Post on 13-Dec-2020
Burst Ensemble MultiplexingLinking dendritic activity to inhibitory
microcircuits
Richard NaudBrain and Mind Research InstituteDepartment of Cellular and Molecular MedicineUniversity of Ottawa, Canada
Neocortical Neural Code is Hierarchical
Gilbert and Li, Nat Rev Neurosci (2013)Felleman and van Essen, Cereb Cortex (1991) Hubel and Wiesel, J Physiol (1962)
Synaptic inputs
or sensory
stimulation
FiringRate
Rate 1Inputs 1
Inputs 2 Rate 2
Outline
Introducing Bursting and the Neural CodePart I: Burst Ensemble MultiplexingPart II: Information-Limiting Factors in MultiplexingPart III: Role of Inhibitory MicrocircuitryHierarchical Codes: A Role for Multiplexing?
Burst Ensemble Multiplexing
PART I
Ensemble Firing Rate
Input (sensory)
time
Ensemble Neural Decoding
Firing Rate
Gerstner Neural Comp (2000)
Tchumatchenko et al., J Neurosci (2011)
Knight J Gen Physiol (1972)Wilson and Cowan Biophys J (1972)
Membrane Potential
time
London et al., Nature (2010)Banerjee et al., Neural Comput. (2010)
Input-derivative encoding Gabbiani et al. Nature (1996)Kepecs et al. (2001)
Larkum et al. Nature (1999)Xu et al. Nat. Neurosci. (2013)Conjunction of inputs
Burst Ensemble Multiplexing
1 Burst
Firing times
Events}
Firing Rate
Burst Rate
Event Rate
Singlet Rate
1 Singlet
Distinct Nature of Inputs to Apical VS Perisomatic
SomaticSensory - Bottom-up
Gilbert and Sigman Neuron (2007)Petreanu et al. Nature (2009)
Larkum Trends Neurosci (2013)Xu et al. Nature (2012)
Deep-layer (L5B)pyramidal cells
Top-down (Attention,
expectation, top-down partial credit)
Dendritic
Cortical Microcircuits
Gilbert and Li, Nat Rev Neurosci (2013)
+ STD
PV+
VIP
+STD
STD+
STF+-
SOM+-
-
-Pyr
Tsodyks and Markram PNAS (1998)
Pala and Petersen, Neuron (2015)Jiang et al. Science (2016)
Reyes et al. Nat Neurosci (1998) Pfeffer et al. Nat Neurosci (2013)Pi et al. Nature (2013)
Lovett-Baron Nat Neurosci (2012)Pi et al. Nature (2013)
Bursts of Action Potentials in vivo
Bursts are sparseBursts are shortBursts are stereotypical
In vivo ISI distributions are bimodal: Bursts and single spikesP (ISI)
Interspike interval (schematic)
de Kock et al. J Phys (2008)
Bursting in L5B cells: BAC-Firing
Deep-layer (L5B)pyramidal cell
population
20 ms
10 ms
Larkum et al. Nature (1999)
Naud, Bathellier and Gerstner, Front Comp Neuro (2014)
Characterization of Active Dendrites
Two-compartment model fitted on electrophysiological data- Predicts 85% of spike times- Morris-Lecar dendritic compartment and LIF soma (+
adaptation)- Back-propagating action potential and Forward propagating
calcium spike
Experiment Model
Mensi, et al. J Neurophys (2012)
Background noise
Each compartment receives background noiseAmplitude of noise tuned to yield 5 mV standard deviation (Polack et al. Nat Neurosci 2013)Background noise replaces E-I balance and synaptic bombardment
background noise
background noise
Each compartment receives independent noise Simulate ensemble
Naud & Sprekeler, Submitted
Simulations of Deep Cortical Cells show Burst Ensemble Multiplexing
Deep-layerpyramidal cell
population
Simulations of Deep Cortical Cells show Burst Ensemble Multiplexing
Naud & Sprekeler, Submitted
S Dx
S
DS
Sx
DecodingEncoding
A single ensemble of pyramidal neurons can encode two streams of information simultaneously with different spike
timing patterns
Information Limiting Factors in Multiplexing
PART II
Encoding Time-dependent Stimuli
Multiplexing holds for quickly changing inputs up to approximately 40 Hz.
Mutual Information of Firing Rate vs Multiplexing
Shannon (1948)Bialek et al. (1991)
Lindner IEEE (2016)
~420+210 = 630 bits/s~300 + 40 = 340 bits/s
Multiplexing info.Firing Rate info.
I(A; B) = �Z W
0log2(1� C(!))d!
Burst Ensemble Multiplexing can almost double information rate
Burst Ensemble Multiplexing is works with larger ensembles
Information-Limiting Factors
Bandwidth
Number of cells
E0
F0
N
Stationary event rateStationary Burst ProbabilityNumber of neurons in the ensembleEffective membrane potential input-driven varianceBandwidth
Ps Pd
Theoretical Estimates of Information Rate
E0
F0
N
Stationary event rateStationary Burst ProbabilityNumber of neurons in the ensembleEffective membrane potential input-driven varianceBandwidth
Ps Pd
Renewal Theory and Information Theory
Theoretical limits to multiplexing
0 20 40 60 80 100Avg. Burst Prob. [%]
1.0
1.5
2.0To
tal I
nfo.
[bits
/ms] 2 sp./bst.
3 sp./bst.6 sp./bst.eq. rate
0 5 10 15Burst Size [sp./bst]
0.0
0.5
1.0
1.5
Info
. [bi
ts/m
s]
N =104ca
0 5 10 15Burst Size [sp/bst.]
0
10
20
30
40
Opt
imal
Bur
st P
rob.
[%]b d
100
Pop. Size [# cells]
0.5
1.0
1.5
2.0In
fo. B
EM /
Info
. Eq.
Rat
e
102 104 106
Rate advantageBEM advantage
N = 103
N = 102
Sparse and short bursts are optimal
Compare Total Multiplexing Information with Classical firing rate info, constrained for matched total number of spikes
Naud & Sprekeler, Submitted
Can Neurons Read a Multiplexed Code?
PART III
Neural Demixing: Short-Term Plasticity and Cortical Microcircuits
STD
STF
Short-term Facilitation
Short-termDepressionEvents}
Pre-syn. Spike pattern
Post-syn. Membrane potential
+ STD
PV+
VIP
+STD
STD+
1 Burst
1 Singlet
STF+-
SOM+-
-
-
Simulations of Neocortical Networks show Demultiplexing
Naud & Sprekeler, Submitted
Time [ms]
S Dx
S
DS
Sx
Simulations of Neocortical Networks show Demultiplexing
+ STD
STF+-
Naud & Sprekeler, Submitted
Theoretical limits to multiplexing
0 20 40 60 80 100Avg. Burst Prob. [%]
1.0
1.5
2.0To
tal I
nfo.
[bits
/ms] 2 sp./bst.
3 sp./bst.6 sp./bst.eq. rate
0 5 10 15Burst Size [sp./bst]
0.0
0.5
1.0
1.5
Info
. [bi
ts/m
s]
N =104ca
0 5 10 15Burst Size [sp/bst.]
0
10
20
30
40
Opt
imal
Bur
st P
rob.
[%]b d
100
Pop. Size [# cells]
0.5
1.0
1.5
2.0In
fo. B
EM /
Info
. Eq.
Rat
e
102 104 106
Rate advantageBEM advantage
N = 103
N = 102
Sparse and short bursts are optimal
Compare Total Multiplexing Information with Classical firing rate info, constrained for matched total number of spikes
Naud & Sprekeler, Submitted
Martinotti Inhibition can Optimize Multiplexing
STF
_
_
STD+
STF+
_
_
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
] *
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
]
*
+
0 300 600 9000
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 900Som. Input [pA]
0
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 9000
20
40
60
80
100
Burs
t Pro
b. [%
]
0 300 600 900
Dend. Input [pA]
0
20
40
60
80
100
Burs
t Pro
b. [%
]
a b c d
e f g h
STF
_
_
STD+
STF+
_
_
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
] *
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
]*
+
0 300 600 9000
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 900Som. Input [pA]
0
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 9000
20
40
60
80
100
Burs
t Pro
b. [%
]
0 300 600 900
Dend. Input [pA]
0
20
40
60
80
100
Burs
t Pro
b. [%
]
a b c d
e f g h
STF
_
_
STD+
STF+
_
_
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
] *
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
]
*
+
0 300 600 9000
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 900Som. Input [pA]
0
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 9000
20
40
60
80
100
Burs
t Pro
b. [%
]0 300 600 900
Dend. Input [pA]
0
20
40
60
80
100
Burs
t Pro
b. [%
]
a b c d
e f g h
STF
_
_
STD+
STF+
_
_
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
] *
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
]
*
+
0 300 600 9000
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 900Som. Input [pA]
0
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 9000
20
40
60
80
100
Burs
t Pro
b. [%
]
0 300 600 900
Dend. Input [pA]
0
20
40
60
80
100
Burs
t Pro
b. [%
]
a b c d
e f g h
STF
_
_
STD+
STF+
_
_
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
] *
-FDI
+FDI
1
2
3
Avg.
Bur
st S
ize
[sp.
]
*
+
0 300 600 9000
20
40
60
80
Firin
g Ra
te [H
z]
0 2000
10
0 300 600 900Som. Input [pA]
0
20
40
60
80Fi
ring
Rate
[Hz]
0 2000
10
0 300 600 9000
20
40
60
80
100
Burs
t Pro
b. [%
]
0 300 600 900
Dend. Input [pA]
0
20
40
60
80
100
Burs
t Pro
b. [%
]
a b c d
e f g h
1) Feedback dendritic inhibition imposes short and sparse bursts, 2) Multiplexing is preserved when inhibition follows the STF + divisive inhibition motif
som. input at 0,200, 400 pA
som. input at 0 pA
som. input at 400 pA
Summary
- Properties of active dendrites is consistent with a mechanism for encoding two streams of information simultaneously
- Burst Ensemble Multiplexing is a distinct for time-division multiplexing and frequency division multiplexing
- Short and sparse bursts are optimal for multiplexing
- Decoding of two streams of information is consistent with physiology of inhibitory microcircuits in the cortex
Bottom-up input
Top Down Input
Bottom-up input
Top Down Input
+STD
STF+
-
STD
-
+
-
+
+
+
++
STD
STF
STF
Top-Down Dendritic Input
Bottom-up Somatic Input
Burst Probability in Low-Level Ensemble
Event Ratein Higher-Level Ensemble
STF and Divisive Inhibitionin Descending Connections
STD inAscendingConnections
STD+
+
+
+
STD
STF
STF
Top-Down Dendritic Input
Bottom-up Somatic Input
Burst Probability of Low-Level Ensemble
Event Rateof Higher-level Ensemble
STF in DescendingConnections
STD in AscendingConnections
Two-way Vertical Communication Layer-wise Top-down Multiplication
Acknowledgments
Henning Sprekeler
Matthew Larkum
Technische Universität BerlinBernstein Center for Computational Neuroscience
Albert Gidon
University of Ottawa Centre for Neural Dynamics
Len Maler
Jean-Claude BéïqueSimon Chen
Humboldt Universität
Filip Vercruysse
Neural Coding LabLouis Vallée Zeke Williams An Duong
We have open Ph.D. and PostDoc positions!
Funding
0 20 40 60 80 100Avg. Burst Prob. [%]
1.0
1.5
2.0To
tal I
nfo.
[bits
/ms] 2 sp./bst.
3 sp./bst.6 sp./bst.eq. rate
0 5 10 15Burst Size [sp./bst]
0.0
0.5
1.0
1.5
Info
. [bi
ts/m
s]
N =104ca
0 5 10 15Burst Size [sp/bst.]
0
10
20
30
40
Opt
imal
Bur
st P
rob.
[%]b d
100
Pop. Size [# cells]
0.5
1.0
1.5
2.0
Info
. BEM
/ In
fo. E
q. R
ate
102 104 106
Rate advantageBEM advantage
N = 103
N = 102
Hypothesis: Burst for Multiplexing
Brain Rhythms and Bursting
Figure 1: Power Spectral Density for TPN population simulated under varying constant
dendritic input and 200pA constant somatic input. (A) Power spectral density for TPN popu-lation with Id = 500pA (red) and Id = -500pA (blue). (B) Neural response (top, raster) and somaticmembrane potential (bottom) to constant 500pA dendritic input. �v = 9.68mV, mean firing of 18 Hzand Fano Factor of 0.52 calculated after 5 repetitions. (C) Normalized peak power of frequencies in the↵/� regime vs. constant dendritic current of power Id. (D) Normalized peak power of frequencies in the↵/� regime vs. average Burst fraction.
1
Figure 1: Power Spectral Density for TPN population simulated under varying constant
dendritic input and 200pA constant somatic input. (A) Power spectral density for TPN popu-lation with Id = 500pA (red) and Id = -500pA (blue). (B) Neural response (top, raster) and somaticmembrane potential (bottom) to constant 500pA dendritic input. �v = 9.68mV, mean firing of 18 Hzand Fano Factor of 0.52 calculated after 5 repetitions. (C) Normalized peak power of frequencies in the↵/� regime vs. constant dendritic current of power Id. (D) Normalized peak power of frequencies in the↵/� regime vs. average Burst fraction.
1
Bursting imposes a strong correlation structure, even in the asynchronous state
Figure 1: Power Spectral Density for TPN population simulated under varying constant
dendritic input and 200pA constant somatic input. (A) Power spectral density for TPN popu-lation with Id = 500pA (red) and Id = -500pA (blue). (B) Neural response (top, raster) and somaticmembrane potential (bottom) to constant 500pA dendritic input. �v = 9.68mV, mean firing of 18 Hzand Fano Factor of 0.52 calculated after 5 repetitions. (C) Normalized peak power of frequencies in the↵/� regime vs. constant dendritic current of power Id. (D) Normalized peak power of frequencies in the↵/� regime vs. average Burst fraction.
1
Louis ValléeuOttawa
Burst Ensemble Multiplexing
Cortical Microcircuits
Tsodyks and Markram PNAS (1998)
Pala and Petersen, Neuron (2015)Jiang et al. Science (2016)
+ STD
PV+
VIP
+STD
STD+
STF+-
SOM+-
-
-
Reyes et al. Nat Neurosci (1998) Pfeffer et al. Nat Neurosci (2013)Pi et al. Nature (2013)
Lovett-Baron Nat Neurosci (2012)Pi et al. Nature (2013)
Short-Term Facilitation
(STF)
Short-Term Depression
(STD)
Pyr
Pyr -> SOM+
Pyr -> PV+
Naud, Bathellier and Gerstner, Front Comp Neuro (2014)
Two-compartment model reproduces BAC-firing
Model reproduces - Spike Timing - BAC-Firing - Critical Frequency
Conditions for Information Enhancement