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Mathematical Modeling of Bio-Macromolecule Dynamics in Living Cells: A Continuum Mechanics Approach

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  2007 ASAE Annual Meeting  077008.(doi:10.13031/2013.23535)
Authors:   Kouroush Sadegh Zadeh, Hubert J Montas, Adel Shirmohammadi
Keywords:   Bio-macromolecule transport in-vivo, Numerical Modeling, Optimization, Preconditioned Conjugate Gradient, Incomplete Cholesky factorization

A robust and efficient numerical model was developed and implemented to solve a system of three coupled nonlinear partial differential equations governing bio-macromolecule transport and reaction in living cells. The Picard fixed point iteration method was coupled with the Incomplete Cholesky factorization, Preconditioned Conjugate Gradient algorithm and adaptive time-stepping to solve the matrix equations. The numerical simulator shows excellent agreement with analytic solutions and is four times faster than the direct algorithm. The model was coupled with the Osborne-Moré extended version of the Levenberg-Marquardt optimization algorithm and an experimental FRAP data set to estimate the optimized values of eight model parameters for GFP-tagged glucocorticoid receptor (GFP-GR). Results indicate that the developed methodology is a powerful approach to quantify biomolecular transport parameters and extract as much physiochemical information from the FRAP protocol as possible. Our study further confirms two basic assumptions of the FRAP protocol in nucleoplasm related to mobility and availability of binding sites.

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