Simplification of a complex signal transduction model using invariants and flow equivalent servers

In this paper we consider the modeling of a portion of the signal transduction pathway involved in the angiogenic process. The detailed model of this process is affected by a high level of complexity due to the functional properties that are represented and the size of its state space. To overcome these problems, we suggest approaches to simplify the detailed representation that result in models with a lower computational and structural complexity, while still capturing the overall behavior of the detailed one. The simplification process must take into account both the structural aspects and the quantitative behavior of the original model. To control the simplification from a structural point of view, we propose a set of reduction steps that maintain the invariants of the original model. To ensure the correspondence between the simplified and the original models from a quantitative point of view we use the flow equivalent method that provides a way of obtaining the parameters of the simplified model on the basis of those of the original one. To support the proposed methodology we show that a good agreement exists among the temporal evolutions of the relevant biological products in the simplified and detailed model evaluated with a large set of input parameters.