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Fig. 3. Learning correlates with an increase Example Target 1 Behavior Fine-timescale Variance
in covariance of the neurons that produce 5 Preceding Target 1 Hit
Illustration using 2 neurons 10 19 kHz
the target pattern. (A) The decoder maps Illustration using 2 neurons
spike counts in 500-ms bins into quantizations Target 1 Target 2
T1 Hit
of (ensemble 1, ensemble 2) space. Neural Example Trial Trial 1 T1 Hit
activity can take multiple routes to achieve %tile:
90th
target 1. (B) Analysis of variance of spike E1 Neuron 90th E1 Neuron
counts with 100-ms bins in a 3-s window E2 Neuron FR %tile: E2 Neuron Trial N E2 Neuron FR 50th
50th
preceding target hit. “x” indicates a spike E2 Neuron 10th 10th
count vector at one time point. (C) Factor Bin Width
Time
analysis was used to analyze the ratio of = 500ms %tile: 10th 50th 90th Bin Width Win Width %tile: 10th 50th 90th
shared variance to total variance (SOT), E1 Neuron FR = 100ms = 3s E1 Neuron FR
which ranges from 0 to 1, for the full
population controlling the BMI. A two-neuron Covariance Index:
illustration shows a neural solution with - Balance of Shared-to-Total Variance (SOT) +
SOT = 0, 0.6, and 1. (D) Correlation of 0 1
change in shared variance before target
1 hit (neural covariance gain) with change
in preference for target 1 over target private variance total variance = private + shared shared variance
2 (learning), over sessions 2, 3, and 4. ChR2
animals (left) showed a significant private SOT = 0 SOT = 0.6 SOT = 1
correlation [ChR2 S4: correlation coefficient 2
–3
(r) = 0.86, P =6.1 ×10 ; ChR2 pool S3, S4: Neuron 2 FR private shared
–3
r =0.71, P =1.0 × 10 ; ChR2 pool S2, S3, S4: 1 shared 1
–4
r =0.62, P =9.8 ×10 ;ChR2 S3: r =0.60, 2 Downloaded from
–2
P =6.5 ×10 ; ChR2 S2: r = 0.62, P = 1.3
–1
×10 ], whereas YFP animals (right) shared space
showed no correlation (YFP pool S2, S3, Neuron 1 FR Neuron 1 FR Neuron 1 FR
–1
S4: r = –0.14, n.s. P =6.4 × 10 ; YFP
–1
S4: r = –0.32, P =6.0 ×10 ; YFP S3: 4 ChR2 YFP
–1
r = –0.69, P = 5.1 × 10 ; YFP S2: r =0.37, S2 4 S2
–1
P =5.4 ×10 ). n.s., not significant. 3 S3 3 S3
S4
S4
(E) SOT of direct and indirect neurons over 2 2 http://science.sciencemag.org/
sessions for ChR2 learners (left, n = 5),
ChR2 poor learners (middle, n = 5), and YFP Learning (Preference Gain T1 vs T2) 1 1
subjects (right, n = 5). ChR2 learners individually 0 0
showed significant preference gain for target
1 versus target 2 in both sessions 3 and 4. -1 -1
ChR2 poor learners constitute the remaining -2 S4: r = 0.86, p = 6.1e-3 -2
animals who as a population showed significant -3 pool: r = 0.62, p = 1.0e-3 pool: r = -0.14, n.s. p = 6.4e-1
target 1 occupancy gain on sessions 3 and 4. For -3
-2 -1 0 1 2 3 4 -2 -1 0 1 2 3 4
direct neurons, ChR2 animals’ and ChR2 on March 1, 2018
learners’ SOT increased from early (sessions Neural Covariance Gain (log2) Neural Covariance Gain (log2)
1 and 2 pooled) to late training (sessions 3 and
4 pooled), whereas ChR2 poor learners and YFP
Learners ChR2 (n = 5) Poor Learners ChR2 (n = 5) YFP (n = 5)
did not (one-sided rank sum test; ChR2, early <
–2
late, P =1.7 × 10 ; ChR2 learners, early < late, direct indirect direct indirect direct indirect
–2
P =1.6 × 10 ; ChR2 poor learners, early < late, 0.5 * 0.5 0.5
–1
n.s. P =2.1 ×10 ; YFP, early < late, n.s. P =8.3 SOT SOT SOT
–1
×10 ). For indirect neurons, SOT showed no
change for all groups (ChR2 learners: early < 0.5 0 0 0
–1
late, n.s. P =4.3 ×10 ; ChR poor learners, 0.4 early late early late early late early late early late early late
–1
early < late, n.s. P =2.7 ×10 ; YFP, early < late,
–1
n.s. P =7.1 × 10 ). Traces in the insets show the 0.3
average of each animal’s SOT in sessions 1 and SOT
2 (early) versus the average of sessions 3 and 0.2
4 (late). Error bars indicate mean ± SEM. The 0.1
asterisk indicates that the population average 0
is significantly larger than the baseline 1 2 3 4 1 2 3 4 1 2 3 4
bootstrap distribution.
Session Session Session
shared inputs to direct neurons and thus increase (private variance), and shared inputs, which drive target 1 (Fig. 3A). We analyzed fine–time scale
covariance over learning (13). We used factor multiple cells simultaneously (shared variance). spike counts (100-ms bins) in a 3-s window pre-
analysis (FA) to partition fine–time scale neural Neural variance changes were not demanded by ceding target hit (Fig. 3B). FA models popula-
variance arising from two sources: private inputs our task, as subjects could use neural activity tion spike counts x = m + x private + x shared as the
to each cell, which drive independent firing drawn from any distribution to ultimately hit sum of a mean firing rate m;private variation
Athalye et al., Science 359, 1024–1029 (2018) 2 March 2018 4of6