6.021/Notes/2006-09-27

Chemical Transport

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