Qualitative Simulation of Genetic Regulatory Networks Using Piecewise-Linear Models

In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics which often provide qualitative and coarse-grained descriptions of genetic regulatory networks. The method is able to deal with nontrivial mathematical problems induced by the discontinuous right-hand sides of the differential equations. Furthermore, it guarantees that the simulation covers all possible solutions of quantitative PL models corresponding to the qualitative PL model used by the method. The qualitative simulation method has been implemented in Java.