TY - JOUR
T1 - The basis of easy controllability in Boolean networks
AU - Borriello, Enrico
AU - Daniels, Bryan C.
N1 - Funding Information:
We thank Cyrus Rashtchian for identifying the number of distinguishing nodes as a problem of witness sets in computational learning theory, and we thank Cole Mathis for useful comments on an early draft. We thank Doug Moore for contributions to the modular analysis code. We acknowledge Research Computing at Arizona State University for providing computing resources. B.C.D. was supported by a fellowship at the Wissenschaftskolleg zu Berlin.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12/1
Y1 - 2021/12/1
N2 - Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the effectiveness of external control in selecting a desired final state when that state is among the original attractors of the dynamics. Analyzing 49 existing biological network models, we find strong numerical evidence that the average number of nodes that must be forced scales logarithmically with the number of original attractors. This suggests that biological networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.
AB - Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the effectiveness of external control in selecting a desired final state when that state is among the original attractors of the dynamics. Analyzing 49 existing biological network models, we find strong numerical evidence that the average number of nodes that must be forced scales logarithmically with the number of original attractors. This suggests that biological networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.
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U2 - 10.1038/s41467-021-25533-3
DO - 10.1038/s41467-021-25533-3
M3 - Article
C2 - 34471107
AN - SCOPUS:85114122699
SN - 2041-1723
VL - 12
JO - Nature communications
JF - Nature communications
IS - 1
M1 - 5227
ER -