Retrospective rationalization of disparities between the concentration dependence of diffusion coefficients obtained by boundary spreading and dynamic light scattering.

This study establishes the existence of substantial agreement between published results from traditional boundary spreading measurements (including synthetic boundary measurements in the analytical ultracenrifuge) on two globular proteins (bovine serum albumin, ovalbumin) and the concentration dependence of diffusion coefficient predicted for experiments conducted under the operative thermodynamic constraints of constant temperature and solvent chemical potential. Although slight negative concentration dependence of the translational diffusion coefficient is the experimentally observed as well as theoretically predicted, the extent of the concentration dependence is within the limits of experimental uncertainty inherent in diffusion coefficient measurement. Attention is then directed toward the ionic strength dependence of the concentration dependence coefficient ([Formula: see text]) describing diffusion coefficients obtained by dynamic light scattering, where, in principle, the operative thermodynamic constraints of constant temperature and pressure preclude consideration of results in terms of single-solute theory. Nevertheless, good agreement between predicted and published experimental ionic strength dependencies of [Formula: see text] for lysozyme and an immunoglobulin is observed by a minor adaptation of the theoretical treatment to accommodate the fact that thermodynamic activity is monitored on the molal concentration scale because of the constraint of constant pressure that pertains in dynamic light scattering experiments.

Experimental support for reclassification of the light scattering second virial coefficient from macromolecular solutions as a hydrodynamic parameter.

This investigation examines the source of the disparity between experimental values of the light scattering second virial coefficient [Formula: see text] (mL.mol/g2) for proteins and those predicted on the statistical mechanical basis of excluded volume. A much better theoretical description of published results for lysozyme is obtained by considering the experimental parameters to monitor the difference between the thermodynamic excluded volume term and its hydrodynamic counterpart. This involves a combination of parameters quantifying concentration dependence of the translational diffusion coefficient obtained from dynamic light scattering measurements. That finding is shown to account for observations of a strong correlation between [Formula: see text] (mL/g), where M2 is the molar mass (molecular weight) of the macromolecule and the diffusion concentration parameter [Formula: see text] (mL/g). On the grounds that [Formula: see text] is regarded as a hydrodynamic parameter, the same status should be accorded the light scattering second virial coefficient rather than its current incorrect thermodynamic designation as [Formula: see text] (mL.mol/g2), or just B, the osmotic second virial coefficient for protein self-interaction.

Thermodynamics of semi-specific ligand recognition: the binding of dipeptides to the E.coli dipeptide binding protein DppA.

This investigation of the temperature dependence of DppA interactions with a subset of three dipeptides (AA. AF and FA) by isothermal titration calorimetry has revealed the negative heat capacity ([Formula: see text]) that is a characteristic of hydrophobic interactions. The observation of enthalpy-entropy compensation is interpreted in terms of the increased structuring of water molecules trapped in a hydrophobic environment, the enthalpic energy gain from which is automatically countered by the entropy decrease associated with consequent loss of water structure flexibility. Specificity for dipeptides stems from appropriate spacing of designated DppA aspartate and arginine residues for electrostatic interaction with the terminal amino and carboxyl groups of a dipeptide, after which the binding pocket closes to become completely isolated from the aqueous environment. Any differences in chemical reactivity of the dipeptide sidechains are thereby modulated by their occurrence in a hydrophobic environment where changes in the structural state of entrapped water molecules give rise to the phenomenon of enthalpy-entropy compensation. The consequent minimization of differences in the value of ΔG0 for all DppA-dipeptide interactions thus provides thermodynamic insight into the biological role of DppA as a transporter of all dipeptides across the periplasmic membrane.

Quantifying the concentration dependence of sedimentation coefficients for globular macromolecules: a continuing age-old problem.

This retrospective investigation has established that the early theoretical attempts to directly incorporate the consequences of radial dilution into expressions for variation of the sedimentation coefficient as a function of the loading concentration in sedimentation velocity experiments require concentration distributions exhibiting far greater precision than that achieved by the optical systems of past and current analytical ultracentrifuges. In terms of current methods of sedimentation coefficient measurement, until such improvement is made, the simplest procedure for quantifying linear s-c dependence (or linear concentration dependence of 1/s) for dilute systems therefore entails consideration of the sedimentation coefficient obtained by standard c(s), g*(s) or G(s) analysis) as an average parameter ( s ¯ ) that pertains to the corresponding mean plateau concentration (following radial dilution) ( c ¯ ) over the range of sedimentation velocity distributions used for the determination of s ¯ . The relation of this with current descriptions of the concentration dependence of the sedimentation and translational diffusion coefficients is considered, together with a suggestion for the necessary improvement in the optical system.

Experimental determination of second virial coefficients by small-angle X-ray scattering: a problem revisited.

This investigation examines the validity of employing single-solute theory to interpret SAXS measurements on buffered protein solutions-the current practice despite the necessity to regard the buffer components as additional non-scattering solutes rather than as part of the solvent. The present study of bovine serum albumin in phosphate-buffered saline supplemented with 20-100 g/L sucrose as small cosolute has certainly verified the prediction that the experimentally obtained second virial coefficient should contain protein-cosolute contributions. Nevertheless, the second virial coefficient determined for protein solutions supplemented with high cosolute concentrations on the basis of single-solute theory remains a valid means for identifying conditions conducive to protein crystallization, because the return of a slightly negative second virial coefficient based on single-solute theory [Formula: see text] still establishes the existence of slightly associative interactions between protein molecules, irrespective of the molecular source-protein self-interactions and/or protein-cosolute contributions.

Use of molecular crowding for the detection of protein self-association by size-exclusion chromatography.

The feasibility of employing molecular crowding cosolutes to facilitate the detection of protein self-association by zonal size exclusion chromatography is investigated. Theoretical considerations have established that although the cosolute-induced displacement of a self-association equilibrium towards the oligomeric state invariably occurs in the mobile phase of the column, that displacement is only manifested as a decreased protein elution volume for cosolutes sufficiently small to partition between the mobile and stationary phases. Indeed, the use of a crowding agent sufficiently large to be confined to the mobile phase gives rise to an increased elution volume that could be misconstrued as evidence of cosolute-induced protein dissociation. Those theoretical considerations are reinforced by experimental studies of α-chymotrypsin (a reversibly dimerizing enzyme) on Superdex 200. The use of cosolutes such as sucrose and small polyethylene glycol fractions such as PEG-2000 is therefore recommended for the detection of protein self-association by molecular crowding effects in size exclusion chromatography.

Quantitative interpretation of isopiestic measurements on aqueous solutions: Urea revisited.

This investigation amends the analysis of isopiestic measurements of solvent thermodynamic activity by taking into account the fact that the solvent activity, traditionally expressed in mole-fraction terms, is a molal parameter because of the constraints (constant temperature and pressure) under which the measurements are made. Application of the revised procedure to published isopiestic measurements on aqueous urea solutions at 25 °C yields a dimerization constant of 0.066 molal-1, which is two-fold larger than an earlier published estimate based on an incorrect definition of the solute activity coefficient. Despite amendments to the quantitative detail, the present study confirms the existence of a large negative entropic contribution that largely counters its enthalpic counterpart arising from the hydrogen bonding responsible for dimer formation. This evidence of enthalpy-entropy compensation is entirely consistent with quantum-mechanical predictions of the adverse effect of water on urea dimerization. Changes in water structure thus contribute significantly to the energetics of urea dimerization in aqueous solution.

Interaction studies of a protein and carbohydrate system using an integrated approach: a case study of the miniagrin-heparin system.

The major challenges in biophysical characterization of human protein-carbohydrate interactions are obtaining monodispersed preparations of human proteins that are often post-translationally modified and lack of detection of carbohydrates by traditional detection systems. Light scattering (dynamic and static) techniques offer detection of biomolecules and their complexes based on their size and shape, and do not rely on chromophore groups (such as aromatic amino acid sidechains). In this study, we utilized dynamic light scattering, analytical ultracentrifugation and small-angle X-ray scattering techniques to investigate the solution properties of a complex resulting from the interaction between a 15 kDa heparin preparation and miniagrin, a miniaturized version of agrin. Results from dynamic light scattering, sedimentation equilibrium, and sedimentation velocity experiments signify the formation of a monodisperse complex with 1:1 stoichiometry, and low-resolution structures derived from the small-angle X-ray scattering measurements implicate an extended conformation for a side-by-side miniagrin‒heparin complex.

Interpretation of results from the competitive Biacore procedure for characterizing immunochemical interactions in solution.

Rigorous consideration of the consequences of antibody bivalence in the published competitive kinetic procedure for quantifying the solution characteristics of an antigen-antibody interaction in solution has rendered redundant the practice of substituting the Fab fragment for the antibody to ensure validity of the analysis of results in terms of theory developed for a univalent analyte. Although the quantitative expressions differ for univalent and bivalent analytes, the additional contribution arising from bivalence is likely to be well within the limits of experimental uncertainty in the measured binding constant.

Allowance for boundary sharpening in the determination of diffusion coefficients by sedimentation velocity: a historical perspective.

This review summarizes endeavors undertaken in the middle of last century to employ the Lamm equation for quantitative analysis of boundary spreading in sedimentation velocity experiments on globular proteins, thereby illustrating the ingenuity required to achieve that goal in an era when an approximate analytical solution of that nonlinear differential equation of second order provided the only means for its application. Application of procedures based on that approximate solution to simulated sedimentation velocity distributions has revealed a slight disparity (about 3%) between returned and input values of the diffusion coefficient-a discrepancy comparable with that of estimates obtained by current simulative analyses based on numerical solution of the Lamm equation. Although the massive technological developments in the gathering and treatment of sedimentation velocity data over the past three to four decades have changed dramatically the manner in which boundary spreading is analyzed, they have not led to any significant improvement in the accuracy of the diffusion coefficient thereby deduced.

Allowance for radial dilution in evaluating the concentration dependence of sedimentation coefficients for globular proteins.

The accuracy with which the concentration dependence of the sedimentation coefficient, s = s 0(1 - kc), can be quantified for globular proteins by commonly used procedures has been examined by subjecting simulated sedimentation velocity distributions for ovalbumin to c(s)‒s analysis. Because this procedure, as well as its g(s)‒s counterpart, is based on assumed constancy of s over the time course of sedimentation coefficient measurement in a given experiment, the best definition of the concentration coefficient k is obtained by associating the measured s with the mean of plateau concentrations for the initial and final distributions used for its determination. The return of a slightly underestimated k (by about 3%) is traced to minor mislocation of the air‒liquid meniscus position as the result of assuming time independence of s in a given experiment. Although more accurate quantification should result from later SEDFIT and SEDANAL programs incorporating the simultaneous evaluation of s 0 and k, the procedures based on assumed constancy of s suffice for determining the limiting sedimentation coefficient s 0-the objective of most s‒c dependence studies.

Rigorous analysis of static light scattering measurements on buffered protein solutions.

Attention is drawn to the thermodynamic invalidity of the current practice of analyzing static light scattering measurements on globular proteins in terms of theory for a single solute because of its disregard of the need to consider small species such as buffer components as additional cosolutes rather than as part of the solvent. This practice continues despite its demonstrated inadequacy in studies of sucrose-supplemented protein solutions, where the aberrant behavior was recognized to be a consequence of physical protein interaction with the small cosolute. Failure to take into account the consequences of small cosolute effects renders extremely difficult any attempt to obtain a rigorous thermodynamic characterization of protein interactions by this empirical technique.

Oligomeric state of hypoxanthine-guanine phosphoribosyltransferase from Mycobacterium tuberculosis.

Sedimentation equilibrium and size-exclusion chromatography experiments on Mycobacterium tuberculosis hypoxanthine-guanine phosphoribosyltransferase (MtHGPRT) have established the existence of this enzyme as a reversibly associating mixture of dimeric and tetrameric species in 0.1 M Tris-HCl-0.012 M MgCl2, pH 7.4. Displacement of the equilibrium position towards the larger oligomer by phosphate signifies the probable existence of MtHGPRT as a tetramer in the biological environment. These data thus add credibility to the relevance of considering enzyme function in the light of a published tetrameric structure deduced from X-ray crystallography. Failure of 5-phospho-α-d-ribosyl-1-pyrophosphate (PRib-PP) to perturb the dimer-tetramer equilibrium position indicates the equivalence and independence of binding for this substrate (the first to bind in an ordered sequential mechanism) to the two oligomers. By virtue of the displacement of the equilibrium position towards dimer that is affected by removing MgCl2 from the Tris-HCl buffer, it can be concluded that divalent metal ions, as well as phosphate, can affect the oligomerization. These characteristics of MtHGPRT in solution are correlated with published crystal structures of four enzyme-ligand complexes.

Measurement of osmotic second virial coefficients by zonal size-exclusion chromatography.

Numerical simulation of protein migration reflecting linear concentration dependence of the partition isotherm has been used to invalidate a published procedure for measuring osmotic second virial coefficients (B22) by zonal exclusion chromatography. Failure of the zonal procedure to emulate its frontal chromatographic counterpart reflects ambiguity about the solute concentration that should be used to replace the applied concentration in the rigorous quantitative expression for frontal migration; the recommended use of the peak concentration in the eluted zone is incorrect on theoretical grounds. Furthermore, the claim for its validation on empirical grounds has been traced to the use of inappropriate B22 magnitudes as the standards against which the experimentally derived values were being tested.

Analytical ultracentrifugation: A versatile tool for the characterisation of macromolecular complexes in solution.

Analytical ultracentrifugation, an early technique developed for characterizing quantitatively the solution properties of macromolecules, remains a powerful aid to structural biologists in their quest to understand the formation of biologically important protein complexes at the molecular level. Treatment of the basic tenets of the sedimentation velocity and sedimentation equilibrium variants of analytical ultracentrifugation is followed by considerations of the roles that it, in conjunction with other physicochemical procedures, has played in resolving problems encountered in the delineation of complex formation for three biological systems - the cytoplasmic dynein complex, mitogen-activated protein kinase (ERK2) self-interaction, and the terminal catalytic complex in selenocysteine synthesis.

Biophysical analysis of a lethal laminin alpha-1 mutation reveals altered self-interaction.

Laminins are key basement membrane molecules that influence several biological activities and are linked to a number of diseases. They are secreted as heterotrimeric proteins consisting of one α, one ß, and one γ chain, followed by their assembly into a polymer-like sheet at the basement membrane. Using sedimentation velocity, dynamic light scattering, and surface plasmon resonance experiments, we studied self-association of three laminin (LM) N-terminal fragments α-1 (hLM α-1N), α-5 (hLM α-5N) and ß-3 (hLM ß-3N) originating from the short arms of the human laminin αßγ heterotrimer. Corresponding studies of the hLM α-1N C49S mutant, equivalent to the larval lethal C56S mutant in zebrafish, have shown that this mutation causes enhanced self-association behavior, an observation that provides a plausible explanation for the inability of laminin bearing this mutation to fulfill functional roles in vivo, and hence for the deleterious pathological consequences of the mutation on lens function.

Evaluation of diffusion coefficients by means of an approximate steady-state condition in sedimentation velocity distributions.

This investigation examined the feasibility of manipulating the rotor speed in sedimentation velocity experiments to spontaneously generate an approximate steady-state condition where the extent of diffusional spreading is matched exactly by the boundary sharpening arising from negative s-c dependence. Simulated sedimentation velocity distributions based on the sedimentation characteristics for a purified mucin preparation were used to illustrate a simple procedure for determining the diffusion coefficient from such steady-state distributions in situations where the concentration dependence of the sedimentation coefficient, s = s(0)/(1 + Kc), was quantified in terms of the limiting sedimentation coefficient as c â†’ 0 (s(0)) and the concentration coefficient (K). Those simulations established that spontaneous generation of the approximate steady state could well be a feature of sedimentation velocity distributions for many unstructured polymer systems because the requirement that Kcoω(2)s(0)/D be between 46 and 183 cm(-2) is not unduly restrictive. Although spontaneous generation of the approximate steady state is also a theoretical prediction for structured macromolecular solutes exhibiting linear concentration dependence of the sedimentation coefficient, s = s(0)(1 - kc), the required value of k is far too large for any practical advantage to be taken of this approach with globular proteins.

Characterization of Intrinsically Disordered Proteins by Analytical Ultracentrifugation.

Intrinsically disordered proteins have traditionally been largely neglected by structural biologists because a lack of rigid structure precludes their study by X-ray crystallography. Structural information must therefore be inferred from physicochemical studies of their solution behavior. Analytical ultracentrifugation yields important information about the gross conformation of an intrinsically disordered protein. Sedimentation velocity studies provide estimates of the weight-average sedimentation and diffusion coefficients of a given macromolecular state of the protein.