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Osmosis dynamics

  • change in both [math]\displaystyle{ A(t) }[/math] (surface area) and [math]\displaystyle{ V^i(t) \rightarrow C^i_\Sigma(t) }[/math]
  • simplest case of concave cell (red blood cell)
    • [math]\displaystyle{ A(t)=A_o }[/math] (constant surface area)
    • not exponential solution. solve differential equation numerically
    • find that shrinking is faster than swelling
    • explained by fact that more water is needed to swell cell to twice volume as water lost to shrink to half volume
  • for spherical cell, dynamics look identical to constant surface area case
  • General conclusion: simple model of swelling agrees with equilirium and kinetic response of simple cells.
  • But there are cases where it doesn't fit

Water channels

  • family of aquaporins
  • first discovered by Agre (AQP1, 28kDa)
  • normal protein dyes don't stain this protein
  • 1D, 2D, 3D structures solved
  • positive charge in middle of this channel
  • on one side water's negative side points towards it. once passed the middle of channel, the water flips direction.