Team:KULeuven/Modeling/Key Antikey

= Key Lock Antikey: Modeling =

Simulation
The input/output behaviour of the key/lock system was investigated using simulations. In the following figures, time is measured in seconds and quantities in molecules.

In the figure below, the blue light input is represented in blue, the vanillin input in green and the amount of unlocked key in red.



Because of the nonlinear relationship between input and (anti)key (Michaelis-Menten), the steady state level of key depends on the level of both blue light sensor and vanillin sensor input and not just the difference between the two.



The most important conclusion is that for good functioning of the differentiator the transcription of both the key and the antikey are operated in the linear region (See figure Michaelis-Menten). It's therefore important that the inputs of this system remain in the same magnitude of the Km of the production of the (anti)key.

Also, the half life of the key and antikey have to be as short as possible, otherwise we subtract the integrated amounts of the signals and not the signals themselves. This should not pose any problem since the half life of non translational mRNA strands is merely 5 minutes, substantially faster than the system requires. This reasoning remains valid for all species in the cell, where the speed of the cell is limited by the slowest degrading species.