Modelling the neurons of the electrosensory lobe in Gymnotus omarorum with differentiable programming

Nervous systems are complex structures in which one can identify different organization levels, from the molecular and subcellular to those describing the whole animal behaviour. One of the challenges of present neuroscience is to understand how different organization levels influence each other, to reach a solid understanding on how the brain works. Formal computational models are powerful tools to bridge the gaps between levels. Taking into account the characteristic features observed in one level they allow to predict the behaviour of the superior level or hypothesize sets of combination factors that explain the emergence of such characteristic features. Here we present ongoing work aiming to construct a model that bridges the gap between the intrinsic properties of the neurons and the circuit behaviour of the electrosensory lobe of the weakly electric fish Gymnotus omarorum.

These fish evaluate their environment and communicate using electric images carried by electric discharges of a specialized electrogenic organ. These images are originated on the heterogeneous distribution of impedance on the fish ́s surrounds and are sensed by cutaneous electroreceptors, each of which provides local information to the electrosensory lobe through a single primary afferent fiber. The electrosensory lobe contains two independent electrosensory paths, called fast and slow somehow analogously to those observed in the auditory system. The fast path is represented by a single type of spherical neurons that receive primary afferent calixes making synaptic contact through electrical and chemical synapses and project to a mesencephalic nuclei where a Jeffress-like circuit (Jeffress, 1948) compares the latency between different incoming inputs. The slow path is represented by a cerebellum-like circuit receiving feed-forward and feed-back connections: such a circuit has two types of output neurons with different intrinsic properties and dynamical responsiveness to changes in the electrosensory image (for details on this system see Caputi et al., 2020).

We focussed first on spherical cells, because their round shape and small number of afferent contacts simplify the modelling and understanding their role in the circuit. These neurons were previously characterized by intracellular recordings in vitro (Nogueira et al., 2006) and their behaviour was studied in freely moving fish (Castelló et al., 1998). Taking into account the previous data (Nogueira et al., 2011, 2014), we used the formalism introduced by Hodgkin and Huxley, including a fast Na+, two K+ currents (high and low threshold) and a mixed cation resonant current. We built a differentiable parametric simulation, and found the set of parameters values that best reproduce the experimental results obtained in vitro and the response of the fast electrosensory path in vivo by means of a gradient-descent-powered maximum likelihood fit.