A two-dimensional spectrum analysis for sedimentation velocity experiments of mixtures with heterogeneity in molecular weight and shape

Abstract

We report a model-independent analysis approach for fitting sedimentation velocity data which permits simultaneous determination of shape and molecular weight distributions for mono- and polydisperse solutions of macromolecules. Our approach allows for heterogeneity in the frictional domain, providing a more faithful description of the experimental data for cases where frictional ratios are not identical for all components. Because of increased accuracy in the frictional properties of each component, our method also provides more reliable molecular weight distributions in the general case. The method is based on a fine grained two-dimensional grid search over s and f/f (0), where the grid is a linear combination of whole boundary models represented by finite element solutions of the Lamm equation with sedimentation and diffusion parameters corresponding to the grid points. A Monte Carlo approach is used to characterize confidence limits for the determined solutes. Computational algorithms addressing the very large memory needs for a fine grained search are discussed. The method is suitable for globally fitting multi-speed experiments, and constraints based on prior knowledge about the experimental system can be imposed. Time- and radially invariant noise can be eliminated. Serial and parallel implementations of the method are presented. We demonstrate with simulated and experimental data of known composition that our method provides superior accuracy and lower variance fits to experimental data compared to other methods in use today, and show that it can be used to identify modes of aggregation and slow polymerization.

Fig. 1

a Initial grid spanning entire $s$ and $k$ parameter space with a sparse representation of each parameter dimension. b Grid evaluation points after one iteration of grid movements. Black initial grid. Purple grid displacement by $\delta k$. Blue grid displacement by $\delta s$. White grid displacement by $\delta s$ and $\delta k$. c Typical storage grid $S$ for a heterogeneous sample after one iteration of grid displacements; darkness of points indicates concentration level; white indicates zero concentration, pink indicates a small concentration, while dark purple indicates high concentration. Solutes get returned with discrete values of $s$ and $k$

Fig. 2

2DSA Monte Carlo analysis of velocity data from a mixture of a 208 bp DNA fragment (black lines) and hen egg lysozyme (blue lines). Heavy lines indicate the mean, thin lines represent 95% confidence intervals for the parameter. The results for several parameters from multiple grid resolutions are compared. a Frictional ratio; b sedimentation coefficient (corrected to standard conditions); c molecular weight, horizontal lines indicate theoretical molecular weight based on sequence; d partial concentration and the residual mean square deviation of the fit (red line). Reliable results are obtained after a minimum of 10,000 iterations, higher resolutions do not improve the results significantly

Fig. 3

Pseudo-3D plots for solute distributions for the 2DSA Monte Carlo results shown in Fig. 2 for the highest and lowest grid resolution examined. a Grid resolution of 100 solutes; b grid resolution of 90,000 solutes. At the low resolution the composition is poorly defined and solute peaks are split, at high-resolution both species are well defined in narrow regions without any significant peak splitting, noise contributions are well separated and identifiable at the upper frictional ratio fitting limit $\left(k=4\right)$. Globular shape of lysozyme and elongated shape of DNA is clearly reproduced by fitting result. The color scale represents the signal of each species in optical density units

Fig. 4

Pseudo-3D plots for Monte Carlo 2DSA analysis results for a simulated five component system described in Sect. 3.2. a Single speed fit of data from conventional centerpiece (10 krpm); b single speed fit of data from conventional centerpiece (60 krpm); c global multi-speed fit of data from conventional centerpiece (10, 30 and 60 krpm); d global multi-speed fit of data from both conventional centerpiece combined with data from band-forming Vinograd centerpiece (10, 30 and 60 krpm for both centerpiece types). Improvement of the results is apparent in reduced peak splitting and improved confidence intervals in going from a → d. Yellow crosses indicate the positions of the known solutes that were simulated for the original data. The color scale represents the signal of each species in optical density units