Control of complex networks requires both structure and dynamics

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.Comment: 15 pages, 6 figure

Unique Information via Dependency Constraints

The partial information decomposition (PID) is perhaps the leading proposal for resolving information shared between a set of sources and a target into redundant, synergistic, and unique constituents. Unfortunately, the PID framework has been hindered by a lack of a generally agreed-upon, multivariate method of quantifying the constituents. Here, we take a step toward rectifying this by developing a decomposition based on a new method that quantifies unique information. We first develop a broadly applicable method---the dependency decomposition---that delineates how statistical dependencies influence the structure of a joint distribution. The dependency decomposition then allows us to define a measure of the information about a target that can be uniquely attributed to a particular source as the least amount which the source-target statistical dependency can influence the information shared between the sources and the target. The result is the first measure that satisfies the core axioms of the PID framework while not satisfying the Blackwell relation, which depends on a particular interpretation of how the variables are related. This makes a key step forward to a practical PID.Comment: 15 pages, 7 figures, 2 tables, 3 appendices; http://csc.ucdavis.edu/~cmg/compmech/pubs/idep.ht

Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.Comment: Accepted for publication in PLOS ON

CANA: A python package for quantifying control and canalization in Boolean Networks

Logical models offer a simple but powerful means to understand the complex dynamics of biochemical regulation, without the need to estimate kinetic parameters. However, even simple automata components can lead to collective dynamics that are computationally intractable when aggregated into networks. In previous work we demonstrated that automata network models of biochemical regulation are highly canalizing, whereby many variable states and their groupings are redundant (Marques-Pita and Rocha, 2013). The precise charting and measurement of such canalization simplifies these models, making even very large networks amenable to analysis. Moreover, canalization plays an important role in the control, robustness, modularity and criticality of Boolean network dynamics, especially those used to model biochemical regulation (Gates and Rocha, 2016; Gates et al., 2016; Manicka, 2017). Here we describe a new publicly-available Python package that provides the necessary tools to extract, measure, and visualize canalizing redundancy present in Boolean network models. It extracts the pathways most effective in controlling dynamics in these models, including their effective graph and dynamics canalizing map, as well as other tools to uncover minimum sets of control variables.Comment: Submitted to the Systems Biology section of Frontiers in Physiolog