6.021/Notes/2006-09-27

Chemical Transport

 * Glucose as example
 * Transport appears faster than expected from diffusion (Transport is facilitated)
 * About $$10^5$$ speedup
 * Structure specific
 * similar sugars transported very differently
 * Transport saturates
 * Can be inhibited by other solutes (not independent)
 * Drugs can completely block transport
 * hormonal control, highly regulated (e.g. insulin)

Model

 * Transport by membrane protein
 * binds solute, flips, releases solute on other side
 * protein can flip with or without solute
 * cannot treat individual solute molecules independently as they are competing for the protein
 * flipping is treated as simple first order reversible reaction
 * $$R\ \overrightarrow{\leftarrow}\ P$$ with a forward rate constant of $$\alpha$$ and reverse rate constant of $$\beta$$
 * At equilibrium, the relatve concentrations of product P to reactant R will be the association constant $$K_a = \frac{\alpha}{\beta}$$
 * the kinetics are exponential with a time constant $$\tau = \frac{1}{\alpha+\beta}$$
 * binding reaction
 * $$S+E\ \overrightarrow{\leftarrow}\ ES$$
 * law of mass action, rate depends on product of concentrations
 * Will usually use dissociation constant $$K=\frac{1}{K_a}$$ (units concentration)
 * total enzyme $$C_{ET}=C_E+C_{ES}$$ is constant
 * Michaelis-Menten (hyperbolic) kinetics of form $$y=\frac{a}{a+x}$$
 * when drawn on doubly reciprocal coordinates, get straight line