Sedimentation Boundary Structure of Multi-Component Solutions with Rapidly Reversible Interactions

Abstract

The coupled transport behavior of macromolecular mixtures with rapidly reversible complex formation is of great interest in the study of protein interactions by many different methods. Complicated transport patterns arise even for simple bimolecular reactions, when all species exhibit different migration velocities, yet are coupled by mass action law. Although partial differential equations are available to describe the spatial and temporal evolution of such systems given particular initial conditions, these are often not useful to fit imperfect experimental data, and do not yield any insight into the transport mechanism and phase behavior of the systems in parameter space. For two-component systems, based on the limit of non-diffusing species migrating under constant force, we have previously derived simple algebraic relationships describing the number, amplitude, and velocity of sedimentation boundaries, which are consistent with the principle that the time-average velocity of all co-sedimenting components must match in each boundary. These can be considered ‘effective particles’, and their properties can be related to parameters extracted from experimental sedimentation profiles. Here, we generalize this effective particle theory to N-component systems. These can have N-2 reaction boundaries of successively lower velocity and number of components. We report algebraic relationships for velocities and composition. The concentration space is subdivided into regions exhibiting different boundary patterns with discontinuous transitions along characteristic subspaces. The extension of the effective particle theory provides physical insights into the coupled co-migration processes, and can be used to interpret boundary patterns derived from experimentally measured sedimentation coefficient distributions. It can be used to plan multi-component sedimentation velocity experiments to determine binding constants and complex stoichiometries.