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


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.