INFERIOR

IN IN IN

n OUT

IN OUT

n n

Figure 5. 21 Stimulus sequence for convergence experiments.

Upper part of figure shows relative positions of patterns: PR in field of right _unit; PLA and PLB in field of left. Lower part of figure shows timing sequence for pattern presentations. All patterns had constant velocity horizontal motion during "on"

period. _PR always had inward motion. P LA and P LB were presented alternately;. their on- and off-times coincided with those for PR. P LA and PLB alternated between inward and outward motion.

- 163 -

pattern sequence as in figure 5. 21. PST histograms for the left (inhibiting) unit were computed for the four stimulus variations:

PLA inward and outward; P LB inward and outward. The two

inward and outward cases for the inhibiting unit were again compared to verify that they did not differ. The corresponding four histograms for the inhibited unit were then computed and the amount of inhibition for PLA and PLB measured as described above. The experiment was performed on four preparations with a total of nine different pairs of patterns. The ratio of difference in amount of inhibition to firing rate of the inhibited unit varied between 0. 5% and 10%.

The average was 5"/o. In all cases, the difference appeared negligible on visual examination of the PST histogram.

Divergence. The variation in amount of inhibition suggested that the effect on the inhibited unit might depend on the particular motion patterns in its field. This was tested in the following way.

Consider the. two very schematic models in figure 5. 22. The left and right units represent a pair of opposite Ila-in' s, with firing

rates pL and pR' respectively. Each has two input branches. Each branch is assumed to be separately excited by patterns Pl and P2.

That is, for model A, it is assumed that if only Pl is present, the rates at the point "a" are

Pru

and 0 for the upper and lower branches.

For pattern P2 only, the rates are 0 and pR

2 for the upper and lower branches. For model A, each branch is separately "inhibited" by the left unit such that the rates at point "b" are

Pru - 11,PL

for the

MODEL A

Left unit .,

PR17

..,__Right unit

a Rate pR

MODEL B Left unit _ . ,

Pru

. - Right unit

k

PRz

Figure 5. 22 Schematic representation of models for testing divergence hypothesis. Left and right units represent a pair of opposite Ila-in units.

Pattern

G

G

- 165 -

upper branch and pRZ - k2pL for the lower branch. (The ki can be thought of as "coefficients of inhibition".) That is:

and

PR= PRl - klpL(Pl) PR = PRz - k2p L(PZ)

for Pl only, for P2 only,

where the notation pL(Pi) is used to allow for dependence of pL on pattern. For model A, the general equation for pR is

where the brackets indicate that each term cannot be less than zero. For model B, the corresponding equation is

The problem is to devise an experiment that will distinguish between models. Suppose Pl only is presented under the condi- tions of two different firing rates for the left unit: p L

>

O; and pL = 0. Then

pR(Pl) = PRl for pL = 0,

pR(Pl) = pRl - klpL(Pl) for pL

>o.

Writing t:ipR(Pl) for the difference in pR(Pl) under these two conditions,

or ( 1}

Similarly, for pattern P2 only,

( 2)

Then for model A,

( 3)

Note that if pL(Pl)

=

pL(P2), then the ratio of the ki's is simply the ratio of the l:ipR's:

(4)

For model B, the right hand side of equation ( 3} is zero, and the ratio in equation (4) is unity.

Thus, an experiment in which the inhibited unit (the right unit in the model) is stimulated with two different patterns should differentiate between model A for unequal ki' s and either model B or model A for equal ki's. For each pattern presented to the

inhibited unit, the inhibiting unit (left unit in the model) is presented both an inward motion pattern (for pL > 0) and an outward motion

pattern (for pL = 0). The rates can be measured and the quantities on the right hand sides of equations (I) and ( 2) computed. If they

- 167 -

are significantly different, model A is a better representation.

A typical arrangement of patterns is shown in figure 5. 23, with Pl and PZ in the field of the right unit and PL in the field of the left unit. Special timing circuitry was used to produce the pattern sequence shown. Pl and PZ always had constant inward motion and, as described earlier, PL was either oscillated back and forth once per presentation or had alternating inward and outward motion.

Figure 5. 24(a) and (b) show typical responses in the form of PST histograms for oscillating and alternating PL' respectively.

The responses of the inhibiting unit for alternating PL (figure 5. 24(b)} are not shown, but were similar to the upper curves in figure 5. l 9(b). The amount of inhibition was measured as

described earlier. Rather than using the SCAN program, however, a special program was written to compute the average number of spikes per pattern presentation for a time interval whose end- points with respect to stimulus-on time were specified by the user. The program also computed the root-mean-squared deviation.

A total of 17 experiments were performed as described above on 8 prepa rations. The experiments were approximately evenly divided between the inhibited unit being the left or right Ila-in. The combinations of patterns used to stimulate the inhibited unit (Pl and PZ) are illustrated schematically below.