## The JPST Diagram

The poststimulus (firing) time (PST) diagram is a well-known neurophysiological tool that is used to illustrate adaptation and habituation in a single responding neuron. Every time a stimulus is given, the time base is triggered on a storage oscilloscope; when the neuron fires, the spike is discriminated and the z-axis (beam intensity) is brightened to make a dot to mark the event on the CRT face. On the next stimulus, the trace is stepped up and another sweep is started, etc. This process builds a raster on the CRT screen full of dots, each one representing the time history of firing of the neuron following a stimulus. (Stimulation can be sensory, i.e., a flash of light,

Stimulus No.

Stimulus No. Post-stimulus time (ms)

FIGURE 8.1-1 Schematic of a PST diagram.

Post-stimulus time (ms)

### FIGURE 8.1-1 Schematic of a PST diagram.

or can be electrical, applied directly to an "input" neuron. Stimulation is generally periodic.) A typical PST diagram is shown schematically in Figure 8.1-1.

Consider another scenario where a stimulus of some type is given to a nervous system and electrical recordings are made from two nearby interneurons, A and B. The responses of A and B can be described statistically by the JPST PST defined as:

§(t, u) dt du = Pr(a neuron A spike occurs in the interval, (t, t + dt) and a B spike occurs in (u, u + du), given a stimulus at t = u = 0} 8.1-1

where the local times t and u are measured from each stimulus event.

The sets of point tallies made in vertical and horizontal columns do not in general correspond to the PST diagrams for the individual neurons. This may be shown by writing the joint density as the product of a conditional density and a marginal density:

£(t, u) = ^A|B(t, u) £b(u) = Sb|aG, u) ^A(t) 8.1-2

where the marginal densities §A(t) and §B(u) are the ordinary PST densities for neurons A and B. The conditional density is defined as

§A|B (t, u) dt = Pr{an A spike occurs in (t, t + dt) |

A JPST diagram is used to estimate §(t, u). It is constructed from N repetitions of a stimulus. At the jth stimulus, spikes from the two neurons are discriminated and converted to a joint point process consisting of their occurrence times. The jth, two-dimensional, scatter diagram is made up as shown in Figure 8.1-2, and its dots are superimposed with the dots from the previous (j - 1) JPST scatter diagrams. Assume neuron A fires on the average 15 spikes in response to a typical stimulus, and B fires 20 in the time frame considered. Thus, there will be on the average 15 x 20 = 300 dots on each scatter diagram. If the stimulus is given N = 25 times, then the final JPST diagram will have about 7.5 x 103 dots. To prevent the loss of information caused by coincident dots, one can overlay a rectangular grid over the JPST surface and have the computer count the number of dots in each differential cell area, At Au. These numbers can be converted to a height above each cell, generating a smooth, three-dimensional surface with contour lines using the proper software, such as found in Matlab.™

In viewing a two-dimensional JPST histogram, point densities taken on lines parallel to the 45o principal diagonal (the t = u line) correspond to the cross-correlation histogram between neurons A and B. Because of obvious geometrical relations, the timescale of a cross-correlation histogram is in the ratio of 1: V2 to that of the JPST scatter diagram.

Gerstein and Perkel (1972) in a paper on statistical techniques for display and analysis of spike trains, presented a number of interesting examples of how two-dimensional, JPST scatter diagrams can be used to deduce parsimonious models for the interaction of three and four neuron groups. The deduced models of neural interaction are qualitative and not unique. They do suggest neural anatomical structures to be searched for, however. Some examples taken from Gerstein and Perkel (1972) are shown in Figure 8.1-3A to H. On these figures, the gray background of the JPST diagrams represents a nearly uniform, random dot density. The darker bars represent wide regions of high-dot-density. Single, bold diagonal lines represent sharp, high-dot-density diagonal plots, and multiple diagonal lines represent broad, high-dot-density diagonal bands. The noise sources are assumed to be present to account for steady-state, random firing of the recorded neurons. Synapses with arrows are excitatory; inhibitory inputs have a small circle synaptic ending. The neural circuits are examples of connections that are capable of producing the associated JPST diagrams, according to Gerstein and Perkel (1972).

In circuit A, there is no functional connection between the stimulus, S, and the recorded neurons, so the JPST diagram has a uniform, random-dot-density; the firing of neurons A and B is uncorrelated. In circuit B, superimposed on the random firing, the stimulus briefly increases the firing rate of A, hence the dark band along the t axis. Both A and B are driven by the stimulus in C, producing two dense dot bands, one along the t axis and the other along the u axis. The uncorrelated background firing is still present.

In circuit D, the stimulus again has no effect on interneurons A and B; however, A drives B in a nearly 1:1 manner, producing a high degree of correlation and a sharp, bold line along the 45° diagonal of the JPST plot. The correlation between A and B in plot E is less sharp because they are each driven by an independent noise source and also by a third, randomly firing neuron, C. The broad, more diffuse

Si ti unit A 