Why?

Hockberger et al (1999) mentions that blue light up to 470 nm can have some phototoxic effect on mammalian cells, from 2 to 6 J/cm². In our experiments, we have observed a much higher cell death rate in the cultures exposed for 24h to blue light than in the control. 24h at 20 mW/cm² is actually more than 1700 J/cm². To stay on the safe side, we can give the cells 32 W/m² for a time span of 30 minutes, which would mean a total of 6 J/m².

• How much activation can we get with this irradiance?
• Will we have to push it up?
• What lighting pattern will give best results?

Other authors, like Marchesini et al (1989) say that 500 W/m² at 488 nm for 5 minutes does have a more beneficial effect on the cells than cytotoxic. But we might need to irradiate the cells for hours to clearly see that the reporter production switched on, depending on the photodynamics of LovTAP-VP16, since the mRNA expression rate might be on order of about 1 per hour per plasmid (Schwanhäusser et al, 2011).

What?

To optimize the number of experiments to perform, we have built a simple model to predict the proportion of photoproduct to be expected at every time point when a sample with LovTAP-VP16 when is illuminated with a time varying light input.

How?

Photoactivation

When light with the appropriate wavelength goes through a solution containing photoactive molecules, a number of photons will be absorbed and transfer their energy to these molecules. In the case of LovTAP-VP16, this energy will favor the conformational change into the “active” state. To simplify the model, we will suppose that the protein will be active once it has received enough energy.

The molar absorptivity, also known as extinction coefficient, ε, is directly related to the absorption cross section, σ, through the formula:

If ε is in L mol⁻¹cm⁻¹ we get σ in m². Therefore we can calculate the number of photons absorbed by a material per unit of distance traveled by the light, using the expression:

where N is the number of photons, m is the number of absorbing molecules per unit volume and x is distance. We can write m in terms of the amount of molecules in the differential volume dV:

and, being dV=Adx, with A the area seen by the light:

Now, the quantum yield of the LOV2 domain, Q, is defined as the number of photons of a particular wavelength required to trigger the photoactivation of one protein. We can use it to relate dN with dM_phot, the variation of the amount of photoproduct:

substituting in the previous expression and defining F as the photon flux:

This will tell us the number of molecules that will be in form of photoproduct. In the case of LovTAP-VP16, since it's a dimer, the proportion of activated dimers will depend on whether both or only one proteins has to be photoactivated to make the dimer active.

Activation parameters

Fig. 1: Comparison of the activation dynamics produced by the model and the experiments by Kasahara

From Kasahara et al (2002) (Table I) we took the values of ε = 14000 L mol⁻¹cm⁻¹ and Q = 0.34 for the LOV2 domain in phot1 in Arabidopsis and rize. They are very similar to the LOV2 domain in phot1 from Avena sativa, according to Salomon et al (2000). Kasahara used a 446 nm light source, at 80 µmol m⁻²s⁻¹, which is 22 mW/m². Using those parameters provides the same dynamics they observed in their experiments for the first 10 s at 4ºC.

To adapt these parameters to the wavelength of the LEDs we are using, the molar absorption has to be modified. Absorbance at 470 nm, the wavelength of the LEDs we use, is some 75% (Kasahara et al (2002), Fig. 1) of the peak absorbance at 450 nm. Since the extinction coefficient, or molar absorption, is proportional to the absorbance, we can expect ε to be between 8000 and 10000 L mol⁻¹cm⁻¹.

Deactivation

Since the ground state, or dark state, is more stable, active LovTAP-VP16 proteins will spontaneously release a photon and go back to the dark state. This rate is parametrized with the half life of the photoproduct.

Deactivation parameters

For 4ºC, Kasahara et al (2002) do not provide a value for the half life of the photoproduct, but provide instead the proportion of photoproduct in equilibrium, which is 0.91. The half life that allows for this is τ_1/2 = 200 s. To verify whether this setup makes sense, we compared it to the experimental results presented in Salomon et al (2000). The only experiment they did with monochromatic light was at 445 nm and 55 µmol m⁻²s⁻¹, or 15 mW/m². In ice, they measured a k_ppf/k_reg of 17, being k_reg = ln(2)/τ_1/2 and k_ppf = F Q σ. Using the previously selected parameters, our model yields exactly 17 for that value.

In both references it is reported that the half-life at room temperature is around 30 s. That would mean the half life is divided by 3.33 for every 10ºC increase. It would then be reasonable to think that at physiological temperature, more than 10ºC over room temperature, the half life would drop to around 9 s.

Interestingly, fig. 3 shows that, at 24ºC, our model predicts a photoactivation of 95% at 180 W/m², quite in agreement with the 200 W/m² saturation irradiance (470 nm) at room temperature mentioned by Strickland et al (2008) for LovTAP. This suggests that our model, built with parameters from the isolated phot1 LOV2 domain, might also provide useful information to predict the photodynamics of LovTAP, which gives us some hope of having it work for LovTAP-VP16.

Kasahara et al also worked with fusion LOV2 proteins, obtaining comparable parameters. We will then assume that the results shown in this page can be extrapolated to LovTAP-VP16.

Results

Fig. 2: Time evolution of the proportion of photoproduct with 4 different lightning cycles.

Fig. 3: Photoproduct in the equilibrium (after 200 s) for different irradiance values at 4ºC, 24ºC and 37ºC.

Let's try to answer the questions proposed in the beginning:

• How much activation can we get with this irradiance?

We said we could go up to 32 W/m², or 3.2 mW/cm², with no damage to the cells. Unfortunately, according to the model we will get only around 45% activation (see fig. 3).

• Will we have to push it up?

Depending on the difference of DNA affinity of LovTAP-VP16 it might be interesting to experiment with irradiances above this value, to get a higher photoconversion rate. Pushing it up to 200 W/m² we should be getting 85% photoactivated LovTAP-VP16. To understand the effect the photoactivation level might have on the expression, we implemented a simple mass-action model.

• What lighting pattern will give best results?

Until now we have talked about average (in time) irradiance values but, with our current bioreactor setup, we can only achieve this by pulse modulation. As seen in fig. 2, the pulse width doesn't affect the average photoactivation. But cycles of several seconds involve minimal instant photoproduct proportion of less than 25% (as in fig. 2 for 25% duty cycle and 20 s cycle length). If a LovTAP-VP16 dimer requires several seconds to bind DNA and recruit all the transcription machinery (as suggested by Darzacq et al), it might be beneficial not to use cycle lengths near the half life of the LovTAP-VP16 photoproduct, or else the recruitment might tend to be aborted at the photoactivation minima.

The code

The MATLAB function we have implemented, as well as he MATLAB script that produces the plots in this page using this function, can be downloaded from: File:Team-EPF-Lausanne photodynamics.zip.

Maximal step size to converge: 2 s for 200 W/m², 0.4 s for 2000 W/m² and 0.04 s for 20000 W/m².

We have implemented it using a pretty rudimentary explicit method, and care should be taken when choosing the time step. In fig. 4 we show the convergence behavior of the function for different light intensities, to get an idea of what step size is safe. Since the fast time constant depends on the light intensity, the step size has to be changed according to it.