Sedimentation velocity analysis of heterogeneous protein-protein interactions: Lamm equation modeling and sedimentation coefficient distributions c(s)

¹ Center for Advanced Research in Biotechnology, University of Maryland
² Medizinische Hochschule Hannover, Hannover, Germany
³ National Institutes of Health

^* To whom correspondence should be addressed. E-mail: pschuck{at}helix.nih.gov.

Submitted on January 12, 2005
Revised on March 19, 2005
Accepted on 19 April 2005

	Abstract

We describe algorithms for solving the Lamm equations for the reaction-diffusion-sedimentation process in analytical ultracentrifugation, and examine the potential and limitations for fitting experimental data. The theoretical limiting case of a small, uniformly distributed ligand rapidly reacting with a larger protein in a 'constant bath' of the ligand is recapitulated, which predicts the reaction boundary to sediment with a single sedimentation and diffusion coefficient. As a consequence, it is possible to express the sedimentation profiles of reacting systems as c(s) distribution of non-interacting Lamm equation solutions, deconvoluting the effects of diffusion. For rapid reactions, the results are quantitatively consistent with the 'constant bath' approximation, showing c(s) peaks at concentration-dependent positions. For slower reactions, the deconvolution of diffusion is still partially successful, with c(s) resolving peaks that reflect the populations of sedimenting species. The transition between c(s) peaks describing reaction boundaries of moderately strong interactions (KD ~ 10(-6) M) or resolving sedimenting species was found to occur in a narrow range of dissociation rate constant between 10(-3) and 10(-4) sec(-1). The integration of the c(s) peaks can lead to isotherms of species populations or s-value of the reaction-boundary, respectively, which can be used for the determination of the equilibrium binding constant.

Key Words: Gilbert-Jenkins theory, Lamm equation, analytical ultracentrifugation, protein-ligand interactions, reaction kinetics, size-distribution

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