## Question

###### Consider two genes controlled by X. Their production rate is g1 = Î² 1X/(K 1 + X) and g2 = Î² 2X/(K 2 + X). The questionis consider the same two genes controlled by X with an FM strategy.Here X is either at level 0 or level X high. The fraction of timethat X is high is proportional to the signal s. Show thatproduction of each gene is proportional to signal, but the ratio g1/g 2 is constant as a function of signal.Hint: Consider what would happen at the limits; when X= 0 andX>>>Ki . Give

Consider two genes controlled by X. Their production rate is g 1 = Î² 1X/(K 1 + X) and g 2 = Î² 2X/(K 2 + X). The question is consider the same two genes controlled by X with an FM strategy. Here X is either at level 0 or level X high. The fraction of time that X is high is proportional to the signal s. Show that production of each gene is proportional to signal, but the ratio g 1/g 2 is constant as a function of signal. Hint: Consider what would happen at the limits; when X= 0 and X>>>Ki . Give also a mathematical explanation.

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