Biomedical Engineering Reference
In-Depth Information
the cell is 0.4 Osm. This will be achieved when the volume inside the cell has been reduced from
2 nl to 1 nl.
C 1 V 1 ¼ C 2 V 2
0
:
2
Osm
Osm
2
nl ¼ V 2
0
:
4
1
nl ¼ V 2
Real cells are much more complex than the simple model just described. In addition to
achieving osmotic balance at equilibrium, real cells must also achieve electrical balance with
regard to the ions that are present in the cytoplasm. The principle of electrical neutrality
requires that the overall concentration of cations in a biological compartment—for example,
a cell—must equal the overall concentration of anions in that compartment. Consider
another model cell (Figure 3.7) with internal and external cation and anion concentrations
similar to those of a typical mammalian cell. Is the cell at equilibrium if the plasma mem-
brane is freely permeable to K þ and Cl but impermeable to Na þ and the internal anions?
The total osmolarity inside the cell is 250 mOsm (12 mM Na þ , 125 mM K þ , 5 mM Cl ,
108 mM anions), while the total osmolarity outside the cell is also 250 mOsm (120 mM
Na þ , 5 mM K þ , 125 mM Cl ), so the cell is in osmotic balance—that is, there will be no
net movement of water across the plasma membrane. If the average charge per molecule
of the anions inside the cell is considered to be -1.2, then the cell is also approximately in
electrical equilibrium (12
125 positive charges for Na þ and K þ ;5
1.2 * 108 negative
charges for Cl and the other anions). Real cells, however, cannot maintain this equilibrium
without expending energy, since real cells are slightly permeable to Na þ . In order to main-
tain equilibrium and keep Na þ from accumulating intracellularly, mammalian cells must
actively pump Na þ out of the cell against its diffusion and electrical gradients. Since Na þ
þ
þ
INTRACELLULAR FLUID
PLASMA MEMBRANE
WATER
K +
Cl
WATER
K +
Cl
108 mM ANIONS
12 mM Na
125 mM K +
5 mM Cl
120 mM Na +
5 mM K +
125 mM Cl
EXTRACELLULAR FLUID
FIGURE 3.7 A model cell with internal and external concentrations similar to those of a typical mammalian cell.
The full extent of the extracellular volume is not shown and is much larger than the cell's volume.
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