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We chose to represent the bioreactor as an infinitely long cylinder. This allows us to consider the problem in two dimensions, yet should stay realistic (the bioreactor will normally be at least two-times longer than its radius, so this model should quite accurately represent what's happening in the middle). From literature (Strickland2008), we know that LovTAP saturates at 20 mW/cm² (note: lower intensities should still work, as saturation isn't necessary, we just want a significant proportion to be activated, but this should keep things easier to calculate).
The results are displayed in a picture at the bottom of the page. Everything that is dark red is fully saturated, but everything between red and green should be enough. The places where the picture is blue represents parts that aren't illuminated enough. However, as the activated LOV-domain has a half-life of 30-40s (and our protein's half-life should be quite close to this), and the bioreactor is operating as an orbital shaker (which results in chaotic movement, meaning every cell has a quasi-uniform probability of going anywhere in the bioreactor), the only thing that matters is that the coverage is high enough (note: "high enough" depends on several parameters, such as the shaker speed).
Parameters
The parameters we have used for the cell culture absorbance have been extracted from the measurements that can be found in this file: File:Team-EPF-Lausanne-cell-culture-absorbance-nanodrop.pdf.
Validation
We have solved a geometrically simple setup: just an onmidirectional light in the center and no reflexions. Then we could compare it to the analytical solution.
Please play with our tool! (If you're unsure about the settings, just click run to use sane defaults).
