Homework 2.2: Autoregulation in a C1-FFL (55 pts)¶

This problem is based off of problem 4.3 from the first edition of Alon’s book.

The type 1 coherent feedforward loop (C1-FFL) is a motif that is found in large numbers in naturally occurring networks. In the figure below, we show two C1-FFL networks in which the regulator Y is autoregulated. In the C1-FFL with AND logic, Y shows autorepression, and in the C1-FFL with OR logic, it shows autoactivation. These “decorations” on C1-FFLs often occur in nature.

Decorated C1-FFL

a) As we learned in lecture, the C1-FFL with AND logic shows sign-sensitive delay. Specifically, if X is suddenly turned on, the response of Z is delayed, but if X is suddenly turned off, the response of Z is instantaneous. Analyze the left circuit in the above figure, and compare its dynamics to the canonical C1-FFL circuit with AND logic. Specifically address how the delay time changes. Assume that the regulation of Y follows AND logic.

b) The C1-FFL with OR logic also shows sign-sensitive delay. With OR logic, though, there is no delay when X is suddenly turned on, but rather delay when X is suddenly turned off. Analyze the right circuit in the above figure and compare its dynamics to the canonical C1-FFL circuit with OR logic. Again, address how the delay time changes, this time assuming that the regulation of Y follows OR logic.