From: Steven Eiger (eiger@montana.edu)
Date: Sat Nov 17 2001 - 09:50:54 PST
Message-Id: <l03102800b81c52123f19@[153.90.150.107]> Date: Sat, 17 Nov 2001 10:50:54 -0700 From: Steven Eiger <eiger@montana.edu> Subject: Re: pinhole Nervous system and voltage
Pinholers, apparently I can not send an encolosure, so I will try and plug
in pieces, in installments; If you want the whole shebang, send me a
personal email address. The pictures help a lot.
Cell Membranes and Transport
A look at our syllabus this semester will reveal that we are going to be
studying nerve, muscle, and transport mechanisms into and out of the body.
We are going to be looking at these physiological mechanisms to a depth
where it will often appear as simple physics; that is precisely our goal -
to reduce these complicated functions to a series of near obvious steps.
While we will be looking at mainly nerve and muscle, these traits are not
unique to these tissues, but are shared to varying extents by all cells,
and therefore have importance beyond our immediate discussions.
Our Electrical System:
The two major modes of signaling in the body are 1. Hormonal, which
involves the bulk flow of chemical messengers moving through the blood
followed by diffusion to specific target cells. This is a slower system,
but requires less hardware, and thus is very cost efficient; and 2.
neuronal, which uses an electrical signal flowing over the surface of
specialized cells. This is a high-speed system, but requires wires
(neurons) to each innervated cell. All cells have an electrical potential
across their cell membrane and are very likely to use this as some form of
signaling mechanism, either to neighboring cells or to different parts of
themselves. Both signaling mechanisms require a means of communicating
signals on the cell surface to the interior, and we will also look at a few
of these.
What is this electrical signal? A change in membrane potential.
What is a membrane potential and how is it formed? It turns out that all
cells have membrane potentials. It is a separation of charge across the
outer cell membrane (plasma membrane) such that the inside of the cell is
generally more negative than the outside. To understand this conceptually
difficult process, we will first look at the plasma membrane.
The plasma membrane.
This figure illustrates the standard fluid mosaic model of a biological
membrane. There are a few interesting things to note.
1. About half of the membrane is made from phospholipids. These are
oriented such that their polar head groups are pulled towards the watery
cytoplasm or extracellular fluid (ECF); and their lipid moieties are all
facing inward where they only need contact each other. This organization
arises due to the differential bond formation which gives us the axiom "oil
and water do not mix", and gives the membrane a structure. Cholesterol
will intercalate between the phospholipids, acting as a fluidity buffer
within the membrane; it binds up other agents, such as alcohols and general
anesthetics which, by virtue of their ability to break up the Van Der Waals
interaction between the hydrophobic tails of the phospholipids would have a
much greater affect on the membrane fluidity alone.
2. The rest of the membrane is made of proteins embedded in this
phospholipid matrix. These proteins are often free to move in this two
dimensional world. They are held in place by the interaction between the
oil:water characteristics of their outer surfaces and that of the membrane.
They are called integral membrane proteins. Their orientation is
determined at their birth (translation) by the signal sequence attached to
the amino end of their mRNA, this is translated into a signal peptide that
binds to a receptor on the rER. Note also that there are often sugar
groups attached to the proteins and phospholipids of the membrane. These
always end up facing the ECF. This is because the process of adding
sugars, or glycosylation, takes place inside of the endoplasmic reticulum
or Golgi apparatus, which is topographically similar to the exterior of the
cell. This topographic similarity is a result of the mechanism by which
membrane material is added to the plasma membrane (by fusion of vesicles -
the vesicles will in essence invert or open up upon fusion, placing the
interior surface of the vesicle on the outside of the cell.
Transport
By Diffusion, i.e. without the help of proteins:
The lipid portion of the membrane is permeable to things that are either
lipid-like and can dissolve in the lipid, or else very small. I am not
sure about the second half of this statement. Water has classically been
thought to diffuse across the lipid portion of membranes, although I have
never believed this. Gases such as carbon dioxide, nitric oxide, and
oxygen certainly can cross the lipid bilayer. It has been stated that each
hydrogen bond made with water will decrease the permeability 40-fold; water
itself makes 3 hydrogen bonds, so that ought to translate to a 64,000-fold
reduction in permeability. Furthermore there are membranes, such as the
renal collecting ducts, which are impermeable to water until aquorins
(water pores) are inserted into them. Make your own judgment. As far as
non-polar solutes crossing the membrane, there have been beautiful studies
showing a direct correlation between a substance's ability to dissolve in
olive oil and its ability to enter the brain.
It is a lot of fun to think about diffusion. It is purely random motion,
although we do have to consider fields. For uncharged substances moving
horizontally, they cross a membrane, if able, according to how often they
hit holes. If there are more on the left, they are more likely to hit from
the left, and move to the right. It is as simple as that. As this is an
advanced course, we have to consider fields and realize that things often
carry charges and therefore the electrochemical gradient is more
appropriate to use than a concentration gradient, but the idea is the same.
Diffusion rate will fit Rate = PADu. Where P is the permeability of the
membrane for the substance, A is the cross sectional area of the membrane
(more area, more diffusion), and Du is the electrochemical gradient.
Facilitated Transport, i.e. with the help of proteins.
Two Types;
… Facilitated diffusion, and
… Active transport
Both are distinguishable from simple diffusion in that:
… Transport is saturable;
… and in the case of active transport, transport requires energy.
The proteins: The electrical characteristics of a particular cell membrane
are due to the nature and quantity of the proteins embedded in it, and the
immediate electrical and chemical milieu (this affects certain transport
proteins).
Facilitated Diffusion:
Two types: channels, and clam-shell transporters.
Clam-shells transport things like amino acids and sugars. They bind the
ligand, change shape, and voila, it appears on the other side.
Facilitated diffusion will only transport material down an electrochemical
gradient.
Channels are essentially holes through which material can diffuse through.
They are specific in terms of what they will allow through, so they have
some characteristics in common with the clam shells.
Many of these channels are involved in ion transport. These have holes in
them. The holes, sometimes described as water-filled pores, will allow
certain polar solutes to pass. It is these pores, or channels that are
going to determine the electrical characteristics of the membrane. The
type of electrical signals a membrane is capable of producing is a direct
result of the types of channels present. The number of known channels is
growing, e.g. there are eight voltage-sensitive channels in cardiac muscle
- genetic defects in some of these lead to dangerous arrythmias.
Channels have three characteristics that are going to be very important:
… Channels conduct ions. The main ions will be K+, Na+, Ca++, and Cl-.
These may go through the channels with water attached. Certainly while
free in solution these ions are solvated.
… Channels recognize and select among specific ions.
… Some channels open or close in response to specific electric, chemical,
or mechanical signals. Channels capable of responding to such signals are
called gated. Other channels that do not change their conducting
capabilities in response to signals are called passive, or leakage channels.
Primary Active Transport:
Protein transporters have structure very, very similar to clam shells, but
require energy (supplied by ATP).
As ATP is supplying the energy, material can be transported against, or up
an electrochemical gradient.
Equilibrium potentials:
Now lets enclose a volume with our membrane so that we have an inside and
an outside. Lets also put a salt such as KCl at equal concentrations on
the inside and outside. Lets also assume that there are ion channels
selective for K+ in the membrane. What will happen?
K+ will diffuse in and out of our cell. However, since the concentration
of K+ is the same on both sides of the membrane, the number of K+ ions
hitting the channels from the inside will be the same as the number hitting
the channels from the outside. The result is that the number of K+ ions
moving into the cell, or the inward flux, will equal the outward flux, and
the net flux will be 0. J will represent flux. We can make our first
equation here. Jnet = Jin - Jout = 0. This is pure statistics, chaos,
chance, or luck. One of Albert Einstein's first papers was on Brownian
motion, where he worked out the speed at which biological molecules would
move in solution!
Now this is dull result, but what would happen if the inside of the cell
had K+Cl- in it and the outside of the cell was bathed in Na+Cl-? Again,
lets assume that there are only K+ channels in the membrane. Our system
would now look like this:
Now there will be a non-zero net K+ flux, Jnet ‚ 0. Can we quantify this
flux? Well the initial net flux can be estimated, and later we will see
why this is the best we can do. Let's try to derive this equation. What
will determine how fast the K+ will leave? First, the larger the
difference in concentration between the inside and outside of the cell, the
quicker will be the Jnet. Therefore: Jnet a Cinside - Coutside. Or, Jnet
a C.
Also, the larger the surface area available for diffusion to occur through,
the larger the flux. Therefore, Jnet a AC.
Now, the thinner the membrane, the greater the flux, so, Jnet a AC/l,
where l is the width of the membrane. C/l, or the difference in
concentration for a given distance is called the concentration gradient.
We can also add a factor, D, which will correct for the size, solubility,
and other characteristics. This leaves us with the Fick diffusion equation.
Jnet = DAC/l
Usually there is a minus sign in front of this equation, which ensures that
one understands that things diffuse from regions of high concentrations to
low concentrations.
Now if we were to do the above experiment, we might expect the K+ to
diffuse out of the cell until the inside concentration equaled the outside
concentration; but this does not happen. Instead very little net K+
actually leaves. Instead, something very interesting happens. As each K+
ion leaves, it takes its little positive charge with it, and leaves behind
an unbalanced negative charge, in this case, a Cl- ion. We begin to get a
separation of charge. The outside of the cell gains + charges and the
inside gets a net - charge. Since unlike charges are attracted to one
another, these charged ions would tend to crowd up next to the membrane,
like so;
Clearly our Fick's diffusion equation must only apply to uncharged, and
simpler situations. In the real world of charged particles, players
respond to not only chemical (concentration) gradients, but electrical ones
as well. The combination of these two gradients, which is related to the
net movement of the particle, is called the electrochemical gradient. A K+
ion leaving the cell will be repulsed by the positive charges on the
exterior, and attracted to the negative charges in the cell's interior.
This electrical gradient, created by the diffusion of K+, i.e. by the
chemical gradient, will tend to push K+ into the cell. This difference in
electrical potential between the inside and the outside of the membrane is
called a potential difference or a voltage. It can be looked at as a
source of energy. If we raise a weight into the air (gain of potential
energy), it can drop and do some work on a spike going into the ground;
likewise, it takes some work to rip apart the positive and negative ions,
and separate them by the width of the membrane. The work in this case is
done by the chemical gradient. This results in an electric field being set
up within the membrane, such that a charged ion placed there will
experience a force, and if mobile, will move. It also points out that the
membrane has a capacitance, i.e. it can store charge.
The equilibrium situation: Now it turns out that after very few K+
ions leave the cell the electrical gradient becomes strong enough to
completely counteract the concentration gradient. This is not at all
intuitive, but it is true. Since an insignificant number, in terms of the
concentration gradient, of K+ ions has left the cell, the concentration
gradient for K+ is essentially unchanged, and still strongly outward; the
electrical gradient, with the inside of the cell negative relative to the
outside, is strongly inward for K+. Again, this idea of just a few ions
leaving the cell and creating a force to balance the concentration gradient
is not intuitive. These apparent pushes on ions arise from entirely
different sources; and have huge differences in strength for a similar
number of ions moving. One force is due to random chance (the chemical
gradient). The other is due to an electric field created by positive and
negative charges being separated in space (electrical gradient). As the
chemical and electrical gradients are oriented in opposite directions, and
are of equal strength, K+ is now in electrochemical equilibrium, its
electrochemical gradient is zero. The electrical potential that will
balance the given concentration gradient for a given ion is called the
equilibrium potential (Eion) for that ion. This can be calculated for any
given concentration gradient using the Nernst equation that states:
for a given ion, RT [ion]o
Eion = ----- ln -------
zF [ion]i
where R is the gas constant, T is temperature in degrees Kelvin, F is
Faraday's constant, and z is the charge on the ion. Note also that it is
the ln of the outside:inside ratio of the ion that is used, not the
concentration gradient, but the basic idea is the same.
In the preceeding discusion we had K+ moving through channels to create a
potential; this is called a diffusion potential. However, for any ion,
which has different concentrations on the inside and outside of the cell,
there will be a theoretical Eion for that particular ion. If our ion of
interest is the only ion that can diffuse across the membrane, it will
generate a diffusion potential, which will be equal to its calculated
equilibrium potential. Note also that if the membrane potential happens to
be equal to the equilibrium potential for that ion, the net flux for that
ion will be zero. Thus, in the situation where there are concentration
gradients, and the membrane is permeable to just a single ion, we can
easily calculate the potential across the membrane from the Nernst
equation: but things are never that simple as we shall soon see.
>I'm trying to teach students what happens inside a nerve cells when signals
>are transmitted. The sources I am reading suggest that the inside of cell
>has a potential relative to the outside of the cell. The value of this
>potential is -70mV.
>
>Should I think about this voltage as I do the voltage in a battery? Are
>electrons getting potential energy from a chemical reaction? What electrons
>are getting this energy? I can only find information about sodium, potassium
>and calcium ions.
>
>So, in short, I'm trying to figure out how the transmission in neurons
>relates to what I know about electrical circuits. I'd appreciate any input.
>
>Thanks,
>Jhumki Basu
>
>
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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