Figure 4 of
Hamer, Mol Vis 2000;
**6**:265-286.

Figure 4. RecRK model accounts for Empirical Response Suite
I with τ_{E} rate-limiting

**A**: The RecRK model (with τ_{E} rate-limiting) was
optimized to both the Murnick & Lamb saturated two-flash data and to
four sub-saturating flash responses from toad rods (four smallest
responses). The model is able to provide a reasonable account of the 4
sub-saturating responses as well as responses to 5 higher intensities
(to which the model was not optimized). **B**: Model step responses
reproduce the "nose" at step onset and the two-phase response at step
offset. **C**: The model T_{sat} versus ln(I) function (blue
solid curve) reproduces the same slope as the Murnick & Lamb data
(~2.8 s/ln unit; red data and dashed line as in Figure 1B).

Finally, the model generates a substantial range of Weber's law LA
flash sensitivity (~3 log units; solid blue curve, panel **D**). For
each of a series of background adaptation levels (I_{b}), model LA
flash sensitivity was defined as the amplitude of the response to a
flash of fixed criterion intensity divided by the intensity of the
criterion flash. The criterion was the flash intensity eliciting a DA
flash response amplitude that was 10% of the full range of circulating
current. The dashed red curve is the Weber-Fechner relation from
Figure 1D, shifted horizontally to fit the model output below a
"cutoff" background intensity (cutoff I_{b}), marked by a dotted
vertical cursor, above which the model was judged to deviate from
Weber's law.

The cutoff I_{b} was defined as the highest I_{b} at which the
value of the model deviated from the best-fit Weber-Fechner curve by a
criterion amount (0.05 log units). The Weber-Fechner curve was fit
(least-squares) to the model over all I_{b} values up to and
including the highest I_{b} where the model slope was still >=-1.
The model slope was estimated by fitting a line to a moving window of 3
adjacent model points (sampling every 2^{0.25} R*/s, or 0.075 log
units).

Note that the model LA flash sensitivity obeys Weber's law over a
significant range (cutoff I_{b} = 8000 R* s^{-1}). At the cutoff
I_{b}, 14% of the model DA circulating current (F_{ss}) remains,
as indicated by the intersection of the vertical cursor line with the
green solid curve. The latter plots the fraction that the steady-state
current is saturated (i.e., 1 - F_{ss}(I_{b})), where F_{ss} is
the steady-state circulating current defined to be 1.0 in the dark, and
zero when all channels are closed. Also, at the cutoff I_{b}, the
steady-state internal Ca^{++} level (c_{ss} in inset) has dropped
by a factor of 5.1, from a dark value of 0.3 μM to 0.059 μM.

Also shown is the LA flash sensitivity of the model under two types
of simulated Ca^{++} clamp conditions: (1) LA flash sensitivity with
Ca^{++} clamped at its dark value (Ca^{++}_{dark} clamp; blue
dash-dot curve). Ca^{++} feedback is fully disabled over the entire
dynamic range, with only static saturation contributing to flash
desensitization. Ca^{++} was fixed at its dark value in the model,
and I_{b} was adjusted to achieve the same steady-state current as in
the unclamped case, ensuring that the steady-state currents were at the
same level in relation to static saturation (i.e., cGMP-gated channel).
Differences in flash sensitivity then can be ascribed to the differing
states of Ca^{++} in the unclamped and clamped cases.

The Ca^{++}_{dark} clamp analysis equates steady-state current
levels (F_{ss}), but does not equate internal Ca^{++} levels at
the time of presentation of the flash. This is achieved in a second
analysis: (2) LA flash sensitivity with Ca^{++} clamped at the new
steady-state level reached in response to each I_{b}
(Ca_{ss}^{++} clamp; blue dashed curve). This approach equates the
F_{ss} (and hence equates the effect of channel saturation), and
equates Ca^{++} at the time of the flash. Thus, in comparing the
unclamped and the Ca_{ss}^{++}-clamped flash sensitivity, the LA
flash response in each case is affected equally by saturation and by the
steady-state level of Ca^{++}-mediated gain. The only additional
factor shaping the LA flash response in the unclamped case is the
dynamic Ca^{++}-mediated gain change evoked by the flash.

Note that at high I_{b} (I_{b}> cutoff I_{b}), the
unclamped model flash sensitivity falls more steeply than a Weber's law
slope of -1, and eventually follows a steep function that parallels the
high - I_{b} behavior of both Ca^{++} clamped curves. In fact, all
3 curves asymptote to a slope of -(n_{cg} + 1), which is predicted by
the instantaneous compressive saturation of the cGMP-gated channels
[30].

Hamer, Mol Vis 2000;

©2000 Molecular Vision <http://www.molvis.org/molvis/>

ISSN 1090-0535