Abstract
Living systems comprise interacting biochemical components in very large networks. Given their high connectivity, biochemical dynamics are surprisingly not chaotic but quite robust to perturbations—a feature C.H. Waddington named canalization. Because organisms are also flexible enough to evolve, they arguably operate in a critical dynamical regime between order and chaos. The established theory of criticality is based on networks of interacting automata where Boolean truth values model presence/absence of biochemical molecules. The dynamical regime is predicted using network connectivity and node bias (to be on/off) as tuning parameters. Revising this to account for canalization leads to a significant improvement in dynamical regime prediction. The revision is based on effective connectivity, a measure of dynamical redundancy that buffers automata response to some inputs. In both random and experimentally validated systems biology networks, reducing effective connectivity makes living systems operate in stable or critical regimes even though the structure of their biochemical interaction networks predicts them to be chaotic. This suggests that dynamical redundancy may be naturally selected to maintain living systems near critical dynamics, providing both robustness and evolvability. By identifying how dynamics propagates preferably via effective pathways, our approach helps to identify precise ways to design and control network models of biochemical regulation and signalling.
Highlights
The complex organization and dynamics of living and social systems have been successfully studied with networks [1,2]
The hypothesis is that effective connectivity, as a measure of the full canalization phenomenon, captures both the connectivity and canalizing logic of automata networks better than the structure parameters used in equation (1.1)
If we use ke to substitute k and even p in the structural theory (ST), we predict the dynamical regime of a Boolean networks (BNs) more accurately
Summary
The complex organization and dynamics of living and social systems have been successfully studied with networks [1,2]. Boolean networks (BNs) are the simplest of such canonical models of complex systems, and exhibit a wide range of dynamical behaviours [5,6]. Logical rules specify the causal mechanisms that lead to state changes and are derived from qualitative (coarse-grained) molecular data, capturing the combinatorial regulation that is pervasive in biochemical networks [7,8,9,10,11,12]. Perhaps the key advantage of using BNs to model biomedical regulation and signalling is precisely that, unlike more traditional continuous dynamical systems, they do not require large amounts of detailed molecular data. Famous examples include the yeast cell cycle BN that reproduces natural dynamical trajectories from known initial conditions [21], an intracellular signal transduction in a breast cancer BN that reproduces known drug resistance mechanisms and has uncovered new drug interventions [22] and a BN model used to reprogramme differentiated cells [23]
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