Control of complex networks requires both structure and dynamics.
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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 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.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.
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PubMed Central - PubMed
Affiliation: School of Informatics and Computing, Indiana University, Bloomington, IN, USA.
ABSTRACT
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. No MeSH data available. |
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Mentions: Let us now consider the N = 3 variable loop motif with self-interactions (Fig. 2D). The full ensemble of BNs constrained by this motif is much larger than the previous example (every variable has ki = 2 inputs); it consists of 4096 networks of which 1352 are NC, 1744 have RES, and 1000 have FES. Figure 4A shows the control portrait of this motif’s BN ensemble for a single (D ≡ {xi}) or pair (D ≡ {xi, xj}) of driver variables. The control portrait of the STG illustrates the difference between the two measures of controllability. While varies greatly, for all BNs. This means that in some BNs, many configurations can be reached simply because the transient dynamics move through many network configurations. Structural control methodologies ignore this natural propensity for control (self-organization). Thus we use the measure to tally only the proportion of transitions that result from control interventions. |
View Article: PubMed Central - PubMed
Affiliation: School of Informatics and Computing, Indiana University, Bloomington, IN, USA.
No MeSH data available.