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.