Handbook of Plant and Crop Physiology

rived from Eq. (2). On assuming equilibrium, namely 
j
0, and substituting EMfor (io), Eq.
(2) becomes

0 
2.3RTloga

a

j

o

ij

zjFEM

or:

log

a

a

jo

ij
2.

z

3

jF

RT

EM (8)

at 30°C, F/2.3RT
1/60 (mV) and

log

a

a

jo

i

j




6

z

0

j

EM

This is one form of the Nernst equation [2]; it gives the relation between the membrane potential and the
expected ion accumulation ratio at equilibrium. Another form of this equation gives the Nernst potential
(EN) at 30°C:

EN


6

z

0

j

log

a

a

jo

ij (9)

This is the membrane potential needed to sustain equilibrium at a certain ion accumulation ratio. Thus at
120 mV, ao/aiwould be 10^2 for K, 10^4 for Ca^2 , and 10^2 for Cl.
The Nernst equation can be employed to determine whether specific ions have been transported pas-
sively. Such an analysis must be performed for tissues in the steady state, namely when net transport has
ceased (Jin
Jout). For this analysis, the membrane potential and the concentration ratio of the ion at the
steady state must be known. Active transport is assumed when the measured EMdiffers from the expected
EN.
Whether transport is active can also be determined for the non–steady state, but the flux ratio must
be known. Using [3] and Theorell [11] have shown that the ratio of passive fluxes (Jin/Jout) of a solute is
proportional to the electrochemical potential difference. The Ussing-Theorell equation is



2.3RTlog

J

J

o

i

u

n

t (10)

Substituting Eq. (2) for 
jandEMfor (io) in Eq. (2) gives

2.3RTlog

a

a

o

i

zFEM
2.3RTlog

J

J

o

i

u

n

t

Dividing by 2.3RTand writing the equation for 30°C results in

log

J

J

o

i

u

n

t
loga

a

o

i



60

z

EM

 (11)

If a flux ratio is larger than expected from this relation, transport is assumed to be active.

V. TRANSPORT PROTEINS

Ion transport across the membranes of plant cells is usually energized by an electrochemical potential gra-
dient of protons (
H) and is facilitated by channels and carriers. The proton electrochemical potential
gradient is formed by primary active [7] proton transport from the cytoplasm to the free space and to the
vacuoles. This proton transport is catalyzed by membrane-embedded electrogenic proton pumps that cat-
alyze the transformation of chemical energy in ATP and PPi to an electrochemical proton gradient.
Ion transport in plant cells that is driven by the electrochemical proton gradient is termed uniport or
cotransport [7] (also see Secs. V.A and V.B.3). Uniport is passive and it occurs via channels in the direc-
tion of the electrical potential gradient of the solute. Cotransport of solutes is secondary active [12] and
derives its energy from concomitant passive transport of another ion. In plants the cotransported ion is, in
most instances, a proton.

MINERAL NUTRIENT TRANSPORT IN PLANTS 341