Diffusion and Osmosis

1
Diffusion and Osmosis
2
Diffusion defined

• Migration of atoms, ions, molecules or even small
  particles through random motion due to thermal
  energy
• A particle at any absolute temperature T has an
  average kinetic energy of 3kT/2, where k is
  Bolzmanns Constant. The value of kT at 300oK is
  4.14X10-14 g/cm2/sec2. Particle size is not a
  factor in this calculation.
• Therefore, the mean velocity of a diffusing
  particle depends on its mass, so that particles
  of different masses have different diffusion
  coefficients.

3
Diffusing particles undergo random walks

• Because of collisions with other particles, a
  diffusing particle changes direction on a
  picosecond time scale. Therefore, individual
  particles move about randomly and tend to return
  to the same spots.
• However, if there is a concentration gradient,
  the average number of particles moving down the
  gradient at any instant will be greater than the
  number moving up the gradient there will be a
  net flux (Jnet) of particles from the higher
  concentration toward the lower concentration.
  Therefore, it helps to think of the concentration
  gradient as a force that drives particle
  movement, even though from the point of view of
  an individual particle, all movements are random.

4
What a random movement looks like
N18,050 steps the particle has moved a
distance made good of 196 step lengths
5
Ficks Law of Diffusion

• The net flux of a solute S in one dimension x is
  described by the Fick Eq.as the product of the
  concentration gradient (dCs) and the diffusion
  coefficient for that solute (Ds).
• Jnet -Ds(dCs/dx)
• The units of J are moles/cm2sec and of the
  concentration gradient, moles/cm3/cm.
• If diffusion is occurring in a 3-dimensional
  setting, a cross-sectional area term must be
  inserted into the equation.

6
Net movement by diffusion is rapid over short
distances, slow over long distances

• Einstein solved the Fick Eq. to show that, on the
  average, in a interval of time t, an average
  diffusing particle will travel a distance of
  (2Dst)1/2 away from its starting point. (For the
  model particle in slide 4, this solution would
  have predicted a distance made good of 190
  steplengths)
• So, the distance gained by diffusional motion
  increases as the square root of time, rather than
  as a direct proportion to time as in linear
  motion.
• For a particle with Ds 2X10-5 cm2/sec,
  instantaneous velocity will average about
  566m/sec,
• but speed made good will be much slower this
  particle will travel a distance of 1 micron in
  about 250 microsec, 10 microns in 25 msec, 100
  microns in 2.5 sec, and a meter in about a month.

7
Permeation through membranes

• If a barrier to free diffusion is inserted into
  the system (such as a cells plasma membrane), a
  permeability coefficient replaces the term for
  the diffusion coefficient.

8
How does diffusion physics relate to physiology?

• Delivery and removal of substances by diffusion
  sets an upper limit on cell diameter of about 100
  microns.
• Since surface area is a term in the 3D Fick
  equation, structures that must maximize
  diffusional flux tend to show expanded surface
  area and attenuated linear dimensions. (Think of
  the anatomy of the lung or the surface of the
  intestine).

9
Osmotic flow

• In osmosis, water diffuses along a gradient of
  water concentration that is the result of
  dilution of water by the presence of solvents
  i.e. the higher the solvent concentration, the
  lower the water concentration
• The potential energy for water movement
  represented by a solute concentration gradient is
  given by the van tHoff Equation
• Posm MRT
• Where the units of Posm are atmospheres, M is the
  osmolality of the solution, R is the gas
  constant, and T is the absolute temperature.
  Generally, a correction has to be added to the
  van tHoff eq. to correct for non-ideal behavior
  of the solute.

10
Colligative properties of solutions

• Osmotic pressure
• Freezing point
• Vapor pressure or boiling point
• Colligative means tied together.The higher the
  solute concentration, the higher the osmotic
  pressure, the lower the freezing point and the
  higher the boiling point, compared to pure water.

11
Two kinds of water potential energy

• Osmotic force a form of chemical potential
  energy
• Hydrostatic force a form of mechanical potential
  energy
• These forces are interconvertible, so the net
  driving force for water between a cell and the
  extracellular solution is
• RT (Osmcell - Osmext) (Pcell Pext)

12
Osmotic swelling is an unavoidable problem for
all cells

• The swelling arises from the presence of
  negatively-charged proteins trapped in the
  cytoplasm
• First, imagine that a water-permeable membrane
  separates two rigid compartments.
• One compartment has a 150 mmolal concentration
  of NaCl.
• The other one has 150 mEq/liter of Na and an
  equal quantity of anionic charge as protein
  however, the protein concentration is only 1
  mmolal.
• Is there an osmotic gradient?
• Is there a solute gradient?

13
Initial conditions
Intermediate conditions Cl- diffused down its
gradient why did Na move against its gradient?
Notice that there is now a gradient of electrical
charge this is a Donnan potential.
Now imagine water trying to move osmotically is
there a gradient of hydrostatic pressure? The
system has come into Gibbs-Donnan equilibrium
all forces are balanced.
14
Animal cells could never attain Gibbs-Donnan
Equilibrium

• Why not? The plasma membrane cannot sustain a
  hydrostatic pressure gradient.
• Without the evolution of some means of avoiding
  Gibbs-Donnan equilibrium, there would be no
  protein-containing cells.

15
The Na/K Pump counteracts G-D equilibration
The Na/K pump undergoes cycles in which it
spends an ATP to eject 3 Na from the cell and at
the same time to take 2 K into the cell. On the
average, this counteracts leakage of Na and K
across the membrane down their electrochemical
gradients. The bottom-line effect of this is to
make the cell effectively impermeable to NaCl.
Gibbs-Donnan equilibrium is not approached and
the cell does not swell, in spite of the presence
of protein anion (X-).
16
What if the Na/K pump stops working?