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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

Enthalpy/entropy compensation effects from cavity desolvation underpin broad ligand binding selectivity for rat odorant binding protein 3.

Evolution has produced proteins with exquisite ligand binding specificity, and manipulating this effect has been the basis for much of modern rational drug design. However, there are general classes of proteins with broader ligand selectivity linked to function, the origin of which is poorly understood. The odorant binding proteins (OBPs) sequester volatile molecules for transportation to the olfactory receptors. Rat OBP3, which we characterize by X-ray crystallography and NMR, binds a homologous series of aliphatic γ-lactones within its aromatic-rich hydrophobic pocket with remarkably little variation in affinity but extensive enthalpy/entropy compensation effects. We show that the binding energetics are modulated by two desolvation processes with quite different thermodynamic signatures. Ligand desolvation follows the classical hydrophobic effect; however, cavity desolvation is consistent with the liberation of "high energy" water molecules back into bulk solvent with a strong, but compensated, enthalpic contribution, which together underpin the origins of broad ligand binding selectivity.

Reconciliation of classical and reacted-site probability approaches to allowance for ligand multivalence in binding studies.

The objective of this investigation is to engender greater confidence in the validity of binding equations derived for multivalent ligands on the basis of reacted-site probability theory. To that end, a demonstration of the theoretical interconnection between expressions derived by the classical stepwise equilibria and reacted-site probability approaches for univalent ligands is followed by the use of the traditional stepwise procedure to derive binding equations for bivalent and trivalent ligands. As well as demonstrating the unwieldy nature of the classical binding equation for multivalent ligand systems, that exercise has allowed numerical simulation to be used to illustrate the equivalence of binding curves generated by the two approaches. The advantages of employing a redefined binding function for multivalent ligands are also confirmed by subjecting the simulated results to a published analytical procedure that has long been overlooked.

Confirmation of the validity of the current characterization of immunochemical reactions by kinetic exclusion assay.

Prior observations that questioned the validity of kinetic exclusion assays were based on the mistaken assumption that the assays quantified the fraction of those antibody molecules that had unoccupied binding sites. Instead, the standard KinExA assay quantifies the fraction of total antibody binding sites that are unoccupied, regardless of the number of unoccupied sites on each antibody molecule. Although the standard KinExA analysis assumes that there is only a small probability of antibody-site capture by the affinity matrix, the results of numerical simulations demonstrate the reliability of dissociation constants obtained by the standard KinExA analysis for capture probabilities as high as 30%. This finding further strengthens the potential of kinetic exclusion assays as the procedure of choice for the rapid and accurate characterization of immunochemical reactions that forms part of screening processes in the search for therapeutic antibodies.

Concentration dependence of translational diffusion coefficients for globular proteins.

This investigation examines published results of traditional diffusion experiments on ovalbumin and bovine serum albumin to determine the extent to which assumed concentration independence of the translational diffusion coefficient is a reasonable approximation in the analysis of boundary spreading in sedimentation velocity experiments on proteins. Although significant positive concentration dependence of the diffusion coefficient (D) for both proteins is predicted by current theories, none has been detected in these experimental diffusion studies performed under the constraints of constant temperature and solvent chemical potential (those also pertinent to sedimentation velocity). Instead, the results are better described by the relatively minor concentration dependence predicted by considering solution viscosity to be an additional source of D-c dependence. Inasmuch as the predicted variation in D for solutions with concentrations below 10 mg mL(-1) is within the uncertainty of experimental estimates, these findings support use of the approximate solution of the Lamm equation developed by Fujita for the quantitative analysis of boundary spreading in sedimentation velocity experiments on proteins.

Allowance for antibody bivalence in the determination of association rate constants by kinetic exclusion assay.

This investigation completes the amendment of theoretical expressions for the characterization of antigen-antibody interactions by kinetic exclusion assay-an endeavor that has been marred by inadequate allowance for the consequences of antibody bivalence in its uptake by the affinity matrix (immobilized antigen) that is used to ascertain the fraction of free antibody sites in a solution with defined total concentrations of antigen and antibody. A simple illustration of reacted site probability considerations in action confirms that the square root of the fluorescence response ratio, R(Ag)/R0, needs to be taken in order to determine the fraction of unoccupied antibody sites, which is the parameter employed to describe the kinetics of antigen uptake in the mixture of antigen and antibody with defined initial composition. The approximately 2-fold underestimation of the association rate constant (k(a)) that emanates from the usual practice of omitting the square root factor gives rise to a corresponding overestimate of the equilibrium dissociation constant (K(d))--a situation that is also encountered in the thermodynamic characterization of antigen-antibody interactions by kinetic exclusion assay.

An analytical solution to the characterization of antigen-antibody interactions by kinetic exclusion assay.

A simpler derivation of the basic expression for the dependence of fluorimetric response ratio (R(Ag)/Ro) on free antigen concentration has demonstrated the universal invalidity of the analysis that is incorporated into the manufacturer's software for determining immunoaffinities by kinetic exclusion assay, and traced the error to inadequate allowance for antibody bivalence in the solution phase of the assay. An analytical solution to the quantitative characterization of antigen-antibody interactions from the dependence of R(Ag)/Ro on total antigen concentration is also described, thereby eliminating the necessity for the extensive simulative procedures employed in current determinations of dissociation constants by kinetic exclusion assay. In the illustrative application of this analytical approach to published results on the interaction between a metal chelate (cadmium-ethylenediaminetetraacetic acid, Cd-EDTA) and an elicited monoclonal antibody, the analytical processing of the data has been performed on a calculator. However, there is no need to replace the more sophisticated procedure that is incorporated into the Sapidyne software provided that programming changes are made to rectify the erroneous equation on which the simulative analysis is based.

A potential for overestimating the absolute magnitudes of second virial coefficients by small-angle X-ray scattering.

Theoretical consideration is given to the effect of cosolutes (including buffer and electrolyte components) on the determination of second virial coefficients for proteins by small-angle X-ray scattering (SAXS)-a factor overlooked in current analyses in terms of expressions for a two-component system. A potential deficiency of existing practices is illustrated by reassessment of published results on the effect of polyethylene glycol concentration on the second virial coefficient for urate oxidase. This error reflects the substitution of I(0,c3,0), the scattering intensity in the limit of zero scattering angle and solute concentration, for I(0,0,0), the corresponding parameter in the limit of zero cosolute concentration (c3) as well. Published static light scattering results on the dependence of the apparent molecular weight of ovalbumin on buffer concentration are extrapolated to zero concentration to obtain the true value (M2) and thereby establish the feasibility of obtaining the analogous SAXS parameter, I(0,0,0), experimentally.

The macromolecular state of A-kinase anchoring protein.

The amendment of the interpretation of recently published size-exclusion chromatography (SEC) data for A-kinase anchoring protein (AKAP12) on Sephacryl-S400 has led to an increase in the estimated size of the supermolecular state from 840 to at least 6000 kDa. Although size-exclusion chromatography has sufficed to demonstrate unequivocally the existence of this 190-kDa scaffold protein in a supermolecular state, any quantitative estimate of the oligomer stoichiometry is shown to be precluded by failure of this empirical procedure to incorporate allowance for any deviation from globular shape--an important consideration in view of the extended structures exhibited by other extracellular matrix proteins.

Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization.

This reexamination of a high-speed sedimentation equilibrium distribution for α-chymotrypsin under slightly acidic conditions (pH 4.1, I(M) 0.05) has provided experimental support for the adequacy of nearest-neighbor considerations in the allowance for effects of thermodynamic nonideality in the characterization of protein self-association over a moderate concentration range (up to 8 mg/mL). A widely held but previously untested notion about allowance for thermodynamic nonideality effects is thereby verified experimentally. However, it has also been shown that a greater obstacle to better characterization of protein self-association is likely to be the lack of a reliable estimate of monomer net charge, a parameter that has a far more profound effect on the magnitude of the measured equilibrium constant than any deficiency in current procedures for incorporating the effects of thermodynamic nonideality into the analysis of sedimentation equilibrium distributions reflecting reversible protein self-association.