Noise and the Neural Response to Current Transients

Thèse No. 2331 (2001) Presentée au Départment d'Informatique, École Polytechnique Fédérale de Lausanne
Alix A. Kamakaokalani Herrmann

Summary

Understanding how neural spike trains encode information is one of the fundamental challenges of neuroscience. Central to this understanding is the 'neural input-output transform', which relates the probability of an action potential to the input. Long-standing neurophysiological evidence shows that the input-output relation, measured using the peristimulus time histogram (PSTH) in response to a transient pulse superimposed on a constant baseline level, is determined not only by a neuron's dynamics and by the input, but also by the level of unsynchronized background input (synaptic noise). However, no theory to date has been able to comprehensively describe the input-output relation across the full range of levels of noise and baseline input.

Using a dynamical mean-field approach, we show how the level of background noise can be taken into account in predicting the PSTH response to a transient pulse. First, we present our method and apply it to the standard leaky integrate-and-fire neuron. Our results show that the effect of background noise can be understood in terms of a linear filter applied to the input. In the low-noise limit, the PSTH response is related to the time derivative if the PSP resulting from the input pulse. In high noise, the response resembles the PSP itself. This is generally consistent with experimental observations.

However, the integrate-and-fire model is too simple and a more quantitative comparison is not possible. After a brief examination we find that the Hodgkin-Huxley model is also unsuitable. Finally, we investigate a varient of the integrate-and-fire model that is biologically realistic, but does not incorporate specifics such as adaptation or ion channel dynamics. We compare our analytical results with simulations and find that this model approximately reproduces the main features of the motoneuron experiments of Poliakov, Powers, Sawczuk, and Binder (1996), using the same inputs and noise levels.

To our knowledge, the effects of uncorrelated background input (synaptic noise) on the PSTH response to a transient pulse have only been experimentally observed in motoneurons firing tonically. Our model predicts that the effects should also be observable below threshold. Furthermore, because the effect does not depend on specific biological details, we predict that the noise has the same effect on the responses of almost any neuron, not just motoneurons. Our model may help in understanding how rate coding and temporal coding can coexist.