# 6.021/Notes/2006-09-27

## Chemical Transport

• Glucose as example
• Transport appears faster than expected from diffusion (Transport is facilitated)
• About $\displaystyle{ 10^5 }$ 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
• $\displaystyle{ R\ \overrightarrow{\leftarrow}\ P }$ with a forward rate constant of $\displaystyle{ \alpha }$ and reverse rate constant of $\displaystyle{ \beta }$
• At equilibrium, the relatve concentrations of product P to reactant R will be the association constant $\displaystyle{ K_a = \frac{\alpha}{\beta} }$
• the kinetics are exponential with a time constant $\displaystyle{ \tau = \frac{1}{\alpha+\beta} }$
• binding reaction
• $\displaystyle{ S+E\ \overrightarrow{\leftarrow}\ ES }$
• law of mass action, rate depends on product of concentrations
• Will usually use dissociation constant $\displaystyle{ K=\frac{1}{K_a} }$ (units concentration)
• total enzyme $\displaystyle{ C_{ET}=C_E+C_{ES} }$ is constant
• Michaelis-Menten (hyperbolic) kinetics of form $\displaystyle{ y=\frac{a}{a+x} }$
• when drawn on doubly reciprocal coordinates, get straight line