An iterative LMA method for parameter estimation in dynamic modeling of TGFβ pathway using ODE

Transforming Growth Factor (TGF) beta signalling pathway is a key regulator of a variety of biological processes in physiological and pathological conditions. In spite of numerous investigations, the dynamics of this complex pathway is largely unknown. Hence, developing mathematical models can pave the way for discovering novel therapeutics. The pathway model has unknown parameters that could be estimated using experimental data. Nonlinear least square methods are commonly used to solve this problem. Because of the difficulties of measuring biological data and its high cost, most of the experiments on this pathway have few data samples. This makes parameter estimation harder and in some cases, with non-unique solutions. In this paper, first a model of TGF beta pathway and its parameters are chosen from the literature. After simulation, model outputs are sampled and used to estimate model parameters. A small number of samples are selected to emulate experimental data. After estimating model parameters multiple times with different initial points, estimation results are compared with the actual value of each parameter by analysing its probability distribution function. In addition, an iterative Levenberg-Marquardt algorithm (LMA) method is proposed in which parameters are divided into groups depending on the state variables they affect. Then, only one group of parameters is estimated in each iteration. Simulation results show the efficiency of the proposed method. By testing the method on the TGF beta model it is shown that it is able to find the optimum point of model residual and solves big network estimation problems with less computation cost.