Abstract
SUMMARY: The biomolecular networks underpinning cell function exhibit canalization, or the buffering of fluctuations required to function in a noisy environment. We present a new major release of CANA, v1.0.0, an open-source Python package for understanding canalization in automata network models, discrete dynamical systems in which activation of biomolecular entities (e.g. transcription of genes) is modeled as the activity of coupled automata. One understudied putative mechanism for canalization is the functional equivalence of biomolecular regulators (e.g. among the transcription factors for a gene). We study this mechanism using the theory of symmetry in discrete functions. We present a new exact method, schematodes, for finding maximal symmetry groups among the inputs to discrete functions, and integrate it into CANA. The schematodes method substantially outperforms the inexact method of previous CANA versions both in speed and accuracy. We apply CANA v1.0.0 to study symmetry in 74 experimentally supported automata network models from the Cell Collective (CC) repository. The symmetry distribution is significantly different in the CC than in random automata with the same in-degree (connectivity) and bias (average output) (Kolmogorov-Smirnov test, P ≪ .001). Its spread is much wider than in a null model (IQR 0.31 versus IQR 0.20 with equal medians), demonstrating that the CC is enriched in functions with extreme symmetry or asymmetry. AVAILABILITY AND IMPLEMENTATION: CANA source is on https://github.com/CASCI-lab/CANA and is installable via pip install cana. Source for schematodes is on https://github.com/CASCI-lab/schematodes. Analysis scripts are on https://github.com/CASCI-lab/symmetryInCellCollective.