Page 45 - Color_Atlas_of_Physiology_5th_Ed._-_A._Despopoulos_2003

Electrical Membrane Potentials and At equilibrium potential, the chemical
Ion Channels gradient will drive just as many ions of species
X in the one direction as the electrical poten-
An electrical potential difference occurs due to tial does in the opposite direction. The electro-
the net movement of charge during ion trans- chemical potential (E m – E x) or so-called elec-
port. A diffusion potential develops for in- trochemical driving “force”, will equal zero,
+
stance, when ions (e.g., K ) diffuse (down a and the sum of ionic inflow and outflow or the
chemical gradient; ! p. 20ff.) out of a cell, net flux (I x) will also equal zero.
Membrane conductance (g x), a concentra-
making the cell interior negative relative to the
Fundamentals and Cell Physiology driven ion transport; ! p. 22). Outward K dif- to a given ion instead of the permeability
tion-dependent variable, is generally used to
outside. The rising diffusion potential then
drives the ions back into the cell (potential-
describe the permeability of a cell membrane
+
coefficient P (see Eq. 1.5 on p. 22 for conver-
fusion persists until equilibrium is reached. At
sion). Since it is relative to membrane surface
equilibrium, the two opposing forces become
area, g x is expressed in siemens (S = 1/Ω) per
equal and opposite. In other words, the sum of
the two or the electrochemical gradient (and
2
m (! p. 22, Eq. 1.9). Ohm’s law defines the net
thereby the electrochemical potential) equals
ion current (I x) per unit of membrane surface
zero, and there is no further net movement of
area as
ions (equilibrium concentration) at a certain
–2
I X ! g X ! (E m – E X) [A ! m ]
[1.19]
voltage (equilibrium potential).
The equilibrium potential (E x) for any spe-
vailing membrane potential, E m, does not equal
(o) a cell can be calculated using the Nernst
1 cies of ion X distributed inside (i) and outside I x will therefore differ from zero when the pre-
the equilibrium potential, E x. This occurs, for
equation: example, after strong transient activation of
+
+
Na -K -ATPase (electrogenic; ! p. 26): hyper-
R ! T [X] o
E X ! ! ln [V] [1.17] polarization of the membrane (! A2), or when
F ! z x [X] i
the cell membrane conducts more than one
where R is the universal gas constant (= 8.314 ion species, e.g., K as well as Cl and Na :
–
+
+
– 1
J ! K – 1 ! mol ), T is the absolute temperature depolarization (! A3). If the membrane is per-
(310 "K in the body), F is the Faraday constant meable to different ion species, the total con-
4
– 1
or charge per mol (= 9.65 # 10 A ! s ! mol ), z is ductance of the membrane (g m) equals the sum
the valence of the ion in question (+ 1 for K , + 2 of all parallel conductances (g 1 + g 2 + g 3 + ...).
+
–
2+
for Ca , – 1 for Cl , etc.), ln is the natural loga- The fractional conductance for the ion species
rithm, and [X] is the effective concentration = X (f x) can be calculated as
activity of the ion X (! p. 376). R ! T/F = 0.0267
V – 1 at body temperature (310 "K). It is some- f X ! g X/g m [1.20]
times helpful to convert ln ([X] o/[X] i) into The membrane potential, E m, can be deter-
–ln ([X] i/[X] o), V into mV and ln into log be- mined if the fractional conductances and equi-
fore calculating the equilibrium potential librium potentials of the conducted ions are
+
+
(! p. 380). After insertion into Eq. 1.17, the known (see Eq. 1.18). Assuming K , Na , and Cl –
Nernst equation then becomes are the ions in question,
1 [X] i E m ! (E K ! f K) + (E Na ! f Na) + (E Cl ! f Cl) [1.21]
E X ! – 61 ! ! log [mV] [1.18]
z X [X] o
Realistic values in resting nerve cells are: f K =
+
+
If the ion of species X is K , and [K ] i = 140, and 0.90, f Na = 0.03, f Cl = 0.07; E K = – 90 mV, E Na =
+
[K ] o = 4.5 mmol/kg H 2O, the equilibrium + 70 mV, E Cl = – 83 mV. Inserting these values
potential E K = – 61 ! log31 mV or – 91 mV. If the into equation 1.21 results in an E m of – 85 mV.
cell membrane is permeable only to K , the Thus, the driving forces (= electrochemical
+
membrane potential (E m) will eventually reach potentials = E m –E x), equal + 5 mV for K , +
–
+
a value of – 91 mV, and E m will equal E K (! A1). – 145 mV for Na , and – 2 mV for Cl . The driv-
32
!
Despopoulos, Color Atlas of Physiology © 2003 Thieme
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