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Dendritic bistability increases the robustness of persistent neural
activity in a model oculomotor neural integrator
Mark Goldman,1 Joseph Levine,1
Guy Major,2 David Tank,2 and Sebastian Seung1
1MIT
2Princeton
The oculomotor neural integrator converts velocity-coded eye movement
commands into eye position signals. In the absence of velocity
commands, integrator neurons maintain a steady rate of firing for tens
of seconds. To achieve these long persistence times, most models use
neurons with a continuous firing rate vs. injected current
relationship and precisely tuned positive feedback. Bistability in
neuronal responses has been proposed as a mechanism to maintain
persistent activity. However, neuronal bistability tends to produce
large discontinuities in firing rate with small changes in eye
position. Thus, the firing rates of bistable neurons do not exhibit an
analog coding of eye position. We show how dendritic bistability can
enhance the robustness of eye fixations to mistuning while preserving
the experimentally observed threshold linear relationship between
firing rate and eye position. We analytically model a network in which
the firing rate of each neuron is a linear sum of the contributions
from multiple bistable dendritic compartments, plus tonic background
and external velocity-command inputs. The network's tolerance to
mistuning is related to the range of bistability of the dendritic
compartments and to the slopes and thresholds of the neurons' firing
rate vs. eye position relationships. Severe mistuning leads to
approximately exponential decay towards a nonzero null eye position,
in agreement with experimental observation. The response of the model
to continuously varying inputs makes testable predictions for the
performance of the vestibuloocular reflex. Analytic model results are
reproduced in a biophysical model.