Analysis of synchronization in the response of neurons to noisy periodic synaptic input
Introduction
The temporal information contained in the responses of neurons plays an important role in neuronal information processing in a number of different parts of the central nervous system (CNS). In auditory processing the degree of phase locking in the neural response to noisy periodic input plays an important role, where studies indicate that spikes in the auditory pathway are phase locked up to frequencies around 3–5 kHz in mammals [19], [12] and up to frequencies of 8 kHz in the Barn Owl [15]. Likewise, a similar phase-locked response is observed in electrosensory systems of a number of fish [1]. This phase-locked response has also been postulated to play a central role in temporal coding in the brain, where it may be used in feature linking and pattern segmentation [24], [8], [11]. For reviews of these and other instances of temporal information processing within the CNS see [22], [6].
In this study we investigate the relationship between the timing of noisy periodic synaptic inputs and the output spikes that are generated in leaky integrate and fire neurons. A recent investigation of this problem [14] examined the input and output rates over the range of input vector strengths [10] (also called the synchronization index) as well as identifying the conditions under which a neuron can act as a coincidence detector and thus convert a temporal code into a rate code. Their results show how the output rate depends upon the neural parameters, such as the number of synapses and the time course of the postsynaptic response to the inputs, as well as upon the input statistics [14]. However, since their analysis concerns only the output rate, they are not able to predict quantities that depend upon the details of the timing of individual output spikes.
Our study provides a significant extension of these results, in which we relate the time-distribution of the output spikes to the phase of the synaptic input, and thus calculate the synchronization index of the output spikes and their phase histogram as a function of the frequency and synchronization of the input. In order to carry out the analysis we make the approximation that the amplitude of the postsynaptic response to an individual input spike is small, which is equivalent to the diffusion approximation [23]. For neurons with large numbers of small amplitude inputs this approximation proves to be very accurate.
Section snippets
Methods
The relationship between the timing of the synaptic inputs and the output spikes requires an analysis of the interspike interval (ISI) distribution of the output spikes, which is obtained using our recently developed integrated-input technique [2], [3], [4]. The membrane potential, V(t), is assumed to be reset to its initial value at time after a spike (action potential, AP) has been generated. The membrane potential is the sum of the excitatory and inhibitory postsynaptic
Results
The typical ISI distribution we obtain is plotted in Fig. 1 and shows the characteristic multimodal response observed in recording from auditory neurons [9].
The dependence of the synchronization index upon the frequency is illustrated in Fig. 2, which shows that the synchronization index decreases for increasing frequencies. The average rate of the inputs, , is the same as the frequency in all cases, i.e., there is on average one incoming spike per fiber per cycle of the stimulus. The
Discussion and conclusions
This study extends that of earlier studies of coincidence detection and the neural response to noisy periodic synaptic input in a number of important ways. Many of the earlier examinations of the question of coincidence detection were numerical, in which the response to a train of spike inputs was simulated, either using a threshold model with a shot-noise response [7], [5], [13], or a membrane-conductance model [21], [20]. The results of such simulations are, of course, subject to statistical
Acknowledgements
This work was funded by The Bionic Ear Institute and the Cooperative Research Center for Cochlear Implant, Speech & Hearing Research.
Graeme M. Clark graduated M.B.B.S. from the University of Sydney in 1957 and is foundation Professor of the Department of Otolaryngology, The University of Melbourne and foundation Director of The Bionic Ear Institute, Melbourne, Australia. He was awarded the Order of Australia in 1983 for his contribution to Medicine and is a Fellow of the Australian Academy of Science. In 1967 Graeme Clark commended basic research to investigate whether a single or multiple-channel (electrode) cochlear
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Graeme M. Clark graduated M.B.B.S. from the University of Sydney in 1957 and is foundation Professor of the Department of Otolaryngology, The University of Melbourne and foundation Director of The Bionic Ear Institute, Melbourne, Australia. He was awarded the Order of Australia in 1983 for his contribution to Medicine and is a Fellow of the Australian Academy of Science. In 1967 Graeme Clark commended basic research to investigate whether a single or multiple-channel (electrode) cochlear implant would be possible for the management of a profound hearing loss. Since 1970 he has led the research team that developed the Australian Bionic Ear (Cochlear Implant) manufactured by Cochlear Limited that now provides hearing to over 20,000 profoundly or totally deaf children and adults.
Anthony N. Burkitt received a B.Sc. degree in theoretical physics and a B.Sc. in psychology from the Australian National University, and Ph.D. degree in theoretical physics from Edinburgh University, UK.
Dr. Burkitt has held research positions at the Universities of Liverpool (UK), Wuppertal (Germany) and the Australian National University. He is currently a research fellow in the Bionic Ear Institute and the Cooperative Research Centre for Cochlear Implant and Hearing Aid Innovation.
Dr. Burkitt's current research interests are in the mathematical and computer modeling of neural systems, especially in relation to the auditory pathway. He is particularly concerned with investigating temporal information processing and the information carried by the timing of individual action potentials (spikes) in biological neural systems.