Redundancy and control in complex networks

Luis Rocha (April 11, 2016)

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The structure of networks has provided many insights into the organization of complex systems. The success of this approach is its ability to capture the organization of multivariate interactions, and how it changes in time (network evolution) without explicit dynamical rules for node variables. As the field matures, however, there is a need to move from understanding to controlling complex systems. This is particularly true in systems biology and medicine, where increasingly accurate models of biochemical regulation have been produced. More than understanding the organization of biochemical regulation, we need to derive control strategies that allow us, for instance, to move a mutant cell to a wild-type state, or revert a mature cell to a pluripotent state. Here I present two concepts developed in our group aimed at supporting this goal. First I will present the schema redescription methodology, used to remove redundancy from automata rules to reveal their canalization properties, thus simplifying the characterization of control in large models of natural networks, such as systems biology models of biochemical regulation [Marques-Pita & Rocha, 2013]. Secondly, we introduce effective connectivity and input redundancy as a measures of canalization, and demonstrate that effective connectivity is an order parameter of Boolean Network (BN) dynamics, and a major factor in network controllability [Marques-Pita et al, 2015; Gates and Rocha, 2015]. We also show that existing structural control methods do not predict the actual controllability of Boolean network models, as they can 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. Finally, we show that controllability can both be hindered or aided by how canalization unfolds in a given network, leaving room for natural selection or human design to effectively control large complex networks