Fluctuations of the proton-electromotive force across the inner mitochondrial membrane
Joaquim Procopio
Instituto de Cie ˆncias Biome ´dicas, Universidade de Sa ˜ o Paulo, Caixa Postal 66208, 05508-970, Sa ˜ o Paulo, SP, Brazil
Jose
´
A. Forne
´
s
*
Instituto de Fı ´sica, Universidade Federal de Goia ´s, Caixa Postal 131, 74001-970, Goia ˆnia, GO, Brazil
Received 17 October 1996
The intermembrane mitochondrial space IMMS is delimited by the inner and outer mitochondrial mem-
branes and defines a region of molecular dimension where fluctuations of the number of free protons and of
transmembrane voltage can give rise to fluctuations in the proton-electromotive force E
PMF
across the inner
mitochondrial membrane IMM. We have applied the fluctuation-dissipation theorem to an electrical equiva-
lent circuit consisting of a resistor R
m
in parallel with a capacitor C
m
representing the passive electrical
properties of the IMM, in series with another capacitor C
b
representing the proton-buffering power of the
IMMS fluid. An access resistance R
a
was defined as a link between the capacitor C
b
and the membrane.
Average E
PMF
fluctuations across the IMM were calculated for different assumptions concerning the inter-
membrane space dimensions. The calculated average E
PMF
fluctuations were in the vicinity of 100 mV for
relaxation times in the few-microseconds range. The corresponding fluctuational protonic free energy is about
10 kJ/mole, which is comparable to the binding energy for protons in different transporters. This suggests that
fluctuations in E
PMF
can be of relevance in the universe of forces influencing the molecular machinery
embedded in the IMM. S1063-651X9701205-1
PACS numbers: 87.10.+e, 51.90.+r
I. INTRODUCTION
The synthesis of ATP in eukariotic cells occurs at the
expense of proton flow driven by the proton electromotive
force ( E
PMF
) across ATP synthase molecules inserted in the
inner mitochondrial membrane IMM. Proton gradients as
high as 1 p H can occur at that location 1 and superposition
with electrical potential difference can lead to E
PMF
’s attain-
ing the 200-mV mark.
Since the intermembrane space in most of its trajectory
has a width of only about 10–20 nanometers, this dimension
limits a region of molecular proportions where fluctuations
in thermodynamic parameters may become an important part
of the forces acting upon the molecular machines inserted
alongside the inner mitochondrial membrane.
This paper analyzes some consequences of the particular
geometry of the intermembrane space IMS in mitochondria
IMMS, which may result in relatively important fluctua-
tions of proton-electromotive force across the IMM.
II. THEORY
The free-energy change G for the creation of an elec-
trochemical gradient by an ion pump is 1the SI system of
units is employed throughout
G =RT ln
c
2
c
1
+zF , 1
where c
2
c
1
-1
is the concentration ratio for the ion that
moves, z is the ion valence, F is Faraday’s constant, R is the
gas constant, T is the absolute temperature, and is the
transmembrane difference in electrical potential measured in
volts. The proton-electromotive force is defined by
E
PMF
=2.3
RT
F
p H+. 2
When G =0 zero chemical driving force, E
PMF
=0), Eq.
3 can be used to relate the variations of p H across the
membrane with voltage changes
p H=-
F
2.3RT
=-
e
2.3kT
, 3
where e is the electronic charge and k the Boltzmann con-
stant.
In order to determine the fluctuations of the E
PMF
across
the IMM, we need to know the susceptibility ( ) of the
system comprised of the following elements see Fig. 1: 1
the inner mitochondrial membrane with its associated resis-
tance and capacitance; 2 the proton buffer compartment
associated with the intermembrane fluid; 3 the access resis-
tance between the first two elements.
In doing the above associations we can model the system
as a set of electrical resistors and capacitors. The IMM and
its surrounding solutions are represented by the membrane
capacitor C
m
. The conductive pathways across the IMM,
which include the pump channel and other leaks including
decouplers, are collectively represented by the term R
m
.
The buffering capacity of the intermembrane fluid is repre-
sented by an electrical equivalent calculated below defined
as C
buffer
=C
b
. This compartment is electrically connected
to the IMM by an access resistance R
a
. *Corresponding author.
PHYSICAL REVIEW E MAY 1997 VOLUME 55, NUMBER 5
55 1063-651X/97/555/62854/$10.00 6285 © 1997 The American Physical Society