BIOPHYSICAL THEORY AND MODELING |
Modeling Analytical Ultracentrifugation Experiments with an Adaptive Space-Time Finite Element Solution for Multi-Component Reacting Systems
Weiming Cao 1 and Borries Demeler 2*
1 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 December 31, 2007
Revised on January 29, 2008
Accepted on 31 January 2008
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Abstract |
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We describe an extension of the adaptive space-time finite element method (ASTFEM) used in the solution of the Lamm equation [Cao W, Demeler B. Modeling analytical ultracentrifugation experiments with an adaptive space-time finite element solution of the Lamm equation. (2005) Biophys J. 89(3):1589-602.] to the case of multi-component reacting systems. We use an operator splitting technique to decouple the sedimentation-diffusion process from the reaction process. The former is solved with an ASTFEM approach based on the Petrov-Galerkin method and on adaptive moving grids, and the latter is solved with the implicit mid-point Euler's method. Our solution can eliminate effectively the sedimentation errors for each component or species involved in the reaction, and it is free from oscillation near the cell bottom. It offers second order accuracy, and guarantees conservation of mass without any additional post-processing, and it permits modeling of multi-component, equilibrating systems where the reaction rate can be kinetically controlled between an instantaneous reaction and a non-interacting mixture. The proposed ASTFEM solution provides improved efficiency and accuracy compared to classical approaches, especially when medium sized and large molecules are modeled.
Key Words:
Adaptive Space Time Finite Element Method, Analytical Ultracentrifugation, Lamm Equation, Reacting Multi-Component Systems, Sedimentation Velocity, Self- and Heteroassociation
