Introduction Linearity for optogenetic inputs in visual cortex b) Linearity ...
Undergraduate Category: Physical and Life Sciences B.S. in Behavioral Neuroscience candidate Abstract ID#: 596
Nicole T. Comfort, Mark H. Histed, Robert T. Ohman, Alan R. Perillo, and John H.R. Maunsell Department of Neurobiology, Harvard Medical School, Boston MA USA
Linear integration for perceptual behavior in mouse primary auditory and visual cortex
Input (Same sum)
−40 −50
Optogenetic + visual Responses
1
10 100 Pulse duration
12 ms
10
100 ms
5 0
50
100
Time from pulse start (ms)
Histed and Maunsell, PNAS 2014
Response change
c) Time
Input (constant)
0 25 Baseline change, spk/s
50
Lever position
45
30
20
Spiking model: linearity requires specific network and cellular properties 3200 excitatory cells
10
...
Visual + ChR2
0
4
0 10 duration (ms)
100
0
Baseline rate (spk/s)
+ ge ( E e − Vm ) + gi ( E i − Vm )
tone duration (ms)
−20
Inhibitory corr.
Baseline rate (spk/s)
Cortex: optimal linearity? LGN neurons
Baseline rate (spk/s)
nonlinearity
50
-75
sum
Σ
Σ
To understand how the brain controls behavior, we wish to identify simple computations that are widely used in the cortex. One such computation is sensory normalization, which is a form of weighted averaging of multiple inputs (Caradini and Heeger, 2012). In contrast, here we have observed purely linear input summation performed by primary visual cortex. In the future, we must determine whether each brain area uses only one of these approaches to combine inputs. Or, if brain areas can use them flexibly for different inputs or behaviors, what circuit mechanisms control the character of input-output computations?
Excitatory corr.
0
100
Conclusions
Independent
0
10
Field and Rieke, 2005, 2006
50
50
0
V1 neuron
20
0
4
1
dVm 1 = − gleak ( E rest − Vm ) + gChR 2 ( E e − Vm ) dt τm
Visual inputs
0
8
Linearity: optimal for detecting changes in a population code?
rod bipolar
Cortical cell
...
−20
12
...
ChR2 conductance input
−40
Figure 3a: We varied the baseline firing rate using ChR2 and recorded the spike responses in ~300 cells. Raising the baseline firing rate slighly raised the spike response by a similar degree; similarly, a large increase in baseline resulted in a large increase in firing rate.
Human
800 inhibitory cells
...
40
200 ms 200
70
Rods ...
Visual alone
20
65
8
sum
Vis ChR2
60
Background inputs
20
−40
0
55
Retina: optimal supralinearity
100 excitatory cells
10
0
rate - baseline (spk / s)
Emx1-ChR2 raises baseline
50
Figure 5: To investigate whether linearity is consistent across cortical areas, we trained mice to do a change detection task, varying tone amplitude and duration. Top left: example psychometric curves from one day. Below: Thresholds plotted across days for varying duration. We also did this in a human subject. This behavioral linearity in humans has been characterized before and is known as Bloch’s Law.
Sublinear
40
Linearity for visual inputs a)
Linear
Baseline change
Figure 2: This figure outlines the two approaches to studying linearity in the cortex. One can use optogenetics only, but there are specific reasons why this may not be the best approach. Therefore, in this study we used both optogenetic and visual stimuli, displaying the same visual stimulus repeatedly and varying the baseline using optogenetics (see above).
Stimulation light pulses (same sum)
Figure 1: Recent published data implies that there is a linearity between ChR2 conductance inputs and spike outputs, despite individual neurons’ many nonlinearities. We varied the pulse duration (3-100ms) and power, keeping the integral the same, and observed a constant spike rate.
0.5
dB SPL
Figure 3c: Cartoon schematic depicting linear, supralinear, and sublinear responses.
Supralinear
77 dB SPL white noise
Response window
0
count
0
−20
−40
−25 0 Baseline change, spk/s
Background
10 ms
Correct release: reward
count
6 ms
100
0
count
15
200
100 ms
1
mean rate (spk/s)
3 ms
Spike count (% of 3 ms)
Population firing rate (spk/s)
20
Same sum:
Signal
20
Figure 3b: Example plots of the inhibitory (left) and excitatory (right) data. The responses are nearly linear on average. There is a trend towards sublinearity for the largest baseline shifts.
raised baseline rate
Linearity for optogenetic inputs in visual cortex
−20
4.8-19.2 kHz tone, 2-100 ms
Thresh (dB re: 200 ms thresh)
Time
0
Task
1
Fract. correct
same sum
20
Mouse
Thresh (dB re: 100 ms thresh)
Responses
Sublinear
Behavioral linearity for auditory stimuli
Excitatory (Emx1-ChR2)
40 Response change (spk/s)
Linear
Supralinear
Inhibitory (PV-ChR2)
40
Response change (spk/s)
This prior result implied that on average, visual cortical neurons transformed optogenetic inputs linearly into outputs. This is surprising given the many nonlinearities in neurons and recurrent networks. Here, by combining visual and optogenetic inputs, we show that visual inputs are transformed into outputs linearly, across a wide range of output firing rates. Also, in an auditory behavioral task, animals show linear integration for tone inputs, suggesting that linear transforms may be one canonical cortical computation.
Optogenetic only
b)
Response change (spk/s)
The brain performs computations as activity patterns are transformed by propagation through neuronal circuits. Using direct stimulation of cortical neurons with channelrhodopsin-2 (ChR2) in a head-fixed change detection task, we have found that animals’ detection abilities depend only on the total number of spikes fired in a 100 ms interval (Histed and Maunsell, 2014). Spike timing has little effect on this behavior.
Input-output transformations: two approaches
Response change (spk/s)
Introduction
This work was supported by NEI, HHMI. -50
Figure 4: A toy model of a cortical neuron demonstrates that linearity can arise, given certain network properties. We expect the responses to be supralinear, however, it is only when there is a relative refractory period and inhibitory cells are correlated that we see the model fit our data.
References Carandini, M., & Heeger, D. J. (2012). Normalization as a canonical neural computation. Nature Reviews Neuroscience, 13(1), 51–62. doi:10.1038/nrn3136 Maunsell, J.H.R., & Histed, M. H. (2014). Cortical neural populations can guide behavior by integrating inputs linearly, independent of synchrony. Proc Natl Acad Sci, 111(1): E178-87. doi: 10.1073/pnas.1318750111
Nicole T. Comfort, Mark H. Histed, Robert T. Ohman, Alan R. Perillo, and John H.R. Maunsell Department of Neurobiology, Harvard Medical School, Boston MA USA
Linear integration for perceptual behavior in mouse primary auditory and visual cortex
Input (Same sum)
−40 −50
Optogenetic + visual Responses
1
10 100 Pulse duration
12 ms
10
100 ms
5 0
50
100
Time from pulse start (ms)
Histed and Maunsell, PNAS 2014
Response change
c) Time
Input (constant)
0 25 Baseline change, spk/s
50
Lever position
45
30
20
Spiking model: linearity requires specific network and cellular properties 3200 excitatory cells
10
...
Visual + ChR2
0
4
0 10 duration (ms)
100
0
Baseline rate (spk/s)
+ ge ( E e − Vm ) + gi ( E i − Vm )
tone duration (ms)
−20
Inhibitory corr.
Baseline rate (spk/s)
Cortex: optimal linearity? LGN neurons
Baseline rate (spk/s)
nonlinearity
50
-75
sum
Σ
Σ
To understand how the brain controls behavior, we wish to identify simple computations that are widely used in the cortex. One such computation is sensory normalization, which is a form of weighted averaging of multiple inputs (Caradini and Heeger, 2012). In contrast, here we have observed purely linear input summation performed by primary visual cortex. In the future, we must determine whether each brain area uses only one of these approaches to combine inputs. Or, if brain areas can use them flexibly for different inputs or behaviors, what circuit mechanisms control the character of input-output computations?
Excitatory corr.
0
100
Conclusions
Independent
0
10
Field and Rieke, 2005, 2006
50
50
0
V1 neuron
20
0
4
1
dVm 1 = − gleak ( E rest − Vm ) + gChR 2 ( E e − Vm ) dt τm
Visual inputs
0
8
Linearity: optimal for detecting changes in a population code?
rod bipolar
Cortical cell
...
−20
12
...
ChR2 conductance input
−40
Figure 3a: We varied the baseline firing rate using ChR2 and recorded the spike responses in ~300 cells. Raising the baseline firing rate slighly raised the spike response by a similar degree; similarly, a large increase in baseline resulted in a large increase in firing rate.
Human
800 inhibitory cells
...
40
200 ms 200
70
Rods ...
Visual alone
20
65
8
sum
Vis ChR2
60
Background inputs
20
−40
0
55
Retina: optimal supralinearity
100 excitatory cells
10
0
rate - baseline (spk / s)
Emx1-ChR2 raises baseline
50
Figure 5: To investigate whether linearity is consistent across cortical areas, we trained mice to do a change detection task, varying tone amplitude and duration. Top left: example psychometric curves from one day. Below: Thresholds plotted across days for varying duration. We also did this in a human subject. This behavioral linearity in humans has been characterized before and is known as Bloch’s Law.
Sublinear
40
Linearity for visual inputs a)
Linear
Baseline change
Figure 2: This figure outlines the two approaches to studying linearity in the cortex. One can use optogenetics only, but there are specific reasons why this may not be the best approach. Therefore, in this study we used both optogenetic and visual stimuli, displaying the same visual stimulus repeatedly and varying the baseline using optogenetics (see above).
Stimulation light pulses (same sum)
Figure 1: Recent published data implies that there is a linearity between ChR2 conductance inputs and spike outputs, despite individual neurons’ many nonlinearities. We varied the pulse duration (3-100ms) and power, keeping the integral the same, and observed a constant spike rate.
0.5
dB SPL
Figure 3c: Cartoon schematic depicting linear, supralinear, and sublinear responses.
Supralinear
77 dB SPL white noise
Response window
0
count
0
−20
−40
−25 0 Baseline change, spk/s
Background
10 ms
Correct release: reward
count
6 ms
100
0
count
15
200
100 ms
1
mean rate (spk/s)
3 ms
Spike count (% of 3 ms)
Population firing rate (spk/s)
20
Same sum:
Signal
20
Figure 3b: Example plots of the inhibitory (left) and excitatory (right) data. The responses are nearly linear on average. There is a trend towards sublinearity for the largest baseline shifts.
raised baseline rate
Linearity for optogenetic inputs in visual cortex
−20
4.8-19.2 kHz tone, 2-100 ms
Thresh (dB re: 200 ms thresh)
Time
0
Task
1
Fract. correct
same sum
20
Mouse
Thresh (dB re: 100 ms thresh)
Responses
Sublinear
Behavioral linearity for auditory stimuli
Excitatory (Emx1-ChR2)
40 Response change (spk/s)
Linear
Supralinear
Inhibitory (PV-ChR2)
40
Response change (spk/s)
This prior result implied that on average, visual cortical neurons transformed optogenetic inputs linearly into outputs. This is surprising given the many nonlinearities in neurons and recurrent networks. Here, by combining visual and optogenetic inputs, we show that visual inputs are transformed into outputs linearly, across a wide range of output firing rates. Also, in an auditory behavioral task, animals show linear integration for tone inputs, suggesting that linear transforms may be one canonical cortical computation.
Optogenetic only
b)
Response change (spk/s)
The brain performs computations as activity patterns are transformed by propagation through neuronal circuits. Using direct stimulation of cortical neurons with channelrhodopsin-2 (ChR2) in a head-fixed change detection task, we have found that animals’ detection abilities depend only on the total number of spikes fired in a 100 ms interval (Histed and Maunsell, 2014). Spike timing has little effect on this behavior.
Input-output transformations: two approaches
Response change (spk/s)
Introduction
This work was supported by NEI, HHMI. -50
Figure 4: A toy model of a cortical neuron demonstrates that linearity can arise, given certain network properties. We expect the responses to be supralinear, however, it is only when there is a relative refractory period and inhibitory cells are correlated that we see the model fit our data.
References Carandini, M., & Heeger, D. J. (2012). Normalization as a canonical neural computation. Nature Reviews Neuroscience, 13(1), 51–62. doi:10.1038/nrn3136 Maunsell, J.H.R., & Histed, M. H. (2014). Cortical neural populations can guide behavior by integrating inputs linearly, independent of synchrony. Proc Natl Acad Sci, 111(1): E178-87. doi: 10.1073/pnas.1318750111
