Page 33 - Color Atlas Physiology

dC
–1
Passive Transport by Means of J diff ! A ! D ! ! " [mol ! s ] [1.2]
dx
Diffusion
where C is the molar concentration and x is the
Diffusion is movement of a substance owing to distance traveled during diffusion. Since the
the random thermal motion (brownian move- driving “force”—i.e., the concentration gradient
ment) of its molecules or ions (! A1) in all (dC/dx)—decreases with distance, as was ex-
directions throughout a solvent. Net diffusion plained above, the time required for diffusion
or selective transport can occur only when the increases exponentially with the distance
Fundamentals and Cell Physiology concentration gradient—i.e., at equilibrium— if the above-water partial pressure of free O 2
traveled (t # x ). If, for example, a molecule
solute concentration at the starting point is
2
travels the first µm in 0.5 ms, it will require 5 s
higher than at the target site. (Note: uni-
directional fluxes also occur in absence of a
to travel 100 µm and a whopping 14 h for 1 cm.
Returning to the previous example (! A2),
but net diffusion is zero because there is equal
diffusion (! A2) is kept constant, the Po 2 in the
flux in both directions.) The driving force of
water and overlying gas layer will eventually
diffusion is, therefore, a concentration gra-
dient. Hence, diffusion equalizes concentra-
equalize and net diffusion will cease (diffusion
tion differences and requires a driving force:
equilibrium). This process takes place within
the body, for example, when O 2 diffuses from
passive transport (= downhill transport).
Example: When a layer of O 2 gas is placed
and when CO 2 diffuses in the opposite direc-
on water, the O 2 quickly diffuses into the water
along the initially high gas pressure gradient
tion (! p. 120).
Let us imagine two spaces, a and b (! B1)
(! A2). As a result, the partial pressure of O 2 the alveoli of the lungs into the bloodstream
1
(Po 2) rises, and O 2 can diffuse further containing different concentrations (C a " C b)
downward into the next O 2-poor layer of water of an uncharged solute. The membrane sepa-
(! A1). (Note: with gases, partial pressure is rating the solutions has pores ∆x in length and
used in lieu of concentration.) However, the with total cross-sectional area of A. Since the
steepness of the Po 2 profile or gradient (dPo 2/ pores are permeable to the molecules of the
dx) decreases (exponentially) in each sub- dissolved substance, the molecules will diffuse
sequent layer situated at distance x from the from a to b, with C –C = ∆C representing the
a
b
O 2 source (! A3). Therefore, diffusion is only concentration gradient. If we consider only the
feasible for transport across short distances spaces a and b (while ignoring the gradients
within the body. Diffusion in liquids is slower dC/dx in the pore, as shown in B2, for the sake
than in gases. of simplicity), Fick’s first law of diffusion
–1
The diffusion rate, J diff (mol·s ), is the (Eq. 1.2) can be modified as follows:
amount of substance that diffuses per unit of ∆C
–1
time. It is proportional to the area available for J diff ! A ! D ! ∆x [mol ! s ]. [1.3]
diffusion (A) and the absolute temperature (T)
and is inversely proportional to the viscosity In other words, the rate of diffusion increases
(η) of the solvent and the radius (r) of the dif- as A, D, and ∆C increase, and decreases as the
fused particles. thickness of the membrane (∆x) decreases.
According to the Stokes–Einstein equation, When diffusion occurs through the lipid
the coefficient of diffusion (D) is derived from T, membrane of a cell, one must consider that hy-
η, and r as drophilic substances in the membrane are
sparingly soluble (compare intramembrane
R ! T
2
–1
D ! [m ! s ], [1.1] gradient in C1 to C2) and, accordingly, have a
N A · 6π ! r ! η
hard time penetrating the membrane by
where R is the general gas constant means of “simple” diffusion. The oil-and-water
–1
(8.3144 J·K –1 · mol ) and N A Avogadro’s con- partition coefficient (k) is a measure of the lipid
23
–1
stant (6.022 · 10 mol ). In Fick’s first law of solubility of a substance (! C).
diffusion (Adolf Fick, 1855), the diffusion rate
20
is expressed as
!
Despopoulos, Color Atlas of Physiology © 2003 Thieme
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