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1.  A Bayesian Approach for Quantifying Trace Amounts of Antibody Aggregates by Sedimentation Velocity Analytical Ultracentrifugation 
The AAPS Journal  2008;10(3):481-493.
Sedimentation velocity analytical ultracentrifugation (SV-AUC) has become an important tool for the characterization of the purity of protein therapeutics. The work presented here addresses a need for methods orthogonal to size-exclusion chromatography for ensuring the reliable quantitation of immunogenic oligomers, for example, in antibody preparations. Currently the most commonly used approach for SV-AUC analysis is the diffusion-deconvoluted sedimentation coefficient distribution c(s) method, previously developed by us as a general purpose technique and implemented in the software SEDFIT. In both practical and theoretical studies, different groups have reported a sensitivity of c(s) for trace oligomeric fractions well below the 1% level. In the present work we present a variant of c(s) designed for the purpose of trace detection, with customized Bayesian regularization. The original c(s) method relies on maximum entropy regularization providing the most parsimonious distribution consistent with the data. In the present paper, we use computer simulations of an antibody system as example to demonstrate that the standard maximum entropy regularization, due to its design, leads to a theoretical lower limit for the detection of oligomeric traces and a consistent underestimate of the trace populations by ∼0.1% (dependent on the level of regularization). This can be overcome with a recently developed Bayesian extension of c(s) (Brown et al., Biomacromolecules, 8:2011–2024, 2007), utilizing the known regions of sedimentation coefficients for the monomer and oligomers of interest as prior expectation for the peak positions in the distribution. We show that this leads to more clearly identifiable and consistent peaks and lower theoretical limits of quantization by approximately an order of magnitude for some experimental conditions. Implications for the experimental design of SV-AUC and practical detection limits are discussed.
doi:10.1208/s12248-008-9058-z
PMCID: PMC2696691  PMID: 18814037
analytical ultracentrifugation; Bayesian analysis; hydrodynamic separation; sedimentation velocity; size-distribution; trace aggregates
2.  Using prior knowledge in the determination of macromolecular size distributions by analytical ultracentrifugation 
Biomacromolecules  2007;8(6):2011-2024.
Analytical ultracentrifugation has reemerged as a widely used tool for the study of ensembles of biological macromolecules to understand, for example, their size-distribution and interactions in free solution. Such information can be obtained from the mathematical analysis of the concentration and signal gradients across the solution column and their evolution in time generated as a result of the gravitational force. In sedimentation velocity analytical ultracentrifugation, this analysis is frequently conducted using high resolution, diffusion-deconvoluted sedimentation coefficient distributions. They are based on Fredholm integral equations, which are ill-posed unless stabilized by regularization. In many fields, maximum entropy and Tikhonov-Phillips regularization are well-established and powerful approaches that calculate the most parsimonious distribution consistent with the data and prior knowledge, in accordance with Occam’s razor. In the implementations available in analytical ultracentrifugation, to date, the basic assumption implied is that all sedimentation coefficients are equally likely, and that the information retrieved should be condensed to the least amount possible. Frequently, however, more detailed distributions would be warranted by specific detailed prior knowledge on the macromolecular ensemble under study, such as, the expectation of the sample to be monodisperse or paucidisperse, or the expectation for the migration to establish a bimodal sedimentation pattern based on Gilbert & Jenkins’ theory for the migration of chemically reacting systems. So far, such prior knowledge has remained largely unused in the calculation of the sedimentation coefficient or molecular weight distributions, or was only applied as constraints. In the present paper, we examine how prior expectations can be built directly into the computational data analysis, conservatively in a way that honors the complete information of the experimental data, whether or not consistent with the prior expectation. Consistent with analogous results in other fields, we find that use of available prior knowledge can have a dramatic effect on the resulting molecular weight, sedimentation coefficient and size-and-shape distributions, and significantly increase both their sensitivity and resolution. Further, the use of multiple alternative priors allows to probe the range of possible interpretations consistent with the data.
doi:10.1021/bm070193j
PMCID: PMC1994561  PMID: 17521163
Analytical ultracentrifugation; sedimentation velocity; sedimentation equilibrium; maximum entropy; Fredholm integral equations; size-distribution; regularization
3.  On the analysis of sedimentation velocity in the study of protein complexes 
European Biophysics Journal   2009;38(8):1079-1099.
Sedimentation velocity analytical ultracentrifugation has experienced a significant transformation, precipitated by the possibility of efficiently fitting Lamm equation solutions to the experimental data. The precision of this approach depends on the ability to account for the imperfections of the experiment, both regarding the sample and the instrument. In the present work, we explore in more detail the relationship between the sedimentation process, its detection, and the model used in the mathematical data analysis. We focus on configurations that produce steep and fast-moving sedimentation boundaries, such as frequently encountered when studying large multi-protein complexes. First, as a computational tool facilitating the analysis of heterogeneous samples, we introduce the strategy of partial boundary modeling. It can simplify the modeling by restricting the direct boundary analysis to species with sedimentation coefficients in a predefined range. Next, we examine factors related to the experimental detection, including the magnitude of optical aberrations generated by out-of-focus solution columns at high protein concentrations, the relationship between the experimentally recorded signature of the meniscus and the meniscus parameter in the data analysis, and the consequences of the limited radial and temporal resolution of the absorbance optical scanning system. Surprisingly, we find that large errors can be caused by the finite scanning speed of the commercial absorbance optics, exceeding the statistical errors in the measured sedimentation coefficients by more than an order of magnitude. We describe how these effects can be computationally accounted for in SEDFIT and SEDPHAT.
doi:10.1007/s00249-009-0514-1
PMCID: PMC2755746  PMID: 19644686
Analytical ultracentrifugation; Hydrodynamics; Direct boundary modeling; Lamm equation
4.  Analytical Ultracentrifugation: Sedimentation Velocity and Sedimentation Equilibrium 
Methods in cell biology  2008;84:143-179.
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, the movement of solutes in high centrifugal fields is interpreted using hydrodynamic theory to define the size, shape and interactions of macromolecules. Sedimentation equilibrium 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 sedimentation velocity 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.
doi:10.1016/S0091-679X(07)84006-4
PMCID: PMC2711687  PMID: 17964931
5.  A new adaptive grid-size algorithm for the simulation of sedimentation velocity profiles in analytical ultracentrifugation 
Computer physics communications  2008;178(2):105-120.
Analytical ultracentrifugation allows one to measure in real-time the concentration gradients arising from the application of a centrifugal force to macromolecular mixtures in solution. In the last decade, the ability to efficiently solve the partial differential equation governing the ultracentrifugal sedimentation and diffusion process, the Lamm equation, has spawned significant progress in the application of sedimentation velocity analytical ultracentrifugation for the study of biological macromolecules, for example, the characterization of protein oligomeric states and the study of reversible multi-protein complexes in solution. The present work describes a numerical algorithm that can provide an improvement in accuracy or efficiency over existing algorithms by more than one order of magnitude, and thereby greatly facilitate the practical application of sedimentation velocity analysis, in particular, for the study of multi-component macromolecular mixtures. It is implemented in the public domain software SEDFIT for the analysis of experimental data.
doi:10.1016/j.cpc.2007.08.012
PMCID: PMC2267755  PMID: 18196178
protein interactions; analytical ultracentrifugation; finite element methods; size distributions
6.  Analysis of high-affinity assembly for AMPA receptor amino-terminal domains 
The Journal of General Physiology  2012;139(5):371-388.
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.
doi:10.1085/jgp.201210770
PMCID: PMC3343374  PMID: 22508847
7.  Assembly, Loading, and Alignment of an Analytical Ultracentrifuge Sample Cell 
The analytical ultracentrifuge (AUC) is a powerful biophysical tool that allows us to record macromolecular sedimentation profiles during high speed centrifugation. When properly planned and executed, an AUC sedimentation velocity or sedimentation equilibrium experiment can reveal a great deal about a protein in regards to size and shape, sample purity, sedimentation coefficient, oligomerization states and protein-protein interactions.
This technique, however, requires a rigorous level of technical attention. Sample cells hold a sectored center piece sandwiched between two window assemblies. They are sealed with a torque pressure of around 120-140 in/lbs. Reference buffer and sample are loaded into the centerpiece sectors and then after sealing, the cells are precisely aligned into a titanium rotor so that the optical detection systems scan both sample and reference buffer in the same radial path midline through each centerpiece sector while rotating at speeds of up to 60, 000 rpm and under very high vacuum
Not only is proper sample cell assembly critical, sample cell components are very expensive and must be properly cared for to ensure they are in optimum working condition in order to avoid leaks and breakage during experiments. Handle windows carefully, for even the slightest crack or scratch can lead to breakage in the centrifuge. The contact between centerpiece and windows must be as tight as possible; i.e. no Newton s rings should be visible after torque pressure is applied. Dust, lint, scratches and oils on either the windows or the centerpiece all compromise this contact and can very easily lead to leaking of solutions from one sector to another or leaking out of the centerpiece all together. Not only are precious samples lost, leaking of solutions during an experiment will cause an imbalance of pressure in the cell that often leads to broken windows and centerpieces. In addition, plug gaskets and housing plugs must be securely in place to avoid solutions being pulled out of the centerpiece sector through the loading holes by the high vacuum in the centrifuge chamber. Window liners and gaskets must be free of breaks and cracks that could cause movement resulting in broken windows.
This video will demonstrate our procedures of sample cell assembly, torque, loading and rotor alignment to help minimize component damage, solution leaking and breakage during the perfect AUC experiment.
doi:10.3791/1530
PMCID: PMC3157848  PMID: 19893484
8.  Current Methods in Sedimentation Velocity and Sedimentation Equilibrium Analytical Ultracentrifugation 
Significant progress in the interpretation of analytical ultracentrifugation (AUC) data in the last decade has led to profound changes in the practice of AUC, both for sedimentation velocity (SV) and sedimentation equilibrium (SE). Modern computational strategies have allowed for the direct modeling of the sedimentation process of heterogeneous mixtures, resulting in 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 AUC, such as the study of protein self- and hetero-association, the study of membrane proteins, and applications in biotechnology. New global multi-signal modeling and mass conservation approaches in SV and 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 multi-protein 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 commentary is to supplement previous AUC protocols, Current Protocols in Protein Science 20.3 (1999) and 20.7 (2003), and 7.12 (2008), and provide an update describing the current tools for the study of soluble proteins, detergent-solubilized membrane proteins and their interactions by SV and SE.
doi:10.1002/0471140864.ps2012s71
PMCID: PMC3652391  PMID: 23377850
sedimentation equilibrium; sedimentation velocity; chemical equilibria; reversible interaction; size-distribution; multi-protein complex; analytical ultracentrifugation; protein hydrodynamics
9.  Investigation of β-carotene–gelatin composite particles with a multiwavelength UV/vis detector for the analytical ultracentrifuge 
European Biophysics Journal   2009;39(3):397-403.
A multiwavelength UV/vis detector for the analytical ultracentrifuge (MWL-AUC) has been developed recently. In this work, β-carotene–gelatin composite particles are investigated with MWL-AUC. Band centrifugation with a Vinograd cell is used to ensure maximum sample separation. Spectral changes of the system are observed in dependence of the sedimentation coefficient and are attributed to a previously unknown inhomogeneity of the β-carotene chemical composition with both H- and J-aggregates coexisting in a mixture. In addition, our data suggest that pure H- and J-aggregates exist in a particle while their relative concentrations in a mixture determine the color characteristics of the sample. The unique abilities and properties of MWL-AUC include sedimentation coefficient distributions for all possible wavelengths, full UV/vis spectra of each different species in the mixture and 3D movies of the sedimentation process. These properties significantly extend the scope of the analytical ultracentrifuge technique and show that complex biopolymer multicomponent mixtures can be resolved into their individual species.
Electronic supplementary material
The online version of this article (doi:10.1007/s00249-009-0412-6) contains supplementary material, which is available to authorized users.
doi:10.1007/s00249-009-0412-6
PMCID: PMC2812708  PMID: 19242689
10.  The Boundary Structure in the Analysis of Reversibly Interacting Systems by Sedimentation Velocity 
Methods (San Diego, Calif.)  2011;54(1):16-30.
Sedimentation velocity (SV) experiments of heterogeneous interacting systems exhibit characteristic boundary structures that can usually be very easily recognized and quantified. For slowly interacting systems, the boundaries represent concentrations of macromolecular species and they can be interpreted directly with population models based solely on the mass action law. For fast reactions, migration and chemical reactions are coupled, and different, but equally easily discernable boundary structures appear. However, these features have not been commonly utilized for data analysis, for the lack of an intuitive and computationally simple model. The recently introduced effective particle theory (EPT) provides a suitable framework. Here, we review the motivation and theoretical basis of EPT, and explore practical aspects for its application. We introduce an EPT-based design tool for SV experiments of heterogeneous interactions in the software SEDPHAT. As a practical tool for the first step of data analysis, we describe how the boundary resolution can be further improved in c(s) with a Bayesian adjustment of maximum entropy regularization to the case of heterogeneous interactions between molecules that have been previously studied separately. This can facilitate extracting the characteristic boundary features by integration of c(s) and their assembly into isotherms as a function of total loading concentrations, which are fitted with EPT in a second stage. Methods for addressing concentration errors in isotherms are discussed. Finally, in an experimental model system of alpha-chymotrypsin interacting with soybean trypsin inhibitor, we show that EPT provides an excellent description of the experimental sedimentation boundary structure of fast interacting systems.
doi:10.1016/j.ymeth.2011.01.010
PMCID: PMC3090504  PMID: 21315155
11.  Extended Fujita Approach to the Molecular Weight Distribution of Polysaccharides and other Polymeric Systems 
Methods (San Diego, Calif.)  2011;54(1):136-144.
In 1962 H. Fujita (Mathematical Theory of Sedimentation Analysis, Academic Press, New York, pp. 182–192) examined the possibility of transforming a quasi-continuous distribution g(s) of sedimentation coefficient s into a distribution f(M) of molecular weight M for linear polymers using the relation f(M) = g(s).(ds/dM) and showed that this could be done if information about the relation between s and M is available from other sources. Fujita provided the transformation based on the scaling relation s = κM0.5, where κ is taken as a constant for that particular polymer and the exponent 0.5 essentially corresponds to a randomly coiled polymer under ideal conditions. This method was successfully applied to mucus glycoproteins (S.E. Harding, Adv. Carbohyd. Chem. Biochem. 47 (1989), 345–381). We now describe an extension of the method to general conformation types via the scaling relation s = κMb, where b = 0.4–0.5 for a coil, ~0.15–0.2 for a rod and ~0.67 for a sphere. We give examples of distributions f(M) vs M obtained for polysaccharides from SEDFIT derived least squares g(s) vs s profiles (P. Schuck, Biophys. J. 78 (2000) 1606–1619) and the analytical derivative for ds/dM performed with Microcal ORIGIN. We also describe a more direct route from a direct numerical solution of the integral equation describing the molecular weight distribution problem. Both routes give identical distributions although the latter offers the advantage of being incorporated completely within SEDFIT. The method currently assumes that solutions behave ideally: sedimentation velocity has the major advantage over sedimentation equilibrium in that concentrations less than 0.2 mg/ml can be employed, and for many systems non-ideality effects can be reasonably ignored. For large, non-globular polymer systems, diffusive contributions are also likely to be small.
doi:10.1016/j.ymeth.2011.01.009
PMCID: PMC3480191  PMID: 21276851
12.  Recorded Scan Times Can Limit the Accuracy of Sedimentation Coefficients in Analytical Ultracentrifugation 
Analytical biochemistry  2013;437(1):104-108.
We report systematic and large inaccuracies in the recorded elapsed time in data files from the analytical ultracentrifuge, leading to overestimates of the sedimentation coefficients of up to 10%. This far exceeds previously considered factors contributing to the uncertainty in this parameter, and has significant ramifications for derived parameters, such as hydrodynamic shape and molar mass estimates. The source of this error is at present unknown, but we found it to be quantitatively consistent across different instruments, increasing with rotor speed. Furthermore, its occurrence appears to correlate with the use of the latest data acquisition software from the manufacturer, in use in some of our laboratories for nearly two years. Many of the recently published sedimentation coefficients may need to be re-examined. The problem can be easily recognized by comparing the file time-stamps provided by the operating system with the elapsed scan times recorded within the data files. We therefore implemented a routine in SEDFIT that can automatically examine the data files, alert the user to significant discrepancies, and correct the scan times accordingly. This eliminates errors in the recorded scan times.
doi:10.1016/j.ab.2013.02.011
PMCID: PMC3676908  PMID: 23458356
sedimentation velocity; hydrodynamic modeling
13.  Multi-Signal Sedimentation Velocity Analysis with Mass Conservation for Determining the Stoichiometry of Protein Complexes 
PLoS ONE  2013;8(5):e62694.
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.
doi:10.1371/journal.pone.0062694
PMCID: PMC3656001  PMID: 23696787
14.  A Multi-Tiered Analytical Approach For the Analysis and Quantitation of High-Molecular-Weight Aggregates in a Recombinant Therapeutic Glycoprotein 
The AAPS Journal  2009;11(2):335-341.
In this study, we have investigated sedimentation velocity ultracentrifugation (AUC-SV), size exclusion chromatography (SEC), and circular dichroism (CD) methods for the detection and quantitation of protein aggregates using recombinant acid alpha-glucosidase (rhGAA) as a model. The results of this study showed that the formation and molecular weight distribution of rhGAA aggregated species were dependent upon the formulation conditions as well as the storage or stress conditions used to induce aggregation. The utility of CD as a probe for non-native, aggregated species was affirmed, as this method was sensitive to rhGAA aggregation levels of ≤4%. An extensive evaluation of AUC-SV variability was performed using nine levels of spiked rhGAA aggregate that were analyzed on six occasions. Based on our data, the precision of the AUC-SV results increased with increasing levels of aggregate, with a mean RSD of 37.2%. The limit of quantitation (LOQ) for the AUC-SV method, which was based on a Precision criterion of RSD <20%, was determined to be ≥3% aggregated rhGAA. The Precision and LOQ of the SEC method, determined using the same rhGAA sample set, was found to be 3.8% and ≥0.2%, respectively. In general, there was good agreement between the levels of aggregated rhGAA determined using the AUC-SV and SEC methods, with a slight positive bias noted for the AUC-SV results. These studies emphasize the value of applying multiple, well-characterized analytical tools in the evaluation of therapeutic protein aggregation.
doi:10.1208/s12248-009-9108-1
PMCID: PMC2691468  PMID: 19430910
aggregation; analytical ultracentrifugation; circular dichroism; size exclusion chromatography
15.  NMR Solution Structure and Condition-Dependent Oligomerization of the Antimicrobial Peptide Human Defensin 5 
Biochemistry  2012;51(48):9624-9637.
Human defensin 5 (HD5) is a 32-residue host-defense peptide expressed in the gastrointestinal, reproductive, and urinary tracts that has antimicrobial activity. It exhibits six cysteine residues that are regiospecifically oxidized to form three disulfide bonds (Cys3—Cys31, Cys5—Cys20, and Cys10—Cys30) in the oxidized form (HD5ox). To probe the solution structure and oligomerization properties of HD5ox, and select mutant peptides lacking one or more disulfide bonds, NMR solution studies and analytical ultracentrifugation experiments are reported in addition to in vitro peptide stability assays. The NMR solution structure of HD5ox, solved at pH 4 in 90:10 H2O/D2O, is presented (PDB: 2LXZ). Relaxation T1/T2 measurements and the rotational correlation time (Tc) estimated from a [15N,1H]-TRACT experiment demonstrate that HD5ox is dimeric under these experimental conditions. Exchange broadening of the Hα signals in the NMR spectra suggests that residues 19-21 (Val19-Cys20-Glu21) contribute to the dimer interface in solution. Exchange broadening is also observed for residues 7-14 comprising the loop. Sedimentation velocity and equilibrium studies conducted in buffered aqueous solution reveal that the oligomerization state of HD5ox is pH-dependent. Sedimentation coefficients of ca. 1.8 S and a molecular weight of 14,363 Da were determined for HD5ox at pH 7, supporting a tetrameric form ([HD5ox] ≥ 30 μM). At pH 2, a sedimentation coefficient of ca. 1.0 S and a molecular weight of 7,079 Da, corresponding to a HD5ox dimer, were obtained. Millimolar concentrations of NaCl, CaCl2, and MgCl2 have negligible effect on the HD5ox sedimentation coefficients in buffered aqueous solution at neutral pH. Removal of a single disulfide bond results in a loss of peptide fold and quaternary structure. These biophysical investigations highlight the dynamic and environment-sensitive behavior of HD5ox in solution, and provide important insights into HD5ox structure/activity relationships and the requirements for antimicrobial action.
doi:10.1021/bi301255u
PMCID: PMC3579768  PMID: 23163963
16.  Analytical Ultracentrifugation as a Tool for Studying Protein Interactions 
Biophysical reviews  2013;5(2):10.1007/s12551-013-0106-2.
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.
doi:10.1007/s12551-013-0106-2
PMCID: PMC3652485  PMID: 23682298
sedimentation equilibrium; sedimentation velocity; multi-protein complexes; multi-signal analysis; global analysis; effective particle theory
17.  Sedimentation Velocity Ultracentrifugation Analysis for Hydrodynamic Characterization of G-Quadruplex Structures 
Summary
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 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 G-quadruplex systems.
doi:10.1007/978-1-59745-363-9_7
PMCID: PMC3008627  PMID: 20012418
analytical ultracentrifugation; sedimentation velocity; sedimentation coefficient; frictional ratio; hydrodynamic; solution conformation; G-quadruplex DNA; data analysis; DCDT+; Sedfit; SedAnal
18.  Analysis of Protein Interactions with Picomolar Binding Affinity by Fluorescence-Detected Sedimentation Velocity 
Analytical Chemistry  2014;86(6):3181-3187.
The study of high-affinity protein interactions with equilibrium dissociation constants (KD) in the picomolar range is of significant interest in many fields, but the characterization of stoichiometry and free energy of such high-affinity binding can be far from trivial. Analytical ultracentrifugation has long been considered a gold standard in the study of protein interactions but is typically applied to systems with micromolar KD. Here we present a new approach for the study of high-affinity interactions using fluorescence detected sedimentation velocity analytical ultracentrifugation (FDS-SV). Taking full advantage of the large data sets in FDS-SV by direct boundary modeling with sedimentation coefficient distributions c(s), we demonstrate detection and hydrodynamic resolution of protein complexes at low picomolar concentrations. We show how this permits the characterization of the antibody–antigen interactions with low picomolar binding constants, 2 orders of magnitude lower than previously achieved. The strongly size-dependent separation and quantitation by concentration, size, and shape of free and complex species in free solution by FDS-SV has significant potential for studying high-affinity multistep and multicomponent protein assemblies.
doi:10.1021/ac500093m
PMCID: PMC3988680  PMID: 24552356
19.  Deriving the ultrastructure of α-crustacyanin using lower-resolution structural and biophysical methods 
Journal of Synchrotron Radiation  2010;18(Pt 1):79-83.
The structure of α-crustacyanin has been determined to 30 Å resolution using negative-stain electron microscopy (EM) single-particle averaging and modelling with the β-crustacyanin dimer from the crystal structure (Protein Data Bank code 1gka), guided by PISA protein subunit interface calculations for 1gka, and compared with the protein arrangements observed in the crystal lattice of 1gka. This α-crustacyanin EM model has been checked against SAXS experimental data, including comparison with rigid-body models calculated from the SAXS data, and finally with analytical ultracentrifugation measurements.
The low-resolution structure of α-crustacyanin has been determined to 30 Å resolution using negative-stain electron microscopy (EM) with single-particle averaging. The protein, which is an assembly of eight β-crustacyanin dimers, appears asymmetrical and rather open in layout. A model was built to the EM map using the X-ray crystallographic structure of β-crustacyanin guided by PISA interface analyses. The model has a theoretical sedimentation coefficient that matches well with the experimentally derived value from sedimentation velocity analytical ultracentrifugation. Additionally, the EM model has similarities to models calculated independently by rigid-body modelling to small-angle X-ray scattering (SAXS) data and extracted in silico from the β-crustacyanin crystal lattice. Theoretical X-ray scattering from each of these models is in reasonable agreement with the experimental SAXS data and together suggest an overall design for the α-crustacyanin assembly.
doi:10.1107/S0909049510034977
PMCID: PMC3004261  PMID: 21169698
α-crustacyanin; EM; SAXS; crystal packing of 1gka; PISA; analytical ultracentrifugation
20.  Macrocyclic β-Sheet Peptides that Mimic Protein Quaternary Structure through Intermolecular β-Sheet Interactions 
This paper reports the design, synthesis, and characterization of a family of cyclic peptides that mimic protein quaternary structure through β-sheet interactions. These peptides are 54-membered-ring macrocycles comprising an extended heptapeptide β-strand, two Hao β-strand mimics [JACS 2000, 122, 7654] joined by one additional α-amino acid, and two δ-linked ornithine β-turn mimics [JACS 2003, 125, 876]. Peptide 3a, as the representative of these cyclic peptides, contains a heptapeptide sequence (TSFTYTS) adapted from the dimerization interface of protein NuG2 [PDB ID: 1mio]. 1H NMR studies of aqueous solutions of peptide 3a show a partially folded monomer in slow exchange with a strongly folded oligomer. NOE studies clearly show that the peptide self-associates through edge-to-edge β-sheet dimerization. Pulsed-field gradient (PFG) NMR diffusion coefficient measurements and analytical ultracentrifugation (AUC) studies establish that the oligomer is a tetramer. Collectively, these experiments suggest a model in which cyclic peptide 3a oligomerizes to form a dimer of β-sheet dimers. In this tetrameric β-sheet sandwich, the macrocyclic peptide 3a is folded to form a β-sheet, the β-sheet is dimerized through edge-to-edge interactions, and this dimer is further dimerized through hydrophobic face-to-face interactions involving the Phe and Tyr groups. Further studies of peptides 3b–3n, which are homologues of peptide 3a with 1–6 variations in the heptapeptide sequence, elucidate the importance of the heptapeptide sequence in the folding and oligomerization of this family of cyclic peptides. Studies of peptides 3b–3g show that aromatic residues across from Hao improve folding of the peptide, while studies of peptides 3h–3n indicate that hydrophobic residues at positions R3 and R5 of the heptapeptide sequence are important in oligomerization.
doi:10.1021/ja068511u
PMCID: PMC2596933  PMID: 17419629
21.  Analysis of PKR-RNA interactions by sedimentation velocity 
Methods in enzymology  2011;488:59-79.
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 interactions. Initially, velocity data obtained at multiple protein:RNA ratios are analyzed using the dc/dt method 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 fit 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.
doi:10.1016/B978-0-12-381268-1.00003-3
PMCID: PMC3058617  PMID: 21195224
22.  Role of analytical ultracentrifugation in assessing the aggregation of protein biopharmaceuticals 
The AAPS Journal  2006;8(3):E590-E605.
In developing and manufacturing protein biopharmaceuticals, aggregation is a parameter that needs careful monitoring to ensure the quality and consistency of the final biopharmaceutical drug product. The analytical method of choice used to perform this task is size-exclusion chromatography (SEC). However, it is becoming more and more apparent that considerable care is required in assessing the accuracy of SEC data. One old analytical tool that is now reappearing to help in this assessment is analytical ultracentrifugation (AUC). Developments in AUC hardware and, more importantly, recent developments in AUC data analysis computer programs have converged to provide this old biophysical tool with the ability to extract very high resolution size information about the molecules in a given sample from a simple sedimentation velocity experiment. In addition, AUC allows sample testing to be conducted in the exact or nearly exact liquid formulation or reconstituted liquid formulation of the biopharmaceutical in the vial, with minimal surface area contact with extraneous materials. As a result, AUC analysis can provide detailed information on the aggregation of a biopharmaceutical, while avoiding many of the major problems that can plague SEC, thus allowing AUC to be used as an orthogonal method to verity SEC aggregation information and the associating properties of biopharmaceuticals.
doi:10.1208/aapsj080368
PMCID: PMC2761066  PMID: 17025277
Protein aggregation; analytical ultracentrifugation; size-exclusion chromatography; SEDFIT
23.  Homooligomerization of the hemagglutinin-neuraminidase glycoprotein of human parainfluenza virus type 3 occurs before the acquisition of correct intramolecular disulfide bonds and mature immunoreactivity. 
Journal of Virology  1991;65(5):2362-2371.
The posttranslational maturation of the hemagglutinin-neuraminidase (HN) glycoprotein of human parainfluenza type 3 virus (PIV3) was investigated in pulse-chase experiments in which folding was monitored by immunoprecipitation with conformation-dependent antibodies and gel electrophoresis under nonreducing conditions and oligomerization was monitored by chemical cross-linking and sedimentation in sucrose gradients. The acquisition of mature immunoreactivity and the formation of correct intramolecular disulfide bonds were concurrent events, with half-times of approximately 10 to 15 min. The finding that newly synthesized HN had little reactivity with postinfection cotton rat serum or with most of the members of a panel of HN-specific monoclonal antibodies indicated that the major epitopes of the PIV3 HN protein are highly conformational in nature. Chemical cross-linking studies indicated that the mature HN protein is present in homoligomers, which are probably tetramers. These findings are consistent with recent observations for the HN protein of Sendai virus (S.D. Thompson, W.G. Laver, K.G. Murti, and A. Portner, J. Virol. 62:4653--4660, 1988; S. Vidal, G. Mottet, D. Kolakofsky, and L. Roux, J. Virol. 63:892--900, 1989). Surprisingly, analysis of pulse-labeled HN protein by sedimentation on sucrose gradients after labeling periods of as little as 2 min indicated that it was present intracellularly only in oligomeric form. The same results were obtained when the labeling period was preceded by a 1.5-h cycloheximide treatment to clear the endoplasmic reticulum of presynthesized HN protein, which indicated that the oligomerization did not involve the incorporation of newly synthesized monomers into partially assembled oligomers. Subsequent chase incubations did not significantly alter the sedimentation profile or stability of the oligomeric forms, suggesting that oligomers detected after short labeling periods were tetramers. Association with cellular proteins did not appear to be responsible for the sedimentation of newly synthesized HN protein as an oligomer. The absence of a detectable monomeric form of intracellular HN protein raised the possibility that oligomerization is cotranslational, and it is possible that the type II membrane orientation of the HN protein might be an important factor in its mode of oligomerization.
Images
PMCID: PMC240588  PMID: 1707981
24.  Structure of viroid replicative intermediates: physico-chemical studies on SP6 transcripts of cloned oligomeric potato spindle tuber viroid. 
Nucleic Acids Research  1986;14(24):9613-9630.
The structure and structural transitions of transcripts of cloned oligomeric viroid were studied in physico-chemical experiments and stability calculations. Transcripts of (+) and (-) polarity, from unit up to sixfold length, were synthesized from DNA clones of the potato spindle tuber viroid (PSTV) with the SP6 transcription system. Their structural properties were investigated by optical denaturation curves, high performance liquid chromatography (HPLC), electron microscopy, sedimentation-diffusion equilibrium and velocity sedimentation. Secondary structures of the RNAs and theoretical denaturation curves were calculated using an energy optimization program. The secondary structure of lowest free energy for unit length and oligomeric transcripts is a rod-like structure similar to that of the mature circular viroids. When this structure is used as a model for calculations, there is a large degree of agreement between the theoretical and the experimental denaturation curves. At high temperatures, however, (+) strand transcripts exhibited a transition which was more stable than expected from the calculations or than was known from curves of mature viroids. This transition arises from a rearrangement of the central conserved region of viroids to a helical region of 28 stable base pairs either intermolecularly leading to bimolecular complexes, or intramolecularly giving rise to a branched secondary structure. The rearrangement could be detected by electron microscopy, HPLC, and analytical ultracentrifugation. The helical region serves to divide up the oligomeric (+) strand into structural units which may be recognized by cleavage and ligation enzymes which process the oligomeric intermediates to circular mature viroids.
Images
PMCID: PMC341324  PMID: 3808953
25.  SEDFIT-MSTAR: Molecular weight and molecular weight distribution analysis of polymers by sedimentation equilibrium in the ultracentrifuge 
The Analyst  2013;139(1):79-92.
Sedimentation equilibrium (analytical ultracentrifugation) is one of the most inherently suitable methods for the determination of average molecular weights and molecular weight distributions of polymers, because of its absolute basis (no conformation assumptions) and inherent fractionation ability (without the need for columns or membranes and associated assumptions over inertness). With modern instrumentation it is also possible to run up to 21 samples simultaneously in a single run. Its application has been severely hampered because of difficulties in terms of baseline determination (incorporating estimation of the concentration at the air/solution meniscus) and complexity of the analysis procedures. We describe a new method for baseline determination based on a smart-smoothing principle and built into the highly popular platform SEDFIT for the analysis of the sedimentation behavior of natural and synthetic polymer materials. The SEDFIT-MSTAR procedure – which takes only a few minutes to perform - is tested with four synthetic data sets (including a significantly non-ideal system) a naturally occurring protein (human IgG1) and two naturally occurring carbohydrate polymers (pullulan and λ–carrageenan) in terms of (i) weight average molecular weight for the whole distribution of species in the sample (ii) the variation in “point” average molecular weight with local concentration in the ultracentrifuge cell and (iii) molecular weight distribution.
doi:10.1039/c3an01507f
PMCID: PMC4064941  PMID: 24244936

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