Canalization and control in automata networks: body segmentation in Drosophila melanogaster

TL;DR

This paper introduces schema redescription as a scalable method to analyze canalization in automata networks, linking micro-level logic redundancy to macro-level dynamics, with applications to biological systems like Drosophila segmentation.

Contribution

The authors develop a novel framework to quantify canalization and control in automata networks, enabling analysis of large-scale biological models and revealing new insights into their dynamics.

Findings

Uncovered dynamical modularity in automata networks.

Identified minimal control conditions and critical nodes.

Enhanced understanding of the robustness and attractor basins in a Drosophila model.

Abstract

We present schema redescription as a methodology to characterize canalization in automata networks used to model biochemical regulation and signalling. In our formulation, canalization becomes synonymous with redundancy present in the logic of automata. This results in straightforward measures to quantify canalization in an automaton (micro-level), which is in turn integrated into a highly scalable framework to characterize the collective dynamics of large-scale automata networks (macro-level). This way, our approach provides a method to link micro- to macro-level dynamics -- a crux of complexity. Several new results ensue from this methodology: uncovering of dynamical modularity (modules in the dynamics rather than in the structure of networks), identification of minimal conditions and critical nodes to control the convergence to attractors, simulation of dynamical behaviour from incomplete information about initial conditions, and measures of macro-level canalization and robustness to perturbations. We exemplify our methodology with a well-known model of the intra- and inter cellular genetic regulation of body segmentation in Drosophila melanogaster. We use this model to show that our analysis does not contradict any previous findings. But we also obtain new knowledge about its behaviour: a better understanding of the size of its wild-type attractor basin (larger than previously thought), the identification of novel minimal conditions and critical nodes that control wild-type behaviour, and the resilience of these to stochastic interventions. Our methodology is applicable to any complex network that can be modelled using automata, but we focus on biochemical regulation and signalling, towards a better understanding of the (decentralized) control that orchestrates cellular activity -- with the ultimate goal of explaining how do cells and tissues 'compute'.