Journal of Computational Neuroscience 17, 149–164, 2004 c  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. A Biophysical Model of Synaptic Delay Learning and Temporal Pattern Recognition in a Cerebellar Purkinje Cell VOLKER STEUBER ∗ AND DAVID WILLSHAW Institute for Adaptive and Neural Computation, University of Edinburgh, 5 Forrest Hill, Edinburgh EH1 2QL, Scotland, UK v.steuber@ucl.ac.uk Received August 6, 2001; Revised March 24, 2004; Accepted April 14, 2004 Action Editor: Xiao-Jing Wang Abstract. It has been suggested that information in the brain is encoded in temporal spike patterns which are decoded by a combination of time delays and coincidence detection. Here, we show how a multi-compartmental model of a cerebellar Purkinje cell can learn to recognise temporal parallel fibre activity patterns by adapting latencies of calcium responses after activation of metabotropic glutamate receptors (mGluRs). In each com- partment of our model, the mGluR signalling cascade is represented by a set of differential equations that reflect the underlying biochemistry. Phosphorylation of the mGluRs changes the concentration of receptors which are available for activation by glutamate and thereby adjusts the time delay between mGluR stimula- tion and voltage response. The adaptation of a synaptic delay as opposed to a weight represents a novel non- Hebbian learning mechanism that can also implement the adaptive timing of the classically conditioned eye-blink response. Keywords: cerebellum, calcium, mGluR, temporal coding Introduction It is widely believed that the patterns of averaged neu- ronal firing rates and that of individual spike times are both important for the representation of information in the brain (e.g. Bialek et al., 1991; Gerstner et al., 1996; Thorpe et al., 1996; Laurent, 1996; Wehr and Laurent, 1996; Rieke et al., 1997). These require different de- coding mechanisms. A pattern of firing rates can be recognised by a system that provides an array of ap- propriately tuned synaptic weights, implemented for example by modifiable conductances of synaptic or in- trinsic ion channels (see e.g. Blackwell et al., 1998). As described by Hopfield (1995), a temporal spike pattern ∗ Present address: Department of Physiology, University College London, Gower Street, London WC1E 6BT, UK. can be decoded by a neuron that uses a combination of time delays and coincidence detection. The response of a temporal decoding neuron is max- imal when the time differences between the spikes in the temporal input pattern are cancelled out by the de- lays between the input spikes and the individual postsy- naptic responses. Thus, a particular temporal decoding neuron specialises onto a temporal template input pat- tern that is encoded in its set of delays. The specific recognition of a template pattern is a property that is shared with radial basis function (RBF) units in artifi- cial neural networks, and Hopfield’s temporal decod- ing neurons are often referred to as RBF neurons (see for example Sejnowski, 1995; Natschl¨ ager and Ruf, 1998). If this form of temporal coding is used in the brain, the decoding RBF neurons must have a mechanism to