After equilibration of the external solution with the free space, the electrochemical potential differ-
ences of cations and anions in the free space (FS) and external solution (sol) is zero. Hence, from Eq. (2):
0 2.3RTloga
aj
jsF
oS
lzjF(
FSsol)The Donnan potential (ED) is the electrical potential difference (EDFSsol), and:
ED
2.3
zR
jT
loga
aj
jFso
Sl
(3)The Donnan potential in cell walls is negative. Equation (3) then shows that cations (z, positive) will ac-
cumulate in the negatively charged cell walls (Donnan phase) and that the anion concentration in the lat-
ter phase will be lower than in the (adjacent) aqueous phase. Donnan potentials from 7 to 289 mV
have been calculated for various cell wall–solution systems [5]. The Donnan potential changes with the
dissociation of the charged sites: it decreases with salt concentration and increases with the dissociation
constants of the various cations.
IV. ELECTRICAL POTENTIALS AT PLANT CELL MEMBRANES
A. Proton Gradients: Uniport and Cotransport
Metabolic solute transport in plant cells is usually energized by an electrochemical potential gradient of
protons (H) across the membranes and is facilitated by channels and carriers. The proton electro-
chemical potential difference is formed by active 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 catalyze the transformation of chemical energy in adenosine-5 -triphosphate (ATP) and py-
rophosphate (PPi), to an electrochemical proton gradient.
Metabolic transport in plant cells that is driven by the electrochemical proton gradient is termed uni-
port[7] (also see Sec. V.A) or cotransport[7] (also see Sec. V.B.3). Uniport is passive and it occurs via
channels in the direction of the electrical potential gradient of the solute. Cotransport of solutes is active
and derives its energy from concomitant passive transport of another ion. In plants the cotransported ion
is, in most instances, a proton.
B. The Membrane Potential
The membrane potential (EM) is the electrical potential difference across a membrane: it consists of a dif-
fusion potential and a potential difference resulting from the action of electrogenic pumps. Diffusion po-
tentials result from different diffusion velocities of anions and cations across a membrane. Membrane po-
tentials of plant cells are measured with reference to the cytoplasm (EMio), where inside (i) is
always the cytoplasm and outside (o) is the free space (with reference to the plasma membrane) and the
vacuole (with reference to the tonoplast). These conventions will be maintained throughout this chapter.
Accordingly, under physiological conditions, the membrane potential is negative at both membranes
(positive charges in the free space as well as the vacuole). An increase in the electrical potential differ-
ence, or hyperpolarization, is synonymous with a decrease of EM(to more negative values), and depolar-
ization is synonymous with an increase of EM.
C. The Diffusion Potential
The unidirectional flux (J) of a solute jacross a membrane depends on the driving force (j) and the
membrane permeability (Pj) of the solute: JPjj(mol sec^1 m^2 ). Thus, if a salt with different an-
ion and cation permeabilities diffuses across the membrane, an excess charge of the more permeable ion
is transported and a diffusion potential (EDM) results. This potential will then retard the diffusion of the
more permeable ion. A small anion-cation concentration difference creates a rather large diffusion po-
tential (see Sec. VI); therefore, practically equivalent amounts of ions of both kinds will pass through the
membrane.
MINERAL NUTRIENT TRANSPORT IN PLANTS 339