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Voltage Clamp

Matt Jones jonesmat at ohsu.edu
Sun Nov 14 17:49:08 EST 1999

In article <80l1qh$aum$1 at new-news.cc.brandeis.edu> Mark Fehr,
wolf at brandeis.edu writes:
>    I'm an aspiring neuroscientist, a junior in college, and was wondering
>if someone could help me out with a concept in my intro to neuroscience
>class.  Can someone explain how the voltage clamp exactly works, and what I
>read from it? I have a vague idea, and would like it to me more grounded.

I'll explain what it's used for, and then if you want to know more about
how a voltage clamp circuit works, you can post a specific question about
that, ok?

Voltage clamp is a technique that electrophysiologists use to study the
ionic conductances that underlie electrical excitability in living cells
(usually nerve or muscle cells, but it can be used to study any cell).

A little background on the biology first (also see Richard Norman's
response elsewhere in this thread):

All cells have a cell membrane that separates the internal components
from the extracellular environment. This membrane is highly resistive to
allowing ions (such as sodium or potassium) to cross from one side to the
other.  But the -regulated- passage of ions is very important for all
cells, so there are special proteins that reside in the membrane for
transporting ions across. Some of these proteins are called "ion
channels", and nowadays we know (because of voltage clamp experiments)
quite a lot about them. Basically they are little pores that allow ions
to pass from one side to the other, but they're not always wide open.
They have "gates" that open and close depending on the membrane potential
(in the case of voltage-gated channels) or on the binding of a
neurotransmitter (in the case of ligand-gated channels). Much of cellular
electrophysiology has to do with studying these channels and trying to
determine the physical parameters (i.e., voltage, ligand concentration)
that get them to open or close, and understanding how this "gating" gives
rise to the transmission of information within and between cells. You
probably already knew about all that.

Anyway, now for the methods: 
The most famous use of the voltage clamp was performed by Hodgkin and
Huxley (for which they won the Nobel prize) in the 40's and 50's. They
knew that nerves were electrically "excitable" because they could put a
nerve (the giant axon of a squid) in a tissue bath and stimulate it, and
it would respond with a very rapid "spike" in potential (i.e., an action
potential). That is, if they draped a wire across its surface, and hooked
that up to a voltage-follower amplifier (i.e., takes a small change in
voltage and turns it into a big change in voltage so that you can see it
on an oscilloscope), the circuit showed very brief pulses in response to
stimulation. These pulses were always the same size (i.e., were
all-or-none events) but could travel for long distances along the nerve,
like a wave that didin't get smaller as it traveled. They knew,
therefore, that these spikes must be important for the axon in doing its
job of sending information from one place to another, but they didn't yet
know exactly what the nature of these spikes were.

Obviously, figuring this out is a problem in electrical engineering, so
they drew on the basic principles of electrical engineering to help them.
The most basic feature of electrical phenomena is the idea of
"conductance", the ability of a material to allow a current to flow from
one place to another. Specifically, if you take a conductor and apply two
different voltages to either end of it (by hooking it up across the + and
- terminals of a battery, say), then charged particles will flow from one
terminal to the other through the conductor. This flow of current follows
a quantitative dependence on both the voltage and the type of material,
which is given by Ohm's Law

deltaV = IR;

where dV is the difference in voltage between one pole of the battery and
the other (in Volts), I is the current that flows through the conductor
(in Amperes, a measure of the number of charges flowing through every
cross section of the conductor per unit of time) and R is a
proportionality constant called the "resistance" of the conductor (in
Ohms). Also, the conductance, G, is just 1/R. If you remember nothing
else about voltage clamp, remember that it depends entirely on Ohm's Law,
and that you can figure it out from there.

So how to use Ohm's Law to understand the action potential? Well first of
all, you need to have electrical access to both sides of the conductor
(or you could also call it the resistor, if you like. They sound
opposite, but remember that you get resistance by taking 1/conductance,
so they're just two different ways of talking about the same thing). For
the squid axon, the conductor is the membrane separating the inside of
the cell from the outside. They therefore ran one wire up the inside of
the axon, and had another wire outside in their bath. The cut ends of the
axon were sealed with vaseline, so any current passing between the two
wires would have to somehow cross the membrane. This is exactly what they
wanted, because they suspected that the action potential was caused by
changes in the conductance of the membrane, and they wanted to measure
those changes.

But, you can't accurately measure voltage and current at the same time,
because Ohm's Law says they change proportionally with each other. To
measure one, you need to hold the other one constant. This is what the
voltage clamp does. One wire is inside the cell, and is hooked up to one
end of the voltage clamp circuit. The other wire is outside the cell, and
hooked to the other end of the voltage clamp circuit. The voltage clamp
then applies a voltage between these two wires that the experimenter
controls (exactly as if they were attached to two ends of an adjustable
battery). Any current that flows between these two wires must pass
through the membrane (and these days we know that the current passes
through specific ion channels in the mambrane, not the membrane itself).
Part of the voltage clamp circuitry enables you to observe this current
on an oscilloscope. So you now have all the pieces you need to figure out
how an action potential is generated by changes in the conductance of the
membrane. You use Ohm's Law:

dV = IR; let's rewrite it as dV = I/G and rearrange to G = I/dV; which
expresses conductance as the ratio of I (which we -measure- during the
experiment) and dV (which we -control- or -clamp- by twiddling the knobs
on our voltage clamp amplifier (actually these days we tell our computer
to twiddle the knobs for us)). We control the voltage (so we know exactly
what it is), we measure the current (so now we also know exactly what it
is) and then we plug them into Ohm's Law to solve for the membrane

It turns out (as shown in some of the most elegant experiments and
analysis ever performed in biology to this very day) that when you change
the voltage, the membrane conductance also changes (so it's not really
Ohmic, because its not linear with voltage as Ohm's Law predicts.  But
the -voltage clamp- still depends on Ohm's Law to work). Also, the
conductances to different ions (sodium and potassium) change differently
with voltage, and also differ in their time course. First there is a
rapid and transient increase in sodium conductance, and that is followed
by a slower but long lasting increase in potassium conductance. This is
what you observe under voltage clamp. However in current clamp (that is,
you hold the current flowing between your wires fixed at a certain level,
and observe the voltage that develops across the membrane (in accordance
with Ohm's Law)), these two different conductance changes give rise to a
brief and large spike in voltage: the action potential.

Hodgkin and Huxley took their measurements of the time and voltage
dependent changes in the potassium and sodium conductances, and wrote
them into a set of coupled differential equations that describes almost
exactly how these changes generate the action potential. Furthermore, by
studying very carefully the details of the conductance changes
themselves, they predicted the existence of discrete ion channels for
each species of ion (which we now know is exactly right because some of
these channels have been cloned and crystalized, and with the advent of
patch clamping, the ion current through an individual channel can now be
routinely recorded. They even essentially predicted how many protein
subunits the potassium channels are composed of (!), decades before
anyone could isolate the molecules involved.

One last thing: neuroscience is really cool, and electrophysiology is
really really cool. You should study it hard, and go to grad school to
learn how to do it for a living. 

Good luck,

Matt Jones

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