Correlation-Induced Oscillations in Spatio-Temporal Excitable Systems

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

2. 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

3. 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)

4. Weakly Electric Fish

5. 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)

6. 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)

7. Higher Brain Sensory Input Sensory Neurons ELL Pyramidal Cell

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

9. Biology: Weakly electric fish

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

11. 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

12. 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

13. Autocorrelation ISI Histogram 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) . Local Stimuli (Dipole) Pyramidal CellResponse to Prey-like Stimuli Fish

14. Autocorrelation ISI Histogram 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) . Global Stimuli Pyramidal Cell Response to Communication-like Stimuli Fish

15. 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 ith neuron obeys the following dynamics Ii(t) – input G(V,t-td) – interactions

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

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

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

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

20. 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. Local Stimuli External Stimulus is applied heterogeneously across the network. No stimulus induced correlations. Oscillation Mechanism

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

22. control block recover Experimental Verification ISI Histogram Autocorrelation

23. Higher Brain Feedback: Open vs Closed Loop Architecture Higher Brain Loop time td

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

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

26. Linear Response Consider the spike train from the ith neuron in our network, . Assuming weak inputs we have that the Fourier transform of the spike train is (1) where A(w) 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 Xi(w).

27. 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

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

29. 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, 77-81 (May 1st 2003).

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

31. 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).