Neuronal populations within local regions frequently undergo oscillatory modulations of their activity. The oscillations of distant populations coupled by long-range connections can lock in various patterns of stable phase differences and the flexible change of such phase locking patterns has been hypothesized to modulate communication and functional connectivity (FC) between them. It is therefore important to understand which factors can affect and control the established interregional phase relations (e.g., FC). Here, we emphasize that while the details of applied local alterations (stimulation or SC link changes) are important, we cannot neglect the global system’s dynamics when predicting effects on FC. A tool which has proved useful to model and predict the behavior of coupled oscillating populations is the phase response curve (PRC). The PRC is a local transformation function that determines the phase-dependent response of an oscillator to any given external or internal input. Importantly, the PRC exclusively depends on parameters of the local regional microcircuit such as the relative strengths of recurrent excitation (E) and inhibition (I) but is ignorant of the oscillatory dynamics of the surrounding large-scale network or the inter-regional connectivity parameters. However, in a complex system of many interacting populations, local and global dynamics are non-trivially coupled and the PRC may be more dependent on them than previously assumed. Considering specific examples of multi-scale circuits, we first show that equivalent changes in FC can be induced by either modifying local connectivity parameters and thereby the PRC, or by modifying features of the long-range inter-regional SC. In this way, diffuse changes of local E and I strengths (induced e.g., by neuromodulation or pharmacological treatments) may be used to compensate for a disrupted connectome (due e.g., to neurodegeneration).
Secondly, we show that the phase-shifting effects of local pulse perturbations do not depend uniquely on the phase at which perturbation is applied, as postulated by the PRC concept, but also on the collective configuration of dynamic FC which the system is transiently visiting. Thus, accounting for changes in collective dynamics beyond local dynamics and structure, is vital for understanding and predicting how the brain will react to internal or external perturbations.

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