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

¹ The University of Texas at San Antonio
² The University of Texas Health Science Center at San Antonio

^* To whom correspondence should be addressed. E-mail: demeler{at}biochem.uthscsa.edu.

Submitted on February 11, 2005
Revised on April 28, 2005
Accepted on 14 June 2005

	Abstract

Analytical ultracentrifugation experiments can be accurately modelled with the Lamm equation [Lamm, O. Die Differentialgleichung der Ultrazentrifugierung. Ark. Mat. Astron. Fys. 21B (1929) 1-4.] 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 s^2/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 paper, 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 [Claverie, J.-M., H. Dreux, and R. Cohen. 1975. Sedimentation of generalized systems of interacting particles. I. Solutions of systems of complete Lamm equations. Biopolymers. 14:1685-1700] and the moving hat method by Schuck [Schuck, P. Sedimentation Analysis of Noninteracting and Self-Associating Solutes Using Numerical Solutions to the Lamm Equation. Biophys. J. 75(3), 1503-1512], our ASTFEM method is not only more accurate but also free from oscillation for any s^2/D without any increase in computational effort. This method is especially superior for cases where large molecules are sedimented at faster rotor speeds where 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. We conclude that ASTFEM is an ideal method for modeling sedimentation experiments.

Key Words: Adaptive Space-Time Finite Element Method, Lamm equation, analytical ultracentrifugation,, fixed mesh, moving mesh, sedimentation velocity analysis

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