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.