The role of feedback in maintaining robustness and modulation across scales: Insights from cellular and network neurophysiology

The brain is a complex system made of many components acting at very different resolution levels, from the microsecond and nanometer scales with ion channels to hours and brain-wide scale with proteins. The brain dynamics and functions emerge from the interactions between these resolution levels. Mathematical modeling is a powerful ally to uncover some of the brain organizing principles and mechanisms. From this perspective, the question of which cellular details must be retained at the network level is largely open. Motifs simplify systems by approximating the wiring diagram and by taking advantage of the timescale separation between processes. Yet, motifs study each resolution level separately and neglect couplings between levels. This approach falls short of system-level questions and multiresolution intrinsic properties. The present dissertation aims at narrowing the gap by looking at the interplay between resolution levels. We propose to extract essential elements, in the form of feedback loops, to be maintained from one resolution to the next in the hope of a better understanding of brain functions and diseases. The focus is on the spatiotemporal upscaling from the neuron to the network level and, in particular, on the maintenance of modulation and robustness properties across scales. This approach is used in a two-neuron network and is extended to a prospective multiresolution excitability framework. The main contributions of this dissertation are the following. We identify the key role of a cellular feedback loop for network oscillation robustness and modulation. Rhythms are crucial in the brain functioning but much awaits to be understood regarding their control, regulation, and function. In a mutually-inhibitory network, we isolate an essential cellular property—a positive feedback loop in the slow timescale—to be retained at the network level to ensure modulation and robustness of network oscillations. We highlight the peculiar role that a cellular feedback loop can play for the regulation of network switches. We identify that a cellular positive feedback loop brings localization properties, both temporally and spatially, to network oscillations. The emerging picture suggests a basal ganglia network model valid both in healthy movement-related oscillations and in parkinsonian conditions. Multiresolution excitability emerges due to localization properties of excitable systems: di erent excitability resolution windows can be superposed and interact, generating multiresolution systems. In each window, the system is characterized via its transfer properties and input-output behavior. Signal processing properties appear in these multiresolution systems and endow multiresolution objects with gating and multiplex signaling capabilities. In conclusion, the present dissertation provides novel insights on the importance of the interplay between cellular and network levels. This multiresolution motif perspective is thought to be general and not specific to neuroscience. Finally, exploiting the concept in multiresolution technologies is suggested.