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Pulse of activation: Consider a cascade of three activators, X -> Y -> Z.Protein X is...

Pulse of activation:

Consider a cascade of three activators, X -> Y -> Z.Protein X is initially present in the cell in its inactive form. The input signal of X, Sx, appears at time t=0. As a result, X rapidly becomes active and binds the promoter of gene Y, so that protein Y starts to be produced at rate β. When Y levels exceed a threshold Ky, gene Z begins to be transcribed. The input signal Sx appears at time t=0 for a pulse of duration D, and then vanishes. (a) What is the concentration Y(t)? (b) What is the minimal pulse duration needed for activation of gene Z? Plot the maximal level reached by the gene product Z as a function of the pulse duration D

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