Correlation-Induced Oscillations in Spatio-Temporal Excitable Systems Andre Longtin Physics Department, University of Ottawa Ottawa, Canada

Co-Workers Brent Doiron Benjamin Lindner Maurice Chacron Physics Department, University of Ottawa Leonard Maler Department of Cellular and Molecular Medicine, University of Ottawa Joseph Bastian Deparment of Zoology, University of Oklahoma

Synopsis Introduction to weakly electric fish Oscillatory activity for communication but not Prey Stimuli Modeling I: Feedback is required Experimental verification Modeling II: stochastic oscillatory dynamics in a spatially extended neural system Doiron, Chacron, Maler, Longtin and Bastian, Nature 421 (Jan 30, 2003)

Weakly Electric Fish

Why study weakly electric fish? (Biology) from molecular to behavioral studies of neural coding peripheral ↔ central feedforward ↔ feedback in vivo ↔ in vitro Stimuli: simple (sines etc…) ↔ natural behaviors: simple ↔ evolved (electrolocation) (electrocommunication)

Why study weakly electric fish? (Mathematical Biology/Biophysics) Single cell dynamics: simple ↔ complex Linear, nonlinear, stochastic (get ready for noise!) Information processing: black box ↔ detailed biophysics  Math, Physics, Neuroscience, Computation Applications: signal detection, novel circuitry, prosthetic design (e.g. with feedback)

Sensory Neurons ELL Pyramidal Cell Sensory Input Higher Brain

Electroreceptor Neurons: Anatomy Pore Sensory Epithelium Axon (To Higher Brain)

Biology: Weakly electric fish

CIRCUITRY Afferent Input Higher Brain Areas The ELL; first stage of sensory processing

Prey Stimuli Electric fish prey on small insects (water fleas). These prey excite only a fraction of the electroreceptors that line the fish’s skin. We label this stimulation geometry local

Communication Stimuli Electric fish communicate by modulating their own electric field, giving a specific input to other fish. These communication calls stimulate the entire surface of the receiving fish’s skin. We label this stimulation geometry global

Pyramidal Cell Response to Prey-like Stimuli AutocorrelationISI Histogram Local Stimuli (Dipole) Fish Random Amplitude Modulations (RAMs) were applied locally to the skin via a small dipole, mimicking prey stimuli. The RAMs were a Gaussian noise process (0-40Hz).

Pyramidal Cell Response to Communication-like Stimuli Global Stimuli AutocorrelationISI HistogramFish RAMs were applied globally to the skin via a large dipole, mimicking communication stimuli. The RAMs were generated by a Gaussian noise process (0-40Hz).

Model Pyramidal Cell We model the ELL pyramidal cell network as an network of Leaky Integrate and Fire (LIF) neurons. The membrane potential of the i th neuron obeys the following dynamics I i (t) – input G(V,t-  d ) – interactions

Pyramidal Cell Interactions – G(t-  d ) The network is coupled through global delayed inhibitory feedback. The inhibitory response is modeled as a fast activating alpha function. dd

Pyramidal Cell Input - I(t) Intrinsic Noise (biased Ornstein-Uhlenbeck process;  =15 ms). Uncorrelated between neurons. External Stimuli (Zero mean band passed Gaussian noise, 0-40Hz). Identical to experiments. Pyramidal Cell I i (t) is composed of two types of “stimuli”

Network Model – Local Input Autocorrelation Histogram To mimic prey stimuli we apply the external stimulus to only one neuron

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

Oscillation Mechanism Local Stimuli External Stimulus is applied heterogeneously across the network. No stimulus induced correlations. Global Stimuli External Stimulus is applied homogenously across the network. Significant stimulus induced correlations. Correlated activity cause a “wave” of inhibition after a delay. This wave carves out the oscillation.

Electrosensory Circuitry The neural sensory system of weakly electric fish has a well characterized feedback pathway. We applied a sodium channel blocker in order to open the feedback loop.

Experimental Verification ISI HistogramAutocorrelation control block recover

Feedback: Open vs Closed Loop Architecture Higher Brain Higher Brain Loop time  d

Correlated Stimuli in Experiments Dipole 1 Dipole 2 Dipole 3 Dipole 4 The random signal emitted from each dipole was composed of an intrinsic,  i (t), and global source,  G (t). The relative strength of these two sources was parameterized by c, representing the covariance between dipoles.

Correlation Induced Oscillation c=1 c=0.5 c=0 Frequency (Hz) Power

Linear Response Consider the spike train from the i th neuron in our network,. Assuming weak inputs we have that the Fourier transform of the spike train is where A(  is the susceptibility of the neuron determined by the intrinsic properties of the cell. The Fourier transform of the input (external + feedback) is given by X i (  ). (1)

Feedback Input Now consider the globally delay coupled LIF network used earlier. Let the “input” into neuron i be Then it can be shown that for an infinite network we have

Fokker-Planck analysis on noisy Leaky Integrate-and-fire neurons

Shift in Coding Strategies The spike train/stimulus coherence shifts from lowpass to highpass as we transition from local to global stimuli Chacron, Doiron, Maler, Longtin, and Bastian, Nature 423, (May 1 st 2003).

Spike Time Reliability When high-frequency stimuli (40-60 Hz) are given, spike time reliability is increased dramatically when the stimulus is applied globally.

Conclusion  Electric fish use delayed inhibitory feedback to differentially respond to communication vs. prey stimuli.  Our work shows how a sensory system adapts its processing to its environment (local vs. global).