Rapid high-resolution size distribution protocol for adeno-associated virus using high speed SV-AUC

Simulated SV-AUC data for an adeno-associated virus (AAV) sample consisting of four components having closely spaced sedimentation coefficients were used to develop a high-speed protocol that optimized the size distribution analysis resolution. The resulting high speed (45K rpm) SV-AUC (hs-SV-AUC) protocol poses several experimental challenges: 1) the need for rapid data acquisition, 2) increased potential for optical artifacts from steep and fast moving boundaries and 3) the increased potential for convection. To overcome these challenges the protocol uses interference detection at low temperatures and data that are confined to a limited radial-time window. In addition to providing higher resolution AAV SV-AUC data and very short run times (<20 min after temperature equilibration), the need to match the sample and reference solvent composition and meniscus positions is relaxed making interference detection as simple to employ as absorbance detection. Finally, experimental data comparing hs-SV-AUC (at 45K rpm) with standard low-speed (15K rpm) SV-AUC on the same AAV sample demonstrate the size distribution resolution improvement. These experiments also validate the use of a radial-time window and show how quickly data can be acquired using the hs-SV-AUC protocol.

Studying Macromolecular Interactions of Cellular Machines by the Combined Use of Analytical Ultracentrifugation, Light Scattering, and Fluorescence Spectroscopy Methods

Cellular machines formed by the interaction and assembly of macromolecules are essential in many processes of the living cell. These assemblies involve homo- and hetero-associations, including protein-protein, protein-DNA, protein-RNA, and protein-polysaccharide associations, most of which are reversible. This chapter describes the use of analytical ultracentrifugation, light scattering, and fluorescence-based methods, well-established biophysical techniques, to characterize interactions leading to the formation of macromolecular complexes and their modulation in response to specific or unspecific factors. We also illustrate, with several examples taken from studies on bacterial processes, the advantages of the combined use of subsets of these techniques as orthogonal analytical methods to analyze protein oligomerization and polymerization, interactions with ligands, hetero-associations involving membrane proteins, and protein-nucleic acid complexes.

SViMULATE: a computer program facilitating interactive, multi-mode simulation of analytical ultracentrifugation data

The ability to simulate sedimentation velocity (SV) analytical ultracentrifugation (AUC) experiments has proved to be a valuable tool for research planning, hypothesis testing, and pedagogy. Several options for SV data simulation exist, but they often lack interactivity and require up-front calculations on the part of the user. This work introduces SViMULATE, a program designed to make AUC experimental simulation quick, straightforward, and interactive. SViMULATE takes user-provided parameters and outputs simulated AUC data in a format suitable for subsequent analyses, if desired. The user is not burdened by the necessity to calculate hydrodynamic parameters for simulated macromolecules, as the program can compute these properties on the fly. It also frees the user of decisions regarding simulation stop time. SViMULATE features a graphical view of the species that are under simulation, and there is no limit on their number. Additionally, the program emulates data from different experimental modalities and data-acquisition systems, including the realistic simulation of noise for the absorbance optical system. The executable is available for immediate download.

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.

Analytical ultracentrifugation sedimentation velocity for the characterization of recombinant adeno-associated virus vectors sub-populations

Recombinant adeno-associated virus virus-derived vectors (rAAVs) are among the most used viral delivery system for in vivo gene therapies with a good safety profile. However, rAAV production methods often lead to a heterogeneous vector population, in particular with the presence of undesired empty particles. Analytical ultracentrifugation sedimentation velocity (AUC-SV) is considered as the gold analytical technique allowing the measurement of relative amounts of each vector subpopulation and components like particle aggregates, based on their sedimentation coefficients. This letter presents the principle and practice of AUC experiments for rAAVs characterization. We discuss our results in the framework of previously published works. In addition to classical detection at 260 nm, using interference optics in the ultracentrifuge can provide an independent estimate of weight percentages of the different populations of capsids, and of the genome size incorporated in rAAV particles.

Generation of unfolded outer membrane protein ensembles defined by hydrodynamic properties

Outer membrane proteins (OMPs) must exist as an unfolded ensemble while interacting with a chaperone network in the periplasm of Gram-negative bacteria. Here, we developed a method to model unfolded OMP (uOMP) conformational ensembles using the experimental properties of two well-studied OMPs. The overall sizes and shapes of the unfolded ensembles in the absence of a denaturant were experimentally defined by measuring the sedimentation coefficient as a function of urea concentration. We used these data to model a full range of unfolded conformations by parameterizing a targeted coarse-grained simulation protocol. The ensemble members were further refined by short molecular dynamics simulations to reflect proper torsion angles. The final conformational ensembles have polymer properties different from unfolded soluble and intrinsically disordered proteins and reveal inherent differences in the unfolded states that necessitate further investigation. Building these uOMP ensembles advances the understanding of OMP biogenesis and provides essential information for interpreting structures of uOMP-chaperone complexes.

Simulation of Gilbert theory for self-association in sedimentation velocity experiments: a guide to evaluate best fitting models

There is a long tradition in the Biophysics community of using simulations as a means to understand macromolecular behavior in various physicochemical methods. This allows a rigorous means to interpret observations in terms of fundamental principles, including chemical equilibrium, reaction kinetics, transport processes and thermodynamics. Here we simulate data for the Gilbert Theory for self-association, a fundamental analytical ultracentrifuge (AUC) technique to understand the shape of sedimentation velocity reaction boundaries that involve reversible monomer-Nmer interactions. Simulating monomer-dimer through monomer-hexamer systems as a function of concentration about the equilibrium constant allows a visual means to differentiate reaction stoichiometry by determining end points and inflection positions. Including intermediates (eg A1-A2-A3-A4-A5-A6) in the simulations reveals the smoothing of the reaction boundary and the removal of sharp inflections between monomers and polymers. The addition of cooperativity restores sharp boundaries or peaks to the observation and allows more discrimination in the selection of possible fitting models. Thermodynamic nonideality adds additional features when applied across wide ranges of concentration that might be appropriate for high-concentration therapeutic monoclonal antibody (mAb) solutions. This presentation serves as a tutorial for using modern AUC analysis software like SEDANAL for selecting potential fitting models.

Strong non-ideality effects at low protein concentrations: considerations for elongated proteins

A recent investigation was aimed at obtaining structural information on a highly extended protein via SEC-MALS-SAXS. Significantly broadened elution peaks were observed, reminiscent of a phenomenon known as viscous fingering. This phenomenon is usually observed above 50 mg/mL for proteins like bovine serum albumin (BSA). Interestingly, the highly extended protein (Brpt5.5) showed viscous fingering at concentrations lower than 5 mg/mL. The current study explores this and other non-ideal behavior, emphasizing the presence of these effects at relatively low concentrations for extended proteins. BSA, Brpt5.5, and a truncated form of Brpt5.5 referred to as Brpt1.5 are studied systematically using size-exclusion chromatography (SEC), sedimentation velocity analytical ultracentrifugation (AUC), and viscosity. The viscous fingering effect is quantified using two approaches and is found to correlate well with the intrinsic viscosity of the proteins-Brpt5.5 exhibits the most severe effect and is the most extended protein tested in the study. By AUC, the hydrodynamic non-ideality was measured for each protein via global analysis of a concentration series. Compared to BSA, both Brpt1.5 and Brpt5.5 showed significant non-ideality that could be easily visualized at concentrations at or below 5 mg/mL and 1 mg/mL, respectively. A variety of relationships were examined for their ability to differentiate the proteins by shape using information from AUC and/or viscosity. Furthermore, these relationships were also tested in the context of hydrodynamic modeling. The importance of considering non-ideality when investigating the structure of extended macromolecules is discussed.

Revisiting macromolecular hydration with HullRadSAS

Hydration of biological macromolecules is important for their stability and function. Historically, attempts have been made to describe the degree of macromolecular hydration using a single parameter over a narrow range of values. Here, we describe a method to calculate two types of hydration: surface shell water and entrained water. A consideration of these two types of hydration helps to explain the "hydration problem" in hydrodynamics. The combination of these two types of hydration allows accurate calculation of hydrodynamic volume and related macromolecular properties such as sedimentation and diffusion coefficients, intrinsic viscosities, and the concentration-dependent non-ideality identified with sedimentation velocity experiments.

Determination of the SLAMF1 self-association affinity constant with sedimentation velocity ultracentrifugation

Signaling lymphocytic activating molecule family member 1 (SLAMF1 or CD150) is a cell surface glycoprotein expressed on various immune populations, regulating cell-cell interactions, activation, differentiation, and inflammatory responses and has been suggested as a potential target for inflammatory diseases. Signaling is believed to be mediated by high-affinity homophilic interactions; the recombinant soluble form of SLAMF1 has optimal activity in the range of 20 μg/mL. This contradicts with a rather weak homo-dimerization binding constant (K_D) value reported previously; however, the analytical approach and data analysis suffered from various technical limitations at the time and therefore warrants re-examination. To address this apparent discrepancy, we determined the K_D of soluble SLAMF1 using sedimentation velocity analytical ultracentrifuge (SV-AUC). A globally fitted monomer-dimer model properly explains the data from a wide concentration range obtained with both UV and fluorescence detection systems. The analysis suggests the dimerization K_D value for human SLAMF1 is 0.48 μM. Additionally, our data show that SLAMF1 self-association is not driven by non-specific binding to glycans supporting the view of specific protein-protein interaction. We anticipate antibody biotherapeutics capable of modulating the biological consequences of SLAMF1 interactions will be readily identified.

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.

Calibrating analytical ultracentrifuges

Analytical ultracentrifugation (AUC) is based on the concept of recording and analyzing macroscopic macromolecular redistribution that results from a centrifugal force acting on the mass of suspended macromolecules in solution. Since AUC rests on first principles, it can provide an absolute measurement of macromolecular mass, sedimentation and diffusion coefficients, and many other quantities, provided that the solvent density and viscosity are known, and provided that the instrument is properly calibrated. Unfortunately, a large benchmark study revealed that many instruments exhibit very significant systematic errors. This includes the magnification of the optical detection system used to determine migration distance, the measurement of sedimentation time, and the measurement of the solution temperature governing viscosity. We have previously developed reference materials, tools, and protocols to detect and correct for systematic measurement errors in the AUC by comparison with independently calibrated standards. This 'external calibration' resulted in greatly improved precision and consistency of parameters across laboratories. Here we detail the steps required for calibration of the different data dimensions in the AUC. We demonstrate the calibration of three different instruments with absorbance and interference optical detection, and use measurements of the sedimentation coefficient of NISTmAb monomer as a test of consistency. Whereas the measured uncorrected sedimentation coefficients span a wide range from 6.22 to 6.61 S, proper calibration resulted in a tenfold reduced standard deviation of sedimentation coefficients. The calibrated relative standard deviation and mean error of 0.2% and 0.07%, respectively, is comparable with statistical errors and side-by-side repeatability in a single instrument.

Sedimentation Velocity Methods for the Characterization of Protein Heterogeneity and Protein Affinity Interactions

Sedimentation velocity analytical ultracentrifugation is a powerful and versatile tool for the characterization of proteins and macromolecular complexes in solution. The direct modeling of the sedimentation process using modern computational strategies allows among others to assess the homogeneity/heterogeneity state of protein samples and to characterize protein associations. In this chapter, we will provide theoretical backgrounds and protocols to analyze the size distribution of protein samples and to determine the affinity of protein-protein hetero-associations.

Multi-wavelength analytical ultracentrifugation as a tool to characterise protein-DNA interactions in solution

Understanding how proteins interact with DNA, and particularly the stoichiometry of a protein-DNA complex, is key information needed to elucidate the biological role of the interaction, e.g. transcriptional regulation. Here, we present an emerging analytical ultracentrifugation method that features multi-wavelength detection to characterise complex mixtures by deconvoluting the spectral signals of the interaction partners into separate sedimentation profiles. The spectral information obtained in this experiment provides direct access to the molar stoichiometry of the interacting system to complement traditional hydrodynamic information. We demonstrate this approach by characterising a multimeric assembly process between the transcriptional repressor of bacterial sialic acid metabolism, NanR and its DNA-binding sequence. The method introduced in this study can be extended to quantitatively analyse any complex interaction in solution, providing the interaction partners have different optical properties.

Analysis of nonideality: insights from high concentration simulations of sedimentation velocity data

The Aviv fluorescence detection system (Aviv-FDS) has allowed the performance of sedimentation velocity experiments on therapeutic antibodies in highly concentrated environments like formulation buffers and serum. Methods were implemented in the software package SEDANAL for the analysis of nonideal, weakly associating AUC data acquired on therapeutic antibodies and proteins (Wright et al. Eur Biophys J 47:709–722, 2018, Anal Biochem 550:72–83, 2018). This involved fitting both hydrodynamic, k_s, and thermodynamic, BM₁, nonideality where concentration dependence is expressed as s = s^o/(1 + k_sc) and D = D^o(1 + 2BM₁c)/(1 + k_sc) and s^o and D^o are values extrapolated to c = 0 (mg/ml). To gain insight into the consequences of these phenomenological parameters, we performed simulations with SEDANAL of a monoclonal antibody as a function of k_s (0–100 ml/g) and BM₁ (0–100 ml/g). This provides a visual understanding of the separate and joint impact of k_s and BM₁ on the shape of high-concentration sedimentation velocity boundaries and the challenge of their unique determination by finite element methods. In addition, mAbs undergo weak self- and hetero-association (Yang et al. Prot Sci 27:1334–1348, 2018) and thus we have simulated examples of nonideal weak association over a wide range of concentrations (1–120 mg/ml). Here we demonstrate these data are best analyzed by direct boundary global fitting to models that account for k_s, BM₁ and weak association. Because a typical clinical dose of mAb is 50–200 mg/ml, these results have relevance for biophysical understanding of concentrated therapeutic proteins.

Aminoethyl substitution enhances the self-assembly properties of an aminocellulose as a potential archaeological wood consolidant

The 6-deoxy-6-aminocelluloses—or “aminocelluloses”—are a class of synthetic natural cellulose derivatives which are mostly aqueous soluble and have excellent film-forming properties. Recent studies have connected these properties at the molecular level with protein-like self-associative behaviour for a range of aminocelluloses including a 6-deoxy-6-(ω-aminoethyl) aminocellulose AEA-1 with the association being a two-stage process—a reversible oligomerisation followed by further (semi-reversible) aggregation into larger structures. Here, we synthesise and compare a new 6-deoxy-6-(ω-aminoethyl) aminocellulose AEA-1′ with different degree of substitution with one with further alkyl derivatisation, namely 6-deoxy-6-(ω-hydroxyethyl) aminocellulose HEA-1′. As with AEA-1, sedimentation velocity and sedimentation equilibrium in the analytical ultracentrifuge still show a two-stage process for both AEA-1′ and HEA-1′, with the latter giving higher molar masses. The consequences of these properties for use as consolidants for archaeological wood are considered.

Resuspending samples in analytical ultracentrifugation

In analytical ultracentrifugation it is often very useful to resuspend samples in situ after sedimentation experiments for further investigation. This can be achieved by manually subjecting the entire sample cell assembly to gentle motion that causes the air bubble in the sample compartment to repeatedly move through the solution and thereby cause convection. Here we describe a cell mixing device that can accomplish the same through axial rotation and slow rocking motion. This cell mixer is low-cost, open-source, and can be easily assembled from readily available components. It can efficiently mix multiple sample cells side-by-side and may be used with various centerpiece designs.

Crossing Species Barriers Relies on Structurally Distinct Prion Assemblies and Their Complementation

Prion replication results from the autocatalytic templated assisted conversion of the host-encoded prion protein PrP^C into misfolded, polydisperse PrP^Sc conformers. Structurally distinct PrP^Sc conformers can give rise to multiple prion strains. Within and between prion strains, the biological activity (replicative efficacy and specific infectivity) of PrP^Sc assemblies is size dependent and thus reflects an intrinsic structural heterogeneity. The contribution of such PrP^Sc heterogeneity across species prion adaptation, which is believed to be based on fit adjustment between PrP^Sc template(s) and host PrP^C, has not been explored. To define the structural-to-fitness PrP^Sc landscape, we measured the relative capacity of size-fractionated PrP^Sc assemblies from different prion strains to cross mounting species barriers in transgenic mice expressing foreign PrP^C. In the absence of a transmission barrier, the relative efficacy of the isolated PrP^Sc assemblies to induce the disease is like the efficacy observed in the homotypic context. However, in the presence of a transmission barrier, size fractionation overtly delays and even abrogates prion pathogenesis in both the brain and spleen tissues, independently of the infectivity load of the isolated assemblies. Altering by serial dilution PrP^Sc assembly content of non-fractionated inocula aberrantly reduces their specific infectivity, solely in the presence of a transmission barrier. This suggests that synergy between structurally distinct PrP^Sc assemblies in the inoculum is requested for crossing the species barrier. Our data support a mechanism whereby overcoming prion species barrier requires complementation between structurally distinct PrP^Sc assemblies. This work provides key insight into the "quasispecies" concept applied to prions, which would not necessarily rely on prion substrains as constituent but on structural PrP^Sc heterogeneity within prion population.

Probing RNA-Protein Interactions and RNA Compaction by Sedimentation Velocity Analytical Ultracentrifugation

Recent advances in multi-wavelength analytical ultracentrifugation (MWL-AUC) combine the power of an exquisitely sensitive hydrodynamic-based separation technique with the added dimension of spectral separation. This added dimension has opened up new doors to much improved characterization of multiple, interacting species in solution. When applied to structural investigations of RNA, MWL-AUC can precisely report on the hydrodynamic radius and the overall shape of an RNA molecule by enabling precise measurements of its sedimentation and diffusion coefficients and identify the stoichiometry of interacting components based on spectral decomposition. Information provided in this chapter will allow an investigator to design experiments for probing ion and/or protein-induced global conformational changes of an RNA molecule and exploit spectral differences between proteins and RNA to characterize their interactions in a physiological solution environment.

Electrokinetic phenomena in a dilute suspension of spherical solid colloidal particles with a hydrodynamically slipping surface in an aqueous electrolyte solution

A review is given on the theory of the electrokinetics in a dilute suspension of spherical solid colloidal particles with a hydrodynamically slipping surface moving in an aqueous liquid medium containing electrolytes. For a solid particle with a slip surface, the Navier boundary condition is employed instead of the usual no-slip boundary condition on the particle surface. The effect of the hydrodynamic slip is characterized by the slipping length. The limiting case of zero slipping length corresponds to a hydrophilic surface. As the hydrophobicity of the particle surface increases, the slipping length increases. The limiting case of infinitely large slipping length corresponds to a completely hydrophobic surface. General formulas and approximate expressions of the electrophoretic mobility, the electrical conductivity, the sedimentation velocity and potential, and the diffusion constant are presented. The magnitudes of the electrophoretic mobility and the sedimentation potential, in particular, are found to increase with increasing slipping length. It is also shown that a spherical solid colloidal particle with a slip surface is hydrodynamically similar to a liquid drop.

Efficient data acquisition with three-channel centerpieces in sedimentation velocity

Three-channel 3D printed centerpieces with two sample sectors next to a joint solvent reference sector were recently described as a strategy to double the throughput of sedimentation velocity analytical ultracentrifugation experiments [Anal. Chem. 91 (2019) 5866-5873]. They are compatible with Rayleigh interference optical detection in commercial analytical ultracentrifuges, but require the rotor angles of data acquisition to be repeatedly adjusted during the experiment to record data from the two sample sectors. Here we present an approach to automate this data acquisition mode through the use of a secondary, general-purpose automation software, and an accompanying data pre-processing software for scan sorting.

Aggregation Profiling of C9orf72 Dipeptide Repeat Proteins Transgenically Expressed in Drosophila melanogaster Using an Analytical Ultracentrifuge Equipped with Fluorescence Detection

The recent development of a fluorescence detection system for the analytical ultracentrifuge has allowed for the characterization of protein size and aggregation in complex mixtures. Protocols are described here to analyze protein aggregation seen in various human neurodegenerative diseases as they are presented in transgenic animal model systems. Proper preparation of crude extracts in appropriate sample buffers is critical for success in analyzing protein aggregation using sedimentation velocity methods. Furthermore, recent advances in sedimentation velocity analysis have led to data collection using single multispeed experiments, which may be analyzed using a wide distribution analysis approach. In this chapter, we describe the use of these new sedimentation velocity methods for faster determination of a wider range of sizes. In Chapter 7 of this book, we describe how agarose gel electrophoresis can be used to complement the analytical ultracentrifugation work, often as a prelude to careful biophysical analysis to help screen conditions in order to improve the success of sedimentation velocity experiments.

ATP hydrolysis inactivating Walker B mutation perturbs E. coli ClpA self-assembly energetics in the absence of nucleotide

E. coli ClpA is an AAA+ (ATPase Associated with diverse cellular Activities) chaperone that catalyzes the ATP-dependent unfolding and translocation of substrate proteins for the purposes of proper proteome maintenance. Biologically active ClpA hexamers contain two nucleotide binding domains (NBD) per protomer, D1 and D2. Despite extensive study, complete understanding of how the twelve NBDs within a ClpA hexamer coordinate ATP binding and hydrolysis to polypeptide translocation is currently lacking. To examine nucleotide binding and coordination at D1 and D2, ClpA Walker B variants deficient in ATP hydrolysis at one or both NBDs have been employed in various studies. In the presence of ATP, it is widely assumed that ClpA Walker B variants are entirely hexameric. However, a thermodynamically rigorous examination of the self-assembly mechanism has not been obtained. Differences in the assembly due to the mutation can be misattributed to the active NBD, leading to potential misinterpretations of kinetic studies. Here we use sedimentation velocity studies to quantitatively examine the self-assembly mechanism of ClpA Walker B variants deficient in ATP hydrolysis at D1, D2, and both NBDs. We found that the Walker B mutations had clear, if modest, effects on the assembly. Most notably, the Walker B mutation stabilizes the population of a larger oligomer in the absence of nucleotide, that is not present for analogous concentrations of wild type ClpA. Our results indicate that Walker B mutants, widely used in studies of AAA+ family proteins, require additional characterization as the mutation affects not only ATP hydrolysis, but also the ligand linked assembly of these complexes. This linkage must be considered in investigations of unfolding or other ATP dependent functions.

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

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

Sedimentation velocity analytical ultracentrifugation for characterization of therapeutic antibodies

Sedimentation velocity analytical ultracentrifugation (SV-AUC) coupled with direct computational fitting of the observed concentration profiles (sedimentating boundary) have been developed and widely used for the characterization of macromolecules and nanoparticles in solution. In particular, size distribution analysis by SV-AUC has become a reliable and essential approach for the characterization of biopharmaceuticals including therapeutic antibodies. In this review, we describe the importance and advantages of SV-AUC for studying biopharmaceuticals, with an emphasis on strategies for sample preparation, data acquisition, and data analysis. Recent discoveries enabled by AUC with a fluorescence detection system and potential future applications are also discussed.

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

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

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

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

Quaternary Structure Analyses of an Essential Oligomeric Enzyme

Here, we review recent studies aimed at defining the importance of quaternary structure to a model oligomeric enzyme, dihydrodipicolinate synthase. This will illustrate the complementary and synergistic outcomes of coupling the techniques of analytical ultracentrifugation with enzyme kinetics, in vitro mutagenesis, macromolecular crystallography, small angle X-ray scattering, and molecular dynamics simulations, to demonstrate the role of subunit self-association in facilitating protein dynamics and enzyme function. This multitechnique approach has yielded new insights into the molecular evolution of protein quaternary structure.

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.

Protein Assembly in Serum and the Differences from Assembly in Buffer

This chapter illustrates how analytical ultracentrifugation methods, coupled with the fluorescence detection system, are an excellent approach to characterizing and comparing protein-binding interactions in dilute solution and concentrated, crowded solutions like serum. We show that in serum, the binding and assembly states for a pair of endogenous protein ligands and an antibody inhibitor are dramatically different than those observed in dilute, simple buffers. This type of analysis approach may be helpful in research efforts intent at discerning the underpinnings to a therapeutic's activity and pharmacokinetic properties in vivo.

Elucidating Complicated Assembling Systems in Biology Using Size-and-Shape Analysis of Sedimentation Velocity Data

Sedimentation velocity analytical ultracentrifugation (SV-AUC) has seen a resurgence in popularity as a technique for characterizing macromolecules and complexes in solution. SV-AUC is a particularly powerful tool for studying protein conformation, complex stoichiometry, and interacting systems in general. Deconvoluting velocity data to determine a sedimentation coefficient distribution c(s) allows for the study of either individual proteins or multicomponent mixtures. The standard c(s) approach estimates molar masses of the sedimenting species based on determination of the frictional ratio (f/f0) from boundary shapes. The frictional ratio in this case is a weight-averaged parameter, which can lead to distortion of mass estimates and loss of information when attempting to analyze mixtures of macromolecules with different shapes. A two-dimensional extension of the c(s) analysis approach provides size-and-shape distributions that describe the data in terms of a sedimentation coefficient and frictional ratio grid. This allows for better resolution of species with very distinct shapes that may co-sediment and provides better molar mass determinations for multicomponent mixtures. An example case is illustrated using globular and nonglobular proteins of different masses with nearly identical sedimentation coefficients that could only be resolved using the size-and-shape distribution. Other applications of this analytical approach to complex biological systems are presented, focusing on proteins involved in the innate immune response to cytosolic microbial DNA.

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.

Measurement of the temperature of the resting rotor in analytical ultracentrifugation

Accurate measurements of rotor temperature are critical for the interpretation of hydrodynamic parameters in analytical ultracentrifugation. We have recently developed methods for a more accurate determination of the temperature of a spinning rotor using iButton temperature loggers. Here we report that the temperature measured with the iButton on the counterbalance of a resting rotor, following thermal equilibration under high vacuum, closely corresponded to the temperature of the spinning rotor with a precision better than 0.2°C. This strategy offers an inexpensive and straightforward approach to monitor the accuracy of the temperature calibration and determine corrective temperature offsets.

Improved measurement of the rotor temperature in analytical ultracentrifugation

Sedimentation velocity is a classical method for measuring the hydrodynamic, translational friction coefficient of biological macromolecules. In a recent study comparing various analytical ultracentrifuges, we showed that external calibration of the scan time, radial magnification, and temperature is critically important for accurate measurements (Anal. Biochem. 440 (2013) 81-95). To achieve accurate temperature calibration, we introduced the use of an autonomous miniature temperature logging integrated circuit (Maxim Thermochron iButton) that can be inserted into an ultracentrifugation cell assembly and spun at low rotor speeds. In the current work, we developed an improved holder for the temperature sensor located in the rotor handle. This has the advantage of not reducing the rotor capacity and allowing for a direct temperature measurement of the spinning rotor during high-speed sedimentation velocity experiments up to 60,000rpm. We demonstrated the sensitivity of this approach by monitoring the adiabatic cooling due to rotor stretching during rotor acceleration and the reverse process on rotor deceleration. Based on this, we developed a procedure to approximate isothermal rotor acceleration for better temperature control.

Improving the thermal, radial, and temporal accuracy of the analytical ultracentrifuge through external references

Sedimentation velocity (SV) is a method based on first principles that provides a precise hydrodynamic characterization of macromolecules in solution. Due to recent improvements in data analysis, the accuracy of experimental SV data emerges as a limiting factor in its interpretation. Our goal was to unravel the sources of experimental error and develop improved calibration procedures. We implemented the use of a Thermochron iButton temperature logger to directly measure the temperature of a spinning rotor and detected deviations that can translate into an error of as much as 10% in the sedimentation coefficient. We further designed a precision mask with equidistant markers to correct for instrumental errors in the radial calibration that were observed to span a range of 8.6%. The need for an independent time calibration emerged with use of the current data acquisition software (Zhao et al., Anal. Biochem., 437 (2013) 104-108), and we now show that smaller but significant time errors of up to 2% also occur with earlier versions. After application of these calibration corrections, the sedimentation coefficients obtained from 11 instruments displayed a significantly reduced standard deviation of approximately 0.7%. This study demonstrates the need for external calibration procedures and regular control experiments with a sedimentation coefficient standard.