From: Steven Eiger (eiger@montana.edu)
Date: Sat Nov 17 2001 - 09:57:01 PST
Message-Id: <l03102801b81c5407b4c4@[153.90.150.107]> Date: Sat, 17 Nov 2001 10:57:01 -0700 From: Steven Eiger <eiger@montana.edu> Subject: Re: pinhole Nervous system and voltage
Here is installment two.
Membrane Potentials: Reality
In the following table are the major ions of interest in mammalian skeletal
muscle. Ionic concentrations are free ions.
Ion Extracellular concentration (mM) Intracellular Concentration
(mM) [Ion]o
[Ion]i Equilibrium Potential (mV)
Na+ 145 12 12 +67
K+ 4 155 0.026 -98
Ca++ 1.5 10-7M 15,000 +129
Cl- 123 4.2 29 -90
A careful look at this table brings up a few questions. First, what is
missing. We must have electrical neutrality in the bulk solutions of ECF
and cytoplasm. Electricity is far too strong a force to settle for
anything other than minute charge separations. It turns out that there are
many organic anions within the cell, such as proteins with anionic side
groups, or phosphorylated molecules. These organic anions make up the
difference in intracellular anions. This is an important point, the bulk
solutions are neutral - very few ions diffuse across the membrane to create
the membrane potential; these stay close to the membrane due to their
mutual attraction, and leave both solutions perfectly neutral.
Secondly, each ion has a different equilibrium potential. These
equilibrium potentials are hypothetical numbers, calculated by the Nernst
Equation. Note that the convention is for the charge inside of the cell to
determine the polarity. The main point is that these Eions are all quite
different. What will the actual membrane potential be?
If we consider a cell with the above ionic concentrations, and with a cell
membrane whose ion channels are selective such that they conduct only K+,
what will happen? First, think about this a bit. The scenario we have
previously described in great detail will occur, and nothing more - since
none of the other ions can move. K+ ions will diffuse out of the cell
until an electrical gradient is created which will balance the chemical
gradient for K+. We have made a K+ diffusion potential. Now the
electrochemical gradient for K+ will be zero. The voltage across the
membrane, or membrane potential, VM, will be the EK+. This is exactly what
happens in a resting glial cell. The V of the membrane potential stands
for voltage, as the units of potential difference are Volts. VM is usually
in the mV range.
But most cells are permeable to more than one ion at any given time. The
membrane potential will be determined by both the ionic ratios and the
relative permeability of the membrane to all ions. Let us assume that the
cell is initially permeable to only K+ and we sequentially add the
influence of each permeable ion. The cell is also a bit permeable to Na+
ions; thus a few Na+ ions will tend to flow into the cell, following their
chemical gradient, and electrical gradient that is pulling cations into the
cell. This makes the inside of the cell a little less negative which will
cause some K+ to leak out (if we assume we had started at EK+ such that the
net flux and electrochemical gradient of potassium started out at zero) and
lessen the drive for Na+ entry. At this point we have K+ diffusing outward
and Na+ inward. The really neat thing is that systems like this will go
towards a stable equilibrium where the net fluxes match one another, and
the membrane potential, VM, reaches a stable or steady state value. Crazy?
To reiterate, in this situation, for every K+ ion leaving the cell, a Na+
ion will enter, and therefore VM will remain constant. Usually, in the
resting situation, the membrane is most permeable to K+, therefore the EM
is close to the EK+, but not quite that low since the membrane is also
permeable to Na+, although to a much lesser extent (1/40). This is a very
important point. Since a normal resting membrane is permeable to both Na+
and K+, the membrane potential will be somewhere in between the EK+ and
ENa+. The vertical axis in the following graph has the equilibrium
potentials on it for each ion. The most common resting membrane potential
is shown. There is an equation, called the Goldman equation, which
predicts the membrane potential. As expected, one needs to plug into this
equation the charges of the various ions, their inside and outside
concentrations and their relative permeability. The Goldman equation
underlines the fact that the membrane potential is a weighted average of
the equilibrium potentials, with the weighting factor being the
permeability of each ion.
RT PK[K+]o + PNa[Na]o + PCl-[Cl]i
Goldman equation Vm = ----- ln
------------------------------------------
F PK[K+]i + PNa[Na]i +
PCl-[Cl]o
I really told a big lie before; the membrane potential is neither at the
Na+ or K+ equilibrium potentials; therefore, these ions are not in
equilibrium, they are moving! Thus, eventually the concentration gradients
will run down; it may take weeks, but left alone this will happen.
Consider K+; it has a large, outward chemical gradient and the electrical
gradient imposed by the membrane potential is inward, but not as strong as
its equilibrium potential, thus the electrochemical gradient is outward and
relatively small; but there is a high permeability. There will be net
outward leakage of K+ from the cell. Na+ experiences strong chemical and
electrical gradients; both directed inward. Na+ will enter the cell, at an
equal rate to K+, because the Na+ permeability is low. In summary, the
balanced fluxes at which the membrane potential is stable as predicted by
the Goldman equation result from a weak K+electrochemical gradient, and a
large gK+; being exactly balanced by a strong Na+ electrochemical gradient
and a small gNa+. While this keeps the VM stable over the short term, it
is not the whole story; although it is the most important part.
Given these steady state fluxes of Na+ and K+, how are the concentration
gradients of these ions maintained? Following is a figure which shows the
important features of the Na+-K+ pump, or the Na+-K+ ATPase.
It pumps 3 Na+ ions out and 2 K+ ions in for each ATP split. This
presents a bit of a problem. I have already told you that the Goldman
equation successfully predicts a membrane potential such that the exchange
is one for one, not two for three. In order to keep things stable, the
membrane potential is about 2 or 3 mV below the Goldman prediction. This
pulls in slightly more sodium and keeps in slightly more potassium such
that the leaks match a 3:2 ratio. This means that the pump is slightly
electrogenic, it affects the Vm, but only a very little bit. It is usually
best to not think about the pump beyond its maintaining the concentration
gradients. The pump is certainly needed, especially in tiny neurons; large
neurons like a squid axon can fire hundreds of thousands of times due to
their large ionic stores even with the pump poisoned, smaller neurons can
not fire as many, but can fire until their concentration gradients are run
down. Remember that very few ions need to cross the membrane to set up a
strong electrical field. "At the resting membrane potential the cell is
not in equilibrium, but rather in a steady state: Metabolic energy must be
used to maintain the ionic gradients across the membrane." KSJ.
Knowing about the pump and how to manipulate it will be useful to you. The
cardiac glycosides (poisons), like oubain and digitalis block the Na+-K+
pump. Digitalis causes an increased strength of heart contraction. How?
Blocking the pump lessens the Na+ gradient. Since Ca++ is pumped out of
the cell using energy form the Na+ gradient, the lessening of the Na+
gradient raises intracellular Ca++. As we will study later, intracellular
Ca++ correlates with strength of contraction. This is a standard treatment
for failing hearts. We will talk about this again.
Note that ECl- is the same value as VM. Cl- is not actively pumped so that
it distributes passively across the membrane. The membrane potential
determines its distribution. Chloride does affect the rate at which the
membrane potential can change, if there is a high chloride conductance, it
acts like molasses on changes in Vm.
While reading the above notes, everything might seem perfectly reasonable,
and one might then assume these ideas ought to be easy to recreate. If you
believe this, you have been tricked. It is quite easy to get off track.
One way to avoid pitfalls is to keep the sequence of your thoughts in
order. These work:
1. In the beginning, there were concentration gradients.
1.a. Hypothetical equilibrium potentials can be calculated from these
ratios; they are only useful as a guide.
2. Given these ionic ratios, and the relative permeability to these ions,
one can determine actual ionic movements and thus, membrane potentials.
Only an afterthought: Pumps maintain the concentration
gradients
#1.is a very good mantra.
It's also a good question. Where did they come from? Active pumping
merely maintains them. They probably come from the fact that cells arise by
cytokinesis. That is, they start off with them.
Signals, or Perturbations in the Vm.
Now things get considerably easier. Since we now understand that Vm is a
function of various permeabilities, and: these permeabilities are a
function of proteins sitting in the membrane, we can describe many signals
by just carefully looking at how these proteins work.
To reiterate: How do cells use membrane potentials as signals?
It is a change in membrane potential, a perturbation from the normal which
is the signal.
How is this done?
By creating fluctuations in the permeability of the membrane. The
concentration gradients (and thus the equilibrium potentials) do not
change. Very few ions need to cross membrane to change Vm.
How do these fluctuations occur?
By opening or closing channels. These channels which open or close in
response to stimulation are called "gated".
Types of Ion Channels
1. Leakage: always open, responsible for the resting membrane potential
2. Gated: open and close; controlled by stimuli
What sort of signals cause these channels to open or close?
1. chemical signals such as neurotransmitters.
2. electrical signals such as a change in membrane potential.
3. mechanical signals such as a pulling on the channel by
cytoskeletal elements.
There are two types of signals which travels down membranes:
1. Local potentials. "Great for short distances"
When a population of chemical or mechanical sensitive channels open, ions
cross the membrane, changing the membrane potential (this is what happened
in the motor end plate as the ACh receptors opened). These ions will then
diffuse through the ECF and the cytoplasm of the neuron and induce other
ions to move as well. This spread of the change in membrane potential by
diffusion of ions is called a local potential. The initial entry of ions
is called a graded or generator potential.
Since the ions will be diluted as they travel and some will leak out of the
cell, the signal dies off with distance and time. These are important
characteristics of local potentials.
In Summary:
Properties:
… Amplitude will decrease with distance
… Signal amplitude will vary according to the strength of
stimulus.
2. Action Potentials
To transmit signals long distances, which the nervous system must do, there
is a special type of signal called the action potential. Other cells such
as muscle cells also use action potentials. Membranes that transmit action
potentials are called excitable, although I think it is a bit close-minded
to just consider voltage-sensitive channels as being excitable and exclude
the other gated channels, but that is what history has done.
Important point -- Action potentials are dependent on the presence of
voltage-sensitive channels.
Their Properties: No decrement in amplitude of signals
"all or none" response; it is either sent or not,
it is never half sent.
Occur due to the presence of voltage-gated channels.
When we talk about membrane potentials which are changing from the resting
potential, we use hyperpolarization to describe the membrane becoming more
polarized, or becoming more negative. Depolarization implies a membrane
potential moving towards zero. It is useful to visualize these ideas on a
plot of Vm over time. Depolarization often leads to attaining threshold
potential but sometimes not. Hyperpolarization will put a membrane further
from threshold. Repolarization describes Vm returning to the resting Vm.
The standard view of an action potential in mammalian nerve.
The key points:
1. Before anything happens the cell is at the resting potential which is
about -70 mV.
2. As the membrane potential depolarizes due to a local potential, it
eventually reaches the threshold potential, at which point a sharp
depolarizing spike occurs.
3. We need to know the cause of each twist and turn of the action
potential trace.
a.. the sharp initial rise is caused by a very large number of
voltage-gated Na+ channels opening. This increases the membrane
permeability to Na+ such that PNa»Pk; as expected Vm will now move close to
ENa+.
b. The sharp fall in Vm is caused by two factors; 1. the Na+
gates remain open for only a set amount of time, they are now closing. 2.
There are voltage-sensitive K+ channels as well, these open slower than the
voltage-sensitive Na+ channels, their opening coincides with the
repolarization of the membrane.
c. As the action potential ends we can see a short period of
hyperpolarization. This is caused by the v-s K+ channels remaining open
for some time after the v-s Na+ channels have closed. When they are again
shut, the Vm will return to the resting potential.
4. There are two refractory periods, one called the absolute refractory
period, when the membrane can not fire; this lasts about a msec and
determines the maximum frequency of firing; and one called the relative
refractory period when the membrane requires a stronger than normal
stimulus to fire again.
The voltage-sensitive Na+ channel.
Below is a schematic representation of the timing and functional elements
of the voltage-sensitive Na+ channel.
A closer look at the key channels:
The voltage-sensitive Na+ channel.
1. There are two gates, an activation gate and an inactivation gate. This
is the simplest way to explain the refractory periods, and there is some
evidence supporting it.
2. At rest the activation gate is closed and the inactivation gate is open.
3. As threshold is reached, the activation gate opens, letting Na+ rush in.
4. At the peak of the action potential the inactivation gates close. This
causes Na+ permeability to rapidly fall resulting in the repolarization of
Vm. It also defines the latter half of the absolute refractory period, for
this channel is now closed until this inactivation gate reopens.
5. As the membrane potential returns to near resting Vm, the activation
gate will close and the inactivation gate gets reset in the open position
again. This ends the absolute refractory period.
Now the voltage-sensitive K+ channel.
1. A single gate
2. Opens slower, such that these channels open as the action potential is
at the peak.
3. Also closes slower which explains the hyperpolarization seen after the
peak has passed.
4. The relative refractory period is a function of two main items: 1) not
all of the Na+ inactivation gates are open (the cell can fire); 2) the
potassium permeability is greater than normal. The Vm is closer to the Ek.
These both result in a cell that requires a bigger bang to reach threshold
potential.
Other details:
The whole action potential lasts just a few msec., if that.
Note that the action potential does not require energy, as long as the
concentration gradients are maintained (this does require energy, of
course). In fact, experimentalists can poison the Na -K pump and create
hundreds to hundreds of thousands of action potentials in an axon (#
depends on the size of axon). During an A.P. only a peq/cm2 of Na and K
move across the membrane. Clinically, the concentration of some ions in the
extracellular fluid may change, and this can make cells hyper, or
hypo-excitable, depending on whether the resting Vm drifts closer to
threshold or further away. Also low Ca has magical stimulatory effects.
Movement or Propagation of the Action Potential:
We have described local changes in ionic flow which cause an event called
the action potential. But an action potential also implies movement over
the surface of the cell. How is this accomplished? The short answer is:
by local potentials. If a cell is not myelinated (only axons are
myelinated) v-s channels are dispersed in the membrane. As channels in one
region reach threshold, the inward Na current changes the ionic
distribution across that section of membrane, and these charges will flow
to neighboring regions. This flow will cause these regions to reach
threshold potential and in turn, fire. Myelination increases the speed of
conduction, local potentials jump from node of Ranvier to node (saltatory
conduction).
Steven Eiger, Ph.D.
Department of Cell Biology and Neuroscience and the WWAMI Medical Education
Program
PO Box 173148
Montana State University - Bozeman
Bozeman, MT 59717-3148
Voice: (406) 994-5672
E-mail: eiger@montana.edu
FAX: (406) 994-7077
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