Model Simplification Procedure for Signal Transduction Pathway Models: An Application to IL-6 Signaling

Mathematical models of signal transduction pathways are characterized by a large number of proteins and uncertain parameters. One challenge involving these models is parameter identifiability as only a limited amount of quantitative data is generally available. One potential solution to this problem is model simplification, as the parts of the model that cannot be identified in experiments can be reduced. It is the main goal of the presented work to derive a model simplification procedure for signal transduction pathways such that: 1) the model size is significantly reduced such that the model can be validated using available experimental data, and 2) the physical interpretation of the remaining states and parameters is retained.
In a first step, sensitivity analysis is performed to determine which parts of the model contain parameters that have highly correlated effects on the outputs of the system. These model parts can then be replaced by a simpler representation as it is not be possible to verify the values of all of the reaction parameters. Representative state variables are then chosen for each part of the model via quantification of the degree of observability of the state variables of the model for potential measurements. A new model structure can be derived based upon this analysis. The initial estimates of the parameters are generated from simulation data of the original model. In a final step, the parameters of the simplified model are re-estimated using available experimental data.

The presented technique is used to derive a simplified version of an IL-6 signal transduction model. The number of equations and parameters in the model has been reduced from 68 to 13 and from 118 to 19, respectively. It is shown that the identifiability of the model has been improved significantly. The new model is able to adequately predict the dynamic behavior of key proteins of the signal transduction pathway both in simulations but also when compared to available experimental data.