Inference of Biochemical S-Systems via Mixed-Variable Multiobjective Evolutionary Optimization

Abstract

Inference of the biochemical systems (BSs) via experimental data is important for understanding how biochemical components in vivo interact with each other. However, it is not a trivial task because BSs usually function with complex and nonlinear dynamics. As a popular ordinary equation (ODE) model, the S-System describes the dynamical properties of BSs by incorporating the power rule of biochemical reactions but behaves as a challenge because it has a lot of parameters to be confirmed. This work is dedicated to proposing a general method for inference of S-Systems by experimental data, using a biobjective optimization (BOO) model and a specially mixed-variable multiobjective evolutionary algorithm (mv-MOEA). Regarding that BSs are sparse in common sense, we introduce binary variables indicating network connections to eliminate the difficulty of threshold presetting and take data fitting error and the L0-norm as two objectives to be minimized in the BOO model. Then, a selection procedure that automatically runs tradeoff between two objectives is employed to choose final inference results from the obtained nondominated solutions of the mv-MOEA. Inference results of the investigated networks demonstrate that our method can identify their dynamical properties well, although the automatic selection procedure sometimes ignores some weak connections in BSs.