J Comput Neurosci (2009) 26:149–155 DOI 10.1007/s10827-008-0106-6 Studying spike trains using a van Rossum metric with a synapse-like filter Conor Houghton Received: 7 December 2007 / Revised: 5 June 2008 / Accepted: 9 June 2008 / Published online: 8 July 2008 © Springer Science + Business Media, LLC 2008 Abstract Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory in- puts is communicated in the form of spike trains. A challenge in understanding spike trains is to assess the significance of individual spikes in encoding in- formation. One approach is to define a spike train metric, allowing a distance to be calculated between pairs of spike trains. In a good metric, this distance will depend on the information the spike trains encode. This method has been used previously to calculate the timescale over which the precision of spike times is significant. Here, a new metric is constructed based on a simple model of synaptic conductances which includes binding site depletion. Including binding site depletion in the metric means that a given individual spike has a smaller effect on the distance if it occurs soon after other spikes. The metric proves effective at classifying neuronal responses by stimuli in the sample data set of electro-physiological recordings from the primary auditory area of the zebra finch fore-brain. This shows that this is an effective metric for these spike trains suggesting that in these spike trains the significance of a spike is modulated by its proximity to previous spikes. This modulation is a putative information-coding prop- erty of spike trains. Action Editor: Jonathan D. Victor C. Houghton (B ) School of Mathematics, Trinity College Dublin, Dublin, Ireland e-mail: houghton@maths.tcd.ie Keywords Spike trains · Information · Metric · Song birds · Auditory pathway 1 Introduction It is not known how the information that is propagating in the sensory pathways is encoded in spike trains. One approach to this question is to use a spike train metric (Victor and Purpura 1996) to cluster responses to repeated presentations of a set of stimuli. If a metric measures a short distance between responses to the same stimulus and a longer distance between responses to different stimuli then the distance measured between two spike trains must be related to the information they encode. A metric can be evaluated by performing distance-based clustering and then calculating how ac- curately the metric clusters together responses to the same stimulus. Using this comparison to optimize a pa- rameter in a family of metrics then gives a measurement of how information is coded in the spike trains. This approach was used by Victor and Purpura (1996). This paper reports the analysis of spike trains collected from areas V1, V2 and V3 of awake monkeys during the transient, 256 ms long, presentation of visual stimuli which differ in texture and contrast level. The spiking responses were clustered using, what is now called, the Victor-Purpura metric: an edit-distance met- ric which has a free parameter q. An indicative time scale for the metric is given by 2/q; roughly speaking, spikes from two different spike trains can be thought of as being related by jitter if their timing difference is less than 2/q. It is a measure of the timescale for which spike timing is significant. In fact, the spike trains are clustered most accurately for 2/q in the range c.