A new notion of criticality: Studies in the pheromone system of the moth

Abstract

Event Abstract Back to Event A new notion of criticality: Studies in the pheromone system of the moth Christopher L. Buckley1* and Thomas Nowotny1 1 University of Sussex, CCNR, Informatics, United Kingdom The concept that the nervous system operates close to a critical point in its dynamics has been receiving a growing amount of attention in the last few years [1,2,3,4]. There are a plethora of computational models that posit critical dynamics as a partial but parsimonious explanation of information transmission [2], storage [5] and computational [6] properties of the nervous system. To date, the majority of computational models of critical brain dynamics have focused on excitatory networks of excitable spiking neurons with sparse activity [3]. This is, perhaps, because such models are thought to be adequate models of the cerebral cortex, [2,3] but also because it has allowed researcher to draw formal comparisons with second order phase transition in 'stick slip' and Ising models. It is well-known that in many brain areas activity is heavily modulated, if not dominated by inhibitory interneurons [7]. For example, we have been investigating a subsystem of the antennal lobe of the moth which is characterised by dominantly inhibitory synapses and high baseline spike rates. It is not clear what relevance the established notion of critical brain dynamics has for such neural subsystems that do not fit into the framework of excitatory networks with sparse activity. In this work we develop, and formally describe, an alternate notion of criticality in terms of the rate dynamics of a network that can be applied to this different regime. In particular, we focus on the macro glomerular complex (MGC) of the moth which plays a key role in pheromone processing. The MGC comprises a set of recurrently connected GABA B inhibitory cells which have baseline firing rates of around 20Hz. We model this system as a set of Hodgkin Huxley neurons with spike frequency adaptation connected via first order (" alpha−beta") synapses [8]. Leveraging the fact that GABA B synapses act at a much slower timescale than the membrane dynamics we are able to reduce this conductance based model to a formally equivalent rate model. This allows us to analyse the nonlinear dynamics of the system in detail. Specifically, we describe the rate response of the MGC to pheromone as transient excursions from a globally asymptotically stable fixed point attractor. We show how this dynamics can account for several of the phenomena observed in the MGC and discuss the relationship of this model to reservoir computing paradigms [9]. In particular we formally show how critical rate dynamics allows sensitive response to inputs while maximizing the dynamic range of the MGC model to inputs of different amplitude. We argue that critical rate dynamics is more general and more widely applicable than current notions of criticality in neuroscience.