Figure 1.
Connectivity of the model. A) Overall connectivity between neural groups. The CB-INs only inhibit the dendrites receiving distal inputs. The PV-INs inhibit the cell bodies of pyramidal neurons as well as each other. B) Disinhibitory short-term plasticity (dSTP). For clarity, local inhibitory INs in the cortex are omitted. Left: If the cortico-thalamic firing in a cortico-reticulo-thalamic (CRT) loop is weak or intermittent, closed-loop inhibition from thalamic reticular nucleus (TRN) is strong, preventing persistent thalamo-cortical signaling and facilitating global phasic or oscillatory firing modes. Right: If the cortico-thalamic firing in a CRT loop is strong and persistent, the dSTP mechanism causes closed-loop inhibition from TRN to be weakened, facilitating strong and focused thalamo-cortical signaling (dark red and green neurons) and a tonic firing mode. MLN = middle-layer neuron; DLN = deep-layer neuron; PV = parvalbumin interneuron; CB = calbindin interneruon; T = thalamo-cortical neuron.
Figure 2.
PV-IN perturbation: smooth pursuit task. The system quickly settles on accurate smooth pursuit of the stimulus. After the 6 s mark (green bar), glutamatergic NMDA conductance on the PV-INs is reduced, leading to increased variability in eye movement. The subplots show the time evolution of model behavior (A–B) and model neural activities (C–I) as well as external thalamic input (J). A) Horizontal position of the model eye (red trace) and the target (blue trace) in absolute coordinates. B) Relative position of the eye with respect to the target. C) Spectrogram of total middle-layer cortical activity. D–I) Raster plots show spiking activity in the model neurons. J) External thalamic input.
Figure 3.
PV-INs perturbation: fixation task. The system quickly settles on accurate fixation of the stationary stimulus. A distractor (magenta trace) is introduced at the 2 s mark, but fixation performance is unaffected. After the 6 s mark (green bar), glutamatergic NMDA conductance on the PV-INs is reduced, causing the model to shift between target and distractor. The subplots show the time evolution of model behavior (A–B) and model neural activities (C–I) as well as external input (J). A) Horizontal position of the model eye (red trace), the target (blue trace), and the distractor (magenta trace, straight line) in absolute coordinates. B) Relative position of the eye with respect to the target. C) Spectrogram of total middle-layer cortical activity. D–I) Raster plots show spiking activity in the model neurons. J) External thalamic input.
Figure 4.
CB-IN perturbation. Left: Smooth pursuit task: final 4 s. After the 6 s mark (green bar), glutamatergic NMDA conductance on the CB-INs is reduced, leading to increased variability and lag in eye movement. The subplots show the time evolution of model behavior (A–B) and model neural activities (C–I) as well as external input (J). A) Horizontal position of the model eye (red trace) and the target (blue trace) in absolute coordinates. B) Relative position of the eye with respect to the target. C) Spectrogram of total middle-layer cortical activity. D–I) Raster plots show spiking activity in the model neurons. J) External thalamic input. Right: Fixation task: final 4 s. The system settles on accurate fixation of the stationary stimulus. A distractor (magenta trace, straight line) is introduced at the 2 s mark, but fixation performance is unaffected. After the 6 s mark (green bar), glutamatergic NMDA conductance on the CB-INs is reduced, causing the model to shift between target and distractor. The subplots show the time evolution of model behavior (K–L) and model neural activities (M–S) as well as external input (T). K) Horizontal position of the model eye (red trace), the target (blue trace), and the distractor (magenta trace) in absolute coordinates. L) Relative position of the eye with respect to the target. M) Spectrogram of total middle-layer cortical activity. N–S) Raster plots show spiking activity in the model neurons. T) External thalamic input.
Figure 5.
TRN perturbation. Left: Smooth pursuit task: final 4 s. After the 6 s mark (green bar), TRN neurons are hyperpolarized, leading to increased variability in eye movement. The subplots show the time evolution of model behavior (A–B) and model neural activities (C–I) as well as external input (J). A) Horizontal position of the model eye (red trace) and the target (blue trace) in absolute coordinates. B) Relative position of the eye with respect to the target. C) Spectrogram of total middle-layer cortical activity. D–I) Raster plots show spiking activity in the model neurons. J) External thalamic input. Right: Fixation task: final 4 s. The system settles on accurate fixation of the stationary stimulus. A distractor (magenta trace, straight line) is introduced at the 2 s mark, but fixation performance is unaffected. After the 6 s mark (green bar), TRN neurons are hyperpolarized, causing the model to shift between target and distractor. The subplots show the time evolution of model behavior (K–L) and model neural activities (M–S) as well as external input (T). K) Horizontal position of the model eye (red trace), the target (blue trace), and the distractor (magenta trace) in absolute coordinates. L) Relative position of the eye with respect to the target. M) Spectrogram of total middle-layer cortical activity. N–S) Raster plots show spiking activity in the model neurons. T) External thalamic input.
Figure 6.
dSTP perturbation. Left: Smooth pursuit task: final 4 s. After the 6 s mark (green bar), the disinhibitory short-term plasticity (dSTP) of reticulo-thalamic inhibition is shut off, leading to increased variability in eye movement. The subplots show the time evolution of model behavior (A–B) and model neural activities (C–I) as well as external input (J). A) Horizontal position of the model eye (red trace) and the target (blue trace) in absolute coordinates. B) Relative position of the eye with respect to the target. C) Spectrogram of total middle-layer cortical activity. D–I) Raster plots show spiking activity in the model neurons. J) External thalamic input. Right: Fixation: final 4 s. The system settles on accurate fixation of the stationary stimulus. A distractor (magenta trace, straight line) is introduced at the 2 s mark, but fixation performance is unaffected. After the 6 s mark (green bar), the dSTP regulation reticulo-thalamic inhibition is shut off, causing the model to shift between the target and the distractor. The subplots show the time evolution of model behavior (K–L) and model neural activities (M–S) as well as external input (T). K) Horizontal position of the model eye (red trace), the target (blue trace), and the distractor (magenta trace) in absolute coordinates. L) Relative position of the eye with respect to the target. M) Spectrogram of total middle-layer cortical activity. N–S) Raster plots show spiking activity in the model neurons. T) External thalamic input.
Figure 7.
Comparison of eye movements across perturbations. Behavioral performance for samples of each type of simulated perturbation, zooming in on the final 4 s of each simulation. The plots on the left (A–D) show the smooth pursuit task, and the plots on the right (E–H) show the fixation task. Blue traces, target; red traces, eye position; magenta traces (straight lines), distractor. Vertical black tick marks indicate temporal locations of “saccade-like” high-velocity movement bursts. The perturbations of PV-INs (A, E), CB-INs (B, F), TRN neurons (C, G), and short-term plasticity (D, H) take place from the 6 s mark onward (green bar). They show broad qualitative similarities, but the detailed performance profiles show differences.
Figure 8.
Comparison of rhythmic activity across perturbations. Each plot shows the power spectrum of the Fourier transform for the 2 s perturbation epoch (red traces) and the 2 s period immediately before the perturbation (blue traces). The plots on the left (A–D) show the smooth pursuit task, and the plots on the right (E–H) show the fixation task. In the perturbations of PV-INs (A, E), there is no evidence of change in alpha power. The perturbations of CB-INs (B, F) and short-term plasticity (D, H) show clear increases in the alpha band for both tasks. The TRN perturbation only shows an increase in alpha power in the fixation task (G).
Figure 9.
Error as a function of perturbation strength. Each subplot shows the root mean square (rms) error as a function of the strength of the simulated perturbation. The blue dashed lines show the average rms error for the normal performance epoch (4 to 6 s period). Red circles show the rms error for the perturbed performance epoch (6 to 8 s period) for a single trial. The black lines shows the trend of the averages across five simulation trials for a given perturbation level. Error bars indicate standard deviation. Plots on the left show results for the smooth pursuit task. Plots on the right show results for the fixation task.
Figure 10.
Number of “saccade-like” transitions as a function of perturbation strength. Each subplot shows the number of high-velocity “saccade-like” movements as a function of the strength of the simulated perturbation. The blue dashed lines show the average “saccade” number for the normal performance epoch (4 to 6 s period). Red circles show the “saccade” number for the perturbed performance epoch (6 to 8 s period) for a single trial. The black lines show the trend of the averages across five simulation trials for a given perturbation level. Error bars indicate standard deviation. Plots on the left show results for the smooth pursuit task. Plots on the right show results for the fixation task.
Table 1.
Inputs to each neuron group
| Region | Excitatory currents | Inhibitory currents |
|---|---|---|
| Thalamus (T) | I ext AMPA + I ext NMDA + I D→T AMPA + I T Ca | P T I R→T GABA B |
| TRN (R) | I T→R AMPA + I D→R AMPA + I R Ca + I R→R gap | I hyp |
| Middle-layer pyramidal neurons (M) | I T→M AMPA (*) | I PV→M GABA A |
| Middle-layer PV neurons (PV) | I M→PV AMPA + I M→PV NMDA | I PV→PV GABA A |
| Middle-layer CB neurons (CB) | I M→CB AMPA + I M→CB NMDA | 0 |
| Deep-layer pyramidal neurons (D) | I M→D AMPA | 0 |
Table 2.
Model parameters
| Term | Value |
|---|---|
| σ D→T | 0.05 |
| σ T→M p | 0.0625 |
| σ T→M d | 0.9375 |
| σ M→D | 0.0125 |
| σ T→R | 0.0938 |
| σ D→R | 0.0125 |
| σ R→R gap | 0.0313 |
| σ PV→PV | 0.0313 |
| σ PV→M | 0.4375 |
| σ CB→M | 1.25 |
| σ M→PV | 0.025 |
| σ M→CB | 0.125 |
| τ rise fast | 2 ms |
| τ fall fast | 10 ms |
| τ rise NMDA | 8 ms |
| τ fall NMDA | 100 ms |
| τ rise PV | 0.1 ms |
| τ fall PV | 0.5 ms |
| τ rise GABA B | 8 ms |
| τ fall GABA B | 30 ms |
| τ rise xslow | 200 ms |
| τ fall xslow | 400 ms |
| τ s | 0.001 ms |
| A D→T | 0.04 |
| A T→M p | 4.8 |
| A T→M d | 1.2 |
| A M→D | 1.4 |
| A T→R | 0.15 |
| A D→R | 1 |
| A R→R gap | 0.3 |
| A PV→PV | 10 |
| A PV→M | 50 |
| A CB→M | 1 |
| A M→PV AMPA | 0.5 |
| A M→PV NMDA | 4 |
| A M→CB AMPA | 0.03 |
| A M→CB NMDA | 1 |
| A R→T | 0.32 |
| A T Ca | 20 |
| A R Ca | 12 |
| A STP | 3,000 |
| N T , N PV, N CB, N R | 40 |
| N M , N D | 120 |