CHAPTER 2 • ELECTRICAL ACTIVITY OF THE HEART
11
membrane (negative inside the cell relative to
outside). The membrane potential that is nec-
essary to oppose the outward movement of
K+ down its concentration gradient is termed
the equilibrium potential for K+ (EK; Nernst
potential). The Nernst potential for K+ at
37°C is as follows:
[K+]
Eq 2-1
EK
= -61 lo g ^-^- = -96 mV
Eq. 2 i
K
a [K+]o
in which the potassium concentration inside
[K+]
,
= 150 mM and the potassium concentra-
tion outside [K+] = 4 mM. The -61 is derived
o
from RT/zF, in which R is the gas constant, z is
the number of ion charges (z = 1 for K+; z = 2 for
divalent ions such as Ca++), F is Faraday con-
stant, and T is temperature (°K).
The equilibrium
potential is the potential difference across the mem-
brane required to maintain the concentration gra-
dient across the membrane.
In other words, the
equilibrium potential for K+ represents the elec-
trical potential necessary to keep K+ from diffus-
ing down its chemical gradient and out of the
cell. If the outside K+ concentration increased
from 4 to 10 mM, the chemical gradient for diffu-
sion out of the cell would be reduced; therefore,
the membrane potential required to maintain
electrochemical equilibrium would be less nega-
tive according to the Nernst relationship.
The Em for a ventricular myocyte is about
-9 0 mV, which is near the equilibrium poten-
tial for K+. Because the equilibrium potential
for K+ is -9 6 mV and the measured resting
membrane potential is -9 0 mV, a net driv-
ing force (net electrochemical force) acts on
the K+, causing it to diffuse out of the cell. In
the case of K+, this net electrochemical driv-
ing force is the Em (-90 mV) minus the E
K
(-96 mV), resulting in +6 mV Because the
resting cell has a finite permeability to K+ and
a small net outward driving force is acting on
K+, K+ slowly leaks outward from the cell.
Sodium ions also play a major role in deter-
mining the membrane potential. Because the
Na+ concentration is higher outside the cell,
this ion would diffuse down its chemical gra-
dient into the cell. To prevent this inward flux
of Na+, a large positive charge is needed inside
the cell (relative to the outside) to balance out
the chemical diffusion forces. This potential is
called the equilibrium potential for Na+ (ENa)
and is calculated using the Nernst equation,
as follows:
Eq. 2-2
ENa = -61 |o g [N jyL = + S2 mV
in which the sodium concentration inside
[Na+]
,
= 20 mM and the sodium concentra-
tion outside [Na+]
o
= 145 mM. The calculated
equilibrium potential for sodium indicates
that to balance the inward diffusion of Na+ at
these intracellular and extracellular concen-
trations, the cell interior has to be +52 mV to
prevent Na+ from diffusing into the cell.
The net driving or electrochemical force act-
ing on sodium (and each ionic species) has two
components. First, the sodium concentration
gradient is driving sodium into the cell; accord-
ing to the Nernst calculation, the electrical force
necessary to counterbalance this chemical gra-
dient is +52 mV. Second, because the interior
of the resting cell is very negative (-90 mV), a
large electrical force is trying to “pull” sodium
into the cell. We can derive the net electro-
chemical force acting on sodium from these
two component forces by subtracting the Em
minus E
Na
: -90 mV - +52 mV equals -142 mV
This large electrochemical force drives sodium
into the cell; however, at rest, the permeability
of the membrane to Na+ is so low that only a
small amount of Na+ leaks into the cell.
The same reasoning can be applied to Ca++
as just described for Na+. Its calculated E
Ca
is
+134 mV and net electrochemical force act-
ing on Ca++ is -224 mV Therefore, like Na+,
there is a very large net electrochemical force
working to drive Ca++ into the resting cell;
however, in the resting cell, little Ca++ leaks
into the cell because of low membrane perme-
ability to Ca++ at rest.
IONIC CONDUCTANCES AND
MEMBRANE POTENTIAL
As explained, the Em in a resting, nonpace-
maker cell is very near E
K
, and quite distant
from E
and E
. This occurs because the
Na
Ca
membrane is much more permeable to K+ in
the resting state than to Na+ or Ca++. Therefore,
Na+ and Ca++ have little contribution to the
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