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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.


(A) Control of the eukaryotic cell cycle of budding yeast Saccharomyces cerevisiae (CCN) for all driver variable subsets of size /D/ = 1, /D/ = 2, /D/ = 3 and /D/ = 4. (inset) The mean fraction of reachable attractors  for each singleton driver variable set. The subset predicted to fully control the network are highlighted in red and labeled  for structural controllability (SC), while those predicted by minimum dominating sets (MDS) are labeled . The driver variable subsets with full attractor control are highlighted in yellow (see SM for further details). (B) Controlled Attractor Graphs (CAGs) for each singleton driver variable set. The wild-type attractor is highlighted in green, all other attractors are in purple.
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f6: (A) Control of the eukaryotic cell cycle of budding yeast Saccharomyces cerevisiae (CCN) for all driver variable subsets of size /D/ = 1, /D/ = 2, /D/ = 3 and /D/ = 4. (inset) The mean fraction of reachable attractors for each singleton driver variable set. The subset predicted to fully control the network are highlighted in red and labeled for structural controllability (SC), while those predicted by minimum dominating sets (MDS) are labeled . The driver variable subsets with full attractor control are highlighted in yellow (see SM for further details). (B) Controlled Attractor Graphs (CAGs) for each singleton driver variable set. The wild-type attractor is highlighted in green, all other attractors are in purple.

Mentions: The eukaryotic cell cycle process of the budding yeast Saccharomyces cerevisiae reflects the cyclical gene expression activity that leads to cell division. Here, we use the 12 variable simplified Boolean model of the yeast Cell-Cycle Network (CCN) derived by Li et al.17. The SC analysis of the CCN interaction graph identifies only one driver variable to be sufficient for fully controlling the BN’s dynamics. Yet, as demonstrated in Fig. 6A, it only achieves negligible configuration control () and very weak attractor control (A_y0 = 0.19). Similarly, MDS analysis identifies 8 driver variable sets of size /D/ = 4 ( to ), none of which achieve full control. It is particularly interesting that the driver sets predicted by MDS lead to values of both and that are essentially random, demonstrating once again that predictions with equivalent support from the point of view of the structure-only theories lead to widely different amounts of real controllability. Our analysis finds 3 driver sets of /D/ = 4 variables that achieve full attractor control (highlighted in yellow in Fig. 6A and detailed in SM). Neither SC nor MDS predict those specific driver sets, which ultimately provide the most useful form of control in such systems. Unlike the SPN, there are no β€œchief controller” variables in this network, as most variables achieve a similar value of when controlled alone (see inset in Fig. 6A).


Control of complex networks requires both structure and dynamics.

Gates AJ, Rocha LM - Sci Rep (2016)

(A) Control of the eukaryotic cell cycle of budding yeast Saccharomyces cerevisiae (CCN) for all driver variable subsets of size /D/ = 1, /D/ = 2, /D/ = 3 and /D/ = 4. (inset) The mean fraction of reachable attractors  for each singleton driver variable set. The subset predicted to fully control the network are highlighted in red and labeled  for structural controllability (SC), while those predicted by minimum dominating sets (MDS) are labeled . The driver variable subsets with full attractor control are highlighted in yellow (see SM for further details). (B) Controlled Attractor Graphs (CAGs) for each singleton driver variable set. The wild-type attractor is highlighted in green, all other attractors are in purple.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4834509&req=5

f6: (A) Control of the eukaryotic cell cycle of budding yeast Saccharomyces cerevisiae (CCN) for all driver variable subsets of size /D/ = 1, /D/ = 2, /D/ = 3 and /D/ = 4. (inset) The mean fraction of reachable attractors for each singleton driver variable set. The subset predicted to fully control the network are highlighted in red and labeled for structural controllability (SC), while those predicted by minimum dominating sets (MDS) are labeled . The driver variable subsets with full attractor control are highlighted in yellow (see SM for further details). (B) Controlled Attractor Graphs (CAGs) for each singleton driver variable set. The wild-type attractor is highlighted in green, all other attractors are in purple.
Mentions: The eukaryotic cell cycle process of the budding yeast Saccharomyces cerevisiae reflects the cyclical gene expression activity that leads to cell division. Here, we use the 12 variable simplified Boolean model of the yeast Cell-Cycle Network (CCN) derived by Li et al.17. The SC analysis of the CCN interaction graph identifies only one driver variable to be sufficient for fully controlling the BN’s dynamics. Yet, as demonstrated in Fig. 6A, it only achieves negligible configuration control () and very weak attractor control (A_y0 = 0.19). Similarly, MDS analysis identifies 8 driver variable sets of size /D/ = 4 ( to ), none of which achieve full control. It is particularly interesting that the driver sets predicted by MDS lead to values of both and that are essentially random, demonstrating once again that predictions with equivalent support from the point of view of the structure-only theories lead to widely different amounts of real controllability. Our analysis finds 3 driver sets of /D/ = 4 variables that achieve full attractor control (highlighted in yellow in Fig. 6A and detailed in SM). Neither SC nor MDS predict those specific driver sets, which ultimately provide the most useful form of control in such systems. Unlike the SPN, there are no β€œchief controller” variables in this network, as most variables achieve a similar value of when controlled alone (see inset in Fig. 6A).

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.