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Background:
Ligands are little molecules (which could be proteins or chemicals or whatever)
which bind to a larger biomolecule (eg, a protein or DNA) called the receptor.
"Receptor/ligand" binding affinity refers to how strongly different ligands
want to attach to different receptors. Both binding (association) and
un-binding (dissociation) is happening all the time, so you get a (dynamic, or
possibly steady state) distribution of binding probability.
ref: https://en.wikipedia.org/wiki/Ligand_(biochemistry)
ODEs (ordinary differential equations) are those involving only a single
independent variable; eg, solving for x in terms of t, only having derivatives
dx/dt, (d^2 x / d x^2), etc. the order of the ODE is the highest order of
derivative.
PDEs (partial differential equations) are those involving multiple independent
variables, and thus partial derivatives. Eg, x in terms of t and r, having
derivatives del x / del t, del x / del r, and del^2 x / (del t * del r).
ref: https://en.wikipedia.org/wiki/Differential_equation#Ordinary_and_partial
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Law of mass action: rate of a reaction involving two quantities is proportional
to the product of the densities of both.
Michaelis-Menten: approximation to solution of enzyme-catalyzed reaction
equation:
d [S] / dt = (max reaction rate) * [S] / (Km + [S])
[S] is concentration of substrate S
Km is Michaelis constant, which is a specific substrate concentration
(max reaction rate) =~ k_2 [E]_total
Km =~ (k_-1 + k_2) / (k_1)
all assuming that enzyme E catalizes S into P with rates k_n:
-> k_1
[E] + [S] [ES] -> k_2 [E] + [P]
<- k_-1
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