Tentative Model for PCP Unit Narrow Sensitivity

A tentative, conceptual neural model to describe the behavior of directionally sharp PP units has been devised. Such a model must necessarily involve inhibition because

FIGURE 2.6-12 Another broadly sensitive PPU that has a sensitivity peak at about 315°, similar to the input LCPI VNC unit.

PP units generally involve the suppression of the background ring (POBL) when the animal is tipped at angles away from the peak angle (e.g., see Figure 2.6-6). Inspection of the four combined angular response plots of the VNC interneurons (see Figure 2.6-4) given by Walthall and Hartman (1981) suggests ways that PP neurons can be driven through excitatory and inhibitory synaptic inputs that may lead to directionally sharp responses.

Figure 2.6-13 illustrates a possible organization of PPUs. Examine, for example, the 315° PPU. Sharpening of its directional response is possible by two mechanisms: (1) by the relative weighting of the excitatory and inhibitory synaptic inputs and (2) by use of feedback inhibition analogous to the reciprocal inhibition in arthropod compound eye systems. (Reciprocal inhibition is introduced in Section 4.2 of this book; it is shown under certain conditions to lead to a sharpening of contrast in a visual image.) Thus, if the animal is tilted away from 315°, either the RCPI or LIPI unit begins to re and reduces the 315° PP unit ring rate via inhibitory interneurons. In the case of a PP unit with a 270° peak sensitivity, sharpening is accomplished by driving the unit excitatorily with the LIPI and LCPI VNC inputs, while inhibiting it with RIPI and RCPI inputs. Further inhibition aids sharpening in the form of reciprocal inhibition from the outputs of the 315° and 225° PP units.

Note that 24 model interneurons are required to simulate the PPU model shown in Figure 2.6-13. (Details of the models used for this size of neural model are discussed in Chapter 3.) To demonstrate sharpening in the model, the input frequencies on the four VNC connectives is preset according to Figure 2.6-4 for each .. At each . assumed, there will be only two connectives ring at rates determined by Figure 2.64. (At the unique angles of . = 45, 135, 225, and 315°, there will be only one connective

FIGURE 2.6-13 A prototype neural model for directional sharpening in PP units. Note that feed-forward inhibition and lateral inhibition is hypothesized to cause directional sharpening. Four input lines diverge to eight output lines in this model, 24 neural elements and a total of 60 synapses must be simulated.

FIGURE 2.6-13 A prototype neural model for directional sharpening in PP units. Note that feed-forward inhibition and lateral inhibition is hypothesized to cause directional sharpening. Four input lines diverge to eight output lines in this model, 24 neural elements and a total of 60 synapses must be simulated.

ring maximally.) Note that, for simplicity, this model is based on constant input frequency ring, rather than the dynamic adapting beha vior seen in the insect.

Because the 24 neuron model contains eight output neurons (PP units assumed recorded), plus 16 inhibitory interneurons, and 60 synapses, each of which has an analog psp emulated by two coupled rst-order ODEs, there is a total of 148 states in the model, including four neurons acting as voltage-to-frequency converters for the four afferent VNC sensory giant bers.

Rather than simulate the entire 148-state model, a reduced model consisting of only three output PPUs (the 45°, 90°, and 135° units in the 24 neuron model) has been chosen. Associated with the three output PPUs, only four inhibitory interneu-rons are needed, giving a total of seven neurons to model. Also, 18 synapses are needed in the reduced model; 4 inhibitory and 14 excitatory. Thus, a total of 7 + 2 • 18 + 4 = 47 states is needed for the reduced model. The model is shown in Figure 2.6-14. The reduced model is simulated using a Simnon program, ARENcns3.t, listed in Appendix 1.

FIGURE 2.6-14 Reduced PPU model. For proof of concept, the model of Figure 2.6-14 was reduced to this 7-neuron, 18-synapse model. The narrow response is expected at the 90° output neuron.

In the program above, each of the four VNC units were modeled by rst generating an analog quantity whose magnitude followed the tilt sensitivity shown in Figure 2.6-4. For example, the response of the RCPI VNC unit was given by frcpi = (maxFj/2) * {1 + cos[2(. - 45)]} 2.6-5

To make this RCPI unit not respond for 135° < . < 315°, use the statements:

rcpil = IF THETA > 135 THEN 1 ELSE 0 " Supresses rcpi for theta rcpi2 = IF THETA < 315 THEN 1 ELSE 0 " between 135 - 315°. rcpi3 = rcpi1*rcpi2

rcpi = IF rcpi3 > 0 THEN 0 ELSE frcpi

The analog signal rcpi is the input to an IPFM voltage-to-frequency converter (state r1). The frequency of uRCPI is proportional to rcpi. The steady-state pulse frequency of uRCPI is one of the inputs to the reduced neural model. The periodic pulses in uRCPI are inputs to the two-pole, ballistic lters, 7, 14, and 17, which generate epsps for neurons 2, 3, and 4, respectively (see Figure 2.6-14). Similar signal processing occurs in the other three VNC unit analogs.

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