Effects of structural and cellular heterogeneity on the control of nonlinear biological oscillator networks

Circadian rhythms are biological processes that have a period of roughly 24 hours. In most animals, these rhythms are orchestrated by a specialized network of neurons that possess a regulatory system involving oscillatory genes and proteins. The dynamics of these regulatory networks are highly nonlinear. In this work, we study the functional consequences of structural and cellular heterogeneity (extrinsic noise) on the control of these oscillator networks. Structural heterogeneity refers to variation in size, topology and edge weights within the network of oscillators. We present two optimal control problems, those of modifying the phase of the population of these oscillators in either minimal time, or using minimum effort. We find there is a sweet spot relating heterogeneity and average coupling strength for which the control cost is minimal, and a limit to which heterogeneity enables greater controllability. Insights relating to heterogeneity also suggest evolutionary advantages heterogeneous populations may carry over homogeneous ones. Our findings also may help provide guidelines for the design of synthetic oscillator networks, a field of growing interest.