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Where we left off

Where we left off. Consider a typical small biological molecule Approximate time to achieve a certain displacement (x) is given by. To cross 1 micron, ~0.5 milliseconds To cross 1 cm, ~14 hours What about us? What about for oxygen to get from our lungs to a finger (~1 m)?

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Where we left off

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  1. Where we left off • Consider a typical small biological molecule • Approximate time to achieve a certain displacement (x) is given by

  2. To cross 1 micron, ~0.5 milliseconds • To cross 1 cm, ~14 hours • What about us? • What about for oxygen to get from our lungs to a finger (~1 m)? • D for O2 in water at 40 C is ~3x10-5 • This is neglecting any additional hindrance due to having to cross cell membranes, etc.

  3. Conclusion? • Bacteria don’t need circulatory systems! • Diffusion is sufficiently rapid to transport molecules throughout the cell • But we do! • Diffusion is far too slow to transport molecules throughout the body • Diffusion limitation is one reason for the cellular nature of life

  4. Diffusion Step Size and Step Rate • Knowing and , we can solve for delta and tau • For comparison, the diameter of a hydrogen atom is 1 angstrom • or 2 picoseconds per step

  5. Sample 2D Random Walks

  6. Random Walks • An individual particle • does not explore space uniformly • has no memory of where it has been • is more likely to explore near where it is than to go far away into a new area, however • if in a new area, it is more likely to stay near there than to wander far away again

  7. Fick’s First Law • Fick’s first law regards the flux of a substance due to diffusion • Consider our simple discrete model (on the board) • Moving across to the right • Moving across to the left • Net Rightward:

  8. Fick’s First Law • What do we need to turn a net number of particles moving into a flux? • Normalize by area (A) and time (tau) • Want to relate to diffusion coefficient • Mult by , rearrange

  9. Fick’s First Law • Flux due to diffusion is proportional to the concentration gradient

  10. Fick’s Second Law • Follows from the first, assuming particles are conserved • Consider a box between x and x+delta, each face of the box has area A • Flux in from the left is Jx(x) and flux out at the right is Jx(x+delta), volume of the box is A*delta

  11. Fick’s Second Law • Concentration change is • proportional to change in flux • proportional to the second derivative of the spatial concentration profile • Diffusion coefficient is the constant of proportionality

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