MULTI-SCALE INVERSE MODELING IN BIOLOGICAL MASS TRANSPORT PROCESSES

Abstract

A state-of-the-art inverse modeling strategy was developed, analyzed, and applied in two different biological mass transport processes. The strategy was developed in the framework of the nonlinear optimization problem in which model parameters were estimated by minimizing an appropriate objective function which represents the discrepancy between the observed and predicted responses of the biological systems. The forward problems were solved numerically using the mass conservative Galerkin based linear finite element and finite difference methods. Before incorporating in the framework of the inverse code, the numerical simulators were validated with either analytical or reference solutions. In the inverse code, the Osborne- Moré extended version of the Levenberg- Marquardt algorithm was used to determine the search direction. The Jacobian matrix was constructed using partial derivatives of the state variables with respect to model parameters by one and two-sided finite difference approximations. A mixed termination criterion was used to end the optimization. The strategy was applied to parameter identification problem in Fluorescence Recovery after Photobleaching (FRAP) protocol to estimate the optimized values of the mass transport and binding rate parameters for GFP-tagged glucocorticoid receptor. Results indicate that the protocol provides enough information to uniquely estimate one parameter. It also provides enough information to uniquely estimate the individual values of the binding rate coefficients given the value of the molecular diffusion coefficient is known. However, the protocol provides insufficient information for unique simultaneous estimation of three parameters (diffusion coefficient and binding rate parameters) owing to the high intercorrelation between the molecular diffusion coefficient and pseudo-association rate parameter. Attempts to estimate macromolecule mass transport and binding rate parameters simultaneously from FRAP data result in misleading conclusions regarding concentrations of free macromolecule and bound complex inside the cell, average binding time per vacant site, average time for diffusion of macromolecules from one site to the next, and slow or rapid mobility of biomolecules in cells. To obtain unique values for molecular diffusion coefficient and binding rate parameters of biomolecule, two FRAP experiments should be conducted on the same class of macromolecule and cell. One experiment should be used to measure the molecular diffusion coefficient independently of binding in an effective diffusion regime and the other should be conducted in a reaction dominant or reaction-diffusion regime to quantify the binding rate parameters. The inverse modeling strategy was also successfully used to identify hydraulic parameters for both single and multi-objective optimization problems in homogeneous and heterogeneous variably saturated soils. Incorporating both soil water content information and soil water pressure head data in the framework of the multi-objective parameter optimization, produced excellent result for both soil water content and pressure head profiles.