{"title": "Temporal coding in the sub-millisecond range: Model of barn owl auditory pathway", "book": "Advances in Neural Information Processing Systems", "page_first": 124, "page_last": 130, "abstract": null, "full_text": "Temporal coding \n\nin the sub-millisecond range: \n\nModel of barn owl auditory pathway \n\nRichard Kempter* \n\nWulfram Gerstner \n\nInstitut fur Theoretische Physik \n\nPhysik-Department der TU Munchen \n\nD-85748 Garching bei Munchen \n\nInstitut fur Theoretische Physik \n\nPhysik-Department der TU Munchen \n\nD-85748 Garching bei Munchen \n\nGermany \n\nGermany \n\nJ. Leo van Hemmen \n\nInstitut fur Theoretische Physik \n\nPhysik-Department der TU Munchen \n\n0-85748 Garching bei Munchen \n\nGermany \n\nHermann Wagner \nInstitut fur Zoologie \n\nFakultiit fur Chemie und Biologie \nD-85748 Garching bei Munchen \n\nGermany \n\nAbstract \n\nBinaural coincidence detection is essential for the localization of \nexternal sounds and requires auditory signal processing with high \ntemporal precision. We present an integrate-and-fire model of spike \nprocessing in the auditory pathway of the barn owl. It is shown that \na temporal precision in the microsecond range can be achieved with \nneuronal time constants which are at least one magnitude longer. \nAn important feature of our model is an unsupervised Hebbian \nlearning rule which leads to a temporal fine tuning of the neuronal \nconnections. \n\n\u00b7email: kempter.wgerst.lvh@physik.tu-muenchen.de \n\n\fTemporal Coding in the Submillisecond Range: Model of Bam Owl Auditory Pathway \n\n125 \n\n1 \n\nIntroduction \n\nOwls are able to locate acoustic signals based on extraction of interaural time dif(cid:173)\nference by coincidence detection [1, 2]. The spatial resolution of sound localization \nfound in experiments corresponds to a temporal resolution of auditory signal pro(cid:173)\ncessing well below one millisecond. It follows that both the firing of spikes and their \ntransmission along the so-called time pathway of the auditory system must occur \nwith high temporal precision. \n\nEach neuron in the nucleus magnocellularis, the second processing stage in the \nascending auditory pathway, responds to signals in a narrow frequency range. Its \nspikes are phase locked to the external signal (Fig. 1a) for frequencies up to 8 \nkHz [3]. Axons from the nucleus magnocellularis project to the nucleus laminaris \nwhere signals from the right and left ear converge. Owls use the interaural phase \ndifference for azimuthal sound localization. Since barn owls can locate signals with a \nprecision of one degree of azimuthal angle, the temporal precision of spike encoding \nand transmission must be at least in the range of some 10 J.lS. \n\nThis poses at least two severe problems. First, the neural architecture has to be \nadapted to operating with high temporal precision. Considering the fact that the \ntotal delay from the ear to the nucleus magnocellularis is approximately 2-3 ms [4], \na temporal precision of some 10 J.lS requires some fine tuning, possibly based on \nlearning. Here we suggest that Hebbian learning is an appropriate mechanism. Sec(cid:173)\nond, neurons must operate with the necessary temporal precision. A firing precision \nof some 10 J.ls seems truly remarkable considering the fact that the membrane time \nconstant is probably in the millisecond range. Nevertheless, it is shown below that \nneuronal spikes can be transmitted with the required temporal precision. \n\n2 Neuron model \n\nWe concentrate on a single frequency channel of the auditory pathway and model \na neuron of the nucleus magnocellularis. Since synapses are directly located on the \nsoma, the spatial structure of the neuron can be reduced to a single compartment. \nIn order to simplify the dynamics, we take an integrate-and-fire unit. Its membrane \npotential changes according to \n\nu \n\nd \n-u = -- + 1(t) \ndt \n\nTO \n\n(1) \n\nwhere 1(t) is some input and TO is the membrane time constant. The neuron fires, \nif u(t) crosses a threshold {) = 1. This defines a firing time to. After firing u is reset \nto an initial value uo = O. Since auditory neurons are known to be fast, we assume \na membrane time constant of 2 ms. Note that this is shorter than in other areas of \nthe brain, but still a factor of 4 longer than the period of a 2 kHz sound signal. \n\nThe magnocellular neuron receives input from several presynaptic neurons 1 ~ k ~ \nJ{. Each input spike at time t{ generates a current pulse which decays exponentially \nwith a fast time constant Tr = 0.02 ms. The magnitude of the current pulse depends \non the coupling strength h. The total input is \n\n1(t) = L h: exp( --=-.!. ) O(t - t{) \n\ntf \n\nt \n\nk,f \n\nTr \n\n(2) \n\nwhere O(x) is the unit step function and the sum runs over all input spikes. \n\n\fR. KEMPTER, W. GERSTNER, J. L. VAN HEMMEN, H. WAGNER \n\n/ \\ h \n\nfoE- T~ \nb \n\n-\nI \nI \nI \n