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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)


  • 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