(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 Mar;266(3):44-51.
2.- Doyle et al, “The structure of the potassium channel:
molecular basis of K+ conduction and selectivity”
Science. 1998 Apr 3;280(5360):69-77.
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)
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
Ultrastructure of a typical animal cell
The cell membrane contains
many proteins including ion
channels
Phospholipids and a phospholipid bilayer
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 highmagnification 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.)
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 (homooligomer); (2) distinct
subunits that are
homologous but not
identical (heterooligomer); or (3)
repetitive subunit-like
domains within a single
polypeptide (pseudooligomer). 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.
Formation of an aqueous pore by an ion channel. The dielectric constant of water
(ε= 80)is about 40-fold higher than the dielectric constant of the lipid bilayer(ε = 2).
Diffusion potential across a planar lipid bilayer containing a K+-selective channel
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 391:85-100,
1981.)
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
336:247-250, 1988.)
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).
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 12:1183-1194, 1994.)
Some mutations of human Na+ channels. At least two genetic diseases are caused by mutations in the Na+ channe
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 membranespanning 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 72:S15-S48, 1992.)
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 280:69-77, 1998.)
Ohm’s law
An open ion channel follows Ohm’s law!
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) 385:243-286, 1987.)
Goldman-Hodgkin-Katz equation.
Valid when the total membrane current equals zero;
Im=IK+INa+ICl=0




PK [ K ]O  PNa [ Na ]O  PCl [Cl ]i 
RT

Vm 
 ln 



F
 PK [ K ]i  PNa [ Na ]i  PCl [Cl ]o 
 [ K  ]O  a [ Na  ]O 
RT

Vm 
 ln 


F
 [ K ]i  a [ Na ]i 
Dependence of the
resting membrane
potential on [K+]o 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 [K+]o, where
the [K+]o is relatively
larger.
DP=RTDOsm
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.
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.