Extracting equilibrium constants from kinetically limited reacting systems

Hydrodynamic and thermodynamic analysis of PEGylated human serum albumin

Covalent labeling of therapeutic drugs and proteins with polyethylene glycol (PEGylation) is an important modification for improving stability, solubility, and half-life. PEGylation alters protein solution behavior through its impact on thermodynamic nonideality by increasing the excluded volume, and on hydrodynamic nonideality by increasing the frictional drag. To understand PEGylation's impact, we investigated the thermodynamic and hydrodynamic properties of a model system consisting of PEGylated human serum albumin derivatives using analytical ultracentrifugation (AUC) and dynamic light scattering (DLS). We constructed PEGylated human serum albumin derivatives of single, linear 5K, 10K, 20K, and 40K PEG chains and a single branched-chain PEG of 40K (2 × 20K). Sedimentation velocity (SV) experiments were analyzed using SEDANAL direct boundary fitting to extract ideal sedimentation coefficients so, hydrodynamic nonideality ks, and thermodynamic nonideality 2BM1SV terms. These quantities allow the determination of the Stokes radius Rs, the frictional ratio f/fo, and the swollen or entrained volume Vs/v, which measure size, shape, and solvent interaction. We performed sedimentation equilibrium experiments to obtain independent measurements of thermodynamic nonideality 2BM1SE. From DLS measurements, we determined the interaction parameter, kD, the concentration dependence of the apparent diffusion coefficient, D, and from extrapolation of D to c = 0 a second estimate of Rs. Rs values derived from SV and DLS measurements and ensemble model calculations (see complementary study) are then used to show that ks + kD = theoretical 2B22M1. In contrast, experimental BM1 values from SV and sedimentation equilibrium data collectively allow for similar analysis for protein-PEG conjugates and show that ks + kD = 1.02-1.07∗BM1, rather than the widely used ks + kD = 2BM1 developed for hard spheres. The random coil behavior of PEG dominates the colloidal properties of PEG-protein conjugates and exceeds the sum of a random coil and hard-sphere volume due to excess entrained water.

Sedimentation velocity FDS studies of antibodies in pooled human serum

The biotech industry has great interest in investigating therapeutic proteins in high concentration environments like human serum. The fluorescence detection system (Aviv-FDS) allows the performance of analytical ultracentrifuge (AUC) sedimentation velocity (SV) experiments in tracer or BOLTS protocols. Here, we compare six pooled human serum samples by AUC SV techniques and demonstrate the potential of this technology for characterizing therapeutic antibodies in serum. Control FDS SV experiments on serum alone reveal a bilirubin-HSA complex whose sedimentation is slowed by solution nonideality and exhibits a Johnston-Ogston (JO) effect due to the presence of high concentrations of IgG. Absorbance SV experiments on diluted serum samples verify the HSA-IgG composition as well as a significant IgM pentamer boundary at 19 s. Alexa-488 labeled Simponi (Golimumab) is used as a tracer to investigate the behavior of a therapeutic monoclonal antibody (mAb) in serum, and the sedimentation behavior of total IgG in serum. Serum dilution experiments allow extrapolation to zero concentration to extract so, while global direct boundary fitting with SEDANAL verifies the utility of a matrix of self- and cross-term phenomenological nonideality coefficients (ks and BM1) and the source of the JO effect. The best fits include weak reversible association (~ 4 × 103 M-1) between Simponi and total human IgG. Secondary mAbs to human IgG and IgM verify the formation of a 10.2 s 1:1 complex with human IgG and a 19 s complex with human IgM pentamers. These results demonstrate that FDS AUC allows a range of approaches for investigating therapeutic antibodies in human serum.

Energetic Dissection of Mab-Specific Reversible Self-Association Reveals Unique Thermodynamic Signatures

PURPOSE

Reversible self-association (RSA) remains a challenge in the development of therapeutic monoclonal antibodies (mAbs). We recently analyzed the energetics of RSA for five IgG mAbs (designated as A-E) under matched conditions and using orthogonal methods. Here we examine the thermodynamics of RSA for two of the mAbs that showed the strongest evidence of RSA (mAbs C and E) to identify underlying mechanisms.

METHODS

Concentration-dependent dynamic light scattering and sedimentation velocity (SV) studies were carried out for each mAb over a range of temperatures. Because self-association was weak, the SV data were globally analyzed via direct boundary fitting to identify best-fit models, accurately determine interaction energetics, and account for the confounding effects of thermodynamic and hydrodynamic nonideality.

RESULTS

mAb C undergoes isodesmic self-association at all temperatures examined, with the energetics indicative of an enthalpically-driven reaction offset by a significant entropic penalty. By contrast, mAb E undergoes monomer-dimer self-association, with the reaction being entropically-driven and comprised of only a small enthalpic contribution.

CONCLUSIONS

Classical interpretations implicate van der Waals interactions and H-bond formation for mAb C RSA, and electrostatic interactions for mAb E. However, noting that RSA is likely coupled to additional equilibria, we also discuss the limitations of such interpretations.

The staphylococcal biofilm protein Aap forms a tetrameric species as a necessary intermediate before amyloidogenesis

The accumulation-associated protein (Aap) from Staphylococcus epidermidis is a biofilm-related protein that was found to be a critical factor for infection using a rat catheter model. The B-repeat superdomain of Aap, composed of 5-17 B-repeats, each containing a Zn²⁺-binding G5 and a spacer subdomain, is responsible for Zn²⁺-dependent assembly leading to accumulation of bacteria during biofilm formation. We previously demonstrated that a minimal B-repeat construct (Brpt1.5) forms an antiparallel dimer in the presence of 2-3 Zn²⁺ ions. More recently, we have reported the presence of functional amyloid-like fibrils composed of Aap within S. epidermidis biofilms and demonstrated that a biologically relevant construct containing five and a half B-repeats (Brpt5.5) forms amyloid-like fibrils similar to those observed in the biofilm. In this study, we analyze the initial assembly events of the Brpt5.5 construct. Analytical ultracentrifugation was utilized to determine hydrodynamic parameters of reversibly associating species and to perform linked equilibrium studies. Linkage studies indicated a mechanism of Zn²⁺-induced dimerization similar to smaller constructs; however, Brpt5.5 dimers could then undergo further Zn²⁺-induced assembly into a previously uncharacterized tetramer. This led us to search for potential Zn²⁺-binding sites outside of the dimer interface. We developed a Brpt5.5 mutant that was unable to form the tetramer and was concordantly incapable of amyloidogenesis. CD and dynamic light scattering indicate that a conformational transition in the tetramer species is a critical step preceding amyloidogenesis. This mechanistic model for B-repeat assembly and amyloidogenesis provides new avenues for potential therapeutic targeting of staphylococcal biofilms.

Modeling the Early Stages of Phase Separation in Disordered Elastin-like Proteins

Elastin-like proteins (ELPs) are known to undergo liquid-liquid phase separation reversibly above a concentration-dependent transition temperature. Previous studies suggested that, as temperature increases, ELPs experience an increased propensity for type II β-turns. However, how the ELPs behave below the phase transition temperature itself is still elusive. Here, we investigate the importance of β-turn formation during the early stages of ELP self-association. We examined the behavior of two ELPs, a 150-repeat construct that had been investigated previously (ELP[V5G3A2-150] as well as a new 40-repeat construct (ELP40) suitable for nuclear magnetic resonance measurements. Structural analysis of ELP40 reveals a disordered conformation, and chemical shifts throughout the sequence are insensitive to changes in temperature over 20°C. However, a low population of β-turn conformation cannot be ruled out based on chemical shifts alone. To examine the structural consequences of β-turns in ELPs, a series of structural ensembles of ELP[V5G3A2-150] were generated, incorporating differing amounts of β-turn bias throughout the chain. To mimic the early stages of the phase change, two monomers were paired, assuming preferential interaction at β-turn regions. This approach was justified by the observation that buried hydrophobic turns are commonly observed to interact in the Protein Data Bank. After dimerization, the ensemble-averaged hydrodynamic properties were calculated for each degree of β-turn bias, and the results were compared with analytical ultracentrifugation experiments at various temperatures. We find that the temperature dependence of the sedimentation coefficient (s20,wo) can be reproduced by increasing the β-turn content in the structural ensemble. This analysis allows us to estimate the presence of β-turns and weak associations under experimental conditions. Because disordered proteins frequently exhibit weak biases in secondary structure propensity, these experimentally-driven ensemble calculations may complement existing methods for modeling disordered proteins generally.

Determination of Interaction Parameters for Reversibly Self-Associating Antibodies: A Comparative Analysis

Monoclonal antibodies (mAbs) represent a major class of biotherapeutics and are the fastest growing category of biologic drugs on the market. However, mAb development and formulation are often impeded by reversible self-association (RSA), defined as the dynamic exchange of monomers with native-state oligomers. Here, we present a comparative analysis of the self-association properties for 5 IgG mAbs, under matched conditions and using orthogonal methods. Concentration-dependent dynamic light scattering and sedimentation velocity studies revealed that the majority of mAbs examined exhibited weak to moderate RSA. However, because these studies were carried out at mAb concentrations in the mg/mL range, we also observed significant nonideality. Noting that nonideality frequently masks RSA and vice versa, we conducted direct boundary fitting of the sedimentation velocity data to determine stoichiometric binding models, interaction affinities, and nonideality terms for each mAb. These analyses revealed equilibrium constants from micromolar to millimolar and stoichiometric models from monomer-dimer to isodesmic. Moreover, even for those mAbs described by identical models, we observed distinct kinetics of self-association. The accuracy of the models and their corresponding equilibrium constants were addressed using sedimentation equilibrium and simulations. Overall, these results serve as the starting point for the comparative dissection of RSA mechanisms in therapeutic mAbs.

Analytical ultracentrifugation in structural biology

Researchers in the field of structural biology, especially X-ray crystallography and protein nuclear magnetic resonance, are interested in knowing as much as possible about the state of their target protein in solution. Not only is this knowledge relevant to studies of biological function, it also facilitates determination of a protein structure using homogeneous monodisperse protein samples. A researcher faced with a new protein to study will have many questions even after that protein has been purified. Analytical ultracentrifugation (AUC) can provide all of this information readily from a small sample in a non-destructive way, without the need for labeling, enabling structure determination experiments without any wasting time and material on uncharacterized samples. In this article, I use examples to illustrate how AUC can contribute to protein structural analysis. Integrating information from a variety of biophysical experimental methods, such as X-ray crystallography, small angle X-ray scattering, electrospray ionization-mass spectrometry, AUC allows a more complete understanding of the structure and function of biomacromolecules.

Use of fluorescence-detected sedimentation velocity to study high-affinity protein interactions

Sedimentation velocity (SV) analytical ultracentrifugation (AUC) is a classic technique for the real-time observation of free macromolecular migration in solution driven by centrifugal force. This enables the analysis of macromolecular mass, shape, size distribution, and interactions. Although traditionally limited to determination of the sedimentation coefficient and binding affinity of proteins in the micromolar range, the implementation of modern detection and data analysis techniques has resulted in marked improvements in detection sensitivity and size resolution during the past decades. Fluorescence optical detection now permits the detection of recombinant proteins with fluorescence excitation at 488 or 561 nm at low picomolar concentrations, allowing for the study of high-affinity protein self-association and hetero-association. Compared with other popular techniques for measuring high-affinity protein-protein interactions, such as biosensing or calorimetry, the high size resolution of complexes at picomolar concentrations obtained with SV offers a distinct advantage in sensitivity and flexibility of the application. Here, we present a basic protocol for carrying out fluorescence-detected SV experiments and the determination of the size distribution and affinity of protein-antibody complexes with picomolar KD values. Using an EGFP-nanobody interaction as a model, this protocol describes sample preparation, ultracentrifugation, data acquisition, and data analysis. A variation of the protocol applying traditional absorbance or an interference optical system can be used for protein-protein interactions in the micromolar KD value range. Sedimentation experiments typically take ∼3 h of preparation and 6-12 h of run time, followed by data analysis (typically taking 1-3 h).

Transient-State Kinetic Analysis of the RNA Polymerase I Nucleotide Incorporation Mechanism

Eukaryotes express three or more multisubunit nuclear RNA polymerases (Pols) referred to as Pols I, II, and III, each of which synthesizes a specific subset of RNAs. Consistent with the diversity of their target genes, eukaryotic cells have evolved divergent cohorts of transcription factors and enzymatic properties for each RNA polymerase system. Over the years, many trans-acting factors that orchestrate transcription by the individual Pols have been described; however, little effort has been devoted to characterizing the molecular mechanisms of Pol I activity. To begin to address this gap in our understanding of eukaryotic gene expression, here we establish transient-state kinetic approaches to characterize the nucleotide incorporation mechanism of Pol I. We collected time courses for single turnover nucleotide incorporation reactions over a range of substrate ATP concentrations that provide information on both Pol I's nucleotide addition and nuclease activities. The data were analyzed by model-independent and model-dependent approaches, resulting in, to our knowledge, the first minimal model for the nucleotide addition pathway for Pol I. Using a grid searching approach we provide rigorous bounds on estimated values of the individual elementary rate constants within the proposed model. This work reports the most detailed analysis of Pol I mechanism to date. Furthermore, in addition to their use in transient state kinetic analyses, the computational approaches applied here are broadly applicable to global optimization problems.

Analysis of Linked Equilibria

The ATPases associated with diverse cellular activities (AAA+) is a large superfamily of proteins involved in a broad array of biological processes. Many members of this family require nucleotide binding to assemble into their final active hexameric form. We have been studying two example members, Escherichia coli ClpA and ClpB. These two enzymes are active as hexameric rings that both require nucleotide binding for assembly. Our studies have shown that they both reside in a monomer, dimer, tetramer, and hexamer equilibrium, and this equilibrium is thermodynamically linked to nucleotide binding. Moreover, we are finding that the kinetics of the assembly reaction are very different for the two enzymes. Here, we present our strategy for determining the self-association constants in the absence of nucleotide to set the stage for the analysis of nucleotide binding from other experimental approaches including analytical ultracentrifugation.

Calculations and Publication-Quality Illustrations for Analytical Ultracentrifugation Data

The analysis of analytical ultracentrifugation (AUC) data has been greatly facilitated by the advances accumulated in recent years. These improvements include refinements in AUC-based binding isotherms, advances in the fitting of both sedimentation velocity (SV) and sedimentation equilibrium (SE) data, and innovations in calculations related to posttranslationally modified proteins and to proteins with a large amount of associated cosolute, e.g., detergents. To capitalize on these advances, the experimenter often must prepare and collate multiple data sets and parameters for subsequent analyses; these tasks can be cumbersome and unclear, especially for new users. Examples are the sorting of concentration-profile scans for SE data, the integration of sedimentation velocity distributions (c(s)) to arrive at weighted-average binding isotherms, and the calculations to determine the oligomeric state of glycoproteins and membrane proteins. The significant organizational and logistical hurdles presented by these approaches are streamlined by the software described herein, called GUSSI. GUSSI also creates publication-quality graphics for documenting and illustrating AUC and other biophysical experiments with minimal effort on the user's part. The program contains three main modules, allowing for plotting and calculations on c(s) distributions, SV signal versus radius data, and general data/fit/residual plots.

A histogram approach to the quality of fit in sedimentation velocity analyses

The quality of fit of sedimentation velocity data is critical to judge the veracity of the sedimentation model and accuracy of the derived macromolecular parameters. Absolute statistical measures are usually complicated by the presence of characteristic systematic errors and run-to-run variation in the stochastic noise of data acquisition. We present a new graphical approach to visualize systematic deviations between data and model in the form of a histogram of residuals. In comparison with the ideally expected Gaussian distribution, it can provide a robust measure of fit quality and be used to flag poor models.

Accounting for photophysical processes and specific signal intensity changes in fluorescence-detected sedimentation velocity

Fluorescence detected sedimentation velocity (FDS-SV) has emerged as a powerful technique for the study of high-affinity protein interactions, with hydrodynamic resolution exceeding that of diffusion-based techniques, and with sufficient sensitivity for binding studies at low picomolar concentrations. For the detailed quantitative analysis of the observed sedimentation boundaries, it is necessary to adjust the conventional sedimentation models to the FDS data structure. A key consideration is the change in the macromolecular fluorescence intensity during the course of the experiment, caused by slow drifts of the excitation laser power, and/or by photophysical processes. In the present work, we demonstrate that FDS-SV data have inherently a reference for the time-dependent macromolecular signal intensity, resting on a geometric link between radial boundary migration and plateau signal. We show how this new time-domain can be exploited to study molecules exhibiting photobleaching and photoactivation. This expands the application of FDS-SV to proteins tagged with photoswitchable fluorescent proteins, organic dyes, or nanoparticles, such as those recently introduced for subdiffraction microscopy and enables FDS-SV studies of their interactions and size distributions. At the same time, we find that conventional fluorophores undergo minimal photobleaching under standard illumination in the FDS. These findings support the application of a high laser power density for the detection, which we demonstrate can further increase the signal quality.

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.

Microtubule-associated proteins and tubulin interaction by isothermal titration calorimetry

Microtubules play an important role in a number of vital cell processes such as cell division, intracellular transport, and cell architecture. The highly dynamic structure of microtubules is tightly regulated by a number of stabilizing and destabilizing microtubule-associated proteins (MAPs), such as tau and stathmin. Because of their importance, tubulin-MAPs interactions have been extensively studied using various methods that provide researchers with complementary but sometimes contradictory thermodynamic data. Isothermal titration calorimetry (ITC) is the only direct thermodynamic method that enables a full thermodynamic characterization (stoichiometry, enthalpy, entropy of binding, and association constant) of the interaction after a single titration experiment. This method has been recently applied to study tubulin-MAPs interactions in order to bring new insights into molecular mechanisms of tubulin regulation. In this chapter, we review the technical specificity of this method and then focus on the use of ITC in the investigation of tubulin-MAPs binding. We describe technical issues which could arise during planning and carrying out the ITC experiments, in particular with fragile proteins such as tubulin. Using examples of stathmin and tau, we demonstrate how ITC can be used to gain major insights into tubulin-MAP interaction.

Analysis of a glucocorticoid-estrogen receptor chimera reveals that dimerization energetics are under ionic control

Steroid receptors assemble at DNA response elements as dimers, resulting in coactivator recruitment and transcriptional activation. Our work has focused on dissecting the energetics associated with these events and quantitatively correlating the results with function. A recent finding is that different receptors dimerize with large differences in energetics. For example, estrogen receptor-α (ER-α) dimerizes with a ΔG=-12.0 kcal/mol under conditions in which the glucocorticoid receptor (GR) dimerizes with a ΔG≤-5.1 kcal/mol. To determine the molecular forces responsible for such differences, we created a GR/ER chimera, replacing the hormone-binding domain (HBD) of GR with that of ER-α. Cellular and biophysical analyses demonstrate that the chimera is functionally active. However, GR/ER dimerization energetics are intermediate between the parent proteins and coupled to a strong ionic linkage. Since the ER-α HBD is the primary contributor to dimerization, we suggest that GR residues constrain an ion-regulated HBD assembly reaction.

Bovine β-lactoglobulin is dimeric under imitative physiological conditions: dissociation equilibrium and rate constants over the pH range of 2.5-7.5

The oligomerization of β-lactoglobulin (βLg) has been studied extensively, but with somewhat contradictory results. Using analytical ultracentrifugation in both sedimentation equilibrium and sedimentation velocity modes, we studied the oligomerization of βLg variants A and B over a pH range of 2.5-7.5 in 100 mM NaCl at 25°C. For the first time, to our knowledge, we were able to estimate rate constants (k(off)) for βLg dimer dissociation. At pH 2.5 k(off) is low (0.008 and 0.009 s(-1)), but at higher pH (6.5 and 7.5) k(off) is considerably greater (>0.1 s(-1)). We analyzed the sedimentation velocity data using the van Holde-Weischet method, and the results were consistent with a monomer-dimer reversible self-association at pH 2.5, 3.5, 6.5, and 7.5. Dimer dissociation constants K(D)(2-1) fell close to or within the protein concentration range of ∼5 to ∼45 μM, and at ∼45 μM the dimer predominated. No species larger than the dimer could be detected. The K(D)(2-1) increased as |pH-pI| increased, indicating that the hydrophobic effect is the major factor stabilizing the dimer, and suggesting that, especially at low pH, electrostatic repulsion destabilizes the dimer. Therefore, through Poisson-Boltzmann calculations, we determined the electrostatic dimerization energy and the ionic charge distribution as a function of ionic strength at pH above (pH 7.5) and below (pH 2.5) the isoelectric point (pI∼5.3). We propose a mechanism for dimer stabilization whereby the added ionic species screen and neutralize charges in the vicinity of the dimer interface. The electrostatic forces of the ion cloud surrounding βLg play a key role in the thermodynamics and kinetics of dimer association/dissociation.

The interdomain linker of AAV-2 Rep68 is an integral part of its oligomerization domain: role of a conserved SF3 helicase residue in oligomerization

The four Rep proteins of adeno-associated virus (AAV) orchestrate all aspects of its viral life cycle, including transcription regulation, DNA replication, virus assembly, and site-specific integration of the viral genome into the human chromosome 19. All Rep proteins share a central SF3 superfamily helicase domain. In other SF3 members this domain is sufficient to induce oligomerization. However, the helicase domain in AAV Rep proteins (i.e. Rep40/Rep52) as shown by its monomeric characteristic, is not able to mediate stable oligomerization. This observation led us to hypothesize the existence of an as yet undefined structural determinant that regulates Rep oligomerization. In this document, we described a detailed structural comparison between the helicase domains of AAV-2 Rep proteins and those of the other SF3 members. This analysis shows a major structural difference residing in the small oligomerization sub-domain (OD) of Rep helicase domain. In addition, secondary structure prediction of the linker connecting the helicase domain to the origin-binding domain (OBD) indicates the potential to form α-helices. We demonstrate that mutant Rep40 constructs containing different lengths of the linker are able to form dimers, and in the presence of ATP/ADP, larger oligomers. We further identified an aromatic linker residue (Y224) that is critical for oligomerization, establishing it as a conserved signature motif in SF3 helicases. Mutation of this residue critically affects oligomerization as well as completely abolishes the ability to produce infectious virus. Taken together, our data support a model where the linker residues preceding the helicase domain fold into an α-helix that becomes an integral part of the helicase domain and is critical for the oligomerization and function of Rep68/78 proteins through cooperative interaction with the OBD and helicase domains.

Dynamic light scattering to study allosteric regulation

The Escherichia coli ClpA protein, like many AAA+ motor proteins, is allosterically regulated by nucleotide binding. We have combined analytical ultracentrifugation approaches with dynamic light scattering (DLS) to examine the self-association properties and the allosteric linkage of assembly to nucleotide binding. Here we present a protocol for the rapid and precise determination of the diffusion coefficient using DLS measurements in a model-independent fashion. When combined with analytical ultracentrifugation experiments, such an approach can yield a more complete understanding of the hydrodynamic and thermodynamic properties of the system.

Mapping the Deltex-binding surface on the notch ankyrin domain using analytical ultracentrifugation

The Notch signal transduction pathway controls cell fate determination during metazoan development. The Notch gene encodes a transmembrane receptor that is cleaved upon activation, liberating the Notch intracellular domain, which enters the nucleus and assembles transcriptional activation complexes that drive expression of Notch-responsive genes. The most conserved region of the Notch intracellular domain is an ankyrin domain (Nank), which binds directly to the cytosolic effector protein Deltex (Dx), controlling intracellular Notch activity. However, the structural and energetic basis for this interaction remains unknown. Here, we analyze the thermodynamics and hydrodynamics of the Nank:Dx heteroassociation, as well as a weaker Nank self-association, using sedimentation velocity analytical ultracentrifugation. By comparing g(s*) and c(s) distributions, and by direct fitting of sedimentation boundaries with thermodynamic association models, we were able to characterize the Nank:Dx heterodimer, measure its affinity, and map the interaction on the surface on Nank. N- and C-terminal deletions of whole ankyrin units implicate repeats 3 and 4 as key for mediating heteroassociation. An alanine scan across the interaction loops of Nank identifies a conserved hot spot in repeats 3 and 4, centered at R127, as critical for Dx binding. In addition, we were able to detect weak but reproducible Nank homodimerization (K(d) in the millimolar range). This association is disrupted by substitution of a conserved arginine (R107) with alanine, a residue previously implicated in a functionally relevant mode of interaction within dimeric transcription complexes. The distinct binding surfaces on Nank for homotypic versus Dx interaction appear to be compatible with teterameric Notch(2):Dx(2) assembly.

Analysis of PKR-RNA interactions by sedimentation velocity

PKR is an interferon-induced kinase that plays a pivotal role in the innate immunity pathway for defense against viral infection. PKR is activated to undergo autophosphorylation upon binding to RNAs that contain duplex regions. Some highly structured viral RNAs do not activate and function as PKR inhibitors. In order to define the mechanisms of activation and inhibition of PKR by RNA, it is necessary to characterize the stoichiometries, affinities, and free energy couplings governing the assembly of the relevant complexes. We have found sedimentation velocity analytical ultracentrifugation to be particularly useful in the study of PKR-RNA interactions. Here, we describe protocols for designing and analyzing sedimentation velocity experiments that are generally applicable to studies of protein-nucleic acid interactions. Initially, velocity data obtained at multiple protein:RNA ratios are analyzed using the dc/dt method's to define the association model and to test whether the system is kinetically limited. The sedimentation velocity data obtained at multiple loading concentrations are then globally fitted to this model to determine the relevant association constants. The frictional ratios of the complexes are calculated using the fitted sedimentation coefficients to determine whether the hydrodynamic properties are physically reasonable. We demonstrate the utility of this approach using examples from our studies of PKR interactions with simple dsRNAs, the HIV TAR RNA, and the VAI RNA from adenovirus.

Effect of kinetics on sedimentation velocity profiles and the role of intermediates

We have previously presented a tutorial on direct boundary fitting of sedimentation velocity data for kinetically mediated monomer-dimer systems [Correia and Stafford, 2009]. We emphasized the ability of Sedanal to fit for the k(off) values and measure their uncertainty at the 95% confidence interval. We concluded for a monomer-dimer system the range of well-determined k(off) values is limited to 0.005-10(-5) s(-1) corresponding to relaxation times of approximately 70 to approximately 33,000 s. More complicated reaction schemes introduce the potential complexity of low concentrations of an intermediate that may also influence the kinetic behavior during sedimentation. This can be seen in a cooperative ABCD system (A+B --> C; B+C --> D) where C, the 1:1 complex, is sparsely populated (K(1)=10(4) M(-1), K(2)=10(8) M(-1)). Under these conditions a k(1,off)<0.01 s(-1) produces slow kinetic features. The low concentration of species C contributes to this effect while still allowing the accurate estimation of k(1,off) (although k(2,off) can readily compensate and contribute to the kinetics). More complex reactions involving concerted assembly or cooperative ring formation with low concentrations of intermediate species also display kinetic effects due to a slow flux of material through the sparsely populated intermediate states. This produces a kinetically limited reaction boundary that produces partial resolution of individual species during sedimentation. Cooperativity of ring formation drives the reaction and thus separation of these two effects, kinetics and energetics, can be challenging. This situation is experimentally exhibited by systems that form large oligomers or rings and may especially contribute to formation of micelles and various protein aggregation diseases including formation of beta-amyloid and tau aggregates. Simulations, quantitative parameter estimation by direct boundary fitting and diagnostic features for these systems are presented with an emphasis on the features available in Sedanal to simulate and analyze kinetically mediated systems.

Sedimentation velocity ultracentrifugation analysis for hydrodynamic characterization of G-quadruplex structures

Analytical ultracentrifugation (AUC) is a powerful technique for the characterization of hydrodynamic and thermodynamic properties. The intent of this article is to demonstrate the utility of sedimentation velocity (SV) studies to obtain hydrodynamic information for G-quadruplex (GQ) systems and to provide insights into one part of this process, namely, data analysis of existing SV data. An array of data analysis software is available, mostly written and continually developed by established researchers in the AUC field, with particularly rapid advances in the analysis of SV data. Each program has its own learning curve, and this article is intended as a resource in the data analysis process for beginning researchers in the field. We discuss the application of three of the most commonly used data analysis programs, DCDT+, Sedfit, and SedAnal, to the interpretation of SV data obtained in our laboratory on two GQ systems.

The Escherichia coli ClpA molecular chaperone self-assembles into tetramers

The Escherichia coli ATP-dependent protease, ClpAP, is composed of the hexameric ATPase/protein-unfoldase, ClpA, and the tetradecameric proteolytic component, ClpP. ClpP proteolytically degrades folded proteins only when associated with the motor protein ClpA or ClpX, both of which use ATP binding and/or hydrolysis to unfold and translocate proteins into the tetradecameric serine protease ClpP. In addition to ClpA's role in regulating the proteolytic activity of ClpP, ClpA catalyzes protein unfolding of proteins that display target sequences to "remodel" them, in vivo, for regulatory roles beyond proteolytic degradation. In order for ClpA to bind protein substrates targeted for removal or remodeling, ClpA first requires nucleoside triphosphate binding to assemble into an oligomeric form with protein substrate binding activity. In addition to this nucleotide driven assembly activity, ClpA self-associates in the absence of nucleoside triphosphate binding. An examination of the energetics of the nucleotide driven assembly process cannot be performed without a thermodynamic model of the self-assembly process in the absence of nucleotide cofactor. Here we report an examination of the self-association properties of the E. coli ClpA protein unfoldase through the application of analytical ultracentrifugation and light scattering techniques, including sedimentation velocity, sedimentation equilibrium, and dynamic light scattering approaches. In contrast to published results, application of these approaches reveals that ClpA exists in a monomer-tetramer equilibrium (300 mM NaCl, 10 mM MgCl(2), and 25 mM HEPES, pH 7.5 at 25 degrees C). The implications of these results for the E. coli ClpA self-association and ligand linked association activities are discussed.

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis.