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.

AUC measurements of diffusion coefficients of monoclonal antibodies in the presence of human serum proteins.

The goal of this work is to develop a preclinical method for quantitative hydrodynamic and thermodynamic analysis of therapeutic proteins in crowded environments like human serum. The method utilizes tracer amounts of fluorescently labeled monoclonal antibodies and the Aviv AU-FDS optical system. We have performed sedimentation velocity experiments as a function of mAb, human serum albumin and human IgG concentration to extract self- and cross-term hydrodynamic nonideality effects. SV measurements are consistently complicated by weak mAb-mAb and mAb-IgG interactions (Wright et al. in Anal Biochem 550:72-83, 2018). In an attempt to explore different approaches we have investigated measurements of diffusion coefficients by traditional synthetic boundary experiments. Here we present a new technique incorporated into SEDANAL that can globally analyze the full time course of synthetic boundary experiments. This approach also utilizes F-mAb against a high concentration of unlabeled carrier protein (HSA or IgG). In principle both diffusion and sedimentation coefficient information can be extracted including hydrodynamic and thermodynamic nonideality. The method can be performed at a traditional low speed (5-7K rpm) or at high speeds. The high speed method can also be used to measure D and s for small molecules like fluorescein (often contaminants of F-HSA and F-mAb). The advantage of synthetic boundary over the standard sedimentation velocity method is that it allows for higher precision determination of diffusion coefficients. The concentration dependence of D can be corrected for hydrodynamic nonideality effects by plotting D * (1 + kijcj) vs total carrier concentration. The slope of the fitted data allows an alternate approach to determine self- and cross-term thermodynamic nonideality. This method can also explore cross-term diffusion coefficient effects. These results are compared to dynamic light scattering approaches which are limited to kD determinations for solutions of pure protein.

Characterization of therapeutic antibodies in the presence of human serum proteins by AU-FDS analytical ultracentrifugation.

The preclinical characterization of biopharmaceuticals seeks to determine the stability, state of aggregation, and interaction of the antibody/drug with other macromolecules in serum. Analytical ultracentrifugation is the best experimental method to understand these factors. Sedimentation velocity experiments using the AU-FDS system were performed in order to quantitatively characterize the nonideality of fluorescently labeled therapeutic antibodies in high concentrations of human serum proteins. The two most ubiquitous serum proteins are human serum albumin, HSA, and γ-globulins, predominantly IgG. Tracer experiments were done pairwise as a function of HSA, IgG, and therapeutic antibody concentration. The sedimentation coefficient for each fluorescently labeled component as a function of the concentration of the unlabeled component yields the hydrodynamic nonideality (ks). This generates a 3x3 matrix of ks values that describe the nonideality of each pairwise interaction. The ks matrix is validated by fitting both 2:1 mixtures of HSA (1-40 mg/ml) and IgG (0.5-20 mg/ml) as serum mimics, and human serum dilutions (10-100%). The data are well described by SEDANAL global fitting with the ks nonideality matrix. The ks values for antibodies are smaller than expected and appear to be masked by weak association. Global fitting to a ks and K2 model significantly improves the fits.

Simultaneous analysis of hydrodynamic and optical properties using analytical ultracentrifugation equipped with multiwavelength detection.

Analytical ultracentrifugation (AUC) has proven to be a powerful tool for the study of particle size distributions, particle shapes, and interactions with high accuracy and unrevealed resolution. In this work we show how the analysis of sedimentation velocity data from the AUC equipped with a multiwavelength detector (MWL) can be used to gain an even deeper understanding of colloidal and macromolecular mixtures. New data evaluation routines have been integrated in the software SEDANAL to allow for the handling of MWL data. This opens up a variety of new possibilities because spectroscopic information becomes available for individual components in mixtures at the same time using MWL-AUC. For systems of known optical properties information on the hydrodynamic properties of the individual components in a mixture becomes accessible. For the first time, the determination of individual extinction spectra of components in mixtures is demonstrated via MWL evaluation of sedimentation velocity data. In our paper we first provide the informational background for the data analysis and expose the accessible parameters of our methodology. We further demonstrate the data evaluation by means of simulated data. Finally, we give two examples which are highly relevant in the field of nanotechnology using colored silica and gold nanoparticles of different size and extinction properties.

Simulation and analysis of a multi-order imaging Fabry-Perot interferometer for the study of thermospheric winds and temperatures.

We describe an analysis procedure for estimating the thermospheric winds and temperatures from the multi-order two-dimensional (2D) interferograms produced by an imaging Fabry-Perot interferometer (FPI) as imaged by a CCD detector. We also present a forward model describing the 2D interferograms. To investigate the robustness and accuracy of the analysis, we perform several Monte Carlo simulations using this forward model for an FPI that has recently been developed and deployed to northeastern Brazil. The first simulation shows that a slight cross-contamination at high temperatures exists between neighboring orders in the interferogram, introducing a bias in the estimated temperatures and increasing errors in both the estimated temperatures and winds when each order is analyzed in full. The second simulation investigates how using less than an entire order in the analysis reduces the cross contamination observed in the first set of simulations, improving the accuracy of the estimated temperatures. The last simulation investigates the effect of the signal-to-noise ratio on the errors in the estimated parameters. It is shown that, for the specific FPI simulated in this study, a signal-to-noise ratio of 1.5 is required to obtain thermospheric wind errors of 5 m/s and temperature errors of 20 K.

Analysis of heterologous interacting systems by sedimentation velocity: curve fitting algorithms for estimation of sedimentation coefficients, equilibrium and kinetic constants.

Analytical ultracentrifugation (AUC) has played and will continue to play an important role in the investigation of protein-protein, protein-DNA and protein-ligand interactions. A major advantage of AUC over other methods is that it allows the analysis of systems free in solution in nearly any buffer without worry about spurious interactions with a supporting matrix. Large amounts of high-quality data can be acquired in relatively short times. Advances in software for the treatment of AUC data over the last decade have eliminated many of the tedious aspects of AUC data analysis, allowing relatively rapid analysis of complicated systems that were previously unapproachable. A software package called sedanal is described that can perform global fits to AUC sedimentation velocity data obtained for both interacting and non-interacting, macromolecular multi-species, multi-component systems, by combining data from multiple runs over a range of sample concentrations and component ratios. Interaction parameters include both forward and reverse rate constants, or equilibrium constants, for each reaction, as well as concentration dependence of both sedimentation and diffusion coefficients. sedanal fits to time-difference data to eliminate time-independent systematic errors inherent in AUC data. The sedanal software package is based on the use of finite-element numerical solutions of the Lamm equation.