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Analysis and simulation of optogenetic perturbations in efficiently balanced networks
Nuno Calaim1, Pedro Gonçalves2, David Barrett3 Sophie Denève4 and Christian Machens1
1Champalimaud Neuroscience Programme, Champalimaud Centre for the Unknown 2Gatsby Computational Neuroscience Unit, UCL 3University of Cambridge 4École Normale Supérieure, Paris

How do neural networks respond to instantaneous perturbations of their activity? Can a network be able to compensate for these manipulations? In this work, we build a spiking network model following the approach of Boerlin et al. 2013 [1] based on the following first principles: we assume that the network's output is a linear readout of the firing rates and that it operates in order to minimize a given Loss Function that describes mathematically the objective of the network. Previous work has shown that the resulting networks are robust against neural death [2]. This robustness is possible through the rapid adjustment of the activity of the unperturbed neurons. Here, we test this framework under a variety of optogenetic-type perturbations.

Through analytical studies we find that instantaneously perturbing the voltage dynamics of each neuron can be interpreted as an extra L1 cost term on the Loss Function that describes the goal of the network. We compare the analytical predictions to results in silico and we find that the network is able to compensate for inhibitory perturbations either by reducing the activity of oppositely tuned neurons or by increasing it for the similar tuned ones. In the case of excitation we find that perturbations are always able to change the system unless we further assume a saturation for the firing rates of each neuron.

We apply this framework to describe the impact of optogenetic perturbations on the oculomotor integrator (OI). The OI is a neural structure in the hindbrain which is responsible for controlling eye position by integrating eye movement signals to produce eye position signals. The implemented spiking network replicates key properties of the OI, such as the typical distribution of tuning curves and accurate eye position representation. Moreover we find that the total inhibition is tightly balanced by the total excitation carried by the recurrent connections within the network. We apply the optogenetic perturbations to this system to find that the resulting changes in eye position are consistent with recent optogenetic experiments in which the OI was optogenetically perturbed [3]. This indicates that the OI acts to instantaneously adjust the activities of the unperturbed neurons in order to compensate for any error in the computation performed by the OI. These results suggest that our framework may provide a useful and timely tool for characterizing the impact of optogenetic manipulations.

[1] M. Boerlin, C.K. Machens, S. Denève, PLoS Comput. Biol. 9, e1003258 (2013).
[2] D. Barrett, S. Denève, C.K. Machens, under revision.
[3] P.J. Gonçalves, A.B. Arrenberg, B. Hablitzel, H. Baier, C.K. Machens, Front. Neural Circuits 8:10 (2014).