A key effort of the project has been to bridge the separate worlds of neurophysiology and control theory through the common modelling language of circuit theory.
Mixed feedback has been the central concept of the project: multi-resolution systems that can dynamically and robustly signal across scales are modelled as interconnections of simple mixed-feedback motifs. Each mixed-feedback motif controls one threshold localised in amplitude and in time by the balance between a fast/local positive feedback loop and a slow/global negative feedback loop. Such systems are realised as nonlinear circuits that interconnect positive and negative conductance elements with specific amplitude and temporal activation ranges. Interconnections of such motifs and modulation of the thresholds via the modulation of maximal is the central control principle studied to signal across scales.
Four key results can be singled out at the end of the switchlet project:
1. The project has identified a novel role of cellular bursting in the organisation of neural circuits. By modeling cellular bursting as a motif with two distinct thresholds, we demonstrated that the modulation of the slow threshold is an ubiquitous control mechanism to shape the functional topology of large networks. This mechanism was shown to be robust to uncertainty and far more efficient than the classical view that topology is controlled by synaptic interactions. This result, published in [Drion et al,, Plos Computational Biology, 2018], establishes for the first time the significance of a classical cellular phenomenon for circuit organisation. By highlighting the distinct roles of a fast and a slow negative conductances, our theory also challenges established views in neurodynamics that bursting only requires a fast negative conductance.
2. Dissipativity theory is the state-of-the art methodology to analyse nonlinear feedback systems. A key limitation of that theory is that it is only concerned with dynamical systems that converge to equilibrium when disconnected from their environment. A key outcome of the switchlet project is the novel dominance theory, that leverages the existing theory of dissipativity to analyse feedback systems that switch and oscillate. This new result, published in [Forni and Sepulchre, IEEE Transactions on Automatic Control, 2019], was awarded the Axelby best paper award 2021. It opens the way to analyze novel types of nonlinear feedback systems, that include the mixed feedback circuits of neuroscience.
3. A third major outcome of the action is a novel adaptive online estimator for the maximal conductances of an arbitrary neural circuit model. This result provides a novel bridge between neurophysiology and the classical theory of adaptive control. While adaptive control has been traditionally driven by and applied to robotics and the control of electro-mechanical systems, its application to neuronal circuits is novel and significant. It opens novel estimation algorithms of relevance for experimental neurophysiology. More fundamentally, it suggests that the neuromodulatory principles of neuroscience closely resemble conventional adaptation schemes of control engineering.
4. A fourth major outcome of the action is the first application of neuromodulation principles in a neuromorphic circuit. While previous neuromorphic circuits have successfully replicated specific behaviors observed in neural circuits, the article [Ribar and Sepulchre, IEEE Transactions on Circuits and Systems, 2019] is the first experimental demonstration of a neuromorphic circuit that replicates the robust neuromodulation of a single cell between spiking and bursting.
