Transcript Lecture 10 - Washington State University

The Resting Potential
Cells are electrical batteries
•Virtually all cells have a steady transmembrane voltage, the
“resting potential”, across their plasma membranes.
•The negative pole of the battery is the interior of the cell; the
positive the exterior.
•All voltage values are measured relative to some baseline – in this
case, we usually take the solution surrounding the cell as the
ground or baseline, and so resting potential values are expressed as
negative numbers.
•We can measure the resting potential by inserting a metal or glass
electrode across the plasma membrane, placing a second (ground)
electrode near the cell surface, and connecting a voltmeter to the
electrodes.
The set-up for recording membrane potentials
What are the sources of this
electrical potential energy?
• Direct contributions from pumps that move
charge – this would include both the
Na+/K+ pump (almost all cells) and the Vtype H+ ATPase (restricted to a few cell
types).
• Diffusion potentials arising from ionic
gradients
Diffusion potentials and the concept of
electrochemical equilibrium
• Imagine two solutions of differing ionic
composition, separated by a barrier. For
example, let’s let the solute be KCl and the
gradient be 10:1.
KCl
KCl
• Depending on the permeability properties
of the barrier, there are 4 possible
outcomes (but two of them are boring):
The non-boring outcomes
• 1. barrier permeable to K+ but not to Cl-: K+ will attempt to
diffuse from left to right – but very soon the pull of the leftbehind Cl- will become equal to the “push” of the concentration
gradient, and the system will come into electrochemical
equilibrium with a net negative charge on the left side of the
barrier and a net positive charge on the right side.
• 2. barrier permeable to Cl- but not to K+: exactly the
opposite will happen, resulting in a net negative charge on the
right side and an opposing positive one on the left side.
• These are equilibria, so they will persist without any energy
expenditure as long as the system is not disturbed.
The boring outcomes
• 1. barrier permeable to both ions: a
temporary diffusion potential will exist
because the diffusion coefficient of K+ and
Cl- differ, but ultimately concentrations will
be equal on both sides and there will be
no voltage at equilibrium – boring!
• 2. barrier permeable to neither ion: no
change at all – very boring!
The Nernst Equation relates chemical and
electrical driving forces
R and T have their usual meanings, Z is the ionic charge (+1 for K+),
and F is Faraday’s Number, a fudge factor that converts from
coulombs (a measure of static charge) to molar units.
For ease of calculation, it helps to know that if we fill in constants
and convert to 10-base logs, the equation yields 55 mV of potential
for every additional decade of ionic gradient at room temperature or
about 60 mV at mammalian body temperature.
+60
ENa
This diagram shows the
Nernstian equilibrium potential
values for Na+ and K+ when the
concentration ratios across the
membrane barrier are 1/10 for
Na+ and 1/30 for K+ - these are
typical values for real cells
0
mV
-90
EK
Possible misconceptions: typical illustrations grossly underrepresent the numbers of ions, so that it seems that the cell
below has more than twice as many negatively charged
ions inside it as positively charged ions…
The real situation:
• The charge on the membrane is generated by
an extremely small charge imbalance and
represents very few ions. The oppositelycharged ions clustered on the inside and outside
of the membrane are such a small portion of the
total number of each category of ion, that for a
large neuron, if one K+ diffuses out of the cell for
every 10 million K+ inside the cell, the effect is to
produce a membrane potential of 100mV insidenegative!
+60
ENa
Where is the resting potential in
this?
0
mV
-70
-90
EK
Implications of the previous
slide
• The resting potential cannot be explained
as a pure K+ or pure Na+ diffusion potential
• Neither K+ nor Na+ is in electrochemical
equilibrium – K+ is close, but Na+ is way
off.
The Na+/K+ pump explains the nonequilibrium distributions of Na+ and
K+
• If an ion’s concentration gradient is not in
agreement with what the Nernst Equation
predicts, work is being done to keep the
system out of equilibrium.
• Na+ and K+ distributions across the plasma
membrane are kept away from diffusional
equilibrium by the Na+/K+ pump. The
energy is provided by hydrolysis of ATP.
Now, how do we explain the
resting potential?
The magnitude and polarity of the
resting potential are determined by two
factors:
• 1. The magnitude of the concentration
gradients for Na+ and K+ between
cytoplasm and extracellular fluid.
• 2. The relative permeabilities of the
plasma membrane to Na+ and K+.
Since the Na+ and K+ concentration
gradients are opposite, you could think of
the membrane potential as the outcome of a
tug-of-war between the two gradients. The
winner (defined as the ion that can bring the
membrane potential the closest to its own
equilibrium potential) is determined by the
relative magnitudes of the K+ and Na+
gradients and the relative permeability of
the membrane to the two ions.
K+ is the winner on both counts: its
gradient is about 30/1 as compared to
Na+’s 10/1, and the membranes of most
cells are 50-75 times more permeable to
K+ than Na+.
Leak Channels
Despite the overall high resistance of the
membrane, some leak channels are open in the
”resting” membrane. A few of the leak channels
allow Cl- through, a few allow Na+ through, but
most of the leak channels allow K+ to pass
through.
Given that there are leak channels, which way will
each ion move through the leak channels, on
average?
We can quantify the effects of the
Na+ and K+ gradients
• We just have to know the relative
magnitudes of the concentration gradients
and the relative permeabilities
The Goldman Equation describes the
membrane potential in terms of gradients
and permeabilities
In words, the Goldman equation says:
“The membrane potential is determined by the relative
magnitudes of the concentration gradients, each
weighted by its relative permeability.”
What ions have to appear in the
Goldman equation?
• To be accurate, the Goldman equation
must include a term for each ion that is:
• a. not at equilibrium, and
• b. for which there is significant
permeability
• So, for those cells which actively transport
Cl-, a Cl- term must be added. To do so,
[Cl-]in and [Cl-]out have to be inverted
relative to the cation terms, because of the
charge difference.
+60
ENa
0
This diagram shows the sizes of
the driving forces that act on
Na+ and K+ when the
concentration ratios across the
membrane are 1/10 for Na+ and
1/30 for K+ and the resting
potential is -70 mV.
Driving force on Na+ = 130 mV
mV
Resting potential
Driving force on K+ = 20 mV
-70
-90
EK
How do things look to Na+?
Na+ is not conflicted!
• Both the concentration gradient and the
internally-negative membrane potential
favor entry into the cell….
The way things look to K+
• The forces on K+ are outward, down its concentration
gradient, and inward, responding to the attraction of
the negative interior…
The way things look to Cl-
Chloride is often passively distributed…..
• Cl- is driven out, repulsed by the negative
charge inside, but it is driven in by its
concentration gradient. The result can be
that Cl- is “contented” at the resting
membrane potential, with its two forces
balanced.
A little review of electrical terms
Ohm’s Law ( I = V/R ) is the relationship between
electrical force and flow.
The driving force (V or E; units of volts); this is
potential energy.
Resistance is R (units: ohms); conductance (G) is the
inverse of resistance (units: mohs or siemens)
Current (I) is in units of amps: One amp is the current
that flows when the driving force is 1 volt and the
resistance is one ohm (or the conductance is 1 Siemen).
Relevant membrane properties:
resistance and capacitance
• The lipid bilayer has a high electrical resistance
(i.e., charged particles do not move easily
across it) and it separates two very conductive
(“salty”) solutions.
• The lipid bilayer is thin (about 50 Angstroms).
The thinness of the membrane allows it to store
a relatively large amount of charge, i.e., have a
high capacitance: very small differences in the
electrical balance of charges inside the cell
easily attract opposite charges to the outside of
the cell.
Net current flow across the membrane
is zero at rest.(or at any time when the
potential is stable)
An important corollary of Ohm’s law is that when
the membrane potential is stable, net current flow
across it is zero. If net current flow is not zero,
Vmembrane has to be changing.
Current Flow causes the membrane
potential to change
In physiology (unlike physics), current is
defined as the flow of positive charge. A net
inward current is thus equivalent to flow of
cation into the cell (or anion out of the cell),
either of which would cause depolarization change toward a less inside-negative membrane
potential. The opposite change is
hyperpolarization.
Membrane response to injected current
After the injected current is turned off, the membrane
potential moves pretty quickly back to the resting
level: What is going on?.
Some factors that cause
depolarization
[K+] extracellular
[Na+] extracellular
Na+ permeability
K+ permeability