Adaptive neural-based fuzzy modeling for biological systems.

The inverse problem of identifying dynamic biological networks from their time-course response data set is a cornerstone of systems biology. Hill and Michaelis-Menten model, which is a forward approach, provides local kinetic information. However, repeated modifications and a large amount of experimental data are necessary for the parameter identification. S-system model, which is composed of highly nonlinear differential equations, provides the direct identification of an interactive network. However, the identification of skeletal-network structure is challenging. Moreover, biological systems are always subject to uncertainty and noise. Are there suitable candidates with the potential to deal with noise-contaminated data sets? Fuzzy set theory is developed for handing uncertainty, imprecision and complexity in the real world; for example, we say "driving speed is high" wherein speed is a fuzzy variable and high is a fuzzy set, which uses the membership function to indicate the degree of a element belonging to the set (words in Italics to denote fuzzy variables or fuzzy sets). Neural network possesses good robustness and learning capability. In this study we hybrid these two together into a neural-fuzzy modeling technique. A biological system is formulated to a multi-input-multi-output (MIMO) Takagi-Sugeno (T-S) fuzzy system, which is composed of rule-based linear subsystems. Two kinds of smooth membership functions (MFs), Gaussian and Bell-shaped MFs, are used. The performance of the proposed method is tested with three biological systems.