Identification of parameters for large-scale kinetic models

Abstract

Numerical method for the inverse problem on the identification of parameters for large-scale systems of nonlinear ordinary differential equations (ODEs) arising in systems biology is introduced. The method combines Pontryagin optimization or Bellman's quasilinearization with sensitivity analysis and Tikhonov regularization. Embedding a method of staggered corrector for sensitivity analysis and by enhancing multi-objective optimization enables application of the method to large-scale models with practically non-identifiable parameters based on multiple data sets, possibly with partial and noisy measurements. The method is tested in two canonical benchmark models, such as three-step pathway modeled by 8 nonlinear ODEs with 36 unknown and two control input parameters, and a model of central carbon metabolism of Escherichia coli described by a system of 18 linear ODEs with 116 unknown parameters. The numerical results demonstrate superlinear convergence with a minimum data sets and with minimum measurements per data set, and possibly with partial and noisy measurements. Software package qlopt is developed and posted in GitHub. MATLAB package AMIGO2 is used to demonstrate advantage of qlopt over most popular methods/software such as lsqnonlin, fmincon and nl2sol.