3

Gene expression can be very well described by Hill functions, i.e.: $$c_Y(c_X) = \frac{c_X^n}{1+c_X^n}$$ when $X$ activates $Y$ and $$c_Y(c_X) = \frac{1}{1+c_X^n}$$ when $X$ represses $Y$ (omitting units and all sorts of constants for simplicity). For the common case that $n>1$, these functions look like this: As you can see, they are far from linear, ...


1

Just to expand on @Wrzlprmft's great answer with a concrete example: Sticking to your simple gene circuit with $X$, $Y$, and $Z$, now consider the possibility that $Y$ also activates its own expression via a positive feedback loop: $X \to \underset{\circlearrowright}Y \to Z$ Here activation of $Y$ will be only minimally dependent on $X$. Once $Y$ is ...


Only top voted, non community-wiki answers of a minimum length are eligible