BioSystems 48 (1998) 105 – 112 How the threshold of a neuron determines its capacity for coincidence detection Richard Kempter a, *, Wulfram Gerstner b , J. Leo van Hemmen a a Physik Department der TU Mu ¨nchen, D-85747 Garching bei Mu  nchen, Germany b Swiss Federal Institute of Technology, Center of Neuromimetic Systems,EPFL-DI, CH-1015 Lausanne, Switzerland Abstract Coherent oscillatory activity of a population of neurons is thought to be a vital feature of temporal coding in the brain. We focus on the question of whether a single neuron can transform a spike code into a rate code. More precisely, how does a neuron vary its mean output firing rate, if its input changes from random to coherent? We investigate the coincidence detection properties of an integrate-and-fire neuron in dependence upon internal parameters and input statistics. In particular, we show how coincidence detection depends on the membrane time constant and the threshold. Furthermore, we demonstrate that there is an optimal threshold for coincidence detection and that there is a broad range of near-optimal threshold values. Fine-tuning is not necessary. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Coincidence detection; Voltage threshold; Coherent activity; Temporal coding; Rate coding; Integrate-and- fire neuron 1. Introduction The issue of how neurons read out the temporal structure of the input and how they transform this structure into a firing rate pattern has been ad- dressed by several authors and is attracting an increasing amount of interest. Ko ¨nig et al. (1996) have argued that the main prerequisite for coinci- dence detectors is that the mean interspike inter- val is long as compared to the integration time which neurons need to effectively sum synaptic potentials. The importance of the effective (mem- brane) time constant of neurons has also been emphasized by Softky (1994). In addition, Abeles (1982) has shown that the value of the spike threshold and the number of synapses are relevant parameters as well. In summary, some general principles have al- ready been outlined, but not verified, and a de- tailed investigation of conditions under which neurons can act as coincidence detectors is not available yet. In the following we will substantiate some of the above statements and show explicitly * Corresponding author. E-mail: kempter@physik.tu-muenchen.de 0303-2647/98/$ - see front matter © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0303-2647(98)00055-0