How Precise is the Timing of Action Potentials?

Distributed spiking activity underlies the dynamics and function of neuronal circuits and thus their computational capabilities. Beyond a simple rate, often the timing of spikes also essentially contributes to information processing in these systems A thorough understanding and analysis of the very notion of spike timing is therefore pivotal for understanding brain function. For instance, it is widely accepted that abstract discrete time models of interacting neurons, with spike times fixed to a temporal grid, may well describe the spike rates of neurons, e.g., for balanced cortical activity (van Vreeswijk and Sompolinsky, 1996), but the timing of spikes is not modeled exactly. In this respect, even simple integrate-and-fire type models are more accurate because they describe neural dynamics in continuous time and thus may exhibit spikes at any chosen time (Brette et al., 2007). One may argue that the manually implemented reset in integrate-and-fire models, leading to exact spike times, merely serves as a low-level compromise between detailed biological modeling and mathematical trac-tability. Generating an action potential takes a time of the order of 1 ms, but one may easily introduce a defined time of a spike by interpreting it, e.g., as the time of peak voltage during a biophysical action potential (cf. Figure 1). Nevertheless, continuous time models, in general, face the conceptual problem that information contained in the timing of only a single spike is infinite. In contrast , discrete time models exhibit bounds on the information carried by a spike but it may seem questionable how real biological systems would conform to time discretization. Moreover, in raster plots displaying experimentally recorded spike trains of neurons there is actually a raster, a non-zero time resolution discretizing time into small but positive intervals. However, the current high temporal resolution, often 10 kHz or more, may make us forget such discretization issues. In their recent contribution to Frontiers in Neuroscience, Cessac and Viéville (2008) emphasize that the main issue is not about how fine the resolution actually is, in models or data, but whether or not there is a discretization at all. So not even the most subtle description, neither experimentally nor in modeling, can characterize the timing of spikes with arbitrarily high precision. The authors now show an alternative way of modeling spiking neural circuits by lifting a recent mathematical work (Cessac, 2008) to the level of networks with conductance-based synapses and by pointing out (and explicitly highlighting for …