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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.


The state transition graph (STG) and the controlled variants (CSTG) for an exemplar Boolean Network using the Feed-Forward network structure (Fig. 2A), with the logical transition functions given in the upper right.Configurations are shown as green nodes, attractors are highlighted green nodes, and transitions are illustrated as solid black arrows. The CSTG  for the three singleton driver variable sets D ≡ {x1}, {x2}, {x3} are shown with controlled transitions denoted by dashed, orange arrows. The controlled attractor graphs CAG  are also depicted for the singleton driver variable sets with the attractors shown as purple highlighted nodes and dashed orange arrows denoting the existence of at least one perturbed transition between attractor basins (if any exist).
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f1: The state transition graph (STG) and the controlled variants (CSTG) for an exemplar Boolean Network using the Feed-Forward network structure (Fig. 2A), with the logical transition functions given in the upper right.Configurations are shown as green nodes, attractors are highlighted green nodes, and transitions are illustrated as solid black arrows. The CSTG for the three singleton driver variable sets D ≡ {x1}, {x2}, {x3} are shown with controlled transitions denoted by dashed, orange arrows. The controlled attractor graphs CAG are also depicted for the singleton driver variable sets with the attractors shown as purple highlighted nodes and dashed orange arrows denoting the existence of at least one perturbed transition between attractor basins (if any exist).

Mentions: At time t, the network is in a configuration of states Xt, which is a vector of all variable states at t. The set of all possible network configurations is denoted by , where . The complete dynamical behavior of the system for all initial conditions is captured by the state-transition graph (STG): , where each node is a configuration , and an edge denotes that a system in configuration Xα at time t will be in configuration Xβ at time t + 1. Under deterministic dynamics, only a single transition edge Tα,β is allowed out of every configuration node Xα. Because is finite, it contains at least one attractor, as some configuration or cycle of configurations must repeat in time43. An exemplar STG is shown in Fig. 1 (top, left).


Control of complex networks requires both structure and dynamics.

Gates AJ, Rocha LM - Sci Rep (2016)

The state transition graph (STG) and the controlled variants (CSTG) for an exemplar Boolean Network using the Feed-Forward network structure (Fig. 2A), with the logical transition functions given in the upper right.Configurations are shown as green nodes, attractors are highlighted green nodes, and transitions are illustrated as solid black arrows. The CSTG  for the three singleton driver variable sets D ≡ {x1}, {x2}, {x3} are shown with controlled transitions denoted by dashed, orange arrows. The controlled attractor graphs CAG  are also depicted for the singleton driver variable sets with the attractors shown as purple highlighted nodes and dashed orange arrows denoting the existence of at least one perturbed transition between attractor basins (if any exist).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: The state transition graph (STG) and the controlled variants (CSTG) for an exemplar Boolean Network using the Feed-Forward network structure (Fig. 2A), with the logical transition functions given in the upper right.Configurations are shown as green nodes, attractors are highlighted green nodes, and transitions are illustrated as solid black arrows. The CSTG for the three singleton driver variable sets D ≡ {x1}, {x2}, {x3} are shown with controlled transitions denoted by dashed, orange arrows. The controlled attractor graphs CAG are also depicted for the singleton driver variable sets with the attractors shown as purple highlighted nodes and dashed orange arrows denoting the existence of at least one perturbed transition between attractor basins (if any exist).
Mentions: At time t, the network is in a configuration of states Xt, which is a vector of all variable states at t. The set of all possible network configurations is denoted by , where . The complete dynamical behavior of the system for all initial conditions is captured by the state-transition graph (STG): , where each node is a configuration , and an edge denotes that a system in configuration Xα at time t will be in configuration Xβ at time t + 1. Under deterministic dynamics, only a single transition edge Tα,β is allowed out of every configuration node Xα. Because is finite, it contains at least one attractor, as some configuration or cycle of configurations must repeat in time43. An exemplar STG is shown in Fig. 1 (top, left).

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.