COVOL: an interactive program for evaluating second virial coefficients from the triaxial shape or dimensions of rigid macromolecules

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.

Analytical Ultracentrifugation as a Matrix-Free Probe for the Study of Kinase Related Cellular and Bacterial Membrane Proteins and Glycans

Analytical ultracentrifugation is a versatile approach for analysing the molecular mass, molecular integrity (degradation/aggregation), oligomeric state and association/dissociation constants for self-association, and assay of ligand binding of kinase related membrane proteins and glycans. It has the great property of being matrix free-providing separation and analysis of macromolecular species without the need of a separation matrix or membrane or immobilisation onto a surface. This short review-designed for the non-hydrodynamic expert-examines the potential of modern sedimentation velocity and sedimentation equilibrium and the challenges posed for these molecules particularly those which have significant cytoplasmic or extracellular domains in addition to the transmembrane region. These different regions can generate different optimal requirements in terms of choice of the appropriate solvent (aqueous/detergent). We compare how analytical ultracentrifugation has contributed to our understanding of two kinase related cellular or bacterial protein/glycan systems (i) the membrane erythrocyte band 3 protein system-studied in aqueous and detergent based solvent systems-and (ii) what it has contributed so far to our understanding of the enterococcal VanS, the glycan ligand vancomycin and interactions of vancomycin with mucins from the gastrointestinal tract.

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 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{s} $$\end{document}s¯) that pertains to the corresponding mean plateau concentration (following radial dilution) (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{c} $$\end{document}c¯) over the range of sedimentation velocity distributions used for the determination of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{s} $$\end{document}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.

Quantifying Protein-Protein Interactions in Molecular Simulations

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B₂. As a measure of nonspecific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid–liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B₂ from insertion and removal energies by applying Bennett’s acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K_d and B₂ allow us to separate out the contributions of nonbinding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K_d and B₂ calculations make them well suited for high-throughput studies of large interactomes.

Effects of Hydrodynamic Interactions on the Near-Surface Diffusion of Spheroidal Molecules

We investigated diffusion of spheroidal molecules near a planar surface, accounting for spatially dependent translational and rotational mobilities of molecules resulting from their hydrodynamic interactions with the plane. Rigid-body Brownian dynamics simulations of prolate ellipsoids of revolution of an axial ratio in the range of 1.5 to 3.0, suspended in a viscous fluid, with a no-slip flat boundary confining the suspension were employed. Mobility tensor matrices of molecules were evaluated as functions of spheroids' distance and orientation with respect to the plane. Hydrodynamic interactions with the surface lead to substantial changes of spheroids' translational diffusion coefficients both in the direction perpendicular and parallel to the plane when compared with the values characterizing the bulk diffusion. Moreover, the short-time translational diffusion of molecules, measured in the laboratory frame, both in an unbounded fluid and under the confinement, is non-Gaussian, with much larger deviations from Gaussianity observed in the latter case. In an unbounded fluid, distributions of translational displacements of molecules deviate from those expected for a simple Brownian motion as a result of shape anisotropy. In the presence of the plane, spheroids experience an additional anisotropic drag, and consequently, their mobilities depend on their positions and orientations. Therefore, anomalies in the short-time dynamics observed under confinement can be explained in terms of the so-called diffusing-diffusivity mechanism. Our findings have implications for understanding of a wide range of biological and technological processes that involve diffusion of anisotropic molecules near surfaces of natural and model cell membranes, biosensors and nanosensors, and electrodes.

A Comprehensive Brownian Dynamics Approach for the Determination of Non-ideality Parameters from Analytical Ultracentrifugation

Brownian dynamics (BD) has been applied as a comprehensive tool to model sedimentation and diffusion of nanoparticles in analytical ultracentrifugation (AUC) experiments. In this article, we extend the BD algorithm by considering space-dependent diffusion and solvent compressibility. With this, the changes in the sedimentation and diffusion coefficient from altered solvent properties at increased pressures are accurately taken into account. Moreover, it is demonstrated how the concept of space-dependent diffusion is employed to describe concentration-dependent sedimentation and diffusion coefficients, in particular, through the Gralen coefficient and the second virial coefficient. The influence of thermodynamic nonideality on diffusional properties can be accurately simulated and agree with well-known evaluation tools. BD simulations for sedimentation equilibrium and sedimentation velocity (SV) AUC experiments including effects of hydrodynamic and thermodynamic nonideality are validated by global evaluation in SEDANAL. The interplay of solvent compressibility and retrieved nonideality parameters can be studied utilizing BD. Finally, the second virial coefficient is determined for lysozyme from SV AUC experiments and BD simulations and compared to membrane osmometry. These results are in line with DLVO theory. In summary, BD simulations are established for the validation of nonideal sedimentation in AUC providing a sound basis for the evaluation of complex interactions even in polydisperse systems.

IgG Charge: Practical and Biological Implications

Practically, IgG charge can contribute significantly to thermodynamic nonideality, and hence to solubility and viscosity. Biologically, IgG charge isomers exhibit differences in clearance and potency. It has been known since the 1930s that all immunoglobulins carry a weak negative charge in physiological solvents. However, there has been no systematic exploration of this fundamental property. Accurate charge measurements have been made using membrane confined electrophoresis in two solvents (pH 5.0 and pH 7.4) on a panel of twelve mAb IgGs, as well as their F(ab’)₂ and Fc fragments. The following observations were made at pH 5.0: (1) the measured charge differs from the calculated charge by ~40 for the intact IgGs, and by ~20 for the Fcs; (2) the intact IgG charge depends on both Fv and Fc sequences, but does not equal the sum of the F(ab)’₂ and Fc charge; (3) the Fc charge is consistent within a class. In phosphate buffered saline, pH 7.4: (1) the intact IgG charges ranged from 0 to −13; (2) the F(ab’)₂ fragments are nearly neutral for IgG1s and IgG2s, and about −5 for some of the IgG4s; (3) all Fc fragments are weakly anionic, with IgG1 < IgG2 < IgG4; (4) the charge on the intact IgGs does not equal the sum of the F(ab’)₂ and Fc charge. In no case is the calculated charge, based solely on H⁺ binding, remotely close to the measured charge. Some mAbs carried a charge in physiological salt that was outside the range observed for serum-purified human poly IgG. To best match physiological properties, a therapeutic mAb should have a measured charge that falls within the range observed for serum-derived human IgGs. A thermodynamically rigorous, concentration-dependent protein–protein interaction parameter is introduced. Based on readily measured properties, interaction curves may be generated to aid in the selection of proteins and solvent conditions. Example curves are provided.

The Svedberg Lecture 2017. From nano to micro: the huge dynamic range of the analytical ultracentrifuge for characterising the sizes, shapes and interactions of molecules and assemblies in Biochemistry and Polymer Science

The analytical ultracentrifuge (AUC) invented by T. Svedberg has now become an extremely versatile and diverse tool in Biochemistry and Polymer Science for the characterisation of the sizes, shapes and interactions of particles ranging in size from a few nanometres to tens of microns, or in molecular weight, M (molar mass) terms from a few hundred daltons to hundreds of megadaltons. We illustrate this diversity by reviewing recent work on (1) small lignin-like isoeugenols of M ~ 0.4–0.9 kDa for archaeological wood conservation, (2) protein-like association of a functional amino-cellulose M = 3.25 kDa, (3) a small glycopeptide antibiotic (M ~ 1.5 kDa) and its association with a protein involved in antibiotic resistance (M ~ 47 kDa), (4) tetanus toxoid protein TTP (M ~ 150 kDa) and (5) the incorporation of TTP into two huge glycoconjugates considered in glycovaccine development with molecular weight species in a broad distribution appearing to reach 100 MDa. In illustrating the diversity, we will highlight developments in hydrodynamic analysis which have made the AUC such an exciting and important instrument, and point to a potential future development for extending its capability to highly concentrated systems.

Glargine and degludec: Solution behaviour of higher dose synthetic insulins

Single, double and triple doses of the synthetic insulins glargine and degludec currently used in patient therapy are characterised using macromolecular hydrodynamic techniques (dynamic light scattering and analytical ultracentrifugation) in an attempt to provide the basis for improved personalised insulin profiling in patients with diabetes. Using dynamic light scattering and sedimentation velocity in the analytical ultracentrifuge glargine was shown to be primarily dimeric under solvent conditions used in current formulations whereas degludec behaved as a dihexamer with evidence of further association of the hexamers ("multi-hexamerisation"). Further analysis by sedimentation equilibrium showed that degludec exhibited reversible interaction between mono- and-di-hexamer forms. Unlike glargine, degludec showed strong thermodynamic non-ideality, but this was suppressed by the addition of salt. With such large injectable doses of synthetic insulins remaining in the physiological system for extended periods of time, in some case 24-40 hours, double and triple dose insulins may impact adversely on personalised insulin profiling in patients with diabetes.

Foreword to 'Quantitative and analytical relations in biochemistry'-a special issue in honour of Donald J. Winzor's 80th birthday

The purpose of this special issue is to honour Professor Donald J. Winzor's long career as a researcher and scientific mentor, and to celebrate the milestone of his 80th birthday. Throughout his career, Don has been renowned for his development of clever approximations to difficult quantitative relations governing a range of biophysical measurements. The theme of this special issue, 'Quantitative and analytical relations in biochemistry', was chosen to reflect this aspect of Don's scientific approach.

Assessing sedimentation equilibrium profiles in analytical ultracentrifugation experiments on macromolecules: from simple average molecular weight analysis to molecular weight distribution and interaction analysis

Molecular weights (molar masses), molecular weight distributions, dissociation constants and other interaction parameters are fundamental characteristics of proteins, nucleic acids, polysaccharides and glycoconjugates in solution. Sedimentation equilibrium analytical ultracentrifugation provides a powerful method with no supplementary immobilization, columns or membranes required. It is a particularly powerful tool when used in conjunction with its sister technique, namely sedimentation velocity. Here, we describe key approaches now available and their application to the characterization of antibodies, polysaccharides and glycoconjugates. We indicate how major complications, such as thermodynamic non-ideality, can now be routinely dealt with, thanks to a great extent to the extensive contribution of Professor Don Winzor over several decades of research.

Recent advances in the analysis of macromolecular interactions using the matrix-free method of sedimentation in the analytical ultracentrifuge

Sedimentation in the analytical ultracentrifuge is a matrix free solution technique with no immobilisation, columns, or membranes required and can be used to study self-association and complex or “hetero”-interactions, stoichiometry, reversibility and interaction strength of a wide variety of macromolecular types and across a very large dynamic range (dissociation constants from 10⁻¹² M to 10⁻¹ M). We extend an earlier review specifically highlighting advances in sedimentation velocity and sedimentation equilibrium in the analytical ultracentrifuge applied to protein interactions and mucoadhesion and to review recent applications in protein self-association (tetanus toxoid, agrin), protein-like carbohydrate association (aminocelluloses), carbohydrate-protein interactions (polysaccharide-gliadin), nucleic-acid protein (G-duplexes), nucleic acid-carbohydrate (DNA-chitosan) and finally carbohydrate-carbohydrate (xanthan-chitosan and a ternary polysaccharide complex) interactions.

Self crowding of globular proteins studied by small-angle x-ray scattering

Small-angle x-ray scattering (SAXS) was used to study the behavior of equine metmyoglobin (Mb) and bovine pancreatic trypsin inhibitor (BPTI) at concentrations up to 0.4 and 0.15 g/mL, respectively, in solutions also containing 50% D2O and 1 M urea. For both proteins, significant effects because of interference between x-rays scattered by different molecules (interparticle interference) were observed, indicating nonideal behavior at high concentrations. The experimental data were analyzed by comparison of the observed scattering profiles with those predicted by crystal structures of the proteins and a hard-sphere fluid model used to represent steric exclusion effects. The Mb scattering data were well fit by the hard-sphere model using a sphere radius of 18 Å, only slightly smaller than that estimated from the three-dimensional structure (20 Å). In contrast, the scattering profiles for BPTI in phosphate buffer displayed substantially less pronounced interparticle interference than predicted by the hard-sphere model and the radius estimated from the known structure of the protein (15 Å). Replacing the phosphate buffer with 3-(N-morpolino)propane sulfonic acid (MOPS) led to increased interparticle interference, consistent with a larger effective radius and suggesting that phosphate ions may mediate attractive intermolecular interactions, as observed in some BPTI crystal structures, without the formation of stable oligomers. The scattering data were also used to estimate second virial coefficients for the two proteins: 2.0 ×10(-4) cm(3)mol/g(2) for Mb in phosphate buffer, 1.6 ×10(-4) cm(3)mol/g(2) for BPTI in phosphate buffer and 9.2 ×10(-4) cm(3)mol/g(2) for BPTI in MOPS. The results indicate that the behavior of Mb, which is nearly isoelectric under the conditions used, is well described by the hard-sphere model, but that of BPTI is considerably more complex and is likely influenced by both repulsive and attractive electrostatic interactions. The hard-sphere model may be a generally useful tool for the analysis of small-angle scattering data from concentrated macromolecular solutions.

SEDFIT-MSTAR: molecular weight and molecular weight distribution analysis of polymers by sedimentation equilibrium in the ultracentrifuge

Sedimentation equilibrium (analytical ultracentrifugation) is one of the most inherently suitable methods for the determination of average molecular weights and molecular weight distributions of polymers, because of its absolute basis (no conformation assumptions) and inherent fractionation ability (without the need for columns or membranes and associated assumptions over inertness). With modern instrumentation it is also possible to run up to 21 samples simultaneously in a single run. Its application has been severely hampered because of difficulties in terms of baseline determination (incorporating estimation of the concentration at the air/solution meniscus) and complexity of the analysis procedures. We describe a new method for baseline determination based on a smart-smoothing principle and built into the highly popular platform SEDFIT for the analysis of the sedimentation behavior of natural and synthetic polymer materials. The SEDFIT-MSTAR procedure - which takes only a few minutes to perform - is tested with four synthetic data sets (including a significantly non-ideal system), a naturally occurring protein (human IgG1) and two naturally occurring carbohydrate polymers (pullulan and λ-carrageenan) in terms of (i) weight average molecular weight for the whole distribution of species in the sample (ii) the variation in "point" average molecular weight with local concentration in the ultracentrifuge cell and (iii) molecular weight distribution.

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.

Reactions of dipolar bio-molecules in nano-capsules--example of folding-unfolding process

The confinement of chemical reactions in nano-capsules can lead to a dramatic effect on the equilibrium constant of these latter. Indeed, capillary effects due to the curvature and surface energy of nano-capsules can alter in a noticeable way the evolution of reactions occurring within. Nano-encapsulation of bio-materials has attracted lately wide interest from the scientific community because of the great potential of its applications in biomedical areas and targeted therapies. The present paper focuses one's attention on alterations of conformation mechanisms due to extremely confining and interacting solvated dipolar macromolecules at their isoelectric point. As a specific example studied here, the folding-unfolding reaction of proteins (particularly RNase A and creatine kinase CK) is drastically changed when encapsulated in solid inorganic hollow nano-capsules. The effects demonstrated in this work can be extended to a wide variety of nano-encapsulation situations. The design and sizing of nano-capsules can even make use of the effects shown in the present study to achieve better and more effective encapsulation.

Insight into protein-protein interactions from analytical ultracentrifugation

Analytical ultracentrifugation is a free solution technique with no supplementary immobilization, columns or membranes required, and can be used to study self-association and hetero-interactions, stoichiometry, reversibility and interaction strength across a very large dynamic range (dissociation constants from 10(-12) M to 10(-1) M). In the present paper, we review some of the advances that have been made in the two different types of sedimentation experiment--sedimentation equilibrium and sedimentation velocity--for the analysis of protein-protein interactions and indicate how major complications such as thermodynamic and hydrodynamic non-ideality can be dealt with.

Insight into the integrase-DNA recognition mechanism. A specific DNA-binding mode revealed by an enzymatically labeled integrase

Integration catalyzed by integrase (IN) is a key process in the retrovirus life cycle. Many biochemical or structural human immunodeficiency virus, type 1 (HIV-1) IN studies have been severely impeded by its propensity to aggregate. We characterized a retroviral IN (primate foamy virus (PFV-1)) that displays a solubility profile different from that of HIV-1 IN. Using various techniques, including fluorescence correlation spectroscopy, time-resolved fluorescence anisotropy, and size exclusion chromatography, we identified a monomer-dimer equilibrium for the protein alone, with a half-transition concentration of 20-30 mum. We performed specific enzymatic labeling of PFV-1 IN and measured the fluorescence resonance energy transfer between carboxytetramethylrhodamine-labeled IN and fluorescein-labeled DNA substrates. FRET and fluorescence anisotropy highlight the preferential binding of PFV-1 IN to the 3'-end processing site. Sequence-specific DNA binding was not observed with HIV-1 IN, suggesting that the intrinsic ability of retroviral INs to bind preferentially to the processing site is highly underestimated in the presence of aggregates. IN is in a dimeric state for 3'-processing on short DNA substrates, whereas IN polymerization, mediated by nonspecific contacts at internal DNA positions, occurs on longer DNAs. Additionally, aggregation, mediated by nonspecific IN-IN interactions, occurs preferentially with short DNAs at high IN/DNA ratios. The presence of either higher order complex is detrimental for specific activity. Ionic strength favors catalytically competent over higher order complexes by selectively disrupting nonspecific IN-IN interactions. This counteracting effect was not observed with polymerization. The synergic effect on the selection of specific/competent complexes, obtained by using short DNA substrates under high salt conditions, may have important implications for further structural studies in IN.DNA complexes.

Hydrodynamic modeling: the solution conformation of macromolecules and their complexes

Hydrodynamic bead modeling (HBM) is the representation of a macromolecule by an assembly of spheres (or beads) for which measurable hydrodynamic (and related) parameters are then computed in order to understand better the macromolecular solution conformation. An example-based account is given of the main stages in HBM of rigid macromolecules, namely: model construction, model visualization, accounting for hydration, and hydrodynamic calculations. Different types of models are appropriate for different macromolecules, according to their composition, to what is known about the molecule or according to the types of experimental data that the model should reproduce. Accordingly, the construction of models based on atomic coordinates as well as much lower resolution data (e.g., electron microscopy images) is described. Similarly, several programs for hydrodynamic calculations are summarized, some generating the most basic set of solution parameters (e.g., sedimentation and translational diffusion coefficients, intrinsic viscosity, radius of gyration, and Stokes radius) while others extend to data determined by nuclear magnetic resonance, fluorescence anisotropy, and electric birefringence methods. An insight into the topic of hydrodynamic hydration is given, together with some practical suggestions for its satisfactory treatment in the modeling context. All programs reviewed are freely available.

Self-assembly of medium-chain alkyl monoglucosides in ammonium sulfate solutions with poly(ethylene glycol)

We study the phase behavior and microstructure of alkyl-beta-monoglucosides with intermediate chain lengths (octyl- and nonyl-beta-glucoside) in aqueous solutions containing ammonium sulfate and poly(ethylene glycol) (PEG). When the glucoside surfactants are mixed with PEG of molecular weight 3350 or larger, two different phase transitions are observed in the temperature range 0-100 degrees C, with lower and upper miscibility gaps separated by a one-phase isotropic region. Isothermal titration calorimetry is used to quantify the effect of PEG on the micellization properties of the alkyl monoglucosides, whereas small-angle neutron scattering gives insight into the microstructure of the surfactant/polymer mixtures near the liquid-liquid phase boundary. Results show that the range and the strength of the interactions in these solutions are highly affected by the presence of PEG. Solutions with nonyl-beta-glucoside contain larger micelles than those with octyl-beta-glucoside, and the intermicellar interactions are much stronger and longer ranged. The relevance of these findings for membrane protein crystallization is discussed.

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.

A new level of architectural complexity in the human pyruvate dehydrogenase complex

Mammalian pyruvate dehydrogenase multienzyme complex (PDC) is a key metabolic assembly comprising a 60-meric pentagonal dodecahedral E2 (dihydrolipoamide acetyltransferase) core attached to which are 30 pyruvate decarboxylase E1 heterotetramers and 6 dihydrolipoamide dehydrogenase E3 homodimers at maximal occupancy. Stable E3 integration is mediated by an accessory E3-binding protein (E3BP) located on each of the 12 E2 icosahedral faces. Here, we present evidence for a novel subunit organization in which E3 and E3BP form subcomplexes with a 1:2 stoichiometry implying the existence of a network of E3 "cross-bridges" linking pairs of E3BPs across the surface of the E2 core assembly. We have also determined a low resolution structure for a truncated E3BP/E3 subcomplex using small angle x-ray scattering showing one of the E3BP lipoyl domains docked into the E3 active site. This new level of architectural complexity in mammalian PDC contrasts with the recently published crystal structure of human E3 complexed with its cognate subunit binding domain and provides important new insights into subunit organization, its catalytic mechanism and regulation by the intrinsic PDC kinase.

Negative second virial coefficients as predictors of protein crystal growth: evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (BAA/MA) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, BAA/MA assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to BAA/MA but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive.

Protein charge determination

The most popular current method of determining protein valence entails the calculation of net charge from amino acid sequence/composition. However, the inaccuracy of that approach was recognized long before the advent of the protein data banks and computer programs to facilitate its adoption. Capillary zone electrophoresis affords the simplest and most economical procedure for obtaining a reliable estimate of the net charge of a protein in the buffer system of interest. This unit explains the major pitfalls in the calculation of net charge from protein sequence data.

Determination of protein charge by capillary zone electrophoresis

The feasibility of employing classical electrophoresis theory to determine the net charge (valence) of proteins by capillary zone electrophoresis is illustrated in this paper. An outline of a procedure to facilitate the interpretation of mobility measurements is demonstrated by its application to a published mobility measurement for Staphylococcal nuclease at pH 8.9 that had been obtained by capillary zone electrophoresis. The significantly higher valence of +7.5 (cf. 5.6 from the same series of measurements) that has been reported on the basis of a "charge ladder" approach for charge determination signifies the likelihood that the latter generic approach may be prone to error arising from nonconformity of the experimental system with an inherent assumption that chemical modification or mutation of amino acid residues has no effect on the overall three-dimensional size and shape of the protein.

Hydrodynamic properties of rigid macromolecules composed of ellipsoidal and cylindrical subunits

A procedure is devised for the calculation of hydrodynamic properties of rigid macromolecules composed subunits that are modeled as ellipsoids of revolution and cylinders. Owing to the axial symmetry of these shapes, smooth shell models can be constructured for the subunit structure. The bead shell model so constructed is employed for the calculation of the properties. A computer program, HYDROSUB, has been written implementing both the model building and the hydrodynamic calculation. A detailed example of the use of this methodology is presented for the case of the solution properties of the human antibody molecule immunoglobulin G3 (IgG3). Finally, hints are given on other uses and applications of the procedure.

Analysis of thermodynamic non-ideality in terms of protein solvation

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical-mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation parameter delta are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein-protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected.

Non-ideality by sedimentation velocity of halophilic malate dehydrogenase in complex solvents

We have investigated the potential of sedimentation velocity analytical ultracentrifugation for the measurement of the second virial coefficients of proteins, with the goal of developing a method that allows efficient screening of different solvent conditions. This may be useful for the study of protein crystallization. Macromolecular concentration distributions were modeled using the Lamm equation with the approximation of linear concentration dependencies of the diffusion constant, D = D(o) (1 + k(D)c), and the reciprocal sedimentation coefficient s = s(o)/(1 + k(s)c). We have studied model distributions for their information content with respect to the particle and its non-ideal behavior, developed a strategy for their analysis by direct boundary modeling, and applied it to data from sedimentation velocity experiments on halophilic malate dehydrogenase in complex aqueous solvents containing sodium chloride and 2-methyl-2,4-pentanediol, including conditions near phase separation. Using global modeling for three sets of data obtained at three different protein concentrations, very good estimates for k(s) and s degrees and also for D degrees and the buoyant molar mass were obtained. It was also possible to obtain good estimates for k(D) and the second virial coefficients. Modeling of sedimentation velocity profiles with the non-ideal Lamm equation appears as a good technique to investigate weak inter-particle interactions in complex solvents and also to extrapolate the ideal behavior of the particle.

A small-angle X-ray solution scattering study of bovine alpha-crystallin

The native high molecular mass form of alpha-crystallin, the most important soluble protein in the eye lens, and its low molecular mass form obtained at 37 degrees C in dilute solutions were investigated by synchrotron radiation small-angle X-ray scattering. The alpha-crystallin solutions are polydisperse and good fits to the experimental data can be obtained using distributions of spheres with radii varying between about 5 and 10 nm. In spite of the polydispersity, two different ab initio methods were used to retrieve low resolution shapes from the scattering data. These shapes correspond to the z-average structure of the oligomers. In the absence of any symmetry constraints, the scattering curves of the two forms of alpha-crystallin yield bean-like shapes. The shape corresponding to the low molecular mass form has about 20% less mass at the periphery. Imposing tetrahedral symmetry on the average structures worsens the fit to the experimental data. We emphasized the apparent contradiction between hydrodynamic and molecular properties of alpha-crystallin. An explanation was put forward based on the presence of solvent-exposed flexible C-terminal extensions. We present two bead models ('hollow globule with tentacles' and 'bean with tentacles') based on NMR and cryo-electron microscopy studies and discuss how well they correspond with our data from X-ray scattering, light scattering and analytical ultracentrifugation.

Viscosity analysis of the temperature dependence of the solution conformation of ovalbumin

The viscosity of ovalbumin aqueous solutions was studied as a function of temperature and of protein concentration. Viscosity-temperature dependence was discussed on the basis of the modified Arrhenius formula at temperatures ranging from 5 to 55 degrees C. The activation energy of viscous flow for hydrated and unhydrated ovalbumin was calculated. Viscosity-concentration dependence, in turn, was discussed on the basis of Mooney equation. It has been shown that the shape parameter S decreases with increasing temperature, and self-crowding factor K does not depend on temperature. At low concentration limit the numerical values of the intrinsic viscosity and of Huggins coefficient were calculated. A master curve relating the specific viscosity etasp to the reduced concentration c[eta], over the whole range of temperature, was obtained and the three ranges of concentrations: diluted, semi-diluted and concentrated, are discussed. It has been proved that the Mark-Houvink-Kuhn-Sakurada (MHKS) exponent for ovalbumin does not depend on temperature.

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.

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.

Novel size-independent modeling of the dilute solution conformation of the immunoglobulin IgG Fab' domain using SOLPRO and ELLIPS

The proliferation of hydrodynamic modeling strategies to represent the shape of quasirigid macromolecules in solution has been hampered by ambiguities caused by size. Universal shape parameters, independent of size, developed originally for ellipsoid modeling, are now available for modeling using the bead-shell approximation via the algorithm SOLPRO. This paper validates such a "size-independent" bead-shell approach by comparison with the exact hydrodynamics of 1) an ellipsoid of revolution and 2) a general triaxial ellipsoid (semiaxial ratios a/b, b/c) based on a fit using the routine ELLIPSE (. J. Mol. Graph. 1:30-38) to the chimeric (human/mouse) IgG Fab' B72.3; a similar fit is obtained for other Fabs. Size-independent application of the bead-shell approximation yields errors of only approximately 1% in frictional ratio based shape functions and approximately 3% in the radius of gyration. With the viscosity increment, errors have been reduced to approximately 3%, representing a significant improvement on earlier procedures. Combination of the Perrin frictional ratio function with the experimentally measured sedimentation coefficient for the same Fab' from B72.3 yields an estimate for the molecular hydration of the Fab' fragment of approximately (0.43 +/- 0.07) g/g. This value is compared to values obtained in a similar way for deoxyhemoglobin (0.44) and ribonuclease (0.27). The application of SOLPRO to the shape analysis of more complex macromolecules is indicated, and we encourage such size-independent strategies. The utility of modern sedimentation data analysis software such as SVEDBERG, DCDT, LAMM, and MSTAR is also clearly demonstrated.