Spike Train Analysis Research Articles

STAP-12: A library system for on-line assimilation and off-line analysis of event/time data

An open ended library system for neuronal spike train analysis is presented. The design is based on the experience with STAP-8, a spike train analysis program for the PDP-8/AX08 system. The system software and all I/O and analysis programs are written in assembly language for the standard PDP-12/A equipment. Single- or multi-channel assimilation of unit activity is possible by means of either AD-conversion of membrane potentials or event recording with Schmitt-trigger inputs. Multi-unit records of a single, non-selelctive electrode are sorted with respect to pre-defined threshold parameters. Data files (spike trains) with up to 2048 event times are saved on a LINC tape train library for off-line analysis. A set of 12 analysis programs is part of the basic STAP-12 system and covers the standard procedures, as interval histogram, autocorrelogram, crosscorrelogram, latency crosscorrelogram, auto- and crosscovariance estimates, serial correlogram, and Poisson parameter estimates. The user may extend the capacity of STAP-12, implementing his own specific programs.

STAP-8: A subroutine package for statistical online analysis of simultaneous neuronal spike trains

This paper presents a computer program including a subroutine package for the statistical analysis of neuronal spike trains. Extended use was made of an information display concept, on-line control via teletype intercommunication and the use of a versatile laboratory peripheral, including, among other features, Schmitt-Trigger inputs, multiplexed analog-digital converters, and a variable RC-clock. The software, written exclusively in the system's specific symbolic assembler language, was compiled and tested on a LAB-8 System of DEC, extended with the Arithmetic Element MP8/1, the Mini-Disk DF32, and the Tektronix Type 601 Storage Oscilloscope, and is available as an assembly listing together with the binary paper tape. From the neuronal spike trains recorded simultaneously by two Schmitt-Trigger inputs, interspike intervals are counted by the RC-clock counting chain and translated into 12-bit positive integers. These interval data files stored on the disk are available to eight different analysis programs: Interval histogram, autocorrelogram, cumulative distribution function, conditioned probability density, serial correlogram, cross-correlogram, post-stimulus time histogram, and time interval sequence. The results are given as a function or histogram display, or may be punched on paper tape for further analysis.

Neuronal Spike Trains and Stochastic Point Processes: II. Simultaneous Spike Trains

The statistical analysis of two simultaneously observed trains of neuronal spikes is described, using as a conceptual framework the theory of stochastic point processes.The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. If the null hypothesis is rejected-if dependence is attributed to the trains-the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects of nonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities are shown to have little effect on the detection of interactions.Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons.A companion paper covers the analysis of single spike trains.

Neuronal Spike Trains and Stochastic Point Processes: I. The Single Spike Train

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.

Analysis of spike trains in terms of delayed coincidences.

A particular correlation technique was used in order to analyse the “spontaneous” electrical activity of neurons in the frog's brain, and an electronic device was constructed for analysis of available data. On the basis of the correlograms obtained, two simple models of the net in the neighbourhood of the neuron studied are suggested as explanations for the observed regularities in the spike trains.

Probabilistic Characterization of Simultaneous Nerve Impulse Sequences Controlling Dipteran Flight

A probabilistic method of analysis of spike trains is presented which provides a complete statistical description of spike sequences and allows the elucidation of some of the properties of the neural interconnections producing the output patterns. The flight motor system of the blowfly, Calliphora terraenovae, is analyzed by this method. Individual motor units show large, non-serially correlated, cycle-to-cycle variations in frequency superimposed upon long term frequency trends. These trends are apparently not generated by averaging the cycle-to-cycle variations in input excitation over a long time period. The different motor units share the same short term input excitation and the excitation causing long term trends. Units in different muscles show no preferred phase or latency relationships; they maintain similar frequencies but their phases drift through all possible values. Frequency control without phase control may be accomplished by shared excitation with a total input frequency many times the output frequency. Units in the same muscle maintain strong phase relationships. Constant phase relationships during variations in frequency may, among other models, be due to reciprocal inhibition or a common linearly rising input. Sensory feedback cannot account for the degree of phase or frequency regulation shown. Thus central patterning of the output sequence is necessary, as in the locust, and the two flight systems can be considered as integradable evolutionary variations.

CUTANEOUS SLOWLY ADAPTING MECHANORECEPTORS IN THE CAT.

Cutaneous mechanoreceptors have been anatomically delineated, and the physiological characteristics of the nerve fibers and receptor terminals have been studied. Frequency analysis of spike trains showed two rate processes associated with the rising and plateau phases of the mechanical stimulus. Natural stimulation is capable of evoking firing frequencies which saturate the carrying capacities of the fiber.