Non-Poisson Fluctuation Statistics In Neuronal Inter-Spike Intervals (ISI): Hurst parameter Estimates of Mouse Retinal Ganglion Signals

There is considerable recent interest in both (i) modelling the retinal ganglion cells, so that the models can generate output that approximates the actual response of the retina (such models will help design retinal prosthetics); and (ii) understanding how relevant information is encoded in the spike patterns generated by the ganglion cells (these neuronal codes will help understand how the brain analyzes visual scenes). Since the signals (as captured by ISI) are fundamentally stochastic, any modelling or analysis tool will have to track, and make assumptions about, the fluctuations or noise inherently present in these signals. Even though there have been recent work claiming that the fluctuations are fractal in nature, showing long-range dependencies, almost all modelling and analysis work continue to assume Poisson fluctuations. The widespread use of the Poisson model is partly for the sake of convenience, and partly due to the fact that those claiming on fractal nature of ISI are contradictory: In a paper by Lowen et al. (2001), a long-range dependency (i.e., Hurst parameter as determined by Hurst et al. (1951), H > 0.5) is claimed in cat´s retina, and in a paper by Bahar et al. (2001), an H < 0.5 and a long-range anti-correlation are claimed for paddlefish electroreceptors. We resolve this issue by studying the ISI of more than 50 ganglion cells recorded from two different mouse retinas, and (i) Conclusively show that the Hurst parameter is less than 0.5; we also show why the results presented in a paper by Lowen et al. (2001) are erroneous: methods that do not detrend the data were used, (ii) Even though the fluctuation function is scale free, the auto-correlation function of ISI does not show a long-range anti-correlation behavior as claimed in a paper by Bahar et al. (2001). In fact, the auto-correlation function shows a sharp negative region around the origin, followed by an exponentially decaying tail. Our results generate questions about how the - - non-Poisson and scale-free nature of ISI fluctuations emerges during retinal processing, and how it might affect the accuracy of models based on Poisson assumptions