Biomedical Engineering Reference
In-Depth Information
discussed in Chapter 12, and here we focus on the concentration gradient. For a typical
mammalian cell, the ions of interest are
Na
þ
, with Table 7.2 listing the typical ion
concentrations inside and outside the cell. To maintain ion concentrations at steady-state,
the flow of each ion into the cell must be balanced by the flow of that ion out of the cell.
First consider
K
þ
and
Na
þ
. The concentration gradient drives
Na
þ
into the cell. For
K
þ
, the concen-
K
þ
out of the cell. Osmotically, as long as the
K
þ
loss is balanced by
tration gradient drives
Na
þ
gain, the cell remains isotropic. However, if the loss/gain were allowed to happen,
the ionic concentrations across the cell membrane could not be maintained. To maintain the
ionic concentrations of
the
K
þ
and
Na
þ
, the cell membrane uses the ATP
Na-K
pump, driving
Na
þ
out of the cell and
K
þ
into the cell. Due to the action of the
Na
þ
behaves
Na-K
pump,
as if it is impermeable to the membrane.
The
pump also controls the volume of the cell. The cell contains a large number of
impermeable proteins and molecules that have a negative charge, which attracts positively
charged
Na-K
K
þ
and
Na
þ
, and water driven into the cell by osmosis. Without the
Na-K
pump,
Na
þ
ions for every
the cell would swell and eventually burst. The
Na-K
pump removes 3
K
þ
ions pumped into the cell, thus creating a hypotonic condition that drives water from
the cell by osmosis. If the cell changes volume, the
2
Na-K
pump operates to restore it by
fine-tuning the flow of water into or out of the cell.
Consider the membrane illustrated in Figure 7.6, with two passive channels for
K
þ
and
Na
þ
,an
A
. Assume that there is no pressure differ-
ence between the inside and outside, which is required for a mammalian cell. Thus, the
flow equation using Eq. (7.17) is given by
Na-K
pump and an impermeable anion
RT K
þ
i
K
þ
o
þ
Na
þ
i
Na
þ
o
þ
A
½
½
½
½
½
¼
R
m
Q
ð
7
:
19
Þ
In addition to the flow equation, the flux
10
equation for each of the permeable ions is
given as
J
K
¼
P
K
K
þ
J
p
i
K
þ
½
½
o
ð
7
:
20
Þ
þ
J
p
J
Na
¼
P
Na
Na
þ
i
Na
þ
½
½
o
Na-K Ion Pump
K
+
Na
+
H
2
O
K
+
Na
+
Outside
Inside
Na
+
K
+
A
-
Na
+
K
+
H
2
O
FIGURE 7.6
Cell membrane with two passive channels and a pump. Ions
K
þ
and
Na
þ
diffuse through the
membrane, while anion
A
is impermeable. As indicated, water easily moves through the cell membrane.
10
Flux is the number of particles (ions or molecules) that flow through a unit area per unit time. Flux is a
vector that is given by the symbol
J
.
