A spiking network simulation testing how dopamine level affects whether a working memory bump persists during a delay period.
Ring attractor networks model spatial working memory. Neurons sit on a ring with Mexican-hat connectivity: strong local excitation, weak global inhibition. A bump of activity persists without input, holding a location in memory.
The parameter da multiplies excitatory weights, mimicking D1 receptor gain modulation in prefrontal cortex. The code sweeps 16 DA levels (0.70 to 1.00, 6 trials each) with a no-distractor control to test whether collapse is caused by the distractor or by intrinsic instability.
Each trial is classified as:
- stable: bump survived near the cued location
- relocated: bump moved toward the distractor (rare)
- collapsed: bump died during the delay
0 ms: baseline (50 ms)
50 ms: cue ON (12 mV at position 50, 100 ms)
150 ms: delay (80 ms, no input)
230 ms: distractor ON (4 mV at position 0, 30 ms)
260 ms: post-distractor (40 ms)
300 ms: end
Below da ~ 0.79, bumps collapse even without a distractor. The no-distractor control shows identical collapse rates, so the collapse is intrinsic instability, not distractor-driven. Above da ~ 0.80, bumps persist and resist distractors. One trial at da=0.73 showed distractor-driven relocation (the bump shifted toward the distractor), but with only 1 out of 6 trials this is too thin to treat as a reliable effect.
The key figure
Collapse rate and centroid offset plotted for the normal protocol vs. the no-distractor control, same seeds. The two curves sit on top of each other, which is what shows the collapse is intrinsic rather than caused by the distractor.
DA threshold sweep
Collapse rate and centroid offset across all 16 DA values, distractor condition only. Shows the transition sitting right around da=0.79-0.80.
Failure mode breakdown
Same sweep, broken into stable/relocated/collapsed trial counts per DA level instead of a single averaged number. Makes clear that "collapsed" and "relocated" are different failure modes, not one smeared-together outcome.
Representative trials
Three representative single trials (high, moderate, low DA), spike raster on top and bump centroid trace below. Gives a feel for what a stable vs. a collapsed trial actually looks like at the spike level.
Parameter sensitivity
Same DA sweep repeated at three bump widths (sig_e = 0.04, 0.05, 0.06) to check whether the sharp transition is specific to one width choice. x markers mark DA values where every trial collapsed at that width. Narrower bumps (0.04) collapse across most of the tested range and only survive near da=1.0, and even then the offset estimate is noisy.
Click to expand raw per-DA numbers (n=6 trials/point)
WITH DISTRACTOR
DA stable reloc collap mean_off sd n avg_spk
------------------------------------------------------------------------
0.70 0 0 6 +nan nan 0 0
0.73 0 1 5 +46.0 0.0 1 3
0.76 0 0 6 +nan nan 0 0
0.78 0 0 6 +nan nan 0 0
0.79 2 0 4 -6.7 0.3 2 6
0.80 6 0 0 +6.4 11.3 6 57
0.81 5 0 1 +1.6 9.7 5 75
0.82 6 0 0 +4.5 8.7 6 104
0.83 6 0 0 -4.1 2.8 6 117
0.84 6 0 0 +1.8 7.8 6 128
0.85 6 0 0 -3.5 6.2 6 142
0.88 6 0 0 +0.5 4.4 6 173
0.91 6 0 0 -0.5 1.9 6 211
0.94 6 0 0 -1.0 2.0 6 260
0.97 6 0 0 -0.4 1.6 6 296
1.00 6 0 0 +0.0 0.9 6 340
WITHOUT DISTRACTOR (control)
DA stable reloc collap mean_off sd n avg_spk
------------------------------------------------------------------------
0.70 0 0 6 +nan nan 0 0
0.73 0 0 6 +nan nan 0 0
0.76 0 0 6 +nan nan 0 0
0.78 0 0 6 +nan nan 0 0
0.79 2 0 4 -15.2 2.2 2 18
0.80 4 0 2 -0.5 5.5 4 37
0.81 6 0 0 +2.5 4.0 6 76
0.82 6 0 0 +0.5 2.9 6 102
0.83 6 0 0 +1.9 6.5 6 124
0.84 6 0 0 -0.1 4.3 6 132
0.85 6 0 0 +3.4 5.8 6 144
0.88 6 0 0 +0.4 3.8 6 178
0.91 6 0 0 -0.6 2.5 6 216
0.94 6 0 0 -1.0 1.2 6 260
0.97 6 0 0 -0.1 1.8 6 297
1.00 6 0 0 -0.0 2.3 6 341
Columns: stable/reloc/collap are trial counts out of 6. mean_off/sd are the signed centroid offset from the cue, averaged over non-collapsed trials only (n = how many trials that average is based on). avg_spk is the mean late-window (250-300 ms) spike count across all 6 trials.
python ring_attractor_dopamine.pyOutputs (saved to figures/): control_comparison.png, da_threshold_sweep.png, failure_mode_breakdown.png, ring_attractor_dopamine.png, parameter_sensitivity.png
Runtime: ~4-6 minutes.
| Parameter | Value | Meaning |
|---|---|---|
J_e |
7.0 mV | peak excitatory weight (tuned) |
J_i |
0.2 mV | flat inhibitory offset |
sig_e |
0.05 | gaussian half-width (fraction of ring) |
DIST_AMP |
4.0 mV | distractor amplitude (0 for control) |
- LIF neurons, not Hodgkin-Huxley
- Single gain parameter (real D1 affects multiple conductances)
- No synaptic plasticity
- All-to-all connectivity with distance-dependent weights
- Tuned parameters, not experimentally measured
- Compte, A., Brunel, N., Goldman-Rakic, P. S., & Wang, X.-J. (2000). Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cerebral Cortex, 10(9), 910–923. https://doi.org/10.1093/cercor/10.9.910
- Wang, X.-J. (2001). Synaptic reverberation underlying mnemonic persistent activity. Trends in Neurosciences, 24(8), 455–463. https://doi.org/10.1016/S0166-2236(00)01868-3
- Durstewitz, D., & Seamans, J. K. (2008). The dual-state theory of prefrontal cortex dopamine function with relevance to catechol-O-methyltransferase genotypes and schizophrenia. Biological Psychiatry, 64(9), 739–749. https://doi.org/10.1016/j.biopsych.2008.05.015