Results and comparison to simulations

The electrophysiologically recorded single photon responses, identified by catego-rization with the histogram method and converted to photocurrent, are shown in figure 4.17.

In the figure, I scaled the responses of both data sets separately to an average single photon response of 1 and then pooled the responses from both data sets. We can see that the average failure response is flat, which is a good proof of principle that the categorization worked out well in terms of differentiating between responses and failures to respond. The single photon responses are quite variable, but follow a common shape.

Figure 4.17: The categorized photocurrent responses: upper left, failures to spond; upper right, single photon responses; and lower plot, multiple photon re-sponses. The individual traces are shown in black, with their average in red.

As a first comparison between simulations and experiment, I compared the aver-age single photon response from the electrophysiological recordings to the averaver-age simulated single photon response from the stochastic simulations, see figure 4.18.

Comparing the average responses, they look quite similar in general shape, the rising phase and the shut-off. When doing a more quantitative comparison, we noticed that the simulated single photon responses are a little slower in the rising phase: for the experimental responses, the time to peak is t_TTP = 0.19 s, while for the simulated responses, t_TTP = 0.24 s.

Figure 4.18: Side by side comparison of the average single photon response re-sulting from the categorized experimental dim flash responses, left, and from the stochastically simulated single photon responses, right. Both averages were scaled to an amplitude of 1.

I investigated the origin of this delay more closely and found that it arises in the activation of the PDE. Unfortunately, it was not easily fixed by adapting any parameters. Specifically, it arises in the step of the activation of the PDE from PDE·G_αGTPto PDE^∗·G_αGTP and the further steps towards the double activation of the PDE, as can be seen in figure 4.19.

In the figure, I plotted the normalized molecule numbers of the different species between the activated transducin and the double-activated PDE. We can see that G_αGTPand PDE·G_αGTPreach their peak rapidly, within 0.05 s after the activation of rhodopsin. Thus, the G-protein is rapidly activated and rapidly associates with the PDE. Next, the single-activated form PDE^∗·G_αGTP reaches its peak at 0.21 s.

Thus, it is the activation step of the PDE that introduces a delay.

The same counts for the double-activated form: the pre-complex reaches its peak at 0.15 s, while the double-activated form only peaks at 0.26 s. Since the effector is made up from both the single-activated and the double-activated form of the PDE, its peak lies in between the single- and double-activated maxima, at 0.24 s.

I tried to change the rate of the activation step, but this did not decrease the delay.

To be clear, the delay in itself is not a problem, since the electrophysiological response has its maximum at 0.19 s. Thus, it is fine that a delay is introduced in the activation step, it is just slightly too large.

Figure 4.19: Scaled species numbers for different steps in the activation of the PDE during the single photon response, resulting from a a deterministic simulation.

In the order of activation, the species are GαGTP (red), PDE· GαGTP (yellow), PDE^∗·G_αGTP (green), G_αGTP·PDE^∗·G_αGTP (light blue), G_αGTP·^∗PDE^∗·G_αGTP (blue), as well as the total effector E (magenta).

I also tried to remove the activation step altogether by assuming that the PDE is immediately activated upon binding of the G-protein. However, this also did not significantly decrease the delay: it was then between the single- and double-activated form of the PDE.

The delay could be an artefact of the fact that we do not perform space-resolved simulations, where the activation step would be much faster than the other rates, since it does not require any diffusion. However, though this time-to-peak may be at the upper limit of measured time-to-peaks, it is not completely unrealistic (Cangiano et al., 2012).

Next, let us take a look at the statistical properties of the single photon responses.

Typically, the variability of the responses is quantified by computing the coefficient of variation of their amplitudes and the areas:

CV = σ

µ, (4.8)

with the mean µ and the standard deviation σ, which is the square root of the variance: σ = √

v. Both the mean and the standard deviation are computed for all areas and amplitudes of the single photon responses, respectively.

Before computing the standard deviation from the variance, the variance of the failures is subtracted. This is to quantify the variance arising from just the single photon responses, and to subtract that resulting from dark noise and measurement noise.

For the electrophysiological responses, I computed the coefficients of variability over a duration of 1.5 s after the stimulus. This yielded CV_area = 0.37 and CV_amp = 0.23, which is in line with previously computed values (Hamer et al., 2005).

For the simulated single photon responses, I calculated the coefficients of variability over the same duration of 1.5 s after the stimulus. This resulted in CV_area = 0.87 andCV_amp = 0.34. The CV of the amplitude is well reproduced by the simulations, but the CV of the area is quite high in comparison.

This could be due to several reasons: the shut-off of rhodopsin could be responsi-ble, or a missing shut-off mechanism on the effector, or it could be an effect of the categorization of the responses, which will be investigated in section 4.6. A more detailed discussion of the difference between the measured and simulated CV of the area can be found in chapter 5.

I checked an effect that could have an influence on the calculated CV: the variance of the amplitude and area of the dark noise, which is subtracted from the experi-mental recordings. In the simulations, there is no dark noise or measurement noise, which is why we do not need to subtract it. This could however lead to a larger CV, since the subtraction of dark noise reduces the variance for the experimental recordings. To test this last hypothesis, I tried adding dark noise from the exper-imental traces to the simulated data. This did not lead to any conclusive results, however: the CV was not significantly changed (data not shown).