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Membranes
Written by Tim Sheppard MBBS BSc. Last updated 9/11/10

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What is a membrane?

If you fill a balloon with water, the balloon keeps the water in. The rubbery layer is water tight, and it prevents water seeping out. If you filled that balloon with something else - say, with treacle - that balloon would stop treacle leaking out. If that treacle had lots of pieces of pastry in it, those pieces of pastry would be kept in because the balloon was keeping everything together.

Essentially the membrane plays the role of that balloon. It is the outer layer which keeps everything together - it holds everything in. The contents of the cell, known as the cytoplasm, are kept within this membrane and prevented from leaking out, unless the membrane is broken or ruptured, or deliberately interrupted.

Incidentally, the membrane doesn't just cover the outside of the cell - that's just the cell membrane. The inside of the cell contains objects known as organelles, such as the nucleus or mitochondrion, and each of these is wrapped up in a membrane - to stop it leaking out within the cell. Each of these little packages has its own job to do, and it doesn't want all its contents to be shared with everything else.

Of course, if the membrane were just like a rubber sack, that would be too easy. Unfortunately the membrane does have to let a few other things happen - it has a function. As well as keeping things inside or outside, it also has to allow transport of substances. Also, some reactions happen at membranes. There are lots of things that go on, and for that reason, proteins are often found around membranes - sometimes anchored in the membrane, sometimes just on the periphery, and sometimes embedded - spanning the whole width of the membrane.

The various things that happen at membranes are described elsewhere. The last important thing to remember is that the membrane is generally made of a phospholipid bilayer - two layers of phospholipids against each other. This will be explained more in the next section.


What is a phospholipid?

In diagrams you'll often see a circle with zig-zag legs, and unless you know what a phospholipid is, you'll probably not recognise it. Scientists, in their wisdom, have decided to generalise what a phospholipid looks like, because their presence in membranes makes short-hand very helpful. Essentially they are a polar head and a non-polar base - that is, their head has a charge (in the form of a phosphate group) and their legs do not (because they are long chains). Let me explain...

Triacylglyercol is a glycerol molecule with three fatty acids coming off it. A phospholipid, a cartoon of which is shown to the right, is a glycerol molecule with two fatty acids (seen fading into transparency on the bottom) coming off it, and a phosphate group coming off the third 'space'. The long fatty acids don't have any charge; they're just endless carbon molecules with hydrogens on either side, sometimes with double bonds thrown in. They are relatively simple, and they don't have a charge - they are 'non-polar'. The head on the other hand (where the glycerol backbone is) has a phosphate group coming off it. As you can see from the cartoon, the phosphate group (the orange circle with red circles on every side) has a charge, and this means that it is 'polar'.

Essentially this means that the heads will by hydrophilic - i.e. attracted to water - and the tails (or legs, or fatty acid chains) will be hydrophobic - i.e. repelled by water, attracted to fatty acids and non-polar substances.

In practice this has many important applications, not least their use in the phospholipid bilayer of cellular membranes. The bilayer is arranged in such a way that the heads are on the outside, and the tails of each layer face each other. The image below represents this.

Because of the 'fatty core' of the phospholipid bilayer, formed by all of the tails zig-zagging their way into the centre, water and 'polar' substances are unable to make their way through the layer. However, fatty or non-polar substances - such as fatty acids - have no trouble getting through because the fatty core is exactly the kind of environment they are looking for. Of course, if it is too big, it cannot fit through, but generally fatty acids are only so long, and will slide through.

If something is unable to get through, either because it is polar, or because it is too big - or both - then it needs a specific transporter. That is why there are so many proteins associated with the membrane, embedded between the phospholipids.


What is the resting membrane potential?

According to the laws of diffusion, a substance may move through a partially permeable membrane down its concentration gradient - that is, it will move to where its concentration is lower. According to the laws of physics, voltage is a measure of power, or the energy required to move a charge. Voltage is also expressed as potential difference (i.e. the difference in electrical potential between two points), and it is really this that we're talking about when we refer to membrane potential.

However, the energy required to move a charge will depend on a variety of things - including the tendency of a charge to diffuse, and something called the electrochemical gradient. When we refer to the resting membrane potential, what we actually mean is the voltage (or potential difference) across a normal cell membrane, in normal conditions, taking into account the concentration and electrical gradients.

In 'normal' circumstances, the sodium ion (Na+) concentration outside a cell is around 145mM, but only about 10mM inside the cell. Sodium has a tendency to move into a cell.

The concentration of potassium ions (K+) in a cell is around 120mM, while outside it is less than 5mM. This means that potassium will tend to move out of the cell.

However, we're about to discover that the electrical potential of the membrane is distinctly negative - largely because of the concentration gradient of potassium leading potassium out of the cell. Because of this negativity, positive potassium and sodium ions outside the cell are attracted into the cell.

So potassium tends to want to leave, sodium wants to get in, based on concentration gradients, and both want to get in based on the electrical gradient.

So what happens? Well, we use something called the Nernst Equation. It works on the principle that, at the end of the day, the chemical forces (i.e. the effect of the concentration gradients) and the electrical forces (i.e. the attraction of charge) have to be equal if the system is in balance (after all, your cells aren't exploding everywhere; there's lots going on, but they are still 'in balance'). If the electrical forces (calculated by Ezf) and the chemical forces (calculated by RT ln([ion]o/[ion]i) ) have to be equal, it could be written that Ezf = RT ln([ion]o/[ion]i)

The animation below shows how the terms are rearranged. E stands for the electrical potential difference, so that's what we want on it's own. The other terms are explained as follows:

R - ideal gas constant
T - absolute temperature
z - the charge of the relavant ion
F - Faraday's number, a constant
ln - the logarithm to the base e (it's another constant)
[ion]o - the concentration of the ion outside the cell
[ion]i - the concentration of the ion inside the cell

This is still remarkably complicated, but we can simplify it to make calculations easier. We know the constants because they're constant, and using laws of logarithms we can change the base from e to 10 - which is much nicer to handle. Since the charges of potassium and sodium are both +1, that is also known; so it can be simplified to the equation given below.

If we put the values we know for potassium into this, we get about -90mV, so if the membrane were only permeable to potassium, then this would be the resting membrane potential.

As it happens, neurons have a resting membrane potential of something more like -70mV. So what's going on?

When you put sodium (Na) into the equation, you get about +70mV - which means that if the membrane were only permeable to sodium, the voltage across it would be 70. This is obviously not the case either - it's -70mV in neurons. What we realise is that the membrane must be permeable to both potassium and sodium. Since it's very close to potassium, we realise that the membrane is obviously more permeable to potassium, but we have to take into consideration the values for sodium before we get the right answer. Fortunately, scientists named Goldman, Hodgkin and Katz came up with something called the Goldman-Hodgkin-Katz (Constant Field) Equation, shown below.

This includes something called a, the ion selectivity of the membrane. It changes depending upon which membrane channels are open, but is given by the permeability of the membrane to sodium, divided by the permeability of the membrane to potassium.

If the membrane were 30 times more permeable to potassium than sodium, then the voltage would change to roughly -70mV, the resting membrane potential of neurons.


What is the sodium-potassium pump?

It's probably worth considering at this point a pump which is involved in a lot of membranes. Because membranes, as just discussed, are permeable to ions and let some through, eventually you'd end up with different concentrations. Now, we're talking very small amounts here - at the end of the day, it's not likely to be a problem. However, one of the mechanisms in place to make sure that the concentrations remain constant is the sodium-potassium pump, also known as the sodium potassium exchanger.

There really isn't anything complicated to explain here, except that it swaps 3 sodium ions inside the cell for 2 potassium ions outside the cell, and because this is going to change the charge inside the cell (overall it's getting rid of a positive charge), it requires energy, found through the hydrolysis of ATP. Because it involves ATP, the pump is also known as sodium-potassium-ATPase or Na-K-ATPase.

Importantly, the sodium potassium pump does not have a huge effect on the resting membrane potential. There are drugs that can block this pump, yet the resting membrane potential hardly changes at all.


What is an action potential?

I remember studying action potentials and finding it incredibly daunting - to begin with, they were mentioned and I had no idea what they actually were, yet everyone around me seemed to understand. At the end of the day, they're not that complicated, and the very basics could actually get you quite far: basically, they are simply a very brief fluctuation in resting membrane potential in order to signal something. Or you could think of the signal like a Mexican wave, only instead of arms waving it's an electrical signal, and instead of moving along a crowd of people it's moving along a membrane.

Usually you'll see the action potential in the form shown on the left. A graph of membrane potential against time shows the membrane potential beginning with the resting membrane potential or RMP. If something causes this to change, it may depolarize (or become less negative, more positive). There are lots of things that could cause this depolarization; it may be an action potential has been formed somewhere else on the membrane, and the change in voltage has carried through to here; it may be that a subtance has caused a sodium channel to open - as previously discussed, this would make the membrane more permeable to sodium and therefore make the membrane potential more positive.

Whatever it is that causes the depolarization, if it reaches threshold, it will cause an action potential. The threshold is a particular membrane potential which causes all the voltage gated sodium channels to open, and if it's not reached, the action potential will not happen.

So what are voltage gated sodium channels? Well, there are lots of channels in a membrane that let a particular substance through. Sodium channels, not surprisingly, are channels which allow sodium through. Some sodium channels have 'gates', which will allow sodium through sometimes, but not always. Not surprisingly, voltage gated sodium channels are sensitive to voltage - so if the voltage is right, the gate will be open and it will allow sodium through.

The channels we are interested in are called TTX sensitive sodium channels because tetrodotoxin (TTX) from puffer fish blocks them. These are the sodium channels involved in an action potential (AP) and they have two gates - an activation gate and an inactivation gate, each of which opens and closes at a different voltage.

At rest, the activation gate is closed, the inactivation gate is open; no sodium can get through. When the membrane potential reaches threshold (shown as going red in the animation), the activation gate opens, and sodium is able to get through. However, when the membrane potential passes a certain point (shown as going white again in the animation) the inactivation gate closes, preventing further passage of sodium.

This leads to a characteristic shape. The initial depolarization reaches threshold, and when it does, the activation gates on all the TTX sodium channels open. This increases the permeability to sodium. Let's say that it was increased to the extent that sodium became 10 times more permeable than potassium; this would lead to a membrane potential of +50mV. So the membrane potential shoots up towards +50mv.

However, when the membrane potential reaches, say, 0mV, the inactivation gates begin to close, preventing further sodium influx. The overshoot is caused by the slow decrease in permeability towards sodium; eventually the membrane is 30 times more permeable to potassium again, and the membrane potential shoots down towards the RMP - this is called the repolarization. The membrane potential will overshoot again, and then have to work its way back up towards the RMP; this is called hyperpolarization, and it follows the action potential.

Remember that this is a typical example - not all action potentials are this shape. And generally (though again, not always), all this happens in only a matter of milliseconds - one or two, typically. The action potential is very brief, but it only needs to be. If it's in a nerve, then it just needs to be long enough to signal whatever it is that it is signalling, or to pass on the signal to the next section of nerve. If the signal needs to be longer - such as causing a muscle to contract - then a series of action potentials must be used; however, that is an entirely separate issue.

Notice that if the membrane potential does not reach threshold, the activation gates won't open, so the potential simply returns to RMP when the depolarization is over. This is referred to as a subthreshold response.

One of the important features of an action potential is something called the refractory period. Put simply, it's the time just after an action potential when another action potential cannot be initiated. Let's go back to the TTX sensitive sodium channel. At the end of the action potential, the inactivation gate is shut. While this is shut, you cannot have another action potential. The refractory period will last until the inactivation gate is open and the activation gate is closed - i.e. the resting state is returned. The reason this is so important is that in some cases this controls the rate of action potentials - only so many can come through in a given period of time.


Further Reading