Handbook of Plant and Crop Physiology

The diffusion potential depends on the relative permeabilities of all the cations and anions in the sys-
tem. Equation (4), the Goldman-Hodgkin-Katz equation [8,9], calculates the diffusion potential for Na,
K, and Cl. These are often the quantitatively most important ions in biological systems, and they de-
termine the diffusion potential:

EDM
2.3

R

F

T

log (4)

wherePK,PNa, and PClare the membrane permeabilities of K, Na, and Cl, respectively, and brack-
ets [ ] designate concentration (mol m^3 ). The diffusion potential across a membrane is the membrane po-
tential that can be measured when metabolic transport is inhibited.
Let us calculate the diffusion potential across the plasma membrane for the following situation:
[ KCl]o
10 mM, [ NaCl]o
10 mM, [K]i
100 mM, [ Na]i
10 mM, and [Cl]i
110 mM; the
relative permeabilities of K, Na, and Clare 1, 0.2, and 0.01, respectively. The temperature is 30°C
(303 K) and 2.3RT/F
60 mV. Then:

EDM
60 log 
53.5 mV

D. Proton Motive Force

A proton gradient across a membrane consists of an electrical component and a chemical proton concen-
tration gradient, the pH difference across the membrane. The relations of these two components can be
defined by replacing jin Eq. (2) with Handajwith [ H]:


H
2.3RTlog

[

[

H

H





]

]

o

i

zF(io) (5)

or when (io) is replaced by EM, log [H]i/[H]obypH(io)(orpHoi), and 1 is substituted for
z(the charge of protons):


H
FEM2.3RTpH(oi)(J mol^1 ) (6)

The electrochemical proton gradient can be expressed in electrical units (V) instead of energy units (J
mol^1 ) by division of Eq. (6) with F;
H/ F is then the proton motive force (pmf) [2,10] defined as
follows:

pmf
EM

2.3

F

RT

pH(oi) (7)

When the values for RandF(R
8.3 J mol^1 K^1 ,F
96.49 J mol^1 mV^1 ) are substituted and the
protonmotive force is calculated at 30°C (T
303 K), Eq. (7) becomes

pmf
EM 60 pH (mV)

Thus, when EM
120 mV, pHi
7, and pHo
6, a pmf of 180 mV is obtained.

E. Differentiation of Active and Passive Transport

Nonelectrolytes, such as sugars, are actively transported whenever they are accumulated in the cell to
a higher concentration than outside. For nonelectrolytes, the electrical component of the electrochemi-
cal potential [Eq. (2)] nullifies and the equation becomes a function of the concentration ratio only. The
electrical component of Eq. (2) is important for ions; they can passively accumulate in response to an
electrical potential difference. Suitable transport proteins (channels) may facilitate such passive accu-
mulation. Cations may passively accumulate in the negatively charged cytoplasm and anions in the pos-
itively charged vacuole. Passive ion accumulation is metabolic because energy metabolism is needed to
maintain the necessary membrane potential. The possible passive accumulation ratio of ion j(aij/ajo) de-
pends on the ionic charge of the accumulated ion and on the membrane potential. This ratio can be de-

10 (0.2 10)(0.01 110)



100 (0.2 10)(0.01 20)

PK[K]oPNa[Na]oPCl[Cl]i



PK[K]iPNa[Na]iPCl[Cl]o

340 JACOBY AND MORAN