Sedimentation equilibrium analysis of mixed associations using numerical constraints to impose mass or signal conservation

The Glucagon-Like Peptide 2 Analog Teduglutide Reversibly Associates to Form Pentamers

Glucagon-like peptide 1 and 2 and their analog peptide therapeutics are known to reversibly associate to form oligomers. Here we report the association properties of the glucagon-like peptide 2 analog teduglutide at concentrations up to ∼15 mg/mL. Both sedimentation equilibrium (SE-AUC) and sedimentation velocity (SV-AUC) show that teduglutide dissociates completely to monomers below 0.1 mg/mL. SE-AUC shows that the apparent weight-average molar mass increases substantially between 0.1 and 1 mg/mL, reaching a maximum of ∼14.5 kDa (∼3.9-mer) near 2 mg/mL, and then falling at higher concentrations because of strong solution nonideality effects (highly positive second virial coefficient). Circular dichroism spectra over the range from 0.1 to 2 mg/mL show that self-association is accompanied by significant increases in alpha-helix content, and that the associated state has a distinct tertiary structure. The SV-AUC data up to 2.2 mg/mL are fitted fairly well by an ideal rapidly reversible monomer-pentamer association. The SE-AUC modeling included thermodynamic nonideality effects. SE-AUC data up to ∼15 mg/mL imply a monomer-pentamer association at lower concentrations, but the pentamers also appear to weakly associate to form decamers. These results illustrate the importance of directly modeling the solution nonideality effects, which if neglected would lead to an incorrect preferred stoichiometry.

Optical control of cell signaling by single-chain photoswitchable kinases

Protein kinases transduce signals to regulate a wide array of cellular functions in eukaryotes. A generalizable method for optical control of kinases would enable fine spatiotemporal interrogation or manipulation of these various functions. We report the design and application of single-chain cofactor-free kinases with photoswitchable activity. We engineered a dimeric protein, pdDronpa, that dissociates in cyan light and reassociates in violet light. Attaching two pdDronpa domains at rationally selected locations in the kinase domain, we created the photoswitchable kinases psRaf1, psMEK1, psMEK2, and psCDK5. Using these photoswitchable kinases, we established an all-optical cell-based assay for screening inhibitors, uncovered a direct and rapid inhibitory feedback loop from ERK to MEK1, and mediated developmental changes and synaptic vesicle transport in vivo using light.

A composite polynomial approach for analyzing the indefinite self-association of macromolecules studied by sedimentation equilibrium

A different approach is described for analyzing sedimentation equilibrium experiments of indefinitely self-associating systems. The procedure involves application of conservation of mass criteria, along with local evaluation of the weight average molar mass, to generate a polynomial based on a composite pseudo-independent variable. The outlined method does not depend upon non-linear regression to generate a solution, but instead requires evaluation of the roots of a high-order polynomial.

Variable-Field Analytical Ultracentrifugation: I. Time-Optimized Sedimentation Equilibrium

Sedimentation equilibrium (SE) analytical ultracentrifugation (AUC) is a gold standard for the rigorous determination of macromolecular buoyant molar masses and the thermodynamic study of reversible interactions in solution. A significant experimental drawback is the long time required to attain SE, which is usually on the order of days. We have developed a method for time-optimized SE (toSE) with defined time-varying centrifugal fields that allow SE to be attained in a significantly (up to 10-fold) shorter time than is usually required. To achieve this, numerical Lamm equation solutions for sedimentation in time-varying fields are computed based on initial estimates of macromolecular transport properties. A parameterized rotor-speed schedule is optimized with the goal of achieving a minimal time to equilibrium while limiting transient sample preconcentration at the base of the solution column. The resulting rotor-speed schedule may include multiple over- and underspeeding phases, balancing the formation of gradients from strong sedimentation fluxes with periods of high diffusional transport. The computation is carried out in a new software program called TOSE, which also facilitates convenient experimental implementation. Further, we extend AUC data analysis to sedimentation processes in such time-varying centrifugal fields. Due to the initially high centrifugal fields in toSE and the resulting strong migration, it is possible to extract sedimentation coefficient distributions from the early data. This can provide better estimates of the size of macromolecular complexes and report on sample homogeneity early on, which may be used to further refine the prediction of the rotor-speed schedule. In this manner, the toSE experiment can be adapted in real time to the system under study, maximizing both the information content and the time efficiency of SE experiments.

Sedimentation equilibrium studies

The reversible formation of protein-protein interactions plays a crucial role in many biological processes. In order to carry out a thorough quantitative characterization of these interactions it is essential to establish the oligomerization state of the individual components first. The sedimentation equilibrium method is ideally suited to perform these studies because it allows a reliable, accurate, and absolute value of the solution molecular weight of a macromolecule to be obtained. This technique is independent of the shape of the macromolecule under investigation and allows the determination of equilibrium constants for a monomer-multimer self-associating system.

Multi-signal sedimentation velocity analysis with mass conservation for determining the stoichiometry of protein complexes

Multi-signal sedimentation velocity analytical ultracentrifugation (MSSV) is a powerful tool for the determination of the number, stoichiometry, and hydrodynamic shape of reversible protein complexes in two- and three-component systems. In this method, the evolution of sedimentation profiles of macromolecular mixtures is recorded simultaneously using multiple absorbance and refractive index signals and globally transformed into both spectrally and diffusion-deconvoluted component sedimentation coefficient distributions. For reactions with complex lifetimes comparable to the time-scale of sedimentation, MSSV reveals the number and stoichiometry of co-existing complexes. For systems with short complex lifetimes, MSSV reveals the composition of the reaction boundary of the coupled reaction/migration process, which we show here may be used to directly determine an association constant. A prerequisite for MSSV is that the interacting components are spectrally distinguishable, which may be a result, for example, of extrinsic chromophores or of different abundances of aromatic amino acids contributing to the UV absorbance. For interacting components that are spectrally poorly resolved, here we introduce a method for additional regularization of the spectral deconvolution by exploiting approximate knowledge of the total loading concentrations. While this novel mass conservation principle does not discriminate contributions to different species, it can be effectively combined with constraints in the sedimentation coefficient range of uncomplexed species. We show in theory, computer simulations, and experiment, how mass conservation MSSV as implemented in SEDPHAT can enhance or even substitute for the spectral discrimination of components. This should broaden the applicability of MSSV to the analysis of the composition of reversible macromolecular complexes.

Analytical Ultracentrifugation as a Tool for Studying Protein Interactions

The last two decades have led to significant progress in the field of analytical ultracentrifugation driven by instrumental, theoretical, and computational methods. This review will highlight key developments in sedimentation equilibrium (SE) and sedimentation velocity (SV) analysis. For SE, this includes the analysis of tracer sedimentation equilibrium at high concentrations with strong thermodynamic non-ideality, and for ideally interacting systems the development of strategies for the analysis of heterogeneous interactions towards global multi-signal and multi-speed SE analysis with implicit mass conservation. For SV, this includes the development and applications of numerical solutions of the Lamm equation, noise decomposition techniques enabling direct boundary fitting, diffusion deconvoluted sedimentation coefficient distributions, and multi-signal sedimentation coefficient distributions. Recently, effective particle theory has uncovered simple physical rules for the co-migration of rapidly exchanging systems of interacting components in SV. This has opened new possibilities for the robust interpretation of the boundary patterns of heterogeneous interacting systems. Together, these SE and SV techniques have led to new approaches to study macromolecular interactions across the entire the spectrum of affinities, including both attractive and repulsive interactions, in both dilute and highly concentrated solutions, which can be applied to single-component solutions of self-associating proteins as well as the study of multi-protein complex formation in multi-component solutions.

Overview of current methods in sedimentation velocity and sedimentation equilibrium analytical ultracentrifugation

Modern computational strategies have allowed for the direct modeling of the sedimentation process of heterogeneous mixtures, resulting in sedimentation velocity (SV) size-distribution analyses with significantly improved detection limits and strongly enhanced resolution. These advances have transformed the practice of SV, rendering it the primary method of choice for most existing applications of analytical ultracentrifugation (AUC), such as the study of protein self- and hetero-association, the study of membrane proteins, and applications in biotechnology. New global multisignal modeling and mass conservation approaches in SV and sedimentation equilibrium (SE), in conjunction with the effective-particle framework for interpreting the sedimentation boundary structure of interacting systems, as well as tools for explicit modeling of the reaction/diffusion/sedimentation equations to experimental data, have led to more robust and more powerful strategies for the study of reversible protein interactions and multiprotein complexes. Furthermore, modern mathematical modeling capabilities have allowed for a detailed description of many experimental aspects of the acquired data, thus enabling novel experimental opportunities, with important implications for both sample preparation and data acquisition. The goal of the current unit is to describe the current tools for the study of soluble proteins, detergent-solubilized membrane proteins and their interactions by SV and SE.

Analysis of high-affinity assembly for AMPA receptor amino-terminal domains

Analytical ultracentrifugation (AUC) and steady-state fluorescence anisotropy were used to measure the equilibrium dissociation constant (Kd) for formation of dimers by the amino-terminal domains (ATDs) of the GluA2 and GluA3 subtypes of AMPA receptor. Previous reports on GluA2 dimerization differed in their estimate of the monomer-dimer Kd by a 2,400-fold range, with no consensus on whether the ATD forms tetramers in solution. We find by sedimentation velocity (SV) analysis performed using absorbance detection a narrow range of monomer-dimer Kd values for GluA2, from 5 to 11 nM for six independent experiments, with no detectable formation of tetramers and no effect of glycosylation or the polypeptide linker connecting the ATD and ligand-binding domains; for GluA3, the monomer-dimer Kd was 5.6 µM, again with no detectable tetramer formation. For sedimentation equilibrium (SE) experiments, a wide range of Kd values was obtained for GluA2, from 13 to 284 nM, whereas for GluA3, the Kd of 3.1 µM was less than twofold different from the SV value. Analysis of cell contents after the ∼1-week centrifuge run by silver-stained gels revealed low molecular weight GluA2 breakdown products. Simulated data for SE runs demonstrate that the apparent Kd for GluA2 varies with the extent of proteolysis, leading to artificially high Kd values. SV experiments with fluorescence detection for GluA2 labeled with 5,6-carboxyfluorescein, and fluorescence anisotropy measurements for GluA2 labeled with DyLight405, yielded Kd values of 5 and 11 nM, consistent with those from SV with absorbance detection. However, the sedimentation coefficients measured by AUC using absorbance and fluorescence systems were strikingly different, and for the latter are not consistent with hydrodynamic protein models. Thus, for unknown reasons, the concentration dependence of sedimentation coefficients obtained with fluorescence detection SV may be unreliable, limiting the usefulness of this technique for quantitative analysis.

The analysis of macromolecular interactions by sedimentation equilibrium

The study of macromolecular interactions by sedimentation equilibrium is a highly technical method that requires great care in both the experimental design and data analysis. The complexity of the interacting system that can be analyzed is only limited by the ability to deconvolute the exponential contributions of each of the species to the overall concentration gradient. This is achieved in part through the use of multi-signal data collection and the implementation of soft mass conservation. We illustrate the use of these constraints in SEDPHAT through the study of an A+B+B⇌AB+B⇌ABB system and highlight some of the technical challenges that arise. We show that both the multi-signal analysis and mass conservation result in a precise and robust data analysis and discuss improvements that can be obtained through the inclusion of data from other methods such as sedimentation velocity and isothermal titration calorimetry.

Analysis of PKR activation using analytical ultracentrifugation

Protein kinase R (PKR) is a central component of the interferon antiviral defense pathway. Upon binding to dsRNA, PKR undergoes autophosphorylation reactions that activate the kinase, resulting in the inhibition of protein synthesis in virally-infected cells. We have used analytical ultracentrifugation and related biophysical methods to quantitatively characterize the stoichiometries, affinities, and free energy couplings that govern the assembly of the macromolecular complexes in the PKR activation pathway. These studies demonstrate that PKR dimerization play a key role in enzymatic activation and support a model where the role of dsRNA is to bring two or more PKR monomers in close proximity to enhance dimerization.

Reversibly bound chloride in the atrial natriuretic peptide receptor hormone-binding domain: possible allosteric regulation and a conserved structural motif for the chloride-binding site

The binding of atrial natriuretic peptide (ANP) to its receptor requires chloride, and it is chloride concentration dependent. The extracellular domain (ECD) of the ANP receptor (ANPR) contains a chloride near the ANP-binding site, suggesting a possible regulatory role. The bound chloride, however, is completely buried in the polypeptide fold, and its functional role has remained unclear. Here, we have confirmed that chloride is necessary for ANP binding to the recombinant ECD or the full-length ANPR expressed in CHO cells. ECD without chloride (ECD(-)) did not bind ANP. Its binding activity was fully restored by bromide or chloride addition. A new X-ray structure of the bromide-bound ECD is essentially identical to that of the chloride-bound ECD. Furthermore, bromide atoms are localized at the same positions as chloride atoms both in the apo and in the ANP-bound structures, indicating exchangeable and reversible halide binding. Far-UV CD and thermal unfolding data show that ECD(-) largely retains the native structure. Sedimentation equilibrium in the absence of chloride shows that ECD(-) forms a strongly associated dimer, possibly preventing the structural rearrangement of the two monomers that is necessary for ANP binding. The primary and tertiary structures of the chloride-binding site in ANPR are highly conserved among receptor-guanylate cyclases and metabotropic glutamate receptors. The chloride-dependent ANP binding, reversible chloride binding, and the highly conserved chloride-binding site motif suggest a regulatory role for the receptor bound chloride. Chloride-dependent regulation of ANPR may operate in the kidney, modulating ANP-induced natriuresis.

Analytical ultracentrifugation: sedimentation velocity and sedimentation equilibrium

Analytical ultracentrifugation (AUC) is a versatile and powerful method for the quantitative analysis of macromolecules in solution. AUC has broad applications for the study of biomacromolecules in a wide range of solvents and over a wide range of solute concentrations. Three optical systems are available for the analytical ultracentrifuge (absorbance, interference, and fluorescence) that permit precise and selective observation of sedimentation in real time. In particular, the fluorescence system provides a new way to extend the scope of AUC to probe the behavior of biological molecules in complex mixtures and at high solute concentrations. In sedimentation velocity (SV), the movement of solutes in high centrifugal fields is interpreted using hydrodynamic theory to define the size, shape, and interactions of macromolecules. Sedimentation equilibrium (SE) is a thermodynamic method where equilibrium concentration gradients at lower centrifugal fields are analyzed to define molecule mass, assembly stoichiometry, association constants, and solution nonideality. Using specialized sample cells and modern analysis software, researchers can use SV to determine the homogeneity of a sample and define whether it undergoes concentration-dependent association reactions. Subsequently, more thorough model-dependent analysis of velocity and equilibrium experiments can provide a detailed picture of the nature of the species present in solution and their interactions.

Measuring protein-protein interactions by equilibrium sedimentation

This unit describes basic principles and practice of sedimentation equilibrium analytical ultracentrifugation for the study of reversible protein interactions, such as the characterization of self-association, heterogeneous association, and binding stoichiometry, as well as the determination of association constants. Advanced tools such as mass conservation analysis, multiwavelength analysis, and global analysis are introduced and discussed in the context of the experimental design. A detailed protocol guiding the investigator through the experimental steps and the data analysis is available as an internet resource.

The Effect of Hinge Mutations on Effector Binding and Domain Rotation in Escherichia coli D-3-Phosphoglycerate Dehydrogenase

D-3-phosphoglycerate dehydrogenase (EC 1.1.1.95) from Escherichia coli contains two Gly-Gly sequences that have been shown previously to have the characteristics of hinge regions. One of these, Gly(336)-Gly(337), is found in the loop between the substrate binding domain and the regulatory domain. Changing these glycine residues to valine affected the sensitivity of the enzyme to inhibition by L-serine but not the extent of inhibition. The decrease in sensitivity was caused primarily by a decrease in the affinity of the enzyme for L-serine. These mutations also affected the domain rotation of the subunits in response to L-serine binding. A major conclusion of this study was that it defines a minimal limit on the necessary conformational changes leading to inhibition of enzyme activity. That is, some of the conformational differences seen in the native enzyme upon L-serine binding are not critical for inhibition, whereas others are maintained and may play important roles in inhibition and cooperativity. The structure of G336V demonstrates that the minimal effect of L-serine binding leading to inhibition of enzyme activity requires a domain rotation of approximately only 6 degrees in just two of the four subunits of the enzyme that are oriented diagonally across from each other in the tetramer. Moreover the structures show that both pairs of Asn190 to Asn190 hydrogen bonds across the subunit interfaces are necessary for activity. These observations are consistent with the half-the-sites activity, flip-flop mechanism proposed for this and other similar enzymes and suggest that the Asn190 hydrogen bonds may function in the conformational transition between alternate half-the-site active forms of the enzyme.

Self-association of adrenodoxin studied by using analytical ultracentrifugation

The mitochondrial steroid hydroxylase system of vertebrates utilizes adrenodoxin (Adx), a small iron-sulfur cluster protein of about 14 kDa as an electron carrier between a reductase and cytochrome P450. Although the crystal structure of this protein has been elucidated, the solution structure of Adx was discussed contrary in the literature [I.A. Pikuleva, K. Tesh, M.R. Waterman, Y. Kim, The tertiary structure of full-length bovine adrenodoxin suggests functional dimers, Arch. Biochem. Biophys. 373 (2000) 44-55; D. Beilke, R. Weiss, F. Löhr, P. Pristovsek, F. Hannemann, R. Bernhardt, H. Rüterjans, A new electron mechanism in mitochondrial steroid hydroxylase systems based on structural changes upon the reduction of adrenodoxin, Biochemistry 41 (2002) 7969-7978]. Therefore, it was necessary to study the self-association of this protein by using analytical ultracentrifugation over a larger concentration range. As could be demonstrated in sedimentation velocity experiments, as well as sedimentation equilibrium runs with explicit consideration of thermodynamic non-ideality, the full-length protein (residues 1-128) in the oxidized state resulted in a monomer-dimer equilibrium (K(a) approximately 3 x 10(2) M(-1)). For truncated Adx (1-108), as well as the reduced Adx, the association behavior was strongly reduced. The consequences of this behavior are discussed with respect to the physiological meaning for the Adx system.

Role of the PH domain in regulating in vitro autophosphorylation events required for reconstitution of PDK1 catalytic activity

In addition to its catalytic domain, phosphoinsositide-dependent protein kinase-1 (PDK1) contains a C-terminal pleckstrin homology (PH) domain, which binds the membrane-bound phosphatidylinositol (3,4,5)-triphosphate [PI(3,4,5)P3] second messenger. Here, we report in vitro kinetic, phosphopeptide mapping, and oligomerization studies that address the role of the PH domain in regulating specific autophosphorylation events, which are required for PDK1 catalytic activation. First, 'inactive' unphosphorylated forms of N-terminal His6 tagged full length (His6-PDK1) and catalytic domain constructs [His6-PDK1(Delta PH)] were generated by treatment with Lambda protein phosphatase (lambda PP). Reconstitution of lambda PP-treated His6-PDK1(Delta PH) catalytic activity required activation loop Ser-241 phosphorylation, which occurred only upon trans-addition of 'active' PDK1 with an apparent bimolecular rate constant of (app)k1(S241) = 374+/-29 M(-1) s(-1). In contrast, full length lambda PP-treated His6-PDK1 catalyzed Ser-241 cis-autophosphorylation with an apparent first-order rate constant of (app)k1(S241) = (5.0+/-1.5) x 10(-4) s(-1) but remained 'inactive'. Reconstitution of lambda PP-treated His(6)-PDK1 catalytic activity occurred only when autophosphorylated in the presence of PI(3,4,5)P3 containing vesicles. PI(3,4,5)P3 binding to the PH domain activated apparent first-order Ser-241 autophosphorylation by 20-fold [(app)k1(S241) = (1.1+/-0.1) x 10(-2) s(-1)] and also promoted biphasic Thr-513 trans-autophosphorylation [(app)k2(T513) = (4.9+/-1.1) x 10(2) M(-1) s(-1) and(app)k3(T513) = (1.5+/-0.2) x 10(3) M(-1) s(-1)]. The results of mutagenesis studies suggest that Thr-513 phosphorylation may cause dissociation of autoinhibitory contacts formed between the contiguous regulatory PH and catalytic kinase domains.

Sedimentation equilibrium analysis of protein interactions with global implicit mass conservation constraints and systematic noise decomposition

Sedimentation equilibrium is a powerful tool for the characterization of protein self-association and heterogeneous protein interactions. Frequently, it is applied in a configuration with relatively long solution columns and with equilibrium profiles being acquired sequentially at several rotor speeds. The present study proposes computational tools, implemented in the software SEDPHAT, for the global analysis of equilibrium data at multiple rotor speeds with multiple concentrations and multiple optical detection methods. The detailed global modeling of such equilibrium data can be a nontrivial computational problem. It was shown previously that mass conservation constraints can significantly improve and extend the analysis of heterogeneous protein interactions. Here, a method for using conservation of mass constraints for the macromolecular redistribution is proposed in which the effective loading concentrations are calculated from the sedimentation equilibrium profiles. The approach is similar to that described by Roark (Biophys. Chem. 5 (1976) 185-196), but its utility is extended by determining the bottom position of the solution columns from the macromolecular redistribution. For analyzing heterogeneous associations at multiple protein concentrations, additional constraints that relate the effective loading concentrations of the different components or their molar ratio in the global analysis are introduced. Equilibrium profiles at multiple rotor speeds also permit the algebraic determination of radial-dependent baseline profiles, which can govern interference optical ultracentrifugation data, but usually also occur, to a smaller extent, in absorbance optical data. Finally, the global analysis of equilibrium profiles at multiple rotor speeds with implicit mass conservation and computation of the bottom of the solution column provides an unbiased scale for determining molar mass distributions of noninteracting species. The properties of these tools are studied with theoretical and experimental data sets.

Re-examining the oligomerization state of macrophage migration inhibitory factor (MIF) in solution

The state of oligomerization of macrophage migration inhibitory factor (MIF, also known as glycosylation inhibiting factor, GIF) in solution has been variously reported as monomer, dimer, trimer, or mixtures of all three. Several crystal structures show MIF to be a trimer. Sedimentation velocity shows a recombinant human MIF sample is quite homogeneous, with 98% as a species with s(20,w)=3.07 S and D(20,w)=8.29 x 10(-7) cm(2)/s. Using the partial specific volume calculated from the amino acid composition these values imply a mass of 33.56 kDa, well above that of dimer, but also 9% below the trimer mass of 37.035 kDa. Sedimentation equilibrium data at loading concentrations from 0.01 to 1 mg/ml show unequivocally that the self-association is extremely tight. However, the apparent mass is 33.53 kDa [95% confidence 33.25-33.82], again 9% below that expected for 100% trimer. To examine the possibility this protein has an unusual partial specific volume, sedimentation equilibrium was also done in H(2)O/D(2)O mixtures, giving 0.765+/-0.017 ml/g rather than the calculated 0.735 ml/g. With this revised partial specific volume, the equilibrium and velocity data each give M=37.9+/-2.8 kDa, fully consistent with a strongly-associated trimeric quaternary structure.

Global analysis of non-specific protein-nucleic interactions by sedimentation equilibrium

Protein-nucleic acid interactions govern a variety of processes, including replication, transcription, recombination and repair. These interactions take place in both sequence-specific and non-specific modes, and the latter occur in many biologically significant contexts. Analytical ultracentrifugation is a useful method for the detailed characterization of the stoichiometry and affinity of macromolecular interactions in free solution. There has been a resurgence of interest in the application of sedimentation equilibrium methods to protein-nucleic acid interactions. However, these studies have been generally focused on sequence-specific interactions. Here we describe an approach to analyze non-specific interactions using sedimentation equilibrium. We have adapted an existing model for non-specific interaction of proteins with finite, one-dimensional nucleic acid lattices for global fitting of multiwavelength sedimentation equilibrium data. The model is extended to accommodate protein binding to multiple faces of the nucleic acid, resulting in overlap of consecutive ligands along the sequence of the RNA or DNA. The approach is illustrated in a sedimentation equilibrium analysis of the interaction of the double-stranded RNA binding motif of protein kinase R with a 20-basepair RNA construct.

Spinning with Dave: David Yphantis's contributions to ultracentrifugation

For nearly 50 years David Yphantis has helped advance analytical ultracentrifugation, promoted rigor in the thermodynamic analysis of biochemical data and encouraged students and colleagues to look for the deepest possible understanding of science. This article, written by five of Dave's students, presents some of the impressions he has made over the years.

On the analysis of protein self-association by sedimentation velocity analytical ultracentrifugation

Analytical ultracentrifugation is one of the classical techniques for the study of protein interactions and protein self-association. Recent instrumental and computational developments have significantly enhanced this methodology. In this paper, new tools for the analysis of protein self-association by sedimentation velocity are developed, their statistical properties are examined, and considerations for optimal experimental design are discussed. A traditional strategy is the analysis of the isotherm of weight-average sedimentation coefficients s(w) as a function of protein concentration. From theoretical considerations, it is shown that integration of any differential sedimentation coefficient distribution c(s), ls-g(*)(s), or g(s(*)) can give a thermodynamically well-defined isotherm, as long as it provides a good model for the sedimentation profiles. To test this condition for the g(s(*)) distribution, a back-transform into the original data space is proposed. Deconvoluting diffusion in the sedimentation coefficient distribution c(s) can be advantageous to identify species that do not participate in the association. Because of the large number of scans that can be analyzed in the c(s) approach, its s(w) values are very precise and allow extension of the isotherm to very low concentrations. For all differential sedimentation coefficients, corrections are derived for the slowing of the sedimentation boundaries caused by radial dilution. As an alternative to the interpretation of the isotherm of the weight-average s value, direct global modeling of several sedimentation experiments with Lamm equation solutions was studied. For this purpose, a new software SEDPHAT is introduced, allowing the global analysis of several sedimentation velocity and equilibrium experiments. In this approach, information from the shape of the sedimentation profiles is exploited, which permits the identification of the association scheme and requires fewer experiments to precisely characterize the association. Further, under suitable conditions, fractions of incompetent material that are not part of the reversible equilibrium can be detected.

Modern analytical ultracentrifugation in protein science: a tutorial review

Analytical ultracentrifugation (AU) is reemerging as a versatile tool for the study of proteins. Monitoring the sedimentation of macromolecules in the centrifugal field allows their hydrodynamic and thermodynamic characterization in solution, without interaction with any matrix or surface. The combination of new instrumentation and powerful computational software for data analysis has led to major advances in the characterization of proteins and protein complexes. The pace of new advancements makes it difficult for protein scientists to gain sufficient expertise to apply modern AU to their research problems. To address this problem, this review builds from the basic concepts to advanced approaches for the characterization of protein systems, and key computational and internet resources are provided. We will first explore the characterization of proteins by sedimentation velocity (SV). Determination of sedimentation coefficients allows for the modeling of the hydrodynamic shape of proteins and protein complexes. The computational treatment of SV data to resolve sedimenting components has been achieved. Hence, SV can be very useful in the identification of the oligomeric state and the stoichiometry of heterogeneous interactions. The second major part of the review covers sedimentation equilibrium (SE) of proteins, including membrane proteins and glycoproteins. This is the method of choice for molar mass determinations and the study of self-association and heterogeneous interactions, such as protein-protein, protein-nucleic acid, and protein-small molecule binding.

BetaCore, a designed water soluble four-stranded antiparallel beta-sheet protein

BetaCore is a designed approximately 50-residue protein in which two BPTI-derived core modules, CM I and CM II, are connected by a 22-atom cross-link. At low temperature and pH 3, homo- and heteronuclear NMR data report a dominant folded ('f') conformation with well-dispersed chemical shifts, i, i+1 periodicity, numerous long-range NOEs, and slowed amide hydrogen isotope exchange patterns that is a four-stranded antiparallel beta-sheet with nonsymmetrical and specific association of CM I and CM II. BetaCore 'f' conformations undergo reversible, global, moderately cooperative, non-two-state thermal transitions to an equilibrium ensemble of unfolded 'u' conformations. There is a significant energy barrier between 'f' and 'u' conformations. This is the first designed four-stranded antiparallel beta-sheet that folds in water.

Studies of the ankyrin repeats of the Drosophila melanogaster Notch receptor. 1. Solution conformational and hydrodynamic properties

To gain insight into the structural basis for Notch signaling, and to investigate the relationship between structure and stability in ankyrin repeat proteins, we have examined structural features of polypeptides from the Drosophila melanogaster Notch protein that contain five, six, and a putative seventh ankyrin repeat. Circular dichroism (CD) spectroscopy indicates that Notch ankyrin polypeptides of different length contain a significant amount of alpha-helix, indicating that a folded structure can be maintained despite the loss of individual ankyrin modules. However, the alpha-helical content of the construct with the putative seventh repeat is slightly higher than polypeptides containing fewer repeats, suggesting that the putative seventh repeat may help stabilize other parts of the ankyrin domain. Fluorescence spectroscopy indicates that the single tryptophan in the fifth ankyrin repeat is in a nonpolar environment and is shielded from solvent in all three constructs, although slight differences in spectroscopic properties of the six- and five-repeat constructs are observed, indicating minor structural changes. Near-UV CD indicates that these ankyrin polypeptides contain a significant amount of fixed tertiary structure surrounding their aromatic side chains. Gel filtration chromatography and sedimentation equilibrium studies indicate that these ankyrin repeat polypeptides are monomeric. Sedimentation velocity studies indicate that each polypeptide exhibits significant axial asymmetry, consistent with the elongated structure seen for other for ankyrin repeat proteins. However, the degree of asymmetry is greatest for the construct containing six repeats, suggesting that in the absence of the putative seventh repeat, the sixth repeat is partly unfolded.

Sedimentation studies reveal a direct role of phosphorylation in Smad3:Smad4 homo- and hetero-trimerization

SMAD proteins are known to oligomerize and hetero-associate during their activation and translocation to the nucleus for transcriptional control. Analytical ultracentrifuge studies on Smad3 and Smad4 protein constructs are presented to clarify the model of homo- and hetero-oligomerization and the role of phosphorylation in the activation process. These constructs all exhibit a tendency to form disulfide cross-linked aggregates, primarily dimers, and a strong reducing agent, TCEP, was found to be required to determine the best estimates for reversible association models and equilibrium constants. A Smad4 construct, S4AF, consisting of the middle linker (L) domain and the C-terminal (C) domain, is shown to be a monomer, while a Smad3 construct, S3LC, consisting of the LC domains, is shown to form a trimer with an affinity K(3) = (1.2-3.1) x 10(9) M(-2). A Smad3 construct that mimics phosphorylation at the C-terminal target sequence, S3LC(3E), has 17--35-fold enhanced ability to form trimer over that of the wild-type construct, S3LC. S4AF associates with either S3LC or S3LC(3E) to form a hetero-trimer. In each case, the hetero-trimer is favored over the formation of the homo-trimer. Despite high sequence homology between Smad3 and Smad4, a chimeric Smad4 construct with an engineered Smad3 C-terminal pseudo-phosphorylation sequence, S4AF(3E), shows no tendency to form trimer. This suggests a Smad4-specific sequence insert inhibits homo-trimer formation, or other domains or sequences in S3LC are required in addition to the target sequence to mediate the formation of trimer. These results represent a direct molecular measure of the importance of hetero-trimerization and phosphorylation in the TGF-beta-activated Smad protein signal transduction process.

Vinca alkaloid-induced tubulin spiral formation correlates with cytotoxicity in the leukemic L1210 cell line

The ability of a class of C-20' modified vinca alkaloid congeners to induce tubulin spiral formation was investigated relative to their ability to inhibit microtubule assembly, their cytotoxicity against a leukemic cell line, L1210, and their measured and calculated partition coefficients. These studies were prompted by the observation that the energetics of vinca alkaloid-induced tubulin spiral polymers, or spiraling potential, is inversely related to their clinical dosage and are aimed at the long-term goal of developing the ability to predict the cytotoxic and antineoplastic properties of antimitotic drugs. We demonstrate here that vinca-induced tubulin-spiraling potential is significantly correlated with cytotoxicity against L1210 cells. This is consistent with the size of spirals formed being proportional to the relaxation time for polymer redistribution, the lifetime of cell retention, and effects on microtubule ends and dynamics. Spiraling potential also correlates with calculated but not measured partition coefficients. Surprisingly, spiraling potential does not correlate with the ability to inhibit microtubule formation with purified tubulin or microtubule protein. For the set of C-20' modified compounds studied, the largest inhibitory effects on spiraling potential and cytotoxicity are caused by multiple sites of halogen (-F, -Cl) substitution with the introduction of increased rigidity in the ring. This suggests the C-20' position interacts with a hydrogen bond acceptor or an electrophilic region on the protein that electrostatically disfavors halogen substitutions. These studies are discussed in terms of the cellular mode of action of antimitotic drugs, particularly the importance of microtubule dynamics during mitosis and the factors that regulate those dynamics.