Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions

In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.The authors acknowledge the contribution of Courtney Chancellor, who participated during one year to this research activity, and the first author, Francisco Chinesta, acknowledges the support of the Institute Universitaire de France (IUF). The work of Elias Cueto and Francisco Chinesta has been partially funded by the Spanish Ministry of Economy and Innovation through Grant Number DPI2014-51844-C2-1-R