Lecture 5 Notes
Ion Leaks and the Permeability Barrier - The Third Postulate
Notwithstanding the low diffusive permeability of the inner membrane,
cation and proton leaks occur at significant rates, and they are
physiologically important. Inward K+ leak causes matrix swelling,
and inward proton leak contributes to the basal metabolic rate.
Moreover, nature has engineered the uncoupling proteins to increase
proton leak under certain physiological circumstances.
1) Ion Leaks in Mitochondria (Read Garlid, Beavis and Ratkje
(1989) “On the nature of ion leaks in energy-transducing membranes”
Biochim Biophys Acta 976. 109-120
Diffusive transport of ions obeys the same laws that govern transport
of nonelectrolytes across thin membranes. The rate is
proportional to the concentration difference, and the proportionality
constant (the permeability coefficient) is a function of the energy
barrier that must be crossed during transport.
The ionic charge adds a new complexity that derives
from the long-range effects of the electric field on the local free
energy of the diffusing ions. An ion diffusing across the inner
membrane of mitochondria must cross an energy barrier whose maximum is
located at the center of the membrane, and only those ions having
sufficient energy to reach this peak will cross to the energy well on
the opposite side. Net flux will therefore be proportional to the
differential probability of getting to this peak from either
side. This probability is given by the Boltzmann function,
exp(–Δp/RT), where Δp ≡ p – aq is the Gibbs energy of the
ion at the peak (p) relative to its value in the aqueous energy well at
the surface of the membrane (aq). These considerations lead to
the following expression for diffusive flux of cations across thin
biomembranes:
J =
f P (C1 eu/2 – C2 e–u/2 )
(1)
where u is the reduced voltage (zFΔψ/RT), C1 and C2 are bulk aqueous
concentrations, f is the surface partition coefficient (energy
well/bulk), and P is the permeability constant, given by
P
≡ k e–Δµpo/RT
(2)
where e–Δµpo/RT is the partition coefficient of the ion at the
peak of the barrier (see Fig. 1 of paper).
The factor ½ in the exponents of Eq. 1 arises from the fact that
the maximum energy barrier is found at the midpoint of the membrane.
The second term in Eq. 1 represents back-flux of cations from the
matrix and
becomes negligible at the high values of Δψ maintained by mitochondria
under physiological conditions. Thus, Eq. 1 reduces to a simple
exponential function of Δψ:
J
= f P C1 eu/2
(3)
Equation 3 emphasizes the point that ion flux at high potentials is not
affected by the concentration gradient across the membrane.
(Note that Eq. 3 can also be written as
J =
Jo eu/2
(4)
where Jo is the flux at zero voltage and equals f P C1 .
We have carried out experiments to evaluate Eq. 3 by
measuring the flux of tetraethylammonium (TEA+) cation (Fig. 4 of
paper) and protons (H+) (attached figure). The data for TEA+ and
H+ were normalized to their respective Jo values (J/Jo plot), and it
can be seen that the ions behave identically with respect to the
voltage-dependence of their diffusion across the inner membrane.
2) Other aspects of ion transport
Here are some further points you should understand, using the paper:
a) You might try deriving Eq 1, beginning with the Boltzmann
Equation. Good experience with manipulating exponentials.
b) Derive (and know) Fick’s law from Eq 1.
c) Following the paper, derive (and know) the phenomenological
Flux-force relationship (Eq. 10 in paper).
d) Read and understand the paper generally, especially section IVC.2.