there, I was successful in creating a model for dim light stimuli that reproduces both the result that the main effector is the double-activated PDE, and that 12-14
∗PDE∗ are activated during the single photon response.
The final deterministic model I am working with for bright stimuli is thus the modified model from earlier, where the effector had been scaled to a smaller num-ber, but that does not contain the dimeric activation of the PDE. The effector definition is E = PDE∗+ 2·∗P DE∗ and the main contribution comes from the single-activated PDE. The model is also referred to as the Beelen 2020 model in the following. The parameter changes in the model with respect to the Invergo 2014 model can be found in the appendix in table A.13.
In the figure, the light response to a stimulus consisting of a background lasting for 10 s and a saturating flash at t= 10 s is shown. The four different background intensities lie between 0 photons/µm2s to 4651 photons/µm2s. After the saturat-ing flash, the circulatsaturat-ing current returns to the dark level, since the background stimulus has ended. The larger the background intensity was before the saturating flash, the shorter the time spent in saturation after the flash.
An important mechanism for light adaptation, next to the action of the GC-GCAPs system, is the feedback of calcium on recoverin and the rhodopsin kinase, which regulates the shut-off of the cascade. It is illustrated in figure 3.8. This mecha-nism regulates the availability of the rhodopsin kinase to phosphorylate rhodopsin, which is an essential part of the shut-off of the activated rhodopsin: the phosphory-lation leads to a decreased affinity for the G-protein, and allows binding to arrestin, which completely shuts off rhodopsin.
RK
RecT·Cafree·RK RecT·Cafree
RecR
Cafree
kRec1
kRec2
kRec3 kRec4
RK
kRec3 kRec4
Figure 3.8: The calcium-dependent regulation of the rhodopsin kinase by recoverin.
Recoverin can associate and dissociate to free calcium with rate constantskRec1and kRec2. The calcium-bound form can then associate and dissociate to the rhodopsin kinase with rate constants kRec3 and kRec4.
In the dark state, most of the rhodopsin kinase is unable to interact with rhodopsin, because it is bound to the calcium-bound form of recoverin. As a consequence of the light response, the calcium concentration in the cell drops, which leads to the recoverin losing its calcium ions. This triggers a conformational change in the recoverin and releases the rhodopsin kinase, which can then phosphorylate rhodopsin.
The role of the phosphorylation for the shut-off of rhodopsin is undisputed, but the role of the calcium-dependent regulation in light adaptation is unclear. Using the model, we can investigate the relevance of this mechanism for light adaptation
in more detail.
To study the significance of the recoverin-rhodopsin kinase mediated calcium feed-back for light adaptation, I removed the feedfeed-back from the Beelen 2020 model and looked at light responses in the resulting modified model. The amounts of recov-erin in the calcium-bound and calcium-free state were set to fixed values, which led to the reaction scheme in figure3.9. The rhodopsin kinase could now be consumed and produced with the following rates:
vf = kRec3∗RecR·Ca2+∗RK (3.9) vr = kRec4∗RecR·Ca2+·RK,
where the molecular species RecR·Ca2+and RecR·Ca2+·RK were fixed to their dark concentrations and are therefore not calcium-dependent anymore. The reaction rates are therefore fixed (vf, the rate of the production of rhodopsin kinase) or only dependent on the free concentration of rhodopsin kinase (vr, the rate of the consumption of rhodopsin kinase).
RK
RecT·Cafree·RK RecT·Cafree
RecR
Cafree
kRec1
kRec2
kRec3 kRec4
RK
kRec3 kRec4
Figure 3.9: The calcium-independent regulation of the rhodopsin kinase. The different forms of recoverin are set to constant values which are part of the reaction rates.
I first checked whether there would be any effect of this change on flashes of different intensities without any background. This comparison is shown in figure 3.10. The responses of the two models overlap exactly - thus, there is no effect of the removal of the calcium feedback on recoverin and the rhodopsin kinase for dim to saturating flashes without any background.
Figure 3.10: Comparison of the normal model (solid black lines) to the model with no calcium feedback on the regulation of the rhodopsin kinase (dashed red lines).
The stimulus consisted of flashes of increasing brightness (1.7, 4.8, 15.2, 39.4, 125, 444, 1406 and 4630 photons/µm2) without any background.
Figure 3.11: Responses in the model without calcium feedback on the rhodopsin kinase to a stimulus consisting of a background lasting for 10 s and a saturating flash at t = 10 s. The brightness of the backgrounds was: 0 photons/µm2s (solid black line), 698 photons/µm2s (dashed green line), 1860 photons/µm2s (dot-dashed red line), and 4651 photons/µm2s (dotted blue line). The saturating flash had a brightness of 6968 photons/µm2.
However, when checking the effect on flashes with a background, it became obvious
that there is an effect of the feedback. In figure 3.11, the same stimulus paradigm from figure 3.7 was repeated for the model without calcium feedback. The accel-eration of the recovery phase, a typical feature of light adaptation to background illumination, is lost in the absence of a calcium feedback.
I also calculated the saturation time, which is the time spent over 90% of the maximum amplitude, for saturating flashes after adaptation to backgrounds of different intensities. The comparison of the saturation times can be found in figure 3.12. In the model describing the wild type, there is a clear decrease of saturation time with increasing background intensity. When the calcium feedback is removed, the time spent in saturation even increases slightly with increasing background intensity.
Figure 3.12: The time spent in saturation (over 90% of the maximum ∆J) after adaptation to backgrounds of different intensitiesLand a saturating flash, plotted over ln(L). Black plus signs are for the normal model, while red asterisks are for the model where the calcium feedback on recoverin and the rhodopsin kinase was removed.
To conclude, for the kind of light stimuli presented here, the calcium-mediated feedback on recoverin and the rhodopsin kinase is essential for light adaptation in the model. In the model describing the wild type, the recoverin releases rhodopsin kinase as a response to the decrease in calcium concentration triggered by the background stimulus. This free rhodopsin kinase is then ready to rapidly
phos-phorylate rhodopsin activated by the saturating flash, shutting off the response more quickly than without the background.
In the altered model without the feedback mechanism, production and consump-tion of the rhodopsin kinase are in equilibrium in the dark. As a response to a stimulus, the free rhodopsin kinase can associate to rhodopsin, decreasing the amount of free rhodopsin kinase. This decreases the rate of consumption of the free rhodopsin kinase in equation (3.9). However, there is no increased produc-tion of free rhodopsin kinase due to a change in calcium concentraproduc-tion. Thus, the additional release of rhodopsin kinase by this mechanism is not sufficient for any decrease of the time spent in saturation.