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Control of complex networks requires both structure and dynamics
The study of network structure has uncovered signatures of the organization
of complex systems. However, there is also a need to understand how to control
them; for example, identifying strategies to revert a diseased cell to a
healthy state, or a mature cell to a pluripotent state. Two recent
methodologies suggest that the controllability of complex systems can be
predicted solely from the graph of interactions between variables, without
considering their dynamics: structural controllability and minimum dominating
sets. We demonstrate that such structure-only methods fail to characterize
controllability when dynamics are introduced. We study Boolean network
ensembles of network motifs as well as three models of biochemical regulation:
the segment polarity network in Drosophila melanogaster, the cell cycle of
budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in
Arabidopsis thaliana. We demonstrate that structure-only methods both
undershoot and overshoot the number and which sets of critical variables best
control the dynamics of these models, highlighting the importance of the actual
system dynamics in determining control. Our analysis further shows that the
logic of automata transition functions, namely how canalizing they are, plays
an important role in the extent to which structure predicts dynamics.Comment: 15 pages, 6 figure
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