Click for printer friendely version of this HowTo Assuming Pseudo-Steady-State Also known as Quasi-Steady-State, this assumption allows you to model a small portion of an extremely complex system. Simply put, without this assumption many models would not exist and it allows us to work with a system that has both fast and slow reactions. If you are interested in the portion of the model that contains the slow, or rate limiting reactions, you can (sometimes) assume that the fast reactions are in a state of dynamic equilibrium, and the their derivatives are equal to zero, compared to the slow reactions. If you are interested in the portion of the model that has fast reactions, you can assme that the the slow portion does not change significantly (and thus, it's deriviatve is zero) when compared to the fast. Focus On Slow Reactionsno_title Example 2.7.1.1   Example 2.7.1.2 (Focus On Slow Reactions)   For me, in the drug binding business, the channel switches from closed to open and then it can be bound. The binding reaction is slow and the channel transitions are fast. so C <===> O <===> B Now $dO/dt = k_1 C + k_4 B - (k_2 + k_3) O$ (1,2 are forward and revers for C-O and 3,4 and forward and reverse for O-B. $dB/dt = k_3 O - k_4B$ $dC/dt = k_2O - k_1C$ but this is fast compared with the others so lets assume that it is always in equilibrium: $O = k_1/k_2 C$ and then using $1 = C + O + B$, you know that $1 = k_2/k_1 O + O + B or O = (1 - B)/( 1 + k_2/k_1)$ and now you can sumstitute into the dB/dt equation for O and solve for B in terms of everything else. $\vert\boldsymbol{\vert}$ Focus On Fast Reactionsno_title Example 2.7.1.3   Example 2.7.1.4 (Focus On Fast Reactions)   If we were interested in some intracellular process that required external stimulation, we can often assume that the internal processes are much faster than the externeral ones due to the fact that the concentrations of the various players in the reactions are much higher internally. $\vert\boldsymbol{\vert}$ Click for printer friendely version of this HowTo

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