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Control of complex networks requires both structure and dynamics.

Gates AJ, Rocha LM - Sci Rep (2016)

Bottom Line: 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.

View Article: 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.


Control of the single-cell segment polarity network (SPN) of gene and protein regulation in Drosophila melanogaster for all driver variable subsets of size /D/‚ÄČ=‚ÄČ1, /D/‚ÄČ=‚ÄČ2, /D/‚ÄČ=‚ÄČ3 and /D/‚ÄČ=‚ÄČ4.(inset) The mean fraction of reachable attractors  for each singleton driver variable set. The driver subsets predicted by structural controllability (SC) to fully control the network are highlighted in red and labeled , ,  and . The three variable driver subset with full attractor control is highlighted in yellow and labeled  (see SM for further details).
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f5: Control of the single-cell segment polarity network (SPN) of gene and protein regulation in Drosophila melanogaster for all driver variable subsets of size /D/‚ÄČ=‚ÄČ1, /D/‚ÄČ=‚ÄČ2, /D/‚ÄČ=‚ÄČ3 and /D/‚ÄČ=‚ÄČ4.(inset) The mean fraction of reachable attractors for each singleton driver variable set. The driver subsets predicted by structural controllability (SC) to fully control the network are highlighted in red and labeled , , and . The three variable driver subset with full attractor control is highlighted in yellow and labeled (see SM for further details).

Mentions: Previous analysis has shown that the SPN model is controlled by the upstream value of the Sloppy Pair Protein (SLP) and the extra-cellular signals of the Hedgehog and Wingless proteins from neighboring cells nhh/nHH and nWG55. The control portrait of this model also demonstrates that these three variables (driver set in Fig. 5) are capable of fully controlling the dynamics from any attractor to any other attractor. This is to be expected in segment polarity regulation since it is a highly orchestrated developmental process. The attractor control ability of individual nodes of the SPN in the inset of Fig. 5 further highlights this behavior, only the 3 chemical species mentioned above have a high when controlled alone, while all internal variables have negligible influence.


Control of complex networks requires both structure and dynamics.

Gates AJ, Rocha LM - Sci Rep (2016)

Control of the single-cell segment polarity network (SPN) of gene and protein regulation in Drosophila melanogaster for all driver variable subsets of size /D/‚ÄČ=‚ÄČ1, /D/‚ÄČ=‚ÄČ2, /D/‚ÄČ=‚ÄČ3 and /D/‚ÄČ=‚ÄČ4.(inset) The mean fraction of reachable attractors  for each singleton driver variable set. The driver subsets predicted by structural controllability (SC) to fully control the network are highlighted in red and labeled , ,  and . The three variable driver subset with full attractor control is highlighted in yellow and labeled  (see SM for further details).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834509&req=5

f5: Control of the single-cell segment polarity network (SPN) of gene and protein regulation in Drosophila melanogaster for all driver variable subsets of size /D/‚ÄČ=‚ÄČ1, /D/‚ÄČ=‚ÄČ2, /D/‚ÄČ=‚ÄČ3 and /D/‚ÄČ=‚ÄČ4.(inset) The mean fraction of reachable attractors for each singleton driver variable set. The driver subsets predicted by structural controllability (SC) to fully control the network are highlighted in red and labeled , , and . The three variable driver subset with full attractor control is highlighted in yellow and labeled (see SM for further details).
Mentions: Previous analysis has shown that the SPN model is controlled by the upstream value of the Sloppy Pair Protein (SLP) and the extra-cellular signals of the Hedgehog and Wingless proteins from neighboring cells nhh/nHH and nWG55. The control portrait of this model also demonstrates that these three variables (driver set in Fig. 5) are capable of fully controlling the dynamics from any attractor to any other attractor. This is to be expected in segment polarity regulation since it is a highly orchestrated developmental process. The attractor control ability of individual nodes of the SPN in the inset of Fig. 5 further highlights this behavior, only the 3 chemical species mentioned above have a high when controlled alone, while all internal variables have negligible influence.

Bottom Line: 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.

View Article: 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.