy and precision as the other approach, while being approximately 500 times faster. Using the new method we investigated the effect of hydration layer and protein surface topography on the rotational diffusion properties of a protein. We found that a hydration layer constructed of approximately one monolayer of water molecules smoothens the protein surface and effectively doubles the overall tumbling time. We also calculated the rotational diffusion tensors for a set of 841 protein structures representing the known protein folds. Our analysis suggests that an anisotropic rotational diffusion model is generally required for NMR relaxation data analysis in single-domain proteins, and that the axially symmetric model could be sufficient for these purposes in approximately half of the proteins.

Precise boundary element computation of protein transport properties: Diffusion tensors, specific volume, and hydration

A precise boundary element method for the computation of hydrodynamic properties has been applied to the study of a large suite of 41 soluble proteins ranging from 6.5 to 377 kDa in molecular mass. A hydrodynamic model consisting of a rigid protein excluded volume, obtained from crystallographic coordinates, surrounded by a uniform hydration thickness has been found to yield properties in excellent agreement with experiment. The hydration thickness was determined to be delta = 1.1 +/- 0.1 A. Using this value, standard deviations from experimental measurements are: 2% for the specific volume; 2% for the translational diffusion coefficient, and 6% for the rotational diffusion coefficient. These deviations are comparable to experimental errors in these properties. The precision of the boundary element method allows the unified description of all of these properties with a single hydration parameter, thus far not achieved with other methods. An approximate method for computing transport properties with a statistical precision of 1% or better (compared to 0.1-0.2% for the full computation) is also presented. We have also estimated the total amount of hydration water with a typical -9% deviation from experiment in the case of monomeric proteins. Both the water of hydration and the more precise translational diffusion data hint that some multimeric proteins may not have the same solution structure as that in the crystal because the deviations are systematic and larger than in the monomeric case. On the other hand, the data for monomeric proteins conclusively show that there is no difference in the protein structure going from the crystal into solution.

Numerical path integration technique for the calculation of transport properties of proteins

We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are O(m(3)) where m is the number of finite elements. The new technique, a numerical path integration method, has computation times that are only O(m). We have applied the technique to approximately 1000 different protein structures. The computed translational diffusivities and intrinsic viscosities are, to lowest order, proportional respectively to N(-1/3)(R) and N(0)(R), where N(R) is the number of amino acid residues in the protein. Our calculations also show some correlation with the shape of the molecule, as represented by the ratio m(2)/m(3), where m(2) and m(3) are, respectively, the middle and the smallest of the three principal moments of inertia. Comparisons with a number of experimental results are also performed, with results generally consistent to within experimental error.

Calculation of hydrodynamic properties of globular proteins from their atomic-level structure

The solution properties, including hydrodynamic quantities and the radius of gyration, of globular proteins are calculated from their detailed, atomic-level structure, using bead-modeling methodologies described in our previous article (, Biophys. J. 76:3044-3057). We review how this goal has been pursued by other authors in the past. Our procedure starts from a list of atomic coordinates, from which we build a primary hydrodynamic model by replacing nonhydrogen atoms with spherical elements of some fixed radius. The resulting particle, consisting of overlapping spheres, is in turn represented by a shell model treated as described in our previous work. We have applied this procedure to a set of 13 proteins. For each protein, the atomic element radius is adjusted, to fit all of the hydrodynamic properties, taking values close to 3 A, with deviations that fall within the error of experimental data. Some differences are found in the atomic element radius found for each protein, which can be explained in terms of protein hydration. A computational shortcut makes the procedure feasible, even in personal computers. All of the model-building and calculations are carried out with a HYDROPRO public-domain computer program.

Solution structure of biopolymers: a new method of constructing a bead model

We propose a new, automated method of converting crystallographic data into a bead model used for the calculations of hydrodynamic properties of rigid macromolecules. Two types of molecules are considered: nucleic acids and small proteins. A bead model of short DNA fragments has been constructed in which each nucleotide is represented by two identical, partially overlapping spheres: one for the base and one for the sugar and phosphate group. The optimum radius sigma = 5.0 A was chosen on the basis of a comparison of the calculated translational diffusion coefficients (D(T)) and the rotational relaxation times (tau(R)) with the corresponding experimental data for B-DNA fragments of 8, 12, and 20 basepairs. This value was assumed for the calculation D(T) and tau(R) of tRNA(Phe). Better agreement with the experimental data was achieved for slightly larger sigma = 5.7 A. A similar procedure was applied to small proteins. Bead models were constructed such that each amino acid was represented by a single sphere or a pair of identical, partially overlapping spheres, depending on the amino acid's size. Experimental data of D(T) of small proteins were used to establish the optimum value of sigma = 4.5 A for amino acids. The lack of experimental data on tau(R) for proteins restricted the tests to the translational diffusion properties.