lec06 notes

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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
+---------
+
+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
+