The Neuronal Membrane at Rest
March 9, 2010
정성권 교수 (schung@med.skku.ac.kr)
Lecture Objectives
1. Basic concepts:
hyperpolarization/depolarization, resting membrane potential
equilibrium (Nernst) potential, Goldman equation
2. Two major reasons for the generation of resting membrane potential.
3. Reversal potential for K+ and Na+ ions.
4. Calculating the resting membrane potential using Goldman equation.
Animations for further studies
1. Flow of information through various components of the nervous systems: Reflex Arc
http://www.sumanasinc.com/webcontent/animations/content/reflexarcs2.html
2. Mechanism for the generation of resting membrane potential
http://www.sumanasinc.com/webcontent/animations/content/electricalsignaling.html
http://bcs.whfreeman.com/thelifewire/content/chp44/4401s.swf
3. Molecular structure of K+ ion channel
http://www.rockefeller.edu/interactive/movies/ion_channel.html
Assignments
Q1. How many-helical turns will be need to transverse a 5 nm-thick plasma membrane?
Q2. Calculate resting membrane potential if Na+ permeability is 10 times larger than K+ permeability?
ENa = +62 mV, EK = -80 mV
Q3. What are the molecular mechanisms for the selectivity of Na+, K+ channels towards Na+, K+ ions?
K+ channel, animation #3
Na+ channel, text Figure 4-8
Q4. Once opened, large number of K+ ion (1 x 107) can flow through single K+ channel molecule in
one second!!! Calculate the current level (in pA) through this K+ channel.
elementary charge = 1.6 x 10-19 C (coulombs)
A (ampere) = C / s; pA = 10-12 A
Q5. In order to generate 100 mV potential across cell membrane, how many K+ ions have to move
from the inside of the cell to the outside? (12 m diameter cell)
The farad is defined as the amount of capacitance for which a potential difference of one volt results in a
static charge of one coulomb. 1C(쿨롬)의 전기에 의해서 극판 사이의 전압이 1V(볼트) 변화하는
축전기의 전기용량은 1F이다.
cell membrane capacitance, 0.01 pF/m2
charges from 6x1023 molecules, 105 C
cell volume, 10-12 liter
K+ concentration in cytosol, 150 mM
Q6. A patient is found to be hypokalemic (low levels of potassium) and the physician prescribes
potassium supplements. Describe why potassium supplements are important in relation to
normal neuron function.
Q7. If a toxin were to inhibit the action of the Na+/K+ pumps of a neuron, what would eventually
happen to the membrane potential of that neuron?
Q8. What will happen in the resting membrane potential if there was an increase or decrease of
extracellular K+ concentration?
Q9. What will happen in the resting membrane potential if there was an increase or decrease of
extracellular Na+ concentration?
HODGKIN and HUXLEY'S experiments
(http://physioweb.med.uvm.edu/cardiacep/EP/handh.htm)
Many of the details of the basis of nerve electrical activity came from a series of experiments in the
early 1950's, which led to the awarding of the Nobel prize to the English physiologists A. L. Hodgkin
and A. F. Huxley. As you know, it is now possible to record directly the currents through individual
channels, and the approaches used to analyze individual channel behavior are different from Hodgkin
and Huxley's analysis of conductance properties of many channels acting in concert. Nevertheless,
Hodgkin and Huxley's analysis is a reasonable way of introducing the macroscopic behavior of nerve
membrane conductances.
If voltage is the governing factor, one needs a method that allows control of the membrane voltage, so
that it is possible to explore the voltage dependence of membrane properties. The "voltage clamp" is
a way of doing this. Without going into the details, one controls the membrane voltage electronically,
and measures the currents across the membrane produced by ion movements. For example,
suppose the membrane voltage is forced to change in a stepwise fashion from -70 mV to 0 mV:
The terms
inward or
negative for
current in one
direction and
outward or
positive for
current in the
opposite
direction are
conventions. An
inward
movement of
positive ions is
defined as
negative or
inward current,
whereas
outward movement of positive ions produces positive or outward current. Electrically, inward
movement of negative ions cannot be distinguished from outward movement of positive ions, so
inward movement of negative ions produces a positive or outward current.
The current measured is produced by the movement of ions, but it does not tell one directly what
types of ions moved. An outward current could be produced by potassium or sodium moving out of
the cell, or by chloride moving into the cell. To determine which ions are responsible, one can either
change the concentrations of ions surrounding the membrane, or apply chemicals that interfere with
transmembrane movements of specific types of ions.
If one takes away the sodium bathing the axon, and produces the same depolarization as above, the
current is altered:
Now put the sodium back in, and block the movement of potassium by a drug:
By such experiments, Hodgkin and Huxley determined that, when a nerve membrane is depolarized
above a threshold value, there is a transient inward or negative current produced by inward
movement of sodium, followed by a more slowly developing and sustained current in the opposite
(outward or positive) direction, produced by efflux of potassium.
The influx of positive sodium ions depolarizes the cell. This influx is transient. It is followed by an
increase in the efflux of positive potassium ions, and this repolarizes the cell. It is not really essential
that the potassium conductance increase when the cell is depolarized, because the potassium
conductance is already high (the resting cell has a high potassium conductance). A cell in which the
potassium conductance remained constant at the resting value would repolarize once the transient
increase of sodium conductance was over. However, the increased potassium conductance that takes
place upon depolarization hastens repolarization.
QUANTITATIVE TREATMENT OF THE CONDUCTANCE CHANGES
Hodgkin and Huxley applied Ohm's Law to ionic current:
I=gV
The sodium current, which they called INa, will depend on the membrane's conductance for sodium,
gNa, and on the difference between the existing membrane potential Vm, and the membrane potential
at which there would be no net electrochemical driving force on sodium. The membrane potential at
which there would be no electrochemical driving force on sodium is the Nernst equilibrium potential,
ENa. Thus,
INa = gNa(Vm - ENa)
They wrote a similar
equation for potassium
current:
IK = gK(Vm - EK)
They observed that Vm is
constant when the voltage
is controlled by the voltage
clamp apparatus, and ENa
and EK should not change.
So the fact that the currents
were functions of time
indicated that conductances
to sodium and potassium
were functions of time, as well as of voltage. To show this, they depolarized axons to a variety of
potentials and measured the sodium and potassium currents as functions of time. They divided each
sodium current by the term (Vm - ENa) and each potassium current by the term (Vm - EK). This gave
them the conductance for each ion as a function of time at each voltage:
Depolarization produces a transient increase in gNa, and a slower and sustained increase in gK.
Immediately after a step depolarization, gNa>>gK, but after the cell has been depolarized for a time,
gK>>gNa. Both gNa and gK are functions of voltage and time:
gNa = f(V,t)
gK = f'(V,t)
Hodgkin and Huxley introduced the variables m, h, and n to help them express the time and voltage
dependence of the two conductances. I will just consider the way they described the sodium
conductance, because it is the most difficult. They defined two arbitrary variables, m and h. Each of
these is a function of voltage and time. They used the equation:
gNa = m3h*GNa
In this equation, GNa is the maximum sodium conductance of the axon membrane. Sodium traverses
the membrane through protein channels in the membrane, and these can open and close. GNa is the
conductance for sodium that is seen if all sodium channels are open. The variables m and h each
change between 0 and 1 as functions of time and voltage. The product m 3h represents the fraction of
the total sodium conductance at any given time.
The following graph illustrates the values reached by m and h when the membrane is held at various
potentials for long times:
Next, they described the time dependence of m and h. If the cell is kept at one voltage for a long time,
then voltage is stepped quickly to a new voltage, m and h change to new steady state values, where
the steady state values are given by the above graph.
An all
important fact,
however, is
that m changes
quickly and h
changes more
slowly. For
example, the
following
represents the
approximate
time courses of
change of m
and h if the
voltage is
stepped from 70 mV to 0 mV.
At this point, it
is not
surprising if the
concept of
arbitrary
variables is
disturbing to
you. Hodgkin
and Huxley suggested a simple physical model which might or might not represent reality, but which
helps one see how the time and voltage dependence of currents might arise.
The sodium channel behaves as if it has two sets of gates. One set, the "activation" gates, open
rapidly when the cell is depolarized above a threshold voltage. The other gates, the "inactivation"
gates, close slowly when the cell is depolarized. Suppose each sodium channel has 3 activation gates,
called "m" gates, and 1 inactivation gate, called an "h" gate.
For a single channel, the variable m described by Hodgkin and Huxley is the probability that 1 m gate
will be in the open position. m cubed is the probability that all three m gates will be open. When m is
near 1, as it is when voltage is near 0 mV, there is a very high probability that all 3 m gates are open.
When m equals 0, as it is when voltage is at the resting potential, there is a high probability that the 3
m gates are all shut.
For a single channel, the variable h is the probability that the single h gate will be in the open position.
When h equals 1 (near the resting potential), the h gate is likely to be open. When h equals 0, as it
does in the steady state at depolarized voltages, the h gate is likely to be shut.
The product m3h is the probability that all of the gates are open, so that the channel can conduct
sodium across the membrane. For a large population of channels, the conductance g Na is equal to the
conductance seen when all channels are open (GNa) times the probability that any one channel is
open:
gNa = m3h GNa
Below is an attempt to define the different possible states of these gates at different times after a
sudden depolarization to a voltage above threshold, leading to an action potential:
Problems
1. Which of the following will cause membrane to hyperpolarize?
(a) opening of voltage-dependent K+ channels
(b) opening of voltage-dependent Na+ channels
(c) opening of voltage-dependent Ca2+ channels
(d) opening of non-selective cation channels
(
)
2.
Indicate whether the first item is greater than (G), the same as (S), or less than (L) the second
item.
(a) Increase in Na+ conductance during the rising phase of the action potential (
)
G S L
Increase in K+ conductance during the rising phase of the action potential
(b) Rate of conduction in small-diameter axons (
)
G S L
Rate of conduction in large-diameter axons
3. At rest, all of the following are closed except (
(a) Voltage-gated Na+ channels.
(b) Voltage-gated K+ channels.
(c) Delayed K+ channels.
(d) Non-voltage-gated K+ channels.
)
4. A 65-year-old male on digoxin for atrial fibrillation is told by his physician to get a blood analysis for
K+ on a regular basis because hypokalemia* will increase his risk of digitalis toxicity. Hypokalemia
increases the risk of digitalis toxicity because (
)
(a) The membranes of cardiac muscle cells are hyperpolarized
(b) The intracellular potassium concentration of red blood cells increases
(c) The excitability of nerve cells is increased
(d) The inhibition of sodium-potassium pump is increased
(e) The amplitude of nerve cell action potential is increased
* Abnormally low potassium concentration in the blood
5. If the resting potential of a neuron was -70 mV, potential change to -50 mV is called (
potential change to -80 mV is called (
).
(a) after-hyperpolarization (b) polarization
(c) depolarization
(d) hyperpolarization
6. The resting membrane potential is (
(a) similar to Nernst potential of Na+
(b) similar to Nernst potential of K+
(c) similar to Nernst potential of Ca2+
(d) not related to any ions
), and
).
7. If energy input (in the form of ATP) to the Na+ pump (Na+/K+ ATPase) cease, then (
(a) the resting membrane potential becomes more negative
(b) the resting membrane potential decreases toward zero
(c) the cell lose Na+
(d) non of above
).
8. The Nernst potential of K+ is as following:
EK = -60 log ([K]i / [K]o) (mV).
What do you expect to happen in resting membrane potential if extracellular K+ concentration ([K] o)
increases? (
)
* This symptom is called hyperkalemia, most often due to defective renal excretion)
(a) no change
(b) action potential
(c) depolarization
(d) hyperpolarization
9. A major advantage of reflex arc is that (
).
(a) a response can be elicited before a painful stimulus is consciously perceived
(b) a response can be elicited as soon as a painful stimulus is consciously perceived
(c) only a single neuron is necessary for both the stimulus and response.
10. Cells capable of generating and conducting action potentials are said to have _______________
membrane.
11. Generation of sodium and potassium ionic gradients across membrane is carried out mostly by
__________________.
12. Change of membrane potential from resting to less negative voltage is called _______________.
13. A pharmacological or physiological perturbation that increases the resting PK/PNa ratio for the
plasma membrane of a neuron would (
).
a. lead to depolarization of the cell
b. lead to hyperpolarization of the cell
c. produce no change in the value of the resting membrane potential