Research

Signal Transduction Networks As Information Processing Machinery

The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow simulation and dynamical analysis. Exposing the network to tens of thousands of random combinations of inputs and analyzing the combined dynamics of multiple outputs revealed a robust system capable of clustering widely varying input combinations into equivalence classes of biologically relevant cellular responses. This capability was nontrivial in that the network performed sharp, nonfuzzy classifications even in the face of added noise, a hallmark of real-world decision-making.

Fractal in Biological Networks

One of the major challenges of contemporary science is to understand the nature of complex systems ranging from social networks to molecular networks. Extensive research on real complex networks has focused on static properties including degree distributions, scaling, clustering, and other structural features. The hope is that the architectural properties will yield some clues regarding the dynamics of the networks. Many of these networks are scale-free with the degrees of the nodes having a power law distribution. Also, some of these networks possess self-similar structures. Thus, the existence of a power law and self-similarity suggests an underlying fractal structure may exist and, perhaps, provide some insights on the dynamics. The relationship between complex networks and fractals remains an enigma. In many complex systems the competing forces of freedom and control tend to shape the dynamics. Too much freedom in a system can lead to chaotic, disordered behavior, while too much control can result in totally ordered dynamics. Complex systems seem to function effectively on the border of order and disorder where phase transitions occur and fractals emerge. In our research we analyzed an extensively studied class of discrete networks (Boolean networks) and showed that the dynamics of these networks expressed in terms of their given logical functions are intimately linked to emergent fractals. Applying a combinatorial approach to the state space we can define a complexity (entropy) measure that can discriminate between the different degrees of freedom and control for arbitrary subsets of the state space. We have demonstrated the existence of a global phase transition between order and disorder of these networks that provides mathematical evidence for the fractal nature of complex network dynamics (see our paper Combinatorial Fractal Geometry with a Biological Application, in the journal Fractals (volume 14 (2006) pp. 133-142).