4.6. Biological applications of diffusion[[Student version, December 8, 2002]] 123
10 -610 -50.00010.0010.010.1110 -12 10 -11 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5
BD, cm^2 s-^1Ps, cm s-^1
Figure 4.13: (Experimental data with fit.) Log-log plot of the permeabilityPsof artificial bilayer membranes
(made of egg phosphatidylcholine) to various small molecules, ranging from urea (far left point) to hexanoic acid (far
right point). The horizontal axis gives the productBDof the diffusion constantDof each solute in oil (hexadecane)
times its partition coefficientBin oil versus water.Psis incm s−^1 ,Dincm^2 s−^1 ,andBis dimensionless. The solid
line has slope one, indicating a strict proportionalityPs∝BD.[Data from (Finkelstein, 1987).]
now we only note that this ratio is some measurable constant.
Wewill see in Chapter 8 that a bilayer membrane is essentially a layer of oil (sandwiched between
twolayers of head groups). Thus, a membrane separating two watery compartments with sugar
concentrationsc 1 andc 2 will itself have sugar concentrationBc 1 on one side andBc 2 on the other,
and hence a drop of ∆c=B(c 1 −c 2 )across the membrane. Adapting Your Turn 4e shows that
the resulting flux of sugar gives the membrane a permeabilityPs=BD/L.Thusevenifwedon’t
know the value ofL,wecan still assert that
The permeability of a pure bilayer membrane is roughlyBDtimes a constant
independent of the solute, whereBis the partition coefficient of solute andD
its diffusion constant in oil.(4.22)
The data in Figure 4.13 support this simple conclusion, over a remarkably wide range (six orders
of magnitude) ofBD.
Typical real values arePs≈ 10 −^3 μms−^1 for glucose diffusing across an artificial lipid bilayer
membrane, or three to five orders of magnitude less than this (that is, 0.001 to 0.000 01 times as
great) for charged ions like Cl−or Na+,respectively.
The bilayer membranes surrounding living cells have much larger values ofPsthan the ones
found above. We will see in Chapter 11 that indeed the transport of small molecules across cell
membranes is far more complicated than simple diffusion would suggest. Nevertheless, passive
diffusion is one important ingredient in the full membrane-transport picture.
4.6.2 Diffusion sets a fundamental limit on bacterial metabolism
Let’s idealize a single bacterium as a sphere of radiusR.Suppose that the bacterium is suspended
in a lake, and that it needs oxygen to survive (it’s ærobic). The oxygen is all around it, dissolved