  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.

Discrete Mathematics