Abstract
In a growing class of neurophysiological experiments, the train of impulses (“spikes”) produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- BURNS B. D., SMITH G. K. Transmission of information in the unanaesthetized cat's isolated forebrain. J Physiol. 1962 Nov;164:238–251. doi: 10.1113/jphysiol.1962.sp007017. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Firth D. R. Interspike interval fluctuations in the crayfish stretch receptor. Biophys J. 1966 Mar;6(2):201–215. doi: 10.1016/S0006-3495(66)86651-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- GERSTEIN G. L., MANDELBROT B. RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. Biophys J. 1964 Jan;4:41–68. doi: 10.1016/s0006-3495(64)86768-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- GOLDBERG J. M., ADRIAN H. O., SMITH F. D. RESPONSE OF NEURONS OF THE SUPERIOR OLIVARY COMPLEX OF THE CAT TO ACOUSTIC STIMULI OF LONG DURATION. J Neurophysiol. 1964 Jul;27:706–749. doi: 10.1152/jn.1964.27.4.706. [DOI] [PubMed] [Google Scholar]
- Gerstein G. L. Analysis of Firing Pafferns in Single Neurons. Science. 1960 Jun 17;131(3416):1811–1812. doi: 10.1126/science.131.3416.1811. [DOI] [PubMed] [Google Scholar]
- Junge D., Moore G. P. Interspike interval fluctuations in aplysia pacemaker neurons. Biophys J. 2008 Dec 31;6(4):411–434. doi: 10.1016/S0006-3495(66)86667-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- LAMARRE Y., RAYNAULD J. P. RHYTHMIC FIRING IN THE SPONTANEOUS ACTIVITY OF CENTRALLY LOCATED NEURONS. A METHOD OF ANALYSIS. Electroencephalogr Clin Neurophysiol. 1965 Jan;18:87–90. doi: 10.1016/0013-4694(65)90152-5. [DOI] [PubMed] [Google Scholar]
- Moore G. P., Perkel D. H., Segundo J. P. Statistical analysis and functional interpretation of neuronal spike data. Annu Rev Physiol. 1966;28:493–522. doi: 10.1146/annurev.ph.28.030166.002425. [DOI] [PubMed] [Google Scholar]
- POGGIO G. F., VIERNSTEIN L. J. TIME SERIES ANALYSIS OF IMPULSE SEQUENCES OF THALAMIC SOMATIC SENSORY NEURONS. J Neurophysiol. 1964 Jul;27:517–545. doi: 10.1152/jn.1964.27.4.517. [DOI] [PubMed] [Google Scholar]
- Perkel D. H., Gerstein G. L., Moore G. P. Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J. 1967 Jul;7(4):419–440. doi: 10.1016/S0006-3495(67)86597-4. [DOI] [PMC free article] [PubMed] [Google Scholar]