Medical Studies > QUESTIONS & ANSWERS > University of MichiganBIOMEDE 418BIOMEDE 418 HW 2 Key WITH SOLUTIONS (All)

University of MichiganBIOMEDE 418BIOMEDE 418 HW 2 Key WITH SOLUTIONS

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1. OR-gate logic. Analyze the C1-FFL with OR-logic at the Z promoter. Are there delays following ON or OFF steps of Sx? What could be the biological use of such a design? Solution: After an ON step... of Sx, X becomes active X*. On a rapid timescale it binds the Z promoter. Since Z is regulated by OR-gate logic, X* alone can activate transcription without need of Y. Therefore there are no delays following an ON step of Sx. After an OFF step of Sx, X* rapidly becomes inactive X. However, protein Y is still present in the cell, and if Sy is present, Y is active Y*. Since the Z input function is an OR gate, Y* can continue to activate transcription of Z even in the absence of X*. Therefore, Z production persists, until Y degrades/dilutes below its activation threshold for Z. The dynamics of Y are given by dY / dt= -αY, (there is no production term because X is inactive following removal of Sx) so that Y=Ym exp(-α t), where Ym is the level of Y at time t=0. The OFF delay is given by the time it takes Y to reach its activation threshold for Z, Ky: solving for this time Y(Tof)= Ym exp(-α Tof)=Ky, yields Tof= 1/ α log (Ym/Ky) In summary, the OR-gate C1-FFL shows sign-sensitive delays. It has a delay following OFF but not ON steps of Sx. The delay depends on the presence of Sy. This behavior is opposite to that of the C1-FFL with an AND gate, which shows delay upon ON but not OFF steps. The OR-gate C1-FFL could be useful in systems which need to be protected from sudden loss of activity of their master regulator X. The OR-gate FFL can provide continued production during brief fluctuations in which X activity is lost. This protection works for OFF pulses shorter than Tof. Note that Tof can be tuned by evolutionary selection by adjusting the biochemical parameters of protein Y such as its expression level Ym and its activation threshold Ky [Show More]

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