Maximum entropy formalism to describe transcriptional regulation in cancer
K. Baca-López [1+2], E. Hernández-Lemus [2+3], M. Mayorga [1]

[1] Facultad de Ciencias, Universidad Autonoma del Estado de Mexico, Toluca, Mexico, [2] Departamento de Genomica Computacional, Instituto Nacional de Medicina Genomica, Mexico, D.F., Mexico, [3] Centro de Ciencias de la Complejidad, Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico

Abstract: The vast majority of human diseases is related with the dynamic interaction of many genes and their products as well as environmental constraints. That fact makes them complex phenomena. Cancer (and breast cancer in particular) is a paradigmatic example of such complex behavior. Due to this fact, the analysis of the biochemical interactions involved often is based on the consideration of the related gene regulatory relationships. Since gene regulation is a non-equilibrium process, the inference and analysis of such phenomena could be done following the tenets of non-equilibrium statistical mechanics and irreversible thermodynamics. The traditional program in statistical mechanics consists in inferring the joint probability distribution for either microscopic states (equilibrium) or mesoscopic-states (non-equilibrium) given a model for the particle interactions (e.g. intermolecular potentials).
On the other hand, an inverse problem in statistical mechanics, is based on considering a realization of the probability distribution of micro- or meso-states and using it to infer the interaction potentials between particles. Following this protocol, we analyzed more than 200 whole-genome gene expression experiments in breast cancer patients, and by means of a nonlinear analysis based on an information-theoretical measure, we deconvolute the associated set of transcriptional interactions, i.e. we discover a set of fundamental biochemical reactions related to this pathology. By doing this, we showed how to apply the tools of non-linear statistical physics to generate hypothesis to be tested on clinical and biochemical settings in relation to cancer phenomenology.