Team:ETH Zurich/Modeling/Photoinduction

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Contents

Photoinduction

Introduction

Photoreceptors are light-sensitive proteins, which are able to perform specific actions in the cell (e.g. act as kinases) upon light induction. Photoreceptors typically make use of photopigments (like flavin and bilin), which are structurally changed (Photoisomerization) or reduced (Photoreduction) as reaction to excitation by photons. Some photoreceptors can be activated and deactivated by light; others follow an exponential decay to a ground state after excitation. In either case for an estimation of a receptor’s activity level it is necessary to compute the number of induction events, i.e. light has to be treated as particles.

For E.colipse we needed to know the activation of various receptors (Lov-Tap, BLUF-EAL, Ccas1, Cph8, UVR-8) to predict the behaviour of our system. For each of the receptors we tested several light conditions and computed the effects of visible and UV-light. In particular we analysed whether we can identify the amount of UV radiation with the given receptors.


Methods

Quantification of light

Irradiation spectra for sun light, room light and a 60 W bulb.

For our project we needed to quantify the irradiance of different light sources, like sun light, room light, various bulbs, LEDs and a UV transiluminator. We discretized the irradiance spectra of these sources and converted the energy flux [J m-2 s-1 nm-1] to the photons flux Nλ [mol m-2 s-1 nm-1].

Light sources used:

Name Description Reference Flux at probe Distance
sun natural sun light ISO 9845-1, 1992 640 W m-2 n/a
room sun*0.3, UV part. removed assumption 210 W m-2 n/a
bulb200W Incandescent light bulb GE200Clear 12 W m-2 1 m


We were aware, that light can be polarized, directed and non-coherent, but these characteristics were not relevant for our approximation.


Photoconversion cross section

Figure 1: Photoconversion cross sections calculated for various receptors. "-a/d" indicate activation and deactivation of a receptor.

To compute the fraction of the photon flux, which in fact triggers an event, we used the Absorption cross section or more precise the photoconversion cross section. This is a measure of the probability of such an event and is derived from [http://en.wikipedia.org/wiki/Beer-Lambert_law Beer-Lambert law].

σλ, the photoconversion cross section [m2 mol-1] at wavelength λ, is defined as

ETH photoinduction crosssection.png

where ε [m2 mol-1] is the molar extinction coefficient and Φ is the quantum yield, i.e. the fractions of “hits” causing an event.

Since for most of the receptors only absorption spectra and extinction coefficients at absorption peak wavelengths were available, we assumed the extinction coefficient at each wavelength is proportional to absorption. Furthermore we assumed the quantum yield would be independent of wavelength.


Reaction rate constants

The first order reaction rate constants [s-1] can be computed as integral over all wavelengths of the product of the photoconversion cross section σ times the photon flux Nλ; In our case approximated numerically.

ETH photoinduction rateconstant.png

Additionally our ODE model used dark decay rate constants to approximate the deactivation of receptors.


Validation of the model

The results of our method are consistent with the results of [Mancinelli, 1994] and of the 2010 ETH Zuerich Team’s model. In both cases we reached high accordance. The small difference can be explained by our approximation of the extinction coefficient.

Results & Discussion

Our primary target was to compute rate constants as input for our ODE models. Nevertheless we already gained immediate insights from these rate constants.

Reaction rate constants

Below the reaction rate constants for source-receptor-combinations. The values for activation and deactivation are of the same order of magnitude except for all sun/room and lov/ycgf combinations. This is due a fixed dark decay rate and no light induced deactivation of these receptors.

sunroombulb200W
konkoffkonkoffkonkoff
ycgf4.4e-0015.8e-0031.4e-0015.8e-0031.9e-0035.8e-003
lov2.1e-0015.8e-0036.9e-0025.8e-0036.1e-0045.8e-003
ccas6.6e-0016.2e-0012.2e-0012.0e-0014.8e-0038.9e-003
cph12.6e+0002.8e+0008.7e-0019.2e-0013.7e-0024.6e-002

Receptor activation

Expected steady state activation of receptors for intensities from 0 to 100 % of original source intensity. Read: 90 % of Ycgf is at steady state in active state at 10 % of sun's original irradiance.

We took a frist glimpse on the expected receptor activation by approximating the steady state solution for the ODE system.

ETH photoinduction activation.png

From this results we gained two insights. First, for ycgf and lov (for both of them light on activates) we had to assume that these receptors would be fully activated at low irradiation. "Low" refers to the fraction of original irradiance, e.g. actual sun light intensity or the irradiance caused by a certain light bulb. This was an indication, that we cannot use this receptors in real world applications.

Second, the receptors which are activated and deactivated by light - cph1 and ccas - didn't show different activation levels for different light settings, i.e. they cannot be used to distinguish between them.


Actual UV photon flux

Relative amount of natural sun irradiation. The number of photons (blue) is lowered compared to the power (yellow) at low wavelengths.

Since E.colipse is an UV protection system it is essential to know which receptors detect UV and which fraction of the activation is due to UV radiation. To glance at the emission and absorption spectra only can be misleading because normally emission spectra are given in units of J m-2 s-1 nm-1. However, photons of low wavelength contain higher energy (Ep = h*c/λ), which means the actual flux of low wavelength photons is lower than obvious at first view.

An example is depicted in the figure to the right: The yellow area is the energy flux according irradiance spectrum. In contrast, the blue area is the photon flux. One can see a "shift" to the higher wavelengths, because it needs more "red photons" to transport the same amount of energy as "UV photons". For the sun the fraction of UV photons is 40.49 % less than one would expect from the power spectrum.


Fraction of rate constant due to UV

Fraction of reaction rate constant due to UV radiation, e.g. 16 % of the k_on of lov is caused by photons with λ < 400 nm.

To get an idea of the relevance of UV radiation compared to visible light, we calculated the fraction of the reaction rate constants, which is due to photons with λ < 400 nm, i.e. the integral over all wavelengths up to 400 nm of the product photoconversion cross section times photon flux.

The results shows that the UV fractions for all light source and receptors combinations are always less or equal 15.6 % (for LovTAP). For Cph1 and Ccas, which are activated and deactivated by light, the difference between UV activation and deactivation is small (approx. 5 %).

We assumed these values would be in the order of magnitude of noise and therefore concluded, it would not be possible to measure the amount of UV radiation with a combination of several combined (UV and visible light) receptors.



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