Extracting Time and Space Scales with Feedback and Nonlinearity

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Extracting Time and Space Scales with Feedback
and Nonlinearity
André Longtin Physics Cellular and Molecular
Medicine CENTER FOR NEURAL DYNAMICS UNIVERSITY
OF OTTAWA Funding by NSERC, CIHR, PREA
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Overview

• Processing of spatio-temporal signals
• Global Feedback common noise ?? oscillations
• Spatial scale for feedback and input
• Envelope processing for narrowband in time
• Information resonances
• Coincidence transforms for synchronous firing
• Short term Plasticity and information processing

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Research Program

• Stochastic neural network
• driven by
• Stochastic input in space and time
• Experimental lt-gt Theoretical

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Relevance to this group

• What nonlinearity (if any) supports patterns or
  computations ?

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HIGHER BRAIN AREA II
HIGHER BRAIN AREA I
THALAMUS
RECEPTORS
PHYSICAL STIMULI
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Brain Diagram by Arab philosopher Avicenna (circa
1300)Five ventricles common sense, imagination,
judging, second imagination (composing/combining
images), memory.(University Library, Cambridge)
From Da Vincis notes
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Electrosensory lateralline lobe (ELL)
Courtesy W. Ellis (1991)
Courtesy N. Berman and L. Maler, J. Exp. Biol.,
1999
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The electric sense
Electrosensory Input
Electrosensory Lateral Line Lobe (ELL)
Electric Organ Discharge (EOD)
Higher Brain
Amplitude Modulation (AM)
Electroreceptors
afferents
Krahe and Gabbiani (2004) Nat. Neurosci.Rev.
513-23
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Temporal Characteristics
Spatial Characteristics
global
Harmonic
local
Broadband (noise)
- Frequency tuning is highly correlated with
spatial frequency- Tuning for harmonics or
broadband signals are qualitatively the same
Chacron, et al., Nature, 2003
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Weakly Electric Fish main negative feedback
loop
ELL Pyramidal Cells the first stage of sensory
processing
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Prey Stimuli
Prey (bug) excites a fraction of the
electroreceptors Local stimulation
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Communication Stimuli
Communication calls between fish stimulate the
whole body Global Stimulation
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Oscillation Mechanism(Doiron, Chacron, Bastian,
Longtin, Maler, Nature 2003)
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Electrosensory Circuitry
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Network Model Global Stimuli
Autocorrelation
Histogram
To mimic communication stimuli we apply the
external stimulus to all neurons equally.
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Experimental VerificationDoiron, Chacron, Maler,
Longtin and Bastian, Nature 42, 539 (2003)
ISI Histogram
Autocorrelation
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Correlated Stimuli in Experiments
Each dipole emits an intrinsic noise xi(t), and
global source, xG(t). Their relative strengths
is c, i.e. the covariance between dipoles.
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Integrate-and-fire dynamics
y
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Linear Response
Consider the spike train from the ith neuron in
our network, .
Assuming weak inputs, the Fourier transform of
the spike train is
(1)
A(w) intrinsic frequency response of the noisy
neuron. Xi(w) Fourier transform of input
(external feedback) to neuron i.
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POWER SPECTRUM
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Single Neuron Power Spectrumvspercentage of
common noise (c)

• For an infinite network

(Input-output sync) (spike-spike
sync.)
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Fokker-Planck analysis on noisy Leaky
Integrate-and-fire Neurons Delays Spatial
InputDoiron, Lindner, Longtin, Bastian and
Maler, Phys. Rev. Lett. 93, 048101 (2004)Linear
Fluctuation Theory needs noise.
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Input-output coherence for delayed feedback
network(global feedback)
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Coherence function
Correlation coefficient (in the frequency domain)
between two signals, X and Y
Response spike train
Stimulus
- narrowband stimulus(linear)
- envelope of narrowbandstimulus (non-linear)
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Network of stochastic Perfect IFs with and -
global delayed feedback
S(t) is the stimulus
Chacron, Longtin, Maler, Phys.Rev.E (2005)
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Network of Perfect IFs with global feedback
Information theory
Coherence H(f)2 Pss/Pxx
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INFORMATION RESONANCE(Chacron, Longtin, Maler,
PRE 2005)
Experimental DATA !!
Glt0
G0
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Introducing

• Spatial scale for feedback
• Spatial scale for noise
• Two regimes with respect to
• gamma oscillations

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In linear response, only the ratio of length
scales matters (Hutt, Sutherland, Longtin,
submitted)
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GLOBAL IN SPACE

• NARROWBAND IN TIME
• 2 TIME SCALES

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EOD amplitude
EOD
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EOD amplitude
EOD
Hey guys
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EODamplitude
EOD
Average Df in black (white) waters
Day 35.3 (54.1) HzNight 54.6 (65.8) Hz
Most probable populationsize 3-5 fish
From E. W. Tan et al, Behav.Brain Res.,
16483-92 (2005)
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P-units (primary receptors)
Feed forward
- P-units respond as linear encoders
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Pyramidal Cells

• global stimulation linear
• response to narrowband signal and its low
  frequency envelope- Envelope response is absent
  under local stimulation

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Middleton, Longtin, Benda, Maler, PNAS (2006)
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MECHANISM
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)
input
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transferfunction
output signal
input signal
(rectification)
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signals
Spectral composition
frequency
time
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Network instead of single cell
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Stochastic Envelope Gating(and not SR! See
Middleton et al., PRE 2006)
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Leaky Integrate-and-Fire (LIF) neuron
Mean firing rate
where
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GLOBAL SPATIAL SIGNALS

• EXTRACTING
• HIGH FREQUENCY CHIRPS
• FROM
• LOWER FREQUENCY BEATS
• SYNC-DESYNC CODE

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Context electrocommunication

• Male-male or female-female call causes
  synchronization of receptors
• Male-female or female-male call causes
  desynchronization of receptors
• (Benda, Longtin, Maler, Neuron 2006)

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Encoding a modulatory signal
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Coincidence transforms
Middleton, Longtin, Benda, Maler (submitted)
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Short-term Plasticity
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Broadband Coding
Depression dominates
Facilitation dominates
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• 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

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• Intrinsic noise can gate a signal competing with
  envelope
• Plasticity paradoxical effects on coding
• Importance of spatiotemporal statistics of input

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Brent Doiron
Jan Benda
Len Maler André Longtin
Joe Bastian Connie Sutherland
Maurice Chacron
Benjamin Lindner
Jason Middleton
Carlo Laing
Eric Harvey-Girard
John Lewis
Axel Hutt
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COHERENCE AND STOCHASTIC RESONANCE WITH DELAYED
FEEDBACKMorse and Longtin, Phys. Lett. A (2006)
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MULTIPLE RESONANCES(fixed driving frequency)
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• 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

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• 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

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Apteronotus Leptorhynchus
Electric Fields
Courtesy G. Hupe and J. Lewis (2005)
Courtesy R. Krahe and F. Gabbiani, Nat. Neurosci.
Rev. (2004)
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