Symbolic dynamics of biological feedback networks

TL;DR

This paper introduces a symbolic dynamics framework for analyzing biological feedback networks, revealing dominant feedback loops and robustness in complex systems through coarse-grained analysis of short time series.

Contribution

It develops a general coarse-graining method for feedback network dynamics, identifying dominant loops and robustness in biological modules.

Findings

Dominant symbolic patterns are robust to parameter changes.

Complex networks often exhibit a single dominant feedback loop.

Method can extract feedback loops from transient short time series.

Abstract

We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone 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.