MOTIVATION: The major function of signal transduction pathways in cells is to sense signals from the environment and process the information through signaling molecules in order to regulate the activity of transcription factors. On the molecular level, the information transmitted by a small number of signal molecules is amplified in the internal signaling pathway through enzyme catalysis, molecular modification and via the activation or inhibition of interactions. However, the dynamic system behavior of a signaling pathway can be complex and, despite knowledge of the pathway components and interactions, it is still a challenge to interpret the pathways behavior. Therefore, a systematic method is proposed in this study to quantify the signal transduction ability. RESULTS: Based on the non-linear signal transduction system, signal transduction ability can be investigated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. To avoid difficulties associated with solving a complex HJI-constrained optimization problem for signal transduction ability, the Takagi-Sugeno fuzzy model is introduced to approximate the non-linear signal transduction system by interpolating several local linear systems so that the HJI-constrained optimization problem can be replaced by a linear matrix inequality (LMI)-constrained optimization problem. The LMI problem can then be efficiently solved for measuring signal transduction ability. Finally, the signal transduction ability of two important signal transduction pathways was measured by the proposed method and confirmed using experimental data, which is useful for biotechnological and therapeutic application and drug design.

Signal transduction plays an important role in biological organisms. Here, we proposed a method to access the information of the signal transduction ability of signal transduction pathway in the cells. Due to the nonlinear signal transduction pathway model, we have to solve the Hamilton-Jacobi inequalities (HJIs) to get the measurement. Instead of directly solving HJIs, fuzzy interpolation method was employed such that we can systematically measure signal transduction ability by solving the linear matrix inequalities (LMIs). The measurement will provide an insight to the characteristics of the signal transduction networks.