Effects of Non-Renewal Firing on Information Transfer in Neurons

1. Effects of Non-Renewal Firing on Information Transfer in Neurons Andre Longtin Physics Department University of Ottawa Ottawa, Canada

2. Overview • Weakly Electric Fish • Electroreceptor data • Modeling • Effects of ISI correlations • Linear response models Biology Computation Theory

3. Collaborators Benjamin Lindner, postdoc, Physics, U. Ottawa Maurice Chacron, postdoc, Physics, U. Ottawa Leonard Maler, Cell. Molec. Med, U. Ottawa Khashayar Pakdaman, INSERM, Paris Martin St-Hilaire, M.Sc. Student, U. Ottawa

4. Weakly Electric Fish: Electrolocation

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

6. Electroreceptor Neurons: Electrophysiology data courtesy of Mark Nelson, U. Illinois

7. Modeling Electroreceptors: The Nelson Model (1996) High-Pass Filter Stochastic Spike Generator Input

8. Fit of Nelson Model to Data: Renewal Process (No ISI correlations)

9. Leaky Integrate-and-fire Model with Dynamic Threshold Chacron, Longtin, St-Hilaire, Maler, Phys.Rev.Lett. 85, 1576 (2000) w Ii Ii+1

10. Modeling Electroreceptors: The Extended LIFDT Model High-Pass Filter Input LIFDT Spike Train

11. Fitting the Experimental Data (Part 2): Non-renewal Process

12. Summary of Fitting: Experimental Data: LIFDT Model: Nelson Model:

13. What Else We Know about LIFDT • 1D map for consecutive threshold values • Negative correlation appear when fixed point of map is perturbed by noise: it is a deterministic property. • Strength of correlation depends on system parameters • With sinusoidal forcing, 2D annulus map: simple and complex phase locking, chaos See: Chacron, Pakdaman, Longtin, Neural Comput. (2003). Chacron, Longtin, Pakdaman, Physica D (2004).

14. Comparison Approach to Assess Effects of ISI Correlations: LIFDT Model (non-renewal process) Nelson Model (renewal process) vs.

15. Weak Signal Detection: T=255 msec

16. Regularisation: Fano Factor: Asymptotic Limit (Cox and Lewis, 1966)

17. Stimulation Protocol: Gaussian white noise Low-pass filter Stimulus Stimuli are Gaussian with standard deviation  and cutoff frequency fc

18. Information Theoretic Calculations: ??? Gaussian Noise Stimulus S Neuron Spike Train X Coherence Function: Mutual Information Rate:

19. Comparison using Info Theory

20. An Important Clue: Reduction of Power at Low Frequencies:

21. Theory for why certain correlations are useful: Need simpler models !! • Simple Intrinsic Dynamics only, no extra filtering  perfect integrator neuron instead of leaky: dv/dt = μ + signal(t) • Noise on threshold and reset only • Assume simple noise distribution and action (uniform distribution, piecewise constant in time)

22. Two identical models, except for correlationsChacron, Lindner, Longtin, Phys.Rev.Lett. (in press 2004) Model A: Model B: Successive intervals are not correlated Successive intervals are thus correlated

23. Statistics and Spectra Noise Shaping ISI Statistics: Power Spectra: where β=2πD/µ

24. Linear Response Calculation for Fourier transform of spike train: unperturbed spike train susceptibility It turns out: Spike Train Spectrum= Background Spectrum + Signal Spectrum

25. Linear Response Calculation (Part 2): Coherence Function

26. Linear Response Calculation (Part 3): Mutual Information Rate

27. Conclusions • Weakly electric fish must detect prey (low freq. stimuli, less than 0.1 V) • Negative ISI Correlations Can Regularize a Spike Train through spike count variance reduction and noise reduction at low frequencies. • This is achieved through noise shaping in the power spectrum and this is greatest for weak low frequency stimuli. • Outlook: • Experimentally prove that the negative correlations are really being used for computations. • Deal with mixtures of positive and negative correlations at lags >= 1 • Extend to more realistic models of excitability with memory • Use the ideas presented here in devices to improve SNR and detectability

28. References: • Chacron, Longtin, St-Hilaire, Maler, PRL 85, 1576 (2000). • Chacron, Longtin, Maler, J. Neurosci. 21, 5328 (2001). • Chacron, Lindner, Longtin, (submitted). • Cover, Thomas, Elements of Information Theory (1991). • Cox, Lewis, The Statistical Analysis of Series of Events (1966). • Nelson, Xu, Payne, J. Comp. Physiol. A 181, 532 (1997). • Ratnam, Nelson, J. Neurosci. 20, 6672 (2000).

29. Food for Thought: “Why should we explore exotic sensory systems such as electrosensation in fish or echolocation in bats?... More highly evolved organisms derive their superior qualities not so much from novel mechanisms at the cellular level but rather from a richer complexity in the orchestration of basic designs that they share with simpler organisms. Fundamental mechanisms of perception and neuronal processing of sensory information are shared by animals as diverse as flies and primates, but a larger number of neuronal structures and interconnecting pathways bestow more powerful computational abilities and memory capacities upon the brains of primates.” --Walter Heiligenberg