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There is no known mechanism for exchange of $\ce{O2}$ and $\ce{CO2}$ in a one-for-one fashion. Their transport across the alveolar membrane takes place by diffusion alone: both of them attain their equilibria with blood independently. Note that it is not necessary for inhaled and exhaled tidal volumes to be the same. In fact, under physiologic conditions, ...


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No direct exchange, but there is interaction. I used these wikipedia articles: https://en.wikipedia.org/wiki/Hemoglobin https://en.wikipedia.org/wiki/Bohr_effect For Oxygen transport nearly all is transported bound to hemoglobin. Only one part in 71 is transported as soluble unbound oxygen. For carbon dioxide, only about 20-25% is transported by hemoglobin. ...


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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 ...


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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, ...


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