7.6 Calculation of IMM Electrical Resistance R m
115
dimension limits a cube with 15–20 nm side that defines a fluctuational domain (see
Fig. 7.1).
The inter-membrane space (space between the 2 mithocondrial membranes) can
then be partitioned into a great number of parallel volumes that are considered
to function independently, i.e. are uncorrelated. The I MM patch lining each of
these elementary volumes has then an area of (225–400) nm 2 . The patch electrical
capacity is given by:
C m = 0
A
d
(7.13)
where A is the area of the small I MM patch lining each elementary volume, and
0 are, respectively, the relative dielectric constant of the membrane ( = 2) and
permittivity of vacuum ( 0 = 8.85 × 10 −12 F m −1 ) and d is the I MM membrane
thickness.
7.5 Calculation of Buffer Equivalent Electrical Capacitance
The change of electrical charge, Q, associated with a given change, pH , of the
pH of an elementary volume, V , of the intermembrane fluid is given by:
Q b = F V V[H
+
] = F VββpH
(7.14)
where β is the specific buffering capacitance of the intermembrane fluid equal to
10 mM of acid added per pH unit change, β = [H + ]//pH , see Lauger [4].
This charge, stored in buffer capacitance, corresponds to a voltage change given by:
b =
2.3RT
F
(7.15)
The electrical equivalent of the buffer capacitance will then be:
C b =
Q b
b
=
βF 2 V
2.3RT
(7.16)
7.6 Calculation of IMM Electrical Resistance R m
We assume a density of AT P synthase molecules such that there is an average
of 1 pumping unit facing each cubic fluctuational domain whose lateral area is
about 400 nm 2 . The single-channel conductance of the AT P synthase is taken as
115
dimension limits a cube with 15–20 nm side that defines a fluctuational domain (see
Fig. 7.1).
The inter-membrane space (space between the 2 mithocondrial membranes) can
then be partitioned into a great number of parallel volumes that are considered
to function independently, i.e. are uncorrelated. The I MM patch lining each of
these elementary volumes has then an area of (225–400) nm 2 . The patch electrical
capacity is given by:
C m = 0
A
d
(7.13)
where A is the area of the small I MM patch lining each elementary volume, and
0 are, respectively, the relative dielectric constant of the membrane ( = 2) and
permittivity of vacuum ( 0 = 8.85 × 10 −12 F m −1 ) and d is the I MM membrane
thickness.
7.5 Calculation of Buffer Equivalent Electrical Capacitance
The change of electrical charge, Q, associated with a given change, pH , of the
pH of an elementary volume, V , of the intermembrane fluid is given by:
Q b = F V V[H
+
] = F VββpH
(7.14)
where β is the specific buffering capacitance of the intermembrane fluid equal to
10 mM of acid added per pH unit change, β = [H + ]//pH , see Lauger [4].
This charge, stored in buffer capacitance, corresponds to a voltage change given by:
b =
2.3RT
F
(7.15)
The electrical equivalent of the buffer capacitance will then be:
C b =
Q b
b
=
βF 2 V
2.3RT
(7.16)
7.6 Calculation of IMM Electrical Resistance R m
We assume a density of AT P synthase molecules such that there is an average
of 1 pumping unit facing each cubic fluctuational domain whose lateral area is
about 400 nm 2 . The single-channel conductance of the AT P synthase is taken as