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Modeling Analytical Ultracentrifugation Experiments with an Adaptive Space-Time Finite Element Solution of the Lamm Equation

Weiming Cao ^* and Borries Demeler 

^* Department of Applied Mathematics, The University of Texas at San Antonio, Texas; and Department of Biochemistry, University of Texas Health Science Center at San Antonio, San Antonio, Texas

Correspondence: Address reprint requests to Weiming Cao, E-mail: wcao{at}math.utsa.edu; or Borries Demeler, E-mail: demeler{at}biochem.uthscsa.edu.

Analytical ultracentrifugation experiments can be accurately modeled with the Lamm equation to obtain sedimentation and diffusion coefficients of the solute. Existing finite element methods for such models can cause artifactual oscillations in the solution close to the endpoints of the concentration gradient, or fail altogether, especially for cases where s²/D is large. Such failures can currently only be overcome by an increase in the density of the grid points throughout the solution at the expense of increased computational costs. In this article, we present a robust, highly accurate and computationally efficient solution of the Lamm equation based on an adaptive space-time finite element method (ASTFEM). Compared to the widely used finite element method by Claverie and the moving hat method by Schuck, our ASTFEM method is not only more accurate but also free from the oscillation around the cell bottom for any s²/D without any increase in computational effort. This method is especially superior for cases where large molecules are sedimented at faster rotor speeds, during which sedimentation resolution is highest. We describe the derivation and grid generation for the ASTFEM method, and present a quantitative comparison between this method and the existing solutions.

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