Details

In order to transmit information about a fast-changing world, photoreceptors must recover from previous light stimuli. One measure of this ability is flicker fusion frequency, which depends on ambient light intensity and the type of photoreceptor involved, that is, rods or cones. At the photoreceptor level, this problem translates into the recovery rate constant of the cyclic guanosine monophosphate (cGMP), which keeps the cation channels open and controls the response.

A simplified set of kinetic equations controlling cGMP are as follows:

,

,

with the initial conditions:

, , and ,

where is the number of excited rhodopsins, is the decay rate of excited rhodopsins, controls the stepping of the flash, 375 is the rate of production and is the rate of decay [1], is the cGMP flux, is the kinetic parameter whose value depends on the volume of the compartment [2], and is the hydrolysis rate constant of in the dark. In the realization presented here, one can see how the value of these parameters controls "Td", the so-called Pepperberg's [3] dominant time constant (the spacing between the curves), and "Trec", the slope of the response recovery (best seen when the semilog plot is selected).

It has been found experimentally [1] that the protein , in micromole per square micron, controls in a linear fashion the value of decay rate to a level of 0.037 micron square per second.

Since the value of tracks the value of [1, 4], it is very tempting to suggest that is also controlled by the surface density of Thus appears to control both excited PDE by its action of GTP hydrolysis and unexcited PDE in controlling the value of , the dark rate of cGMP hydrolysis.

References

[1] C. M. Krispel, D. Chen, N. Melling, Y. J. Chen, K. A. Martemyanov, et al., "RGS Expression Rate-Limits Recovery of Rod Photoresponses," Neuron, 51, 2006 pp. 409–416. www.cell.com/neuron/abstract/S0896-6273%2806 %2900550-2.

[2] T. D. Lamb and E. N. Pugh, Jr., "A Quantitative Account of the Activation Steps Involved in Phototransduction in Amphibian Photoreceptors," Journal of Physiology, 449, 1992 pp. 719–758. jp.physoc.org/content/449/1/719.full.pdf.

(3) D. R. Pepperberg, M. C. Cornwall, M. Kahlert, K. P. Hofmann, J. Jin, G. J. Jones, and H. Ripps, "Light-Dependent Delay in the Falling Phase of the Retinal Rod Photoresponse," Visual Neuroscience, 8, 1992 pp. 9–18. doi: 10.1017/S0952523800006441.

[4] M. E. Burns, "Deactivation Mechanisms of Rod Phototransduction: the Cogan lecture," Investigative Ophthalmology & Visual Science, 51, 2010 pp. 1283–1288. www.ncbi.nlm.nih.gov/pmc/articles/PMC2845640/?tool=pubmed.