6.021/Notes/2006-09-27

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Chemical Transport

  • Glucose as example
  • Transport appears faster than expected from diffusion (Transport is facilitated)
    • About 105 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 α and reverse rate constant of β
    • 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 CET = CE + CES is constant
    • Michaelis-Menten (hyperbolic) kinetics of form y=\frac{a}{a+x}
    • when drawn on doubly reciprocal coordinates, get straight line
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