Identification of Parameters for Large-scale Kinetic Models

Inverse problem for the identification of the parameters for large-scale systems of nonlinear ordinary differential equations (ODEs) arising in systems biology is analyzed. In a recent paper in \textit{Mathematical Biosciences, 305(2018), 133-145}, the authors implemented the numerical method suggested by one of the authors in \textit{J. Optim. Theory Appl., 85, 3(1995), 509-526} for identification of parameters in moderate scale models of systems biology. This method combines Pontryagin optimization or Bellman's quasilinearization with sensitivity analysis and Tikhonov regularization. We suggest modification of the method by embedding a method of staggered corrector for sensitivity analysis and by enhancing multi-objective optimization which 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. We apply the modified method to a benchmark model of a three-step pathway modeled by 8 nonlinear ODEs with 36 unknown parameters and two control input parameters. The numerical results demonstrate geometric convergence with a minimum of five data sets and with minimum measurements per data set. Software package \textit{qlopt} is developed and posted in GitHub. MATLAB package AMIGO2 is used to demonstrate advantage of \textit{qlopt} over most popular methods/software such as \textit{lsqnonlin}, \textit{fmincon} and \textit{nl2sol}.