The study of network structure has URLanizational principles in complex systems. However, there is also a need to understand how to control them; for example,  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 multivariate systems can be predicted solely from the graph of interactions between variables, without considering variable dynamics: structural controllability and minimum dominating sets. Both methodologies utilize idealized assumptions about multivariate dynamics, yet most accurate models of real-world systems do not abide by these assumptions. Here, we study the relationship between network structure and the control of multivariate dynamics using three distinct measures of controllability in Boolean Networks. We demonstrate that  structure-only methods fail to properly characterize controllability in these nonlinear systems; even in very simple networks, a large variation of possible dynamics can occur for the same structure, each with different control profiles. Our methodology is also used to characterize critical control variables in three models of biochemical regulation: the Drosophila melanogaster single-cell segment polarity network , the eukaryotic cell cycle of budding yeast Saccharomyces cerevisiae, and the URLan arrangement in Arabidopsis thaliana. Structure-only methods both undershoot and overshoot the number and which sets of variables actually control these models, highlighting the importance of the  system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays a role in the extent to which structure predicts dynamics.
The study of network structure has uncovered signatures of URLanization 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 URLan 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.
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