Assuming that all Vrk are equal,

Vm = - (6KD) ln(Ie/B) = - ln(Ie/B)6KD, Ie > B, Vm < 0 5.2-47

The next step in formulating this speculative model is to assume an electrotonic coupling of the axon of the monopolar cell to a target interneuron in the medulla. The graded potential change in this interneuron, Vi, is also assumed to be hyperpo-larizing, and exponential in shape. Vi is assumed to be directly related to the DCMD spike production rate:

Vm is Vm conditioned by propagating electrotonically down the nonspiking axon of the monopolar cell. For steady-state or average absorbed intensities,

where po is the dc cable attenuation of the axon. Combining the relations above, define the product, Po 6KGD = m:

It will be shown that m must be > 1 for an improvement in the contrast seen in the hyperpolarizing interneuron voltage, CVi. A tacit assumption has been made that an improved contrast in Vi is required for the threshold detection of moving, high-spatial-frequency objects. The contrast in Vi is

The maximum effective intensity in the rhabdoms was shown to be lemax _ Mrca%{^ + (4/n) exp[-a^A]} 5.2-52

If the (p + q)/2 term is factored out, lemax _ M™2lo (p + q)2{l + ^(4/«)exp[-o2u/]} 5.2-53

The exponential term in Equation 5.2.53 is < 1, so when Iemax is raised to the mth power, it becomes possible to use the approximation, (1 + e)m = 1 + me. Thus, lemax = [a% (p + qV2]m{l + m^ (4/rc) exp[-a2u2]} 5.2-54


Cm =[k02na2l0 (p + q)/2]m{l-^C0bj(4/n)exp[-^u2]} 5.2-55

Hence by using Equation 5.2.51, on Equations 5.2.54 and 5.2.55,

As long as m = Po 6KGD > 1, there will be contrast improvement in the membrane voltage of the medullar interneuron, V., as the result of moving a pattern with contrast Cobj over the eye. That is, CVi > CIe > Cobj for m > 1.

It is also of interest to evaluate the contrast function for the retinula cell depolarization voltage, given by

_ d{- ln(B) + ln[(ko 2na 2lo (p + q V^ + ^j (4/ n) exp(-a2 u2 2)]}

_ D{- ln(B) + ln(ko 2na 2lo (p + q y2) + ln[1 + C^ (4/ n) exp(-a2 u2 2)]}

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