Reaction Network Models as a Tool to Study Gene Regulation and Cell Signaling in Development and Diseases

Abstract

Advances in molecular biology and experimental techniques have produced a large amount of data with unprecedented accuracy. In addition to computational methods for handling these massive amounts of data, the development of theoretical models aimed at solving specific questions is essential. Many of these questions reside in the description of gene regulation and cell signaling networks which are key aspects during development and diseases. To deal with this problem, we present in this chapter a set of strategies to describe the dynamic behavior of reaction network models. We present some results selected from broad mathematical results, focused on what is closely related to gene regulation and cell signaling. We give special attention to the so-called Chemical Reaction Network Theory (CRNT) that has been developed since the first half of the past century. Some of the most important and practical results of this theory are the analysis of the conditions for a given network to exhibit emergent proprieties like bistability. The description of this behavior has been recurrent in recent studies of developmental biology or cellular signaling networks [1, 2, 3, 4, 5]. However, while referring to the same phenomena, the connection between bistability or oscillations in CRNT and biology is not obvious and has been a challenge, despite some well-succeeded examples. Contribution to bringing these two areas of knowledge together is the primary purpose of this chapter.