Model of MT spike count variability accounts for
state-dependent tuning disparities
J. A. LOMBARDO , M. MACELLAIO , B. LIU , S. E. PALMER , L. C. OSBORNE
1,2
3
3
1,2
3
Department of Organismal Biology and Anatomy, The University of Chicago, Chicago, IL 60637, USA.
2
Department of Neurobiology, The University of Chicago, Chicago, IL 60637, USA.
3
Committee on Computational Neuroscience, The University of Chicago, Chicago, IL 60637, USA.
1
Summary
500
0
PSTH
90
75
60
45
30
15
0
−15
−30
−45
−60
−75
−90
0
100
200
100
400
Time (ms)
400
Tuning Curve
80
300
200
300
Time (ms)
60
40
0
500
30
20
0
10
20
30
40
Spike Count
−45
0
45
Stimulus Direction (degrees)
60
1
6
0.8
4
2
-2
−90
50
8
0
20
90
•Variance can be decomposed into to two terms reflecting the contributions
from intrinsic variability and gain fluctuations.
•These two contributions have opposing effects on the Fano factor tunings of
neurons.
•This model can fit the distribution of observed Fano factor tunings
•An increase in the gain fluctuations in the anesthetized state can explain the
difference in Fano factor tuning distributions observed.
0
15
30
45
Spike Count
Model
0.6
0.4
0.2
60
0
0
1
2
3
4
Fano factor
5
6
7
•Variability modeled as arising from two independent sources: an
intrinsic variability and input gain fluctuations.
•Intrinsic variability of spike generation is modeled as a normal
distribution with a mean µ and variance µα.
•Input µ is scaled by multiplicative gain.
•Variance of the gain fluctuations and the intrinsic variability parameter α
determine spike count variability.
Neural data: Extracellular spikes were recorded in vivo from both
anaesthetized paralyzed macaques and awake fixating macaques. A total
of 80 single units were collected in cortical area MT/V5 during visual
stimulation.
Stimuli: Smoothly translating random dot textures behind a stationary
aperture presented in the receptive field of the recorded neurons. Stimulus was optimized in size and speed for each cell. Stimulus direction was
randomly chosen from 13 or 24 directions in 15° increments around the
preferred direction.
150
-50
0
50
250
50
150
250
-50
0
50
50
150
-50
0
50
250
150
250
150
250
-50
0
50
50
150
250
-50
0
50
50
50
50
150
250
-50
0
50
50
150
250
Time (ms)
MT Response
50
150
250
-50
0
50
-50
0
50
50
150
250
-50
150
250
-50
0
50
0
50
50
150
250
-50
0
50
0
7
150
250
150
50
150
250
250
50
150
250
50
150
250
-50
0
50
50
150
250
Time (ms)
Awake
7
6
-50
0
50
-50
0
50
50
50
•Responses exhibit gaussian tuning curves relative to stimulus direction
•Shape of responses is the same in awake and anesthetized states.
•Mean response of MT neurons decreases under anesthetsia
FF90
0.5
-50
0
50
50
2
6
5
4
4
3
0.29
0
-135 -90 -45 0
45 90 135
Stimulus Direction (degrees)
-0.03
1
0
2
1
0.5
0
-135 -90 -45 0
0.5
-1
-0.8 -0.6 -0.4 -0.2
45 90 135
Stimulus Direction (degrees)
6 5 41
-1
-0.5
0
FFTI
2
3
0.5
0
FFTI
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
-135 -90 -45
0
45 90 135
0.2
0.4
-135 -90 -45
0.6
0
0.8
1
45 90 135
Stimulus Direction (degrees)
•Spike count variability is stimulus-dependent and Fano factor is directionally
tuned in MT neurons.
•Anesthesia not only increases variability, but diminishes stimulus-dependence
of variability.
•The differences in Fano factor tuning are not attributable solely to differences
in firing rate.
•State-dependent changes in Fano factor tuning can be explained by
differences in gain fluctuations
•This model may extend to other factors that modulate variability structure and
stimulus-dependence
Awake
Anesthetized
1.5
2
1
45 90 135
1
Conclusions
2.5
3
2
-135 -90 -45 0
1.5
Stimulus Direction (degrees)
6
5
FF0
Anesthetized
Probability Density
50
-50
0
50
5
Fano factor
-50
0
50
4
1
Fano factor
-50
0
50
3
1.5
Sample PSTH in Awake MT
Stimulus Direction (degrees)
Stimulus Direction (degrees)
Sample PSTH in Anesthetized MT
2
1
Model Awake FFTI
Model Anesth. FFTI
Observed Awake FFTI
Observed Anesth. FFTI
2
0
Fano factor
Experimental Methods
2.5
Probability Density
400
40
Probability Density
200
300
Time (ms)
•The variance of neural responses depends on such factors as attention,
stimulus presentation, and conscious state.
•MT neurons in awake macaques exhibit a significantly lower Fano factor
than in the anesthetized state.
•Firing in anesthetized state is super-poisson, increasing with spike count
•Firing in awake state is sub-poisson, decreasing with spike count
•Fano factor in anethetized state is consistent with Poisson mixture
model, but awake state is not.
•Many cells in awake MT exhibit a Fano factor that is tuned to stimulus
direction.
•Fano factor has a distinct U- or M-shaped tuning: lower for
preferredmotion direction and increasing for orthogonal directions
•This stimulus-dependence of variance is diminished or absent for
anesthetized MT cells.
•The Fano factor tuning for individual neurons can be quantified with a
tuning index.
50
0
Model Results
Fano Factor Tuning
60
10
Fano factor
100
Awake
Anesthetized
70
Spike Count Variance
PSTH
Firing rate [spk/s]
Stimulus Direction (degrees)
90
75
60
45
30
15
0
−15
−30
−45
−60
−75
−90
0
Raster Plot
80
Stimulus Direction
Stimulus Direction (degrees)
Sensory neurons have variable responses to repeated presentations of
the same stimulus. The structure of this trial-to-trial variability within a
population directly affects the ability to decode stimulus identity. We
compared the spike-count variability of macaque MT neurons in both the
awake and anesthetized state, finding a state-dependence of variability
and variability tuning. In the anesthetized state, the data is well modeled
by a Poisson process with variable multiplicative gain. This model
predicts a variance to mean ratio, or Fano factor (FF), that is strictly
increasing with spike count. However, in the awake state, inverted Fano
factor tuning is observed, with decreasing FF at higher spike counts at
preferred directions of motion. We developed a unified model of spike
count variability that captures the U-shaped Fano factor tuning observed
in the awake state, as well as the super-Poisson variability observed in the
anesthetized state. In our model, the state-dependent FF tuning changes
are mediated by a switch from a low gain fluctuation state in the awake
state to a higher gain fluctuation state when anesthetized.
Spike Count Variance
1
Funding
Alfred P. Sloan Foundation, NEI EY023371, Whitehall Foundation, Brain Research
Foundation, NSF IGERT DGE-0903637