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.
using the function movmean to remove a 50 Hz oscillation.
Figure 3.13: Electrophysiological recordings of the new stimulus paradigm con-sisting of a fixed background and five flashes of increasing intensity. The intensity of the backgrounds was 0 photons/µm2s (black), 8.5 photons/µm2s (green), 252 photons/µm2s (red), and 695 photons/µm2s (blue). The intensi-ties of the flashes was 9.5 photons/µm2, 32.1 photons/µm2, 96.4 photons/µm2, 299 photons/µm2, and 5104 photons/µm2. The responses were shifted to the same resting membrane potential of zero and normalized to the saturating response.
To compare this electrophysiological recording to simulated light responses, we first had to adapt the model to the respective backgrounds. To do this, I ap-plied a steady background illumination by modifying flashBG using an experi-ment. After simulating for 100 seconds, the model had reached a steady state. I saved the current values for all molecular species as initial conditions for a new model, modeladapt, by modifying modeladapt.initialCondition. This model represents the normal Beelen 2020 model which has been adapted to the given background illumination. I did this for each of the 4 background intensities.
Next, I applied the different flashes to the adapted models by modifying flashMag and flashDur according to the stimulus paradigm. I simulated the responses to the flashes one by one, for each combination of background and flash intensity.
When setting the intensity for the experiments in the simulations, we had to scale the intensities with respect to the intensities given in the experiment: in the ex-periment, there is a distance between the light source and the retina and there is some retinal tissue the light has to traverse to reach the rods. By comparing the light responses (especially the fact that the fifth flash is saturating, and the fourth not yet), I arrived at a scaling factor of 0.4 for all intensities given in the experimental description. The dimmest background (intensity 8.5 photons/µm2s) was further scaled with a factor of 3. This is due to the fact that the LED used for the experiments has a nonlinear behaviour at low light intensities, possibly outputting larger intensities than desired at low intensities.
We can then compare the result of the simulations with the electrophysiological recordings. The flashes are shown side by side in figure 3.14: on the left, the experimental flashes are shown in ∆U, and on the right, the simulated flashes are shown in ∆J. The amplitude of the simulated responses was scaled to the amplitudes of the electrophysiological amplitudes, and the resting photocurrent was subtracted to baseline the simulated data like the experimental data.
Figure 3.14: Responses to the bright flash + background paradigm separated by flashes. The experimental data in photovoltage ∆U are on the left and the simulated responses in ∆J are on the right. The simulated responses have been normalized to the same amplitudes as the experimental recordings.
When comparing the responses side by side, it becomes noticeable that the simu-lated responses are slower in terms of the shut-off - this is especially obvious for the brighter flash responses. The responses are also slightly slower in the excitatory phase. However, the general kinetics are reproduced: the brighter the flashes, the longer the response, and the brighter the background, the faster the shut-off.
To compare the experimental data and the simulated responses more quantita-tively, we calculated the time spent over half the maximal amplitude, Thalf, for the simulated and experimental responses. This measure is more stable than the saturation time, which is the time spent in more than 90% of the maximal am-plitude, when we are treating non-saturating flashes. Specifically, we compared the reduction of Thalf for each background, relative to the response without any background. The comparison is shown in figure 3.15.
In this comparison, we can also see that the simulated flash responses are longer,
and that the reduction resulting from the backgrounds is less than in the experi-mental data. But the general trend of the reduction in Thalf by the adaptation to the backgrounds is well reproduced.
Figure 3.15: Comparison of the reduction in the time spent over half the maximal response amplitude,Thalf, for each background with respect to zero background, for the experimental data (left) and the simulated data (right). The background inten-sities were 0 photons/µm2s (black), 8.5 photons/µm2s (green), 252 photons/µm2s (red), and 695 photons/µm2s (blue).
Where do the differences in response kinetics arise from? There are several possi-bilities for this. They could arise because some shut-off mechanism responsible for light adaptation is missing in the model. Furthermore, the discrepancy could be because we are comparing the photovoltage ∆U to the photocurrent ∆J. In prin-ciple it is possible to back-convert ∆U to ∆J by measuring and using the complex impedance of the rod. We do this in section 4.4 for the dim light responses. How-ever, this conversion is not as precise for brighter light responses and we therefore decided against using it in this case. The reasons for the observed discrepancies are further discussed in chapter 5.
In summary, the simulated light responses reproduce the general qualitative fea-tures of the responses and the light adaptation. However, when comparing them more quantitatively, we noticed that the simulated responses have a slower shut-off.