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. 2013;8(2):e57134.
doi: 10.1371/journal.pone.0057134. Epub 2013 Feb 19.

The mechanism of saccade motor pattern generation investigated by a large-scale spiking neuron model of the superior colliculus

Jan Morén  1 , Tomohiro Shibata, Kenji Doya
Affiliations

The mechanism of saccade motor pattern generation investigated by a large-scale spiking neuron model of the superior colliculus

Jan Morén et al. PLoS One. 2013.

Abstract

The subcortical saccade-generating system consists of the retina, superior colliculus, cerebellum and brainstem motoneuron areas. The superior colliculus is the site of sensory-motor convergence within this basic visuomotor loop preserved throughout the vertebrates. While the system has been extensively studied, there are still several outstanding questions regarding how and where the saccade eye movement profile is generated and the contribution of respective parts within this system. Here we construct a spiking neuron model of the whole intermediate layer of the superior colliculus based on the latest anatomy and physiology data. The model consists of conductance-based spiking neurons with quasi-visual, burst, buildup, local inhibitory, and deep layer inhibitory neurons. The visual input is given from the superficial superior colliculus and the burst neurons send the output to the brainstem oculomotor nuclei. Gating input from the basal ganglia and an integral feedback from the reticular formation are also included.We implement the model in the NEST simulator and show that the activity profile of bursting neurons can be reproduced by a combination of NMDA-type and cholinergic excitatory synaptic inputs and integrative inhibitory feedback. The model shows that the spreading neural activity observed in vivo can keep track of the collicular output over time and reset the system at the end of a saccade through activation of deep layer inhibitory neurons. We identify the model parameters according to neural recording data and show that the resulting model recreates the saccade size-velocity curves known as the saccadic main sequence in behavioral studies. The present model is consistent with theories that the superior colliculus takes a principal role in generating the temporal profiles of saccadic eye movements, rather than just specifying the end points of eye movements.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. The model circuit.
Each neuron model layer is spatially extended and organized in the same relative order as in the neural substrate. Feedback connections to the same node indicate layer intraconnections. Primary functional circuits are indicated by coloured connections. Red connections: Burst neuron burst profile circuit. Blue connections: Spreading inhibition and system reset. Grey shaded connections: inputs common to both circuits. See materials and Methods for further details.
Figure 2
Figure 2. Parametrized burst neuron activation profiles based on monkey data.
Curves show peak firing rate and peak-to-end firing time, where the end is taken when the curve drops below 1% of peak. Regenerated from .
Figure 3
Figure 3. Model neuron response to a Poisson spike train input.
Input to a regular excitatory synapse (top) and to an NMDA-type synapse (bottom). A 50 pA input current is added between 50 ms and 100 ms. Model parameters in table 2.
Figure 4
Figure 4. Angle-dependent parameter estimation.
A Model peak-to-end burst time (orange contour plot) and equal peak burst rate (blue contour plot) as functions of QVformula imageburst NMDA synapse strength (horizontal axis) and cMRF inhibitory feedback strength (vertical axis). Axis values are factors of the nominal NMDA synapse and inhibitory synapse strengths (formula imagenS, formula imagenS) as specified in Table 2. The selected contour line values correspond to the peak-to-end burst times and peak burst rates from figure 2. Red marks show intersections of burst time and burst rate for the same magnitude saccade, and signify the combination of parameters that will give us burst neuron activation corresponding to a saccade of that magnitude.B The total peak-to-end spikes (blue contour lines) as a function of NMDA and inhibitory strength. Burst end is determined when activity drops below 10% of peak activity. Red line: the contour line corresponding to the average emitted spikes for all points from 4A (1088 spikes, red marks). Hashed line: the linear approximation of the selected contour line. Cross marks signify the 35 degree and 2 degree points.C NMDA and inhibitory synapse strength across the SC surface is set according to this linear approximation as the radius from the fovea in SC surface coordinates.
Figure 5
Figure 5. Two saccades.
A, B: target input at 9formula image radius, 0formula image angle. C,D: target input at 8formula image radius, 45formula image downward angle. Times are shown relative to the release of external burst neuron inhibition in both cases.A, C: average firing rate in a 0.1 mm radius around the point of peak activity for each saccade, averaged across ten trials. Black marks: spike trains from the peak neuron in each model layer. From top to bottom: SNpr inhibition; superficial wide-field neurons (wide-field); quasivisual neurons (QV); burst neuron (Burst); buildup neuron (Buildup); deep inhibitory neurons (Deep Inhibitory); cMRF neuron integrator units (cMRF integrators); and estimated horizontal (solid) and vertical (hashed) eye position.B, D: 10 ms snapshots of spatial model layer activity at significant points during the saccades. Times are relative to release of external inhibition. B: burst and buildup peak (50 ms), buildup neuron maximum spread (120 ms), deep inhibitory reset (140 ms). D: Preparatory activity during external inhibition (−20 ms), burst and buildup peak (50 ms) buildup maximum spread (125 ms). One point corresponds to one neuron, single trial. Crosses mark peak activity position for the saccade in each layer.
Figure 6
Figure 6. Angle-dependent total burst spike neuron output.
Shown for the same angles as in figure 2, rate estimated by 20 ms sliding window, average of ten runs. The burst end is estimated to be when the rate drops below 10% of the peak rate.
Figure 7
Figure 7. Estimated eye movement profile from model output.
A: Peak saccade speed as a function of saccade distance. Circles are individual trials; solid line is the average per simulated distance; and dotted line is the hypothetical linear relation based on the 2formula image average. B: Saccade time as a function of angular distance. Circles are individual trials; solid line is average per simulated distance; hashed line is parametrized monkey data from . C: Peak saccade speed as function of horizontal distance for 0formula image and 60formula image directions. The oblique saccades show the expected drop in peak speed. D: The estimated final eye position discrepancy as a function of target saccade position for the model with (solid) and without (hashed) deep inhibitory neuron feedback, terminated 300 ms after inhibitory release.
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Publication types

Grants and funding

This study was funded by the Research and Development of the Next-Generation Integrated Simulation of Living Matter, a part of the Development and Use of the Next-Generation Supercomputer Project of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, grant number 06060246 (http://www.csrp.riken.jp/index_e.html and http://www.nsc.riken.jp/index-eng.html). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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