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

Virial Expansions for Ideal Self-Associating Systems

Theoretical virial equations for self-associating systems governed by mass action have been derived assuming the solute to be ideal except for this solutesolute interaction. In particular, monomer-polymer association involving two molecular species and isodesmic association involving an indefinite number of molecular species have been treated analytically. The usefulness of such virial equations is severely limited by their extremely narrow interval of convergence

An extrapolation method for reducing equilibration times in sedimentation equilibrium experiments.

We present a detailed investigation of the use of an extrapolation technique to decrease running times of sedimentation equilibrium experiments. If concentration profiles are available at time delta tau, 2delta tau, 3delta tau,...., cn(r) = c(r, n delta tau), then the Aitken transformation replaces the cn(r) + ĉn(r) = [cn + 1(r) cn - 1(r) - c2n(r)]/[cn + 1(r) + cn - 1(r) - 2cn(r)]. We show that the ĉn(r) converge to the equilibrium values c infinity (r) much more quickly than the cn(r). Savings in time are shown to range from a factor of approximately 2 for meniscus depletion experiments to factors of between 4 and 8 for lower speeds or smaller molecular weights. It is also shown that the technique is quite sensitive to noise, so that an accurate optical system is required to allow its optimal use

QUASI-ELASTIC LIGHT SCATTERING STUDIES OF THE KINETICS OF LYSOZYME DIMERIZATION

On a utilisé la technique de la diffusion de la lumière laser pour étudier les vitesses et le mécanisme de dimérisation du lysozyme en l'absence de substrat. Ces expériences ont été réalisées sur du lysozyme dans du KCl 0,15 molaire, a 20 °C , dans un domaine de pH de 3,0 à 7,0. Les concentrations en protéine ont varié entre 3,6 x 10-4 et 14,6 x 10-4 molaire. L'échantillon de pH = 3,0 (7,3 x 10-4 M) a présenté un Dw20 = (1,04 ± 0,02) x 10-6 cm2/s, correspondant bien à la valeur acceptée pour le coefficient de diffusion translationnel de la forme monomère du lysozyme. Les données de la diffusion ont indiqué que pour un pH 5,0-7,0, le lysozyme subit une transformation de configuration avant de prendre la forme dimère stable. Cela est mis en évidence par un minimum dans la valeur du coefficient de diffusion apparent au-dessous de ce qu'on attend pour le dimère. Une analyse détaillée des spectres observés indique qu'on peut discerner deux étapes dans la réaction. La plus lente de ces étapes correspond à la valeur de saut-T de Owen, Eyring et Cole (1969), qui pour un pH de 7,0 est de (2,0 ± 0,5) x 10-3 s. Les données présentes pour la réaction la plus lente montrent une absence semblable de dépendance avec la température pour pH = 7,0 comme l'ont trouvé Owen et Coll. Cependant, pour des pH de 5,0 et 6,0, il y a une augmentation du temps de relaxation avec une diminution de la concentration (au-dessous de 7 x 10-4 M de concentration de protéine) pour cette étape. D'après les données de la diffusion, il apparaît aussi une composante spectrale correspondant à une étape de réaction avec un temps de relaxation de (3,5 ± 1,0) x 10-5 s. La vitesse de ce processus plus rapide ne varie pas avec le pH ou la concentration en protéine dans les limites des incertitudes expérimentales. On a postulé un modèle pour le mécanisme de dimérisation en deux étapes faisant intervenir un changement de configuration et un processus bimoléculaire. Ce modèle est capable de donner un accord qualitatif avec les données observées bien qu'une nouvelle étude de l'auto-dissociation du lysozyme par ultracentrifugation suggère que pour le pH de 7,0, l'association soit plus élevée que dimère.The laser light scattering technique has been used to probe the rates and mechanism of the dimerization of lysozyme in the absence of substrates. These experiments were performed on lysozyme in 0.15 M KCl and 20 °C over a range of pH from 3.0 to 7.0. Protein concentration varied from 3.6 x 10-4 M to 14.6 x 10-4 M. The pH = 3.0 sample (7.3 x 10-4 M) showed that Dw20 = (1.04 ± .02) x 10-6 cm2/s, corresponding well to the accepted value of the translational diffusion coefficient for the monomeric form of lysozyme. The scattering data indicated that at pH 5.0-7.0, lysozyme undergoes a conformation change before assuming the stable dimer form. This is evidenced by a minimum in the value of the apparent diffusion coefficient below that expected for the dimer. Detailed analysis of the observed spectra indicates that two rate steps can be discerned. The slower of the two rates corresponds to the T-jump value of Owen, Eyring, and Cole, (1969), which at pH = 7.0 is (2.0 ± .5) x 10-3 s. The present data for the slower reaction show a similar lack of concentration dependence at pH = 7.0 as was found by Owen, et al. However, at pH = 5.0 and 6.0, there is an increase of the relaxation time with decreasing concentration (below 7 x 10-4 M protein concentration) for this step. Also evident from the scattering data is a spectral component corresponding to a rate process with a relaxation time of (3.5 ± 1.0) x 10-5 s. The rate of this faster process does not Vary with pH or protein concentration within the bounds of experimental uncertainty. A model for a two-step dimerization mechanism involving a conformation change and a bimolecular process has been postulated. This model is able to give qualitative agreement with the observed data although a reinvestigation of the lysozyme self-dissociation by equilibrium ultracentrifugation suggest that at pH = 7.0, the association may be higher than dimer

Analysis of data from the analytical ultracentrifuge by nonlinear least-squares techniques.

Least-squares analysis of experimental data from the analytical ultracentrifuge is discussed in detail, with particular attention to the use of interference optics in studying nonideal self-associating macromolecular systems. Several samples are given that describe the application of the technique, the expected precision of the results, and some of its limitations. A FORTRAN IV computer program is available from the authors