Symbolic Dynamics of Biological Feedback Networks

We formulate general rules for a coarse graining of the dynamics, which we term “symbolic dynamics,” of feedback networks with monotonic interactions, such as most biological modules. Networks which are more complex than simple cyclic structures can exhibit multiple different symbolic dynamics. Nevertheless, we show several examples where the symbolic dynamics is dominated by a single pattern that is very robust to changes in parameters and is consistent with the dynamics being dictated by a single feedback loop. Our analysis provides a method for extracting these dominant loops from short time series, even if they only show transient trajectories.