Ion transport across the cell membrane underlies cellular

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(Chapters 6-7 of KS)
Ion transport across the cell membrane underlies
cellular Homeostasis and electrical activity
1.- the cell membrane
2.- ion transport across membranes
3.- ion channels structure and function
4.- osmotic balance and ion channels
5.- ion channels and the control of membrane
potential
Readings 1.- Neher E, Sakmann B. "The patch
clamp technique" Sci Am. 1992
Mar266(3)44-51. 2.- Doyle et al, The
structure of the potassium channel
molecular basis of K conduction and
selectivity Science. 1998 Apr
3280(5360)69-77.
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Problems for these chapters
Describe, quantitatively, the series of
electrical events that follow the opening of a
single Na selective ion channel (10 pS) in the
membrane of an isolated vesicle. The lipid
vesicle has a diameter of 3 micrometers. The
concentration of Na outside is 150 mM. The
internal Na concentration is 5 mM. Determine the
polarity, magnitude and time course of the
changes. Five seconds after opening, the Na
channel closes. Then, a K selective ion channel
opens for five seconds (Koutside 5 mM Kinside
150 mM). How much are the internal Na and K
concentrations changed in each cycle. What will
happen if this cycle is repeated several thousand
times? Describe the changes in membrane
potential, cell volume and water flow that occur
after reducing the external Cl- concentration in
the solution bathing a single frog muscle fiber
(slide 39)
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Keywords Bilayer size, properties, membrane
capacitance Ion channel structure, single ion
channel currents Faraday, membrane potential,
charge Nernst equation Donnan
equilibrium electrical equivalent
circuits Permeability ratios Goldman
equation Electrical Driving force
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Ultrastructure of a typical animal cell
The cell membrane contains many proteins
including ion channels
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Phospholipids and a phospholipid bilayer
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Transmission electron micrograph of a cell
membrane. The photograph shows two adjacent cells
of the pancreas of a frog at a magnification of
43,000. The inset is a high-magnification view
(216,000) of the plasma membranes of the cells.
Note that each membrane includes two dense layers
with an intermediate layer of lower density. The
dense layers represent the interaction of the
polar head groups of the phospholipids with the
OsO4 used to stain the preparation. (From Porter
KR, Bonneville MR Fine Structure of Cells and
Tissues, 4th ed., Philadelphia, Lea Febiger,
1973.)
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Structure of ion channels. Most ion channels
consist of four to six subunits that are arranged
like a rosette in the plane of the membrane. The
channel can be made up of (1) identical, distinct
subunits (homo-oligomer) (2) distinct subunits
that are homologous but not identical
(hetero-oligomer) or (3) repetitive subunit-like
domains within a single polypeptide
(pseudo-oligomer). In any case, these "subunits"
surround the central pore of the ion channel.
Note that each "subunit" is itself made up of
several transmembrane segments.
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Formation of an aqueous pore by an ion channel.
The dielectric constant of water (e 80)is about
40-fold higher than the dielectric constant of
the lipid bilayer(e 2).
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Diffusion potential across a planar lipid bilayer
containing a K-selective channel
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Patch clamp methods. (Data from Hamill OP, Marty
A, Neher E, Sakmann B, Sigworth FJ Improved
patch-clamp techniques for high-resolution
current recording from cells and cell-free
membrane patches. Pflugers Arch 39185-100,
1981.)
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Three-dimensional image of the nicotinic
acetylcholine receptor channel. (Data from
Toyoshima C, Unwin N Ion channel of
acetylcholine receptor reconstructed from images
of postsynaptic membranes. Nature 336247-250,
1988.)
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Subunit structure and membrane-folding models of
voltage-gated channels. A, A voltage-gated Na
channel is made up of a pseudo-oligomeric a
subunit, as well as membrane-spanning b1 and b2
subunits. Note that the domains I through IV of
the a subunit are homologous to a single subunit
of a voltage-gated K channel (see C). B, A
voltage-gated Ca2 channel is made up of a
pseudo-oligomeric a1 subunit, as well as an
extracellular a2 subunit, a cytoplasmic b
subunit, and membrane-spanning g and d subunits.
Note that the domains I through IV of the a
subunit are homologous to a single subunit of a
voltage-gated K channel (see C).
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A voltage-gated K channel is made up of four a
subunits, as well as a cytoplasmic a subunit.
(Data from Isom LL, De Jongh KS, Catterall WA
Auxiliary subunits of voltage-gated ion channels.
Neuron 121183-1194, 1994.)
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Some mutations of human Na channels. At least
two genetic diseases are caused by mutations in
the Na channel of human skeletal muscle.
Hyperkalemic periodic paralysis can be caused by
mutations in membrane-spanning segment S5 of
domain II and S6 of domain IV. Paramyotonia
congenita can be caused by mutations in
membrane-spanning segment S3 of domain IV and S4
of domain IV. The disease can also be caused by
mutations in the intracellular segment that links
domains III and IV. (Data from Catterall WA
Cellular and molecular biology of voltage-gated
sodium channels. Physiol Rev 72S15-S48, 1992.)
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Structure of the Streptomyces K channel (KcsA).
A, KcsA is a homotetramer. Each monomer is
represented in a different color and contains
only two membrane-spanning elements, which is
analogous to the S5-P-S6 portion of Shaker-type
K channels. B, This view more clearly shows the
P region, which is very similar to the P region
of the Shaker K channel. The P region appears to
form the selectivity filter of the channel. C,
This is a cut-away view of the pore that shows
three K ions. The top two K ions are bound in a
tight cage that is formed by the peptide
backbones of the P regions of each of the four
channel subunits. (Data from Doyle DA, Morais
Cabral J, Pfuetzner RA, et al The structure of
the potassium channel Molecular basis of K
conduction and selectivity. Science 28069-77,
1998.)
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Ohms law
An open ion channel follows Ohms law!
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Voltage dependence of currents through single Cl
channels in outside-out patches. A, The channel
is a gamma-aminobutyric acid-A (GABAA) receptor
channel, which is a Cl channel activated by
GABA. Identical solutions, containing 145 mM Cl,
were present on both sides of the patch. B, The
magnitudes of the single-channel current
transitions (y-axis) vary linearly with voltage
(x-axis). (Data from Bormann J, Hamill OP,
Sakmann B Mechanism of anion permeation through
channels gated by glycine and g-aminobutyric acid
in mouse cultured spinal neurones. J Physiol
(Lond) 385243-286, 1987.)
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Goldman-Hodgkin-Katz equation. Valid when the
total membrane current equals zero
ImIKINaICl0
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Dependence of the resting membrane potential on
Ko and on the PNa/Pk ratio, a. The blue line
describes an instance in which there is no Na
permeability (i.e., PNa/Pk 0). The three orange
curves describe the Vm predicted by the GHK
Equation for a values greater than zero. The
deviation of these orange curves from linearity
is greater at low values of Ko, where the
Ko is relatively larger.
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DPRTDOsm
Gibbs-Donnan equilibrium. A semipermeable
membrane separates two compartments that have
rigid walls and equal volumes. The membrane is
permeable to Na, Cl, and water, but not to the
macromolecule Y, which carries 150 negative
charges.
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Effect of urea on cell volume. Because the cell
membrane is far more permeable to water than to
urea, we will assume that, during the initial
moments in steps 2 and 3, the cell membrane is
permeable only to water. Later, during steps 4
and 5, we assume that the membrane is permeable
to both water and urea.
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