Table 1.
List of all parameters used in the simulations.
Fig 1.
Responses of three SC model neurons to different microstimulation parameters.
The three neurons differed in their adaptation time constants (A: τq = 84.6ms, B: τq = 70.95ms, and C: τq = 52.4ms). Each row shows the membrane potentials, V(t), for the same electrical stimulus, at a particular intensity (see color code for the different lines, top), and delivered at a particular stimulus duration, DS. Note the clear differences in neuronal membrane responses. Stimulus timings and durations are indicated above the traces by black lines, ranging from DS = 25 ms (bottom) to DS = 225 ms (top). Symbols x, o, and +: selected responses, further analyzed in Fig 2.
Fig 2.
Bursting mechanism of the AdEx neuron model.
Phase plots of V(t) vs. q(t) of the neural dynamics of the same three neurons of Fig 1. Biophysical parameters of the neurons were selected for their bursting responses to a ramp stimulus, with varying current amplitude and durations (traces are marked in Fig 1); the order of spike occurences is denoted next to the traces in the spike initiation zone): A: a burst with 5 spikes (x); B: two burst cycles with 6 and 5 spikes (o); C: a burst cycle with more than 13 spikes (+).
Fig 3.
Spatial properties of input current and neural response.
(A) Input stimulus of 150 pA (100 ms), is presented to the network around the vicinity of the tip of the electrode. Current amplitude drops exponentially with distance from the tip location at 0 with λ = 10mm−1 in every direction on the collicular map. (B,C) Spike counts of neurons activated by microstimulation, without including lateral connections in the motor map. The gaze-motor map is stimulated at the corresponding locations prescribed by the logarithmic afferent mapping function (B: R = 5°, ϕ = 0°;C: R = 31°, ϕ = 30°).
Fig 4.
Population dynamics in the gaze-motor map and eye kinematics.
(A,D) Spike counts from the gaze-motor map represents the recruited population to microstimulation with lateral interactions. Peak firing rates of the cells decrease with distance from the population center. (B,E) Temporal burst profiles of the recruited neurons (taken at 0.1 mm intervals from the central neuron) portray synchronized population activity, here shown along the rostral-caudal direction in the map. Burst durations increase, but the total number of spikes from the population remains the same. (C,F) Emerging eye displacements and eye velocity profiles, generated by the linear dynamic ensemble-coding model (Eqs 2b and 3). Horizontal (green), vertical (yellow), and vectorial (purple) eye-displacement traces.
Fig 5.
Central cell firing properties.
(A) Spike trains and burst profiles for the central neurons of different populations (electrode tip positioned at R = 2, 7, 11, 15, 21 and 31 deg). (B) Peak firing rates (dark green), number of spikes from the central cells (light green), and the durations of the central cell bursts (purple) for different neural populations between R = 2 and 65 deg. Note that the number of spikes for the central cell is constant at about 20 spikes throughout the motor map, while the peak firing rate at caudal sites drops to barely 50% of the rostral stimulation site. Note also that the durations of the central cell bursts increase monotonically with the movement amplitude.
Fig 6.
Saccade endpoints, eye displacement and eye velocity.
(A) Saccade endpoints for stimulation at different sites in the motor map. The scaling parameter of the SC motor map was tuned for a 21 deg horizontal saccade (red circle). (B) Eye displacement traces for horizontal saccades (ϕ = 0 deg) [movement amplitudes are highlighted by the thin horizontal lines]. (C) Saccadic eye velocity profiles for the corresponding position traces in B. Note the clear increase in saccade duration, and the associated saturation of peak eye velocity as function of saccade amplitude.
Fig 7.
Eye-displacement traces and saccadic eye velocity profiles for three directions (ϕ = 0, 30, 60 deg).
(A, B, C) with the same amplitude of R = 21 deg. (purple: total vectorial displacement/velocity, green: horizontal, yellow: vertical saccade component).
Fig 8.
Nonlinear main-sequence behavior of the model.
Shown for stimulation at 16 sites along the horizontal meridian of the motor map. (A) Saturating amplitude-peak eye velocity relation. (B) A straight-line increase of saccade duration with amplitude. (C) Saccade amplitude and the product of peak eye velocity and saccade duration, Vpk ⋅ D, are linearly related with slope, k = 1.7.
Fig 9.
Effect of stimulation parameters.
(A) Peak eye velocity as function of current strength for stimulation at a site corresponding to R = 15 (light), 21 (medium) and 31 (dark) deg, for 100 ms stimulation duration. Beyond the threshold at 140 pA, the evoked eye velocity is virtually independent of the stimulation current. (B) Total eye displacement as function of microstimulation strength for stimulation at a site corresponding to R = 15 (light), 21 (medium) and 31 (dark) deg for 100 ms stimulation duration. Beyond the threshold at 90 pA, the total eye displacement is independent of the stimulation current. (C) Peak eye velocity as a function of microstimulation duration from the same locations at a fixed stimulation strength of 150 pA.