A model for sedimentation in inhomogeneous media. II. Compressibility of aqueous and organic solvents

Flotation Coefficient Distributions of Lipid Nanoparticles by Sedimentation Velocity Analytical Ultracentrifugation

The robust characterization of lipid nanoparticles (LNPs) encapsulating therapeutics or vaccines is an important and multifaceted translational problem. Sedimentation velocity analytical ultracentrifugation (SV-AUC) has proven to be a powerful approach in the characterization of size-distribution, interactions, and composition of various types of nanoparticles across a large size range, including metal nanoparticles (NPs), polymeric NPs, and also nucleic acid loaded viral capsids. Similar potential of SV-AUC can be expected for the characterization of LNPs, but is hindered by the flotation of LNPs being incompatible with common sedimentation analysis models. To address this gap, we developed a high-resolution, diffusion-deconvoluted sedimentation/flotation distribution analysis approach analogous to the most widely used sedimentation analysis model c(s). The approach takes advantage of independent measurements of the average particle size or diffusion coefficient, which can be conveniently determined, for example, by dynamic light scattering (DLS). We demonstrate the application to an experimental model of extruded liposomes as well as a commercial LNP product and discuss experimental potential and limitations of SV-AUC. The method is implemented analogously to the sedimentation models in the free, widely used SEDFIT software.

Comparative Hydrodynamic Study on Non-Aqueous Soluble Archaeological Wood Consolidants: Butvar B-98 and PDMS-OH Siloxanes

Butvar B-98 and PDMS-OH both have a demonstrable ability as consolidants for archaeological wood. This makes them both potential treatment options for the Oseberg collection, which is one of the most important archaeological finds from the Viking era. Both Butvar B-98 and PDMS-OH are soluble in organic solvents, offering a useful alternative to aqueous-based consolidants. Extensive characterisation studies were carried out on both of these polymers, with the use of analytical ultracentrifugation and viscometry, for the benefit of conservators wanting to know more about the physical properties of these materials. Short column sedimentation equilibrium analysis using SEDFIT-MSTAR revealed a weight-average molar mass (weight-average molecular weight) M_w of (54.0 ± 1.5) kDa (kg · mol^-1) for Butvar B-98, while four samples of PDMS-OH siloxanes (each with a different molar mass) had an M_w of (52.5 ± 3.0) kDa, (38.8 ± 1.5) kDa, (6.2 ± 0.7) kDa and (1.6 ± 0.1) kDa. Sedimentation velocity confirmed that all polymers were heterogeneous, with a wide range of molar masses. All molecular species showed considerable conformational asymmetry from measurements of intrinsic viscosity, which would facilitate networking interactions as consolidants. It is anticipated that the accumulated data on these two consolidants will enable conservators to make a more informed decision when it comes to choosing which treatment to administer to archaeological artefacts.

Reincarnation of the Analytical Ultracentrifuge: Emerging Opportunities for Nanomedicine

The analytical ultracentrifuge (AUC) and the modern field of analytical ultracentrifugation found its inception approximately a century ago. We highlight the scope of its major experimental opportunities as a transport-based method, contemporary and up-and-coming investigation potential for polymers, polymer-drug conjugates, polymer assemblies, as well as medical nanoparticles. Special focus lies on molar mass estimates of unimeric polymeric species, self-assemblies in solution, and (co)localization of multicomponent systems in solution alongside the material-biofluid interactions. We close with present challenges and incentives for future research.

Measuring compressibility in the optima AUC™ analytical ultracentrifuge

A method is described to accurately measure the compressibility of liquids using an analytical ultracentrifuge. The method makes use of very large pressure gradients, which can be generated in the analytical ultracentrifuge at high speeds to induce a maximum compression signal. Taking advantage of the new Optima AUC, which offers 10 micron radial resolution, a novel calibration centerpiece for measuring rotor stretch, and a speed-ramping procedure, even the weak compressibility of liquids like water, typically considered to be incompressible, could be detected. A model using the standard expression for the secant-average bulk modulus describing the relative compression of a liquid in the analytical ultracentrifuge is derived. The model is a function of the loading volume and the hydrostatic pressure generated in the analytical ultracentrifuge, as well as the secant-average bulk modulus. The compressibility of water and toluene were measured and the linear secant-average bulk modulus and meniscus positions were fitted. In addition to the measurement of the compressibility of liquids, applications for this method include an improved prediction of boundary conditions for multi-speed analytical ultracentrifugation experiments to better describe highly heterogeneous systems with analytical speed-ramping procedures, and the prediction of radius-dependent density variations.

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

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

[Ag115S34(SCH2C6H4t Bu)47(dpph)6]: synthesis, crystal structure and NMR investigations of a soluble silver chalcogenide nanocluster

With the aim to synthesize soluble cluster molecules, the silver salt of (4-(tert-butyl)phenyl)methanethiol [AgSCH2C6H4t Bu] was applied as a suitable precursor for the formation of a nanoscale silver sulfide cluster. In the presence of 1,6-(diphenylphosphino)hexane (dpph), the 115 nuclear silver cluster [Ag115S34(SCH2C6H4t Bu)47(dpph)6] was obtained. The molecular structure of this compound was elucidated by single crystal X-ray analysis and fully characterized by spectroscopic techniques. In contrast to most of the previously published cluster compounds with more than a hundred heavy atoms, this nanoscale inorganic molecule is soluble in organic solvents, which allowed a comprehensive investigation in solution by UV-Vis spectroscopy and one- and two-dimensional NMR spectroscopy including 31P/109Ag-HSQC and DOSY experiments. These are the first heteronuclear NMR investigations on coinage metal chalcogenides. They give some first insight into the behavior of nanoscale silver sulfide clusters in solution. Additionally, molecular weight determinations were performed by 2D analytical ultracentrifugation and HR-TEM investigations confirm the presence of size-homogeneous nanoparticles present in solution.

Sedimentation coefficient distributions of large particles

The spatial and temporal evolution of concentration boundaries in sedimentation velocity analytical ultracentrifugation reports on the size distribution of particles with high hydrodynamic resolution. For large particles such as large protein complexes, fibrils, viral particles, or nanoparticles, sedimentation conditions usually allow migration from diffusion to be neglected relative to sedimentation. In this case, the shape of the sedimentation boundaries of polydisperse mixtures relates directly to the underlying size-distributions. Integral and derivative methods for calculating sedimentation coefficient distributions g*(s) of large particles from experimental boundary profiles have been developed previously, and are recapitulated here in a common theoretical framework. This leads to a previously unrecognized relationship between g*(s) and the time-derivative of concentration profiles. Of closed analytical form, it is analogous to the well-known Bridgman relationship for the radial derivative. It provides a quantitative description of the effect of substituting the time-derivative by scan differences with finite time intervals, which appears as a skewed box average of the true distribution. This helps to theoretically clarify the differences between results from time-derivative method and the approach of directly fitting the integral definition of g*(s) to the entirety of experimental boundary data.

Analytical Ultracentrifugation as a Tool for Studying Protein Interactions

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

Sedimentation velocity analytical ultracentrifugation in hydrogenated and deuterated solvents for the characterization of membrane proteins

This chapter is a step-by-step protocol for setting up, realizing, and analyzing sedimentation velocity experiments in hydrogenated and deuterated solvents, in the context of the characterization of membrane protein, in terms of homogeneity, association state, and amount of bound detergent, based on a real case study of the membrane protein BmrA solubilized in n-Dodecyl-β-D-Maltopyranoside) detergent.

Effects of rotational speed on the hydrodynamic properties of pharmaceutical antibodies measured by analytical ultracentrifugation sedimentation velocity

Analytical ultracentrifugation sedimentation velocity (AUC-SV) has recently become one of the most important tools for the measurement of hydrodynamic properties of proteins. Although a number of studies using AUC-SV as applied to pharmaceutical antibodies have been conducted, the effect of rotational speed on molecular properties has not been systematically examined. The present study aimed to elucidate the influence of rotational speed on the hydrodynamic parameters of pharmaceutical antibodies. A monoclonal and a polyclonal antibody were studied by using AUC-SV at 5 different rotor speeds, and the acquired data were analyzed either by using the computer programs SEDFIT or UltraScan. The frictional ratio of the studied antibodies decreased at high rotor speeds, resulting in underestimation of molecular weight. The frictional ratio value of the monoclonal antibody measured at the low rotor speed was consistent with that of human immunoglobulin G1 computed from its three-dimensional structure. The best agreement between the measured molecular weight and the value calculated from the antibody sequence was achieved at the lower rotor speed. Similar to the results obtained using antibodies, AUC-SV analysis of human serum albumin revealed that the frictional ratio and apparent molecular weight behave in a speed-dependent manner. We deduced that the findings were mainly attributable to the hydrostatic pressure in the analytical ultracentrifuge. The current study implies that rotor speed should be carefully considered in antibody studies using AUC-SV.

Analytical ultracentrifugation of colloids

In this contribution the use of Analytical Ultracentrifugation (AUC) for the modern analysis of colloids is reviewed. Since AUC is a fractionation technique, distributions of the sedimentation coefficient, particle size and shape, molar mass and density can be obtained for particle sizes spanning the entire colloidal range. The Ångström resolution and the reliable statistics with which particle size distributions can be obtained from analytical ultracentrifugation makes this a high resolution analysis technique for the characterization of nanoparticles in solution or suspension. Several examples showing successful applications of AUC to complex problems in colloid science are given to illustrate the broad range and versatility of questions that can be answered by AUC experiments.

Using analytical ultracentrifugation (AUC) to measure global conformational changes accompanying equilibrium tertiary folding of RNA molecules

Analytical ultracentrifugation (AUC) is a powerful technique to determine the global conformational changes in RNA molecules mediated by cations or small molecule ligands. Although most of the developments in the field of AUC have been centered on studies involving protein molecules, the experimental methods as well as the analytical approaches have been successfully adapted and applied to the study of a variety of RNA molecules ranging from small riboswitches to large ribozymes. Most often AUC studies are performed in conjunction with other structural probing techniques that provide complementary information on local changes in the solvent accessibilities at specific regions within RNA molecules. This chapter provides a brief theoretical background, working knowledge of instrumentation, practical considerations for experimental setup, and guidelines for data analysis procedures to enable the design, execution, and interpretation of sedimentation velocity experiments that detect changes in the global dimensions of an RNA molecule during its equilibrium folding.

Precision of protein aggregation measurements by sedimentation velocity analytical ultracentrifugation in biopharmaceutical applications

Sedimentation velocity analytical ultracentrifugation (SV-AUC) is routinely applied in biopharmaceutical development to measure levels of protein aggregation in protein products. SV-AUC is free from many limitations intrinsic to size exclusion chromatography (SEC) such as mobile phase and column interaction effects on protein self-association. Despite these clear advantages, SV-AUC exhibits lower precision measurements than corresponding measurements by SEC. The precision of SV-AUC is influenced by numerous factors, including sample characteristics, cell alignment, centerpiece quality, and data analysis approaches. In this study, we evaluate the precision of SV-AUC in its current practice utilizing a multilaboratory, multiproduct intermediate precision study. We then explore experimental approaches to improve SV-AUC measurement precision, with emphasis on utilization of high quality centerpieces.

On the analysis of sedimentation velocity in the study of protein complexes

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.

Characterizing protein-protein interactions by sedimentation velocity analytical ultracentrifugation

This unit introduces the basic principles and practice of sedimentation velocity analytical ultracentrifugation for the study of reversible protein interactions, such as the characterization of self-association, heterogeneous association, multi-protein complexes, binding stoichiometry, and the determination of association constants. The analytical tools described include sedimentation coefficient and molar mass distributions, multi-signal sedimentation coefficient distributions, Gilbert-Jenkins theory, different forms of isotherms, and global Lamm equation modeling. Concepts for the experimental design are discussed, and a detailed step-by-step protocol guiding the reader through the experiment and the data analysis is available as an Internet resource.

Dynamics of surfactant-suspended single-walled carbon nanotubes in a centrifugal field

A hydrodynamic model is used to describe the motion of surfactant-suspended single-walled carbon nanotubes in a density gradient, while being subjected to a centrifugal field. The number of surfactant molecules adsorbed on each nanotube determines its effective density and, hence, its position in the gradient after centrifugation has been completed. Analysis of the spatial concentration distributions of CoMoCAT nanotubes suspended with 2 w/v% sodium cholate yielded 2.09, 2.14, and 2.08 surfactant molecules adsorbed per nanometer along the length of the (6,5), (7,5), and (8,7) nanotubes, respectively. The estimates are commensurate with experimental values reported in the literature and can be used to predict the fate of sodium cholate-suspended nanotubes in the separation process. Since the density of the surfactant-nanotube assembly is highly sensitive to the number of adsorbed molecules, a perturbation would cause it to be enriched at a different location in the gradient. The level of sensitivity is also reflected in the 95% confidence levels that are reported in this work.

A new adaptive grid-size algorithm for the simulation of sedimentation velocity profiles in analytical ultracentrifugation

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.

Using prior knowledge in the determination of macromolecular size-distributions by analytical ultracentrifugation

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 the use of available prior knowledge can have a dramatic effect on the resulting molecular weight, sedimentation coefficient, and size-and-shape distributions and can significantly increase both their sensitivity and their resolution. Further, the use of multiple alternative prior information allows us to probe the range of possible interpretations consistent with the data.

Role of analytical ultracentrifugation in assessing the aggregation of protein biopharmaceuticals

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 verify SEC aggregation information and the associating properties of biopharmaceuticals.

Macromolecular size-and-shape distributions by sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation is an important tool in the characterization of macromolecules and nanoparticles in solution. The sedimentation coefficient distribution c(s) of Lamm equation solutions is based on the approximation of a single, weight-average frictional coefficient of all particles, determined from the experimental data, which scales the diffusion coefficient to the sedimentation coefficient consistent with the traditional s approximately M(2/3) power law. It provides a high hydrodynamic resolution, where diffusional broadening of the sedimentation boundaries is deconvoluted from the sedimentation coefficient distribution. The approximation of a single weight-average frictional ratio is favored by several experimental factors, and usually gives good results for chemically not too dissimilar macromolecules, such as mixtures of folded proteins. In this communication, we examine an extension to a two-dimensional distribution of sedimentation coefficient and frictional ratio, c(s,f(r)), which is representative of a more general set of size-and-shape distributions, including mass-Stokes radius distributions, c(M,R(S)), and sedimentation coefficient-molar mass distributions c(s,M). We show that this can be used to determine average molar masses of macromolecules and characterize macromolecular distributions, without the approximation of any scaling relationship between hydrodynamic and thermodynamic parameters.

A model for sedimentation in inhomogeneous media. I. Dynamic density gradients from sedimenting co-solutes

Macromolecular sedimentation in inhomogeneous media is of great practical importance. Dynamic density gradients have a long tradition in analytical ultracentrifugation, and are frequently used in preparative ultracentrifugation. In this paper, a new theoretical model for sedimentation in inhomogeneous media is presented, based on finite element solutions of the Lamm equation with spatial and temporal variation of the local solvent density and viscosity. It is applied to macromolecular sedimentation in the presence of a dynamic density gradient formed by the sedimentation of a co-solute at high concentration. It is implemented in the software SEDFIT for the analysis of experimental macromolecular concentration distributions. The model agrees well with the measured sedimentation profiles of a protein in a dynamic cesium chloride gradient, and may provide a measure for the effects of hydration or preferential solvation parameters. General features of protein sedimentation in dynamic density gradients are described.