About block-parallel Boolean networks: a position paper

TL;DR

This paper advocates for the importance of block-parallel update schedules in Boolean networks, emphasizing their relevance and potential in biological modeling, and calls for further theoretical investigation into their properties.

Contribution

It highlights the significance of block-parallel update schedules in Boolean networks and argues for their consideration in biological modeling, encouraging more research into their theoretical properties.

Findings

Block-parallel schedules admit realistic properties for biological models.

They complement synchronous and asynchronous updates effectively.

Further theoretical study is needed on their intrinsic features.

Abstract

In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or less asymptotic dynamical behaviours such as fixed points or limit cycles. Since such mathematical models have been used in the framework of biological networks modelling, the question of choosing appropriate update schedules has arised soon. In this note, focusing on Boolean networks, our aim is to emphasise that the adequate way of thinking regulations and genetic expression over time is certainly not to consider a wall segregating synchronicity from asynchronicity because they actually complement rather well. In particular, we highlight that specific update schedules, namely block-parallel update schedules, whose intrinsic features are still not known from a theoretical point of view, admit realistic and pertinent properties in the context of biological modelling and deserve certainly more attention from the community.