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

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

Research Program: Stochastic neural network driven by Stochastic input in space and time Experimental Theoretical

Relevance to this group: What nonlinearity (if any) supports patterns or computations ?

HIGHER BRAIN AREA I HIGHER BRAIN AREA II THALAMUS RECEPTORS PHYSICAL STIMULI

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 Vinci’s notes

Courtesy W. Ellis (1991) Electrosensory lateral line 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, Frequency tuning is highly correlated with spatial frequency - Tuning for harmonics or broadband signals are qualitatively the same

Weakly Electric Fish: main negative feedback loop Weakly Electric Fish: main negative feedback loop ELL Pyramidal Cells: the first stage of sensory processing

Prey Stimuli Prey (bug) excites a fraction of the electroreceptors: Local stimulation

Communication Stimuli Communication calls between fish stimulate the whole body: Global Stimulation

Oscillation Mechanism (Doiron, Chacron, Bastian, Longtin, Maler, Nature 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 Circuitry Sodium channel blocker can open the feedback loop.

Network Model – Global Stimuli To mimic communication stimuli we apply the external stimulus to all neurons equally. Autocorrelation Histogram

Experimental Verification Doiron, Chacron, Maler, Longtin and Bastian, Nature 42, 539 (2003) ISI HistogramAutocorrelation controlblockrecover

Correlated Stimuli in Experiments Dipole 1 Dipole 2 Dipole 3 Dipole 4 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 y

Linear Response Consider the spike train from the i th neuron in our network,. Assuming weak inputs, the Fourier transform of the spike train is A(  intrinsic frequency response of the noisy neuron. X i (w): Fourier transform of input (external + feedback) to neuron i. (1)

POWER SPECTRUM

Single Neuron Power Spectrum vs percentage of common noise (c) For an infinite network: (Input-output sync) (spike-spike sync.)

Fokker-Planck analysis on noisy Leaky Integrate-and-fire Neurons + Delays+ Spatial Input Doiron, Lindner, Longtin, Bastian and Maler, Phys. Rev. Lett. 93, (2004) Linear Fluctuation Theory: needs noise.

Input-output coherence for delayed feedback network (global feedback)

Coherence function: Correlation coefficient (in the frequency domain) between two signals, X and Y Response: spike trainStimulus: - narrowband stimulus (linear) - envelope of narrowband stimulus (non-linear)

Network of stochastic Perfect IF’s with + and - global delayed feedback S(t) is the stimulus Chacron, Longtin, Maler, Phys.Rev.E (2005)

Network of Perfect IF’s with global feedback: Information theory Coherence = | H(f)| 2 P ss /P xx

INFORMATION RESONANCE (Chacron, Longtin, Maler, PRE 2005) G<0 G=0 Experimental DATA !!

Introducing… Spatial scale for feedback Spatial scale for feedback Spatial scale for noise Spatial scale for noise  Two regimes with respect to gamma oscillations gamma oscillations

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

GLOBAL IN SPACE NARROWBAND IN TIME: NARROWBAND IN TIME: 2 TIME SCALES 2 TIME SCALES

EOD amplitude EOD

Hey guys EOD amplitude EOD

EOD amplitude EOD From: E. W. Tan et al, Behav. Brain Res., 164:83-92 (2005) Most probable population size 3-5 fish Average  f in black (white) waters: Day: 35.3 (54.1) Hz Night: 54.6 (65.8) Hz

P-units (primary receptors) Feed forward: - P-units respond as linear encoders

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

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

transfer function input signal output signal (rectification)

signalsSpectral composition time frequency

Network instead of single cell

Stochastic Envelope Gating (and not SR! See Middleton et al., PRE 2006)

Leaky Integrate-and-Fire (LIF) neuron: Mean firing rate: where

GLOBAL SPATIAL SIGNALS EXTRACTING EXTRACTING HIGH FREQUENCY CHIRPS FROM LOWER FREQUENCY BEATS “SYNC-DESYNC CODE”

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

Encoding a modulatory signal

Coincidence transforms… Middleton, Longtin, Benda, Maler (submitted)

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 MiddletonCarlo LaingEric Harvey-GirardJohn Lewis Jan Benda Benjamin Lindner Len Maler & André Longtin Joe Bastian Connie Sutherland Axel Hutt

COHERENCE AND STOCHASTIC RESONANCE WITH DELAYED FEEDBACK Morse and Longtin, Phys. Lett. A (2006)

MULTIPLE RESONANCES (fixed driving frequency)

The analytic signal: The Hilbert transform: 90 o phaseshift Mapping of a time varying signal onto a 2D phase plane Allows for the definition of phase and amplitude variables

- 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