Transcript Diffusion and Osmosis - Washington State University

Diffusion and Osmosis
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
Bolzmann’s 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.
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.
What a random movement looks like
N=18,050 steps – the particle
has moved a distance made
good of 196 step lengths
Fick’s 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.
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.
Permeation through membranes
• If a barrier to free diffusion is inserted into
the system (such as a cell’s plasma
membrane), a permeability coefficient
replaces the term for the diffusion
coefficient.
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).
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 t’Hoff
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
t’Hoff eq. to correct for non-ideal behavior of the solute.
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.
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)
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?
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.
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.
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-).
What if the Na+/K+ pump stops working?