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MSP Problem Set #5
Cytoplasm
(mM)
Extracellular
(mM)
ENernst
P1
P2
P3
P4
P5
P6
K+
139
4
-92
1
0
1
25
10
100
Na+
12
145
65
0
1
1
5
100
1
Cl -
9
114
-66
0
0
0
2
2
2
HCO3
-
12.5
21
-14
0
0
1
0
.02
0
Ca++
.0001
1.8
128
0
0
0
0
0
0
-92
65
-1.64
-39.0
42.8
-84.0
Em
1. This problem is designed to give you some practice with the diffusion potential
equations for one and for multiple ions.
A. For a cell with intracellular and extracellular concentrations as shown above,
compute the Nernst Potential for each ion and enter the value in the column
labeled ENernst.
B. If the columns labeled P1…P6 describe six different ionic conductivity patterns
(could be six different membranes or the same membrane in six different states)
fill in the shaded rows of the table labeled Em.
C. Are any of the ions at equilibrium?
Ionic equilibrium occurs when an ion is distributed so that its Nernst potential is equal to the
membrane potential. In the table K+ in P1 and Na+ in P2 are at equilibrium. The ions that are
not at equilibrium have a ‘driving voltage’ which is the difference between Em and the Enernst of
the particular ion. Current flow is proportional to both the driving voltage and the ion’s
conductivity. The students will learn about all of this later though.
2. You have a beaker separated in half by a semi-permeable membrane which is only
permeable to K+. On the left side, you have 9M KCl, and on the right side 1M KCl. At
electrochemical equilibrium, how much K+ (net) will have moved from the left to the
right?
Multiple guess!
a.
b.
c.
>4 moles
4 moles
<4 moles
Answer: c
What will be the final concentrations on each side of the beaker?
(no calculations necessary!)
Answer: they will essentially remain unchanged, because it takes very few molecules moving to
establish an electrical/charge gradient to counterbalance the concentration gradient. So few molecules
move that the change is concentration is undetectable. I think this is important in terms of the Nernst
equation.
3. If the EK for a cell were –90mV, and the ENa were +50 mV, and the cell was sitting at
a potential of –60mV (inside relative to outside), is the cell more permeable to K+ or Na+?
Answer: K+, because the cell is closer to EK.
This is approximately the situation for a neuron at R.P.
4. Epithelia can be described as leaky or tight. Explain how these words relate to
epithelial transport and give examples of where these different kinds of epithelia can
be found. Also describe how the extracellular pathway and the cellular pathway are
created and regulated.
Leaky and tight refer to the ion permeability of the epithelium. It can also be put in terms of electrical
resistance. In tissues like choroid plexus, renal proximal tubule, and the gall bladder the junctions are very
leaky to Na, K, Cl, with a transepithelial resistance of 5 to 25 ohms. This leaky epithelium allows ions to
cross the epithelial layer using the extracellular pathway. However in tight epithelium there are tight
junctions that prevent the extracellular passage of ions through the epithelial layer. All the ions must go
through the intracellular pathway. These epithelial can have electrical resistances as high as 40,000 ohms,
and can be found in tissues like the urinary bladder, collecting tubule, and gastric mucosa.
a) Extracellular Pathway –
Here we are basically talking about the different junctional epithelia that cells have. Tight junctions
are like ‘ring seals’ and limit extracellular passage, while adhering junctions, desmosomes, and gap
junctions allow more passage. The main thing is that tight junctions can block the passage of ions
between cells and can thus maintain an electrochemical gradient across the cell, which is driven by the
basolateral Na/K pump and determined by cellular ion channels. The degree of tightness (i.e.
permeability of tight junctions) ranges from very leaky to very tight and this is reflected in the
electrical resistance of the epithelium.
b) Cellular Pathway
Transport across the cellular pathway is essentially regulated two plasma membranes in series. The cell is
polarized by the presence of the tight junctions which divides the cell into apical and basolateral
membranes, which generally have different composition in terms of lipid composition and transport
proteins. For example, Na/K pumps are limited to the basolateral membranes, while Na/glucose
cotransporters are only present in the apical/brush border surface.
5. Design epithelia like you might find in your small intestine that would allow the
transport of a negatively charged amino acid from the lumen to the blood. Feel free
to use any transporters, pumps, or channels that Dr. Wright has discussed in his
lectures. It might be useful to include a diagram.
The diagram should be very similar to one provided by Dr. Wright (Figure 20). The negatively charged
amino acid would be resistant to facilitated diffusion because the electrical potential of the cell (which is
usually negative) would repel the negatively charge amino acid. The students should recognize the polarity
of the epithelium. On the basolateral side they should have a sodium/potassium pump that shunts Na out of
the cell. This would then set up the gradient for Na/(negatively charged a.a.) co transporter.
6. A researcher is interested in the effect of cell-cell interactions on the transport
characteristics of an epithelial cell. He notes that in a tissue prep obtained from the
small intestine, the cell transports sugars in a unidirectional direction from its luminal
to basolateral face, yet demonstrates a K+ efflux across its luminal surface. If the cell
is detached (e.g. via trypsin) from its neighbors, will its sugar and K+ transfer be
affected? If so, describe how?
Answer: Since unidirectional sugar transport is contingent upon cell surface asymmetry, the destruction of
tight junctions and other cytoskeletal elements responsible for cell-cell and cell-substrate interaction will
have unequivocally alter its transport characteristics. In order maintain unidirectional transport,
Na/Glucose cotransporters are localized to the apical surface, while glucose facilitated transporters are
concentrated on the basolateral surface. If no tight junctions are present, the transporters will laterally
diffuse across the cell’s membrane such that within any given area of membrane, glucose influx (via
Na/glucose cotransporter) will be countered by efflux (facilitated transporter) once the cytosolic
concentration approaches that of the surrounding environment. If the facilitated transporter’s kinetics and
concentration are large enough, no net transport will occur, thus a futile cycle results. In regards to the
observed K+ efflux across the luminal surface, this was due to localization of K+ facilitated transporters
on the apical membrane. Remember, the net flux of K+ across the plasma membrane must be zero (at
equilibrium), hence, the observed efflux was counter-balanced by a K+ influx due to the Na/K pump across
the basolateral membrane. Once cell-cell junctions are destroyed and lateral diffusion occurs, the
observed K+ efflux should approach zero.