Complex recurrent interactions in systems biology: from Henri Poincaré to Robert Rosen

Description/Abstract

In the systems biology era of the life sciences turning the vast amount of biological interaction data into meaningful knowledge requires indisputably methodological advances in data mining and system modelling. Modular hierarchy of complex molecular networks implies that modules have their own dynamics and interaction manifolds. However, when they hierarchically hook together, depending on different stable and unstable attractors of each module, a new organization of interaction with intertwined interacting region will be emerged which represent a complicated higher level complex manifold. To investigate how such higher level complex manifold emerges from integration of lower level modules, this paper presents an Event-Related Recurrent Modular Modelling Approach based on actual systems biology roots. The emphasis of this approach is on recurrence theorem, which is embedded in Henri Poincaré and Robert Rosen points of views as systems and biology roots, and it could be a conceptual strategy for systems identification and design methodology, in systems biology and synthetic biology, respectively. By the use of Iterated Maps, we explain how simple signaling pathways can be embedded in networks to generate more complex behaviours such as toggle switches and oscillators as the basic building blocks of cell cycle engine.