A Novel Finite Volume Solution of the Lamm Equation for Band-Forming Analytical Ultracentrifugation Experiments

Analytical ultracentrifugation (AUC) enables the investigation of a wide variety of systems. However, established analysis methods struggle with variable sedimentation or diffusion coefficients arising from non-constant behavior. While good experimental design can mitigate most non-ideality, some types of experiments depend on non-constant solvent density or viscosity. The band-forming AUC experiment (BFE) is a prime example because diffusive mixing between solvents of different densities results in the formation of dynamic density and viscosity gradients. In this study, we present a solution to the Lamm equation using the adaptive space–time finite volume method (ASTFVM) to model such non-constant behavior. By integrating ASTFVM into all optimization methods available in the UltraScan software, we further demonstrate its potential by analyzing BFEs for the first time since their development without assuming constant density and viscosity. The obtained sedimentation coefficients for our myoglobin system match those of traditional boundary sedimentation velocity experiments while consuming an order of magnitude less sample. ASTFVM represents a significant step towards the analysis of analytical ultracentrifugation experiments performed under non-constant solution conditions, and lends itself to extension to any condition in which sedimentation and diffusion coefficients are non-constant for one or more solutes.