Limits...
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 portrait of the BN ensemble constrained by the Feed-Forward network motif.The mean fraction of reachable configurations  and the mean fraction of controllable configurations  for the full ensemble of 64 BNs with structure given by the Feed-Forward network motif shown in Fig. 2A, as controlled by all driver variable sets of one or two variables. The full effective structure (FES) subset is highlighted by red circles, the reduced effective structure (RES) subset is shown in blue squares, and the non-contingent subset (NC) is shown by green diamonds; the area of the object corresponds to the number of networks at that point.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4834509&req=5

f3: Control portrait of the BN ensemble constrained by the Feed-Forward network motif.The mean fraction of reachable configurations and the mean fraction of controllable configurations for the full ensemble of 64 BNs with structure given by the Feed-Forward network motif shown in Fig. 2A, as controlled by all driver variable sets of one or two variables. The full effective structure (FES) subset is highlighted by red circles, the reduced effective structure (RES) subset is shown in blue squares, and the non-contingent subset (NC) is shown by green diamonds; the area of the object corresponds to the number of networks at that point.

Mentions: Consider the Feed-Forward network motif of N = 3 variables54 shown in Fig. 2A. In this case, the full ensemble consists of 64 distinct BNs of which 36 are NC, 8 have RES, and 20 have FES. Figure 1 depicts the logic of one FES network instance for this motif, along with its STG, CSTGs, and CAGs for various driver sets D. The control portrait of the full BN ensemble is shown in Fig. 3; control measures and are shown for all possible driver sets of one or two variables.


Control of complex networks requires both structure and dynamics.

Gates AJ, Rocha LM - Sci Rep (2016)

Control portrait of the BN ensemble constrained by the Feed-Forward network motif.The mean fraction of reachable configurations  and the mean fraction of controllable configurations  for the full ensemble of 64 BNs with structure given by the Feed-Forward network motif shown in Fig. 2A, as controlled by all driver variable sets of one or two variables. The full effective structure (FES) subset is highlighted by red circles, the reduced effective structure (RES) subset is shown in blue squares, and the non-contingent subset (NC) is shown by green diamonds; the area of the object corresponds to the number of networks at that point.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Control portrait of the BN ensemble constrained by the Feed-Forward network motif.The mean fraction of reachable configurations and the mean fraction of controllable configurations for the full ensemble of 64 BNs with structure given by the Feed-Forward network motif shown in Fig. 2A, as controlled by all driver variable sets of one or two variables. The full effective structure (FES) subset is highlighted by red circles, the reduced effective structure (RES) subset is shown in blue squares, and the non-contingent subset (NC) is shown by green diamonds; the area of the object corresponds to the number of networks at that point.
Mentions: Consider the Feed-Forward network motif of N = 3 variables54 shown in Fig. 2A. In this case, the full ensemble consists of 64 distinct BNs of which 36 are NC, 8 have RES, and 20 have FES. Figure 1 depicts the logic of one FES network instance for this motif, along with its STG, CSTGs, and CAGs for various driver sets D. The control portrait of the full BN ensemble is shown in Fig. 3; control measures and are shown for all possible driver sets of one or two variables.

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.