Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular...
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Transcript of Extracting Time and Space Scales with Feedback and Nonlinearity André Longtin Physics + Cellular...
Extracting Time and Space Extracting Time and Space Scales with Scales with
Feedback and NonlinearityFeedback and Nonlinearity
André Longtin
Physics +Cellular and Molecular Medicine
CENTER FOR NEURAL DYNAMICS
UNIVERSITY OF OTTAWA
Funding by NSERC, CIHR, PREA
Processing of spatio-temporal signals Processing of spatio-temporal signals Global Feedback + common noise: Global Feedback + common noise:
oscillations oscillations Spatial scale for feedback and inputSpatial scale for feedback and input Envelope processing for narrowband in time Envelope processing for narrowband in time Information resonancesInformation resonances Coincidence transforms for synchronous Coincidence transforms for synchronous
firingfiring Short term Plasticity and information Short term Plasticity and information
processingprocessing
Overview
Research Program: Research Program:
Stochastic neural networkStochastic neural network
driven bydriven by
Stochastic input in space and timeStochastic input in space and time
Experimental <-> TheoreticalExperimental <-> Theoretical
Relevance to this group:Relevance to this group:
What nonlinearity (if any) supports What nonlinearity (if any) supports patterns or computations ? patterns or computations ?
HIGHER BRAIN AREA I
HIGHER BRAIN AREA II
THALAMUS
RECEPTORS
PHYSICAL STIMULI
Brain Diagram by Arab philosopher Avicenna (circa 1300)Brain Diagram by Arab philosopher Avicenna (circa 1300)Five ventriclesFive ventricles: common sense, imagination, judging, : common sense, imagination, judging,
second imagination (composing/combining images), memory.second imagination (composing/combining images), memory.((University University LibraryLibrary, Cambridge, Cambridge) )
From Da Vinci’s notes
Courtesy W. Ellis (1991)
Electrosensory lateralline lobe (ELL)
Courtesy N. Berman and L. Maler, J. Exp. Biol., 1999
Electrosensory Lateral Line Lobe (ELL)
Electroreceptors
Higher Brain
Electrosensory Input
Amplitude Modulation (AM)
Krahe and Gabbiani (2004) Nat. Neurosci.Rev. 5:13-23
Electric Organ Discharge (EOD)
afferents
The electric sense
Temporal Characteristics: Spatial Characteristics:
Harmonic
“local”
“global”
Broadband (noise)
Chacron, et al., Nature, 2003
- Frequency tuning is highly correlated with spatial frequency
- Tuning for harmonics or broadband signals are qualitatively the same
Weakly Electric Fish: Weakly Electric Fish: main negative feedback loopmain negative feedback loop
ELL Pyramidal Cells: the first stage of sensory processing
Prey StimuliPrey Stimuli
Prey (bug) excites a fraction of the electroreceptors:
Local stimulation
Communication StimuliCommunication Stimuli
Communication calls between fish stimulate the whole body:
Global Stimulation
Oscillation MechanismOscillation Mechanism(Doiron, Chacron, Bastian, Longtin, Maler, (Doiron, Chacron, Bastian, Longtin, Maler, Nature 2003Nature 2003))
Local Stimuli :applied heterogeneously in space: No stimulus-induced correlations.
Global Stimuli :acts homogenously in space (strong spatial correlations). Correlated activity and delay cause “waves” of inhibition
Electrosensory CircuitryElectrosensory Circuitry
Sodium channel blocker can open the feedback loop.
Network Model – Global Network Model – Global StimuliStimuli
To mimic communication stimuli we apply the external stimulus to all neurons equally.
Autocorrelation Histogram
Experimental VerificationExperimental VerificationDoiron, Chacron, Maler, Longtin and Bastian, Doiron, Chacron, Maler, Longtin and Bastian, NatureNature 42, 539 42, 539
(2003)(2003)
ISI Histogram Autocorrelation
control block recover
Correlated Stimuli in Correlated Stimuli in ExperimentsExperiments
Dipole 1
Dipole 2
Dipole 3
Dipole 4
)()(1)( tctct Gii
Each dipole emits an intrinsic noise i(t), and global source, G(t). Their relative strengths is c, i.e. the covariance between dipoles.
Integrate-and-fire dynamics Integrate-and-fire dynamics
y
Linear ResponseLinear Response
Consider the spike train from the ith neuron in our network, . Assuming weak inputs, the Fourier transform of the spike train is
)()( iji ttty
)()()()( ibgi XAYY
A( intrinsic frequency response of the noisy neuron. Xi(w): Fourier transform of input (external + feedback) to
neuron i.
(1)
POWER SPECTRUMPOWER SPECTRUM
Single Neuron Power SpectrumSingle Neuron Power Spectrumvsvs
percentage of common noise (c) percentage of common noise (c)
For an infinite network: For an infinite network:
2
~2
22
)(~
1
)(~
)(~
Re2
)()()(
AKg
AKgAKg
AcSS
d
dd
bg
)(|)(| 2 inSA
(Input-output sync) (spike-spike sync.)
Fokker-Planck analysis on noisy Leaky Integrate-and-fire Fokker-Planck analysis on noisy Leaky Integrate-and-fire Neurons + Delays+ Spatial InputNeurons + Delays+ Spatial Input
Doiron, Lindner, Longtin, Bastian and Maler, Doiron, Lindner, Longtin, Bastian and Maler, Phys. Rev. LettPhys. Rev. Lett. 93, 048101 (2004). 93, 048101 (2004)
Linear Fluctuation Theory: needs noise. Linear Fluctuation Theory: needs noise. 30
25
20
15
S (
spik
es2 /s
)
140120100806040200
frequency (Hz)
simulation c=1 theory c=1 simulations c=0 theory c=0
Input-output coherence for Input-output coherence for delayed feedback networkdelayed feedback network
(global feedback)(global feedback)
Coherence function:
CXY ( f ) SXY ( f )
2
SXX ( f ) SYY ( f )
Correlation coefficient (in the frequency domain) between two signals, X and Y
R(t) (t tii )
Response: spike trainStimulus:
S(t) - narrowband stimulus(linear)
E(t) - envelope of narrowbandstimulus (non-linear)
Network of stochastic Perfect IF’s Network of stochastic Perfect IF’s with with
+ and - global delayed feedback+ and - global delayed feedback
)2()tt(N
1)t(K
)1()t(Kg)t(Kg)t(S)t(D2VN
1k
)t(M
1jkji,ei,e
iiieeekk
k
S(t) is the stimulus
Chacron, Longtin, Maler, Phys.Rev.E (2005)
Network of Perfect IF’s with Network of Perfect IF’s with global feedback: Information global feedback: Information
theorytheory
0 20 40 60 80
0.0
0.2
0.4
0.6
0.8
1.0
coh
ere
nce
frequency (Hz)
ge=g
i=0
ge=0, g
i=-0.8
ge=0.8, g
i=0
Coherence = | H(f)|2 Pss/Pxx
INFORMATION RESONANCEINFORMATION RESONANCE(Chacron, Longtin, Maler, PRE 2005)(Chacron, Longtin, Maler, PRE 2005)
G<0
G=0
Experimental DATA !!
Introducing…Introducing…
Spatial scale for feedbackSpatial scale for feedback Spatial scale for noiseSpatial scale for noise
Two regimes with respect to Two regimes with respect to
gamma oscillationsgamma oscillations
In linear response, only the ratio of length scales matters(Hutt, Sutherland, Longtin, submitted)
GLOBAL IN SPACEGLOBAL IN SPACE
NARROWBAND IN TIME: NARROWBAND IN TIME:
2 TIME SCALES2 TIME SCALES
EOD amplitude
EOD
Hey guys
EOD amplitude
EOD
EODamplitude
EOD
From: E. W. Tan et al, Behav.Brain Res., 164:83-92 (2005)
Most probable populationsize 3-5 fish
Average f inblack (white) waters:
Day: 35.3 (54.1) HzNight: 54.6 (65.8) Hz
P-units (primary receptors)Feed forward:
- P-units respond as linear encoders
frequency (Hz)
- global stimulation: linear response to narrowband signal and its low frequency envelope
- Envelope response is absent under local stimulation
PyramidalCells
S(t)
E(t)
Middleton, Longtin, Benda, Maler, PNAS (2006)
input
output
- Generation of envelope signal is likely due to spike threshold nonlinearity
- Output spike train is phase- locked to fast oscillation and modulated at lower frequencies
Middleton, Harvey-Girard, Maler, Longtin,
Phys. Rev. E. (2006)
MECHANISM
transferfunction
input signal output signal
(rectification)
signals Spectral composition
time frequency
Network instead of single cellNetwork instead of single cell
Stochastic Envelope GatingStochastic Envelope Gating(and not SR! See Middleton et al., PRE 2006)(and not SR! See Middleton et al., PRE 2006)
Leaky Integrate-and-Fire (LIF) neuron:
dv
dt
v
2D
(t) S(t)
r() dzez2
erfc(z) vR 2 D
vR 2 D
1
(t) o a S(t)
Mean firing rate:
where
GLOBAL SPATIAL SIGNALSGLOBAL SPATIAL SIGNALS
EXTRACTING EXTRACTING
HIGH FREQUENCY CHIRPS HIGH FREQUENCY CHIRPS
FROM FROM
LOWER FREQUENCY BEATSLOWER FREQUENCY BEATS
““SYNC-DESYNC CODE”SYNC-DESYNC CODE”
Context: Context: electrocommunicationelectrocommunication
Male-male or female-female call Male-male or female-female call causes synchronization of receptorscauses synchronization of receptors
Male-female or female-male call Male-female or female-male call causes desynchronization of causes desynchronization of receptorsreceptors
(Benda, Longtin, Maler, Neuron 2006)(Benda, Longtin, Maler, Neuron 2006)
Encoding a modulatory Encoding a modulatory signalsignal
Coincidence transforms…Coincidence transforms…
Middleton, Longtin, Benda, Maler (submitted)
Short-term Plasticity Short-term Plasticity
Broadband Coding
Depression
dominates
Facilitation
dominates
-Gamma rhythms for global correlated inputs
- Gamma strength proportional to correlation
- Spatial feedback can assess spatial correlation of input
- Information resonances with delayed feedback
- Envelope generation due to spike threshold nonlinearity
- Envelope generation is dependent on mean bias and noise
Intrinsic noise can gate a signal competing with envelope
Plasticity: paradoxical effects on coding
Importance of spatiotemporal statistics of input
Brent Doiron
Maurice Chacron
Jason Middleton Carlo Laing Eric Harvey-Girard John Lewis
Jan Benda
Benjamin Lindner
Len Maler & André Longtin
Joe Bastian
Connie Sutherland
Axel Hutt
COHERENCE AND STOCHASTIC RESONANCE COHERENCE AND STOCHASTIC RESONANCE WITH DELAYED FEEDBACKWITH DELAYED FEEDBACK
Morse and Longtin, Phys. Lett. A (2006)Morse and Longtin, Phys. Lett. A (2006)
MULTIPLE RESONANCESMULTIPLE RESONANCES(fixed driving frequency)(fixed driving frequency)
The analytic signal:• The Hilbert transform: 90o phaseshift•Mapping of a time varying signal onto a 2D phase plane•Allows for the definition of phase and amplitude variables
A(t) x(t)2 xH (t)2 (t) arctanxH (t)
x(t)
H[x](t)
A(t)
(t)
z(t) x(t) ixH (t)
xH (t) H[x](t) 1
P
x( )
t
d
- Ovoid Cells are high-pass
- Ovoid spike trains are coherent with narrowband signals (blue) and their envelopes (red)
- Subthreshold voltage shows no coherence with signal envelope
Courtesy R. Krahe and F. Gabbiani,
Nat. Neurosci. Rev. (2004)
Electric Fields
Courtesy G. Hupe and J. Lewis (2005)
Apteronotus Leptorhynchus