andre longtin physics department university of ottawa ottawa, canada effects of non-renewal firing...
TRANSCRIPT
Andre Longtin
Physics Department
University of Ottawa
Ottawa, Canada
Effects of Non-Renewal Firing on Information Transfer in
Neurons
-Weakly Electric Fish
- Electroreceptor data
- Modeling
- Effects of ISI correlations
- Linear response models
Biology
Computation
Theory
Overview
Collaborators
Benjamin Lindner, postdoc, Physics, U. Ottawa
Maurice Chacron, postdoc, Physics, U. Ottawa
Leonard Maler, Cell. Molec. Med, U. Ottawa
Khashayar Pakdaman, INSERM, Paris
Martin St-Hilaire, M.Sc. Student, U. Ottawa
90 100 110 120-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
mV
time (EOD cycles)
transepidermal voltage amplitude
Weakly Electric Fish: Electrolocation
90 95 100 105 110 115 120
0.7
0.8
0.9
1.0
1.1
1.2
1.3
mV
time (EOD cycles)
Electroreceptor Neurons: Anatomy
Pore
SensoryEpithelium
Axon(To Higher Brain)
Electroreceptor Neurons: Electrophysiology
0 10 20-0.5
0.0
0.5
1.0
0 4 80
4
8
0 5000 100000
4
8
(c) i
i 0 4 80
500
1000
1500(d)
Cou
nts
ISI
(b)
ISI i+
1
ISIi
(a)
ISI
ISI Number
data courtesy of Mark Nelson, U. Illinois
2i
2i
2ijii
j II
III
Modeling Electroreceptors: The Nelson Model (1996)
High-PassFilterInput
Stochastic Spike Generator
Fit of Nelson Model to Data:
0 5 10 15 20
0.0
0.4
0.8
0 2 4 6 8 100
2
4
6
8
10
0 5000 10000
2
4
6
8
10
(d)(c)
(b)(a)
i
lag i0 2 4 6 8 10
0
500
1000
1500
2000
# C
oun
tsISI
ISI i+
1
ISIi
ISI
ISI numberRenewal Process(No ISI correlations)
1015 1020 1025 1030 1035 1040
0.00
0.04
0.08
0.12
0.16
membrane potential threshold
time (ms)
Ii Ii+1w
Leaky Integrate-and-fire Model with Dynamic Threshold Chacron, Longtin, St-Hilaire, Maler, Phys.Rev.Lett. 85, 1576 (2000)
)t(w)t(vifw)t(w)t(w
)t(w)t(vif0)t(v
ww)Ttt(Hw
)t()]ft2[sin(H)ft2sin()]t(a[H)t(av
v
firefirefirefire
firefirefire
w
0rfire
v
Modeling Electroreceptors: The Extended LIFDT Model
High-PassFilterInput LIFDT Spike Train
Fitting the Experimental Data (Part 2):
0 5000 10000
2
4
6
8
10
0 5 10 15 20
-0.4
0.0
0.4
0.8
0 2 4 6 8 100
2
4
6
8
10
(d)(c)
(b)(a)
ISI
ISI number
i
lag i0 2 4 6 8 10
0
500
1000
1500
2000
# co
unts
ISIIS
I i+1
ISIi
Non-renewalProcess
Summary of Fitting:
0 5 10 15 20-0.5
0.0
0.5
1.0
0 5 10 15 20-0.5
0.0
0.5
1.0
0 5 10 15 20-0.5
0.0
0.5
1.0
0 2 4 6 8 100
500
1000
1500
2000
SC
C j
lag j0 2 4 6 8 10
0
500
1000
1500
2000
# c
ount
s
ISI
data
0 2 4 6 8 100
500
1000
1500
2000
Experimental Data:
LIFDT Model:
Nelson Model:
What Else We Know about LIFDT
• 1D map for consecutive threshold values
• Negative correlation appear when fixed point of map is perturbed by noise: it is a deterministic property.
• Strength of correlation depends on system parameters
• With sinusoidal forcing, 2D annulus map: simple and complex phase locking, chaos
See: Chacron, Pakdaman, Longtin, Neural Comput. (2003).
Chacron, Longtin, Pakdaman, Physica D (2004).
Comparison Approach to Assess Effects of ISI Correlations:
Nelson Model
(renewal process)
LIFDT Model
(non-renewal process)
vs.
Weak Signal Detection:
2 4 6 8 10 120.0
0.2
0.4
P(n
)
P0(n,T) (no stimulus)
P1(n,T) (with stimulus)
n (spikes)
20
21
01SNR
46 48 50 52 54 56 58
0.0
0.1
0.2
0.3
0.4 (b) baseline LIFDT stimulus LIFDT baseline Nelson stimulus Nelson
P(n
)
n
T=255 msec
10-1 100 101 102 103 104 105 106
10-2
10-1
100
n=5
CV2
LIFDT shuffled LIFDT Nelson
Fan
o fa
ctor
F(T
)
counting time T (msec)
)T(
)T()T(F
2
Fano Factor:
1ii
2 21CV)(F
0 5 10 15-0.5
0.0
0.5
1.0
j
j
Asymptotic Limit(Cox and Lewis, 1966)
Regularisation:
Stimulation Protocol:
f
fc
Gaussian white noise
Low-pass filter Stimulus
Stimuli are Gaussian with standard deviation and cutoff frequency fc
Information Theoretic Calculations:
Gaussian Noise Stimulus S Spike Train XNeuron
???
S~
S~
X~
X~
S~
X~
)f(C**
2*
Coherence Function: Mutual Information Rate:
c
c
f
f
2 )]f(C1[logdf2
1MI
0.00 0.02 0.04
0
30
60
90
120
Nelson LIFDT
MI (
bits
/s)
stimulus contrast (mV)0 50 100 150 200
0
10
20
30
0 50 100 150 200
0
50
100
150
(b)
MI (
bits
/s)
fc (Hz)
(a)
LIFDT NelsonM
I (bi
ts/s
)
fc (Hz)
Comparison using Info Theory
An Important Clue: Reduction of Power at Low Frequencies:
0 100 200 30010-1
100
101
102
103
104
Pow
er (
spk2 /s
ec)
f (Hz)
LIFDT Nelson
1ii
2
21I
CV)0f(P
Theory for why certain correlations are useful: Need simpler models !!
• Simple Intrinsic Dynamics only, no extra filtering
perfect integrator neuron instead of leaky: dv/dt = μ + signal(t)
• Noise on threshold and reset only
• Assume simple noise distribution and action (uniform distribution, piecewise constant in time)
Two identical models, except for correlationsChacron, Lindner, Longtin, Phys.Rev.Lett. (in press 2004)
Model A: Model B:
2VU
VUI
01jj
jjj
Successive intervals are thus correlated
Successive intervals are not correlated
Statistics and Spectra
ISI Statistics: Power Spectra:
)f(sin)fI2cos()f(sin)f(2)f(
I/)f(sin)f()f(S
I
nf
I
11
)f(
)f(sin1
I
1)f(S
4224
44
0B
n2
2
0A
Noise Shaping
where β=2πD/µ
Linear Response Calculation for Fourier transform of spike train:
)(~
)()(~
)(~
0 fSffXfX st
susceptibilityunperturbed spike train
0)()( ff BAIt turns out:
Spike Train Spectrum= Background Spectrum + Signal Spectrum20 )(
Linear Response Calculation (Part 2):
1
st20
2
00B,A
2
B,A )f(S
S
1)f(C
Coherence Function
Linear Response Calculation (Part 3):
)]f(C1[logdf2
1)f(MI
c
c
f
f
2B,A
Mutual Information Rate
Conclusions- Weakly electric fish must detect prey (low freq. stimuli, less than 0.1 V)
- Negative ISI Correlations Can Regularize a Spike Train through spike count variance reduction and noise reduction at low frequencies.
- This is achieved through noise shaping in the power spectrum and this is greatest for weak low frequency stimuli.
- Outlook:
1) Experimentally prove that the negative correlations are really being used for computations.
2) Deal with mixtures of positive and negative correlations at lags >= 1
3) Extend to more realistic models of excitability with memory
4) Use the ideas presented here in devices to improve SNR and detectability
References:- Chacron, Longtin, St-Hilaire, Maler, PRL 85, 1576 (2000).
- Chacron, Longtin, Maler, J. Neurosci. 21, 5328 (2001).
- Chacron, Lindner, Longtin, (submitted).
- Cover, Thomas, Elements of Information Theory (1991).
- Cox, Lewis, The Statistical Analysis of Series of Events (1966).
- Nelson, Xu, Payne, J. Comp. Physiol. A 181, 532 (1997).
- Ratnam, Nelson, J. Neurosci. 20, 6672 (2000).
“Why should we explore exotic sensory systems such as electrosensation in fish or echolocation in bats?...
More highly evolved organisms derive their superior qualities not so much from novel mechanisms at the cellular level but rather from a richer complexity in the orchestration of basic designs that they share with simpler organisms. Fundamental mechanisms of perception and neuronal processing of sensory information are shared by animals as diverse as flies and primates, but a larger number of neuronal structures and interconnecting pathways bestow more powerful computational abilities and memory capacities upon the brains of primates.”
--Walter Heiligenberg
Food for Thought: