Logical and Symbolic Analysis of Robust Biological Dynamics

Logical models provide insight about key control elements of biological networks. Based solely on the logical structure, we can determine state transition diagrams that give the allowed possible transitions in a coarse grained phase space. Attracting pathways and stable nodes in the state transition diagram correspond to robust attractors that would be found in several different types of dynamical systems that have the same logical structure. Attracting nodes in the state transition diagram correspond to stable steady states. Furthermore, the sequence of logical states appearing in biological networks with robust attracting pathways would be expected to appear also in Boolean networks, asynchronous switching networks, and differential equations having the same underlying structure. This provides a basis for investigating naturally occurring and synthetic systems, both to predict the dynamics if the structure is known, and to determine the structure if the transitions are known.