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Sedimentation velocity analytical ultracentrifugation reveals particle size distributions. A new relationship clarifies how time-derivative methods approximate particle size distributions for large particles.

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Area of Science:

  • Biophysics
  • Analytical Chemistry
  • Materials Science

Background:

  • Sedimentation velocity analytical ultracentrifugation (SV-AUC) is crucial for determining particle size distributions.
  • For large particles, diffusion is often negligible compared to sedimentation, simplifying boundary analysis.
  • Previous methods calculated size distributions from boundary profiles, but a unified framework was lacking.

Purpose of the Study:

  • To develop a common theoretical framework for analyzing sedimentation boundaries.
  • To uncover a novel relationship between particle size distributions and concentration profile derivatives.
  • To quantitatively describe approximations in time-derivative methods.

Main Methods:

  • Recapitulation of integral and derivative methods for calculating sedimentation coefficient distributions (g*(s)).
  • Development of a new analytical relationship between g*(s) and the time-derivative of concentration profiles.
  • Analysis of the effect of finite time intervals on time-derivative methods.

Main Results:

  • A new, analytically closed relationship between g*(s) and the time-derivative of concentration profiles was identified.
  • This relationship is analogous to the Bridgman relationship for radial derivatives.
  • Finite time intervals in time-derivative methods introduce a skewed box average of the true distribution.

Conclusions:

  • The study provides a theoretical basis for understanding differences between time-derivative and integral fitting methods in SV-AUC.
  • This work clarifies the impact of experimental approximations on particle size distribution determination.
  • The findings enhance the accuracy and interpretation of SV-AUC data for large particles.