Identification of biomolecule mass transport and binding rate parameters in living cells by inverse modeling

Abstract

Background: Quantification of in-vivo biomolecule mass transport and reaction rate parameters from experimental data obtained by Fluorescence Recovery after Photobleaching (FRAP) is becoming more important.

Parameter estimation in flow through partially saturated porous materials

“…Otherwise, it is increased. The approach avoids calculation of k and step length in each iteration and therefore is computationally cheap [76].…”

A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media

“…(1) and (3), they should be solved numerically. Using Taylor series expansion, the finite difference approximation of the h-based-form Richards equation can be developed as [13,47,55]: …”

“…Experimentation and process-based mathematical modeling are two orthodox approaches which have been extensively used to analyze fluid flow in different systems with varying degree of complexity. While experimentation may better represent the micro-and macro-environment of the systems; they are time-consuming, tedious, expensive, and often impose unrealistic and simplified initial and boundary conditions on transport domain and processes in, especially, open systems [55]. An efficient alternative is developing state-of-the-art process-based mathematical models with enhanced prediction capabilities.…”

Multi-objective optimization in variably saturated fluid flow

“…Table 1 presents eight sets of optimized parameter values obtained by the single-objective optimization using different initial guesses for the hydraulic parameters (the last two columns are from [12] for comparison sake). The Root Mean Squared Error (RMSE) was calculated by [34]: The units for K s and α are cm d −1 and cm −1 , respectively, while other parameters are dimensionless. The last two columns are from [12] for sake of comparison.…”

“…Furthermore, laboratory scale parameters may not be representative of the large scale system and the results obtained by large scale methods may show considerable variations. Finally, information regarding the uncertainty of model parameters is not readily available using these procedures [31,34]. A promising alternative is parameter optimization by inverse modeling which has been widely used in the past few decades [7,[10][11][12][13][14]16,23,[32][33][34].…”