(612c) Evolution of Modular Networks through Optimal Sparse Control

Authors: 
Daoutidis, P., University of Minnesota, Twin Cities
Constantino, P., University of Minnesota
Tang, W., University of Minnesota, Twin Cities
Modularity is ubiquitous in biological networks. However, the understanding of its evolutionary origins remains an open problem in biology. The modelling of biological networks as dynamical systems has allowed the application of control theory to their related problems. Understanding the effect of network topology on its controllability or control performance helps to explain the emergence of different topological features in biological networks and provides principles of designing networked systems. In many natural and artificial systems, networks have sparse topology and are controlled by sparse feedback controllers. Therefore, here we postulate a control cost which comprises of a control performance term and a control sparsity term. We then hypothesize that the minimization of such a control cost can favor network modularity.

To test this hypothesis, we consider Laplacian networks with different topological features and we formulate and solve an optimal control problem, examining the trade-off between control performance and the sparsity of the network and the controllers. When we only allow to vary the sparsity cost of the controller we observe that for moderate and high feedback costs the networks with lowest overall cost are modular and centralized ones, respectively [1, 2]. When we allow to vary (and thus optimize with respect to) both the network and the controller, we observe that with increasing sparsity, modular and hierarchical network features along with distributed and hierarchical control architectures become the optimal features [3]. Finally, we implement genetic algorithms of network populations using the total control cost as the fitness function for natural selection. Our results suggest that blind random mutations do not create modular networks, even though they offer the optimal fitness from a control perspective. However, mutation schemes combining up to 80% of random mutations and 20% of mutations that maximize the diffusion of biological information effectively increase the average modularity of the population [4].

We conclude that control performance and controller sparsity are important factors in the evolution of modularity, especially when the evolutionary mechanism is non-gradualistic, such as observed in developmental biology. These findings offer a plausible hypothesis on the role of modularity in the evolution of biological networks.

References

[1] Tang, W., Daoutidis, P. (2018) The role of community structures in sparse feedback control. Proceedings of the American Control Conference 2018 1790-1795.

[2] Constantino, P.H., Tang, W., Daoutidis, P. (2018) Topology Effects on Sparse Control of Complex Networks with Laplacian Dynamics. Scientific Reports – under review.

[3] Tang, W., Constantino, P.H., Daoutidis, P. (2019) Optimal sparse network topology under sparse control in Laplacian networks. Proceedings of the 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems – submitted.

[4] Constantino, P.H., Daoutidis, P. (2019) A control perspective on the evolution of biological modularity. Proceedings of the 5th IFAC Conference on Intelligent Control and Automation Sciences – submitted.