Each cell in the human body is wrapped in a membrane that separates the inner environment
and outer environment, and positively and negatively charged ions aren’t equally distributed
on both sides of the membrane.
Fundamentally, it’s these differences in concentration and charge as well as permeability
across the membrane that establishes the cell’s resting membrane potential.
Generally speaking there is a higher concentration of Na+ or sodium, Cl- or chloride, and Ca2+
or calcium on the outside of a cell, and a higher concentration of (K+) or potassium
and (A-), which is just what we just write for negatively charged anions, on the inside
of a cell.
These anions include a variety of amino acids and proteins that are produced by the cell.
Let’s start with the sodium-potassium pump which uses ATP to move three sodium ions out
of the cell for every 2 potassium ions that it moves into the cell, this is the workhorse
of the cell and it helps establish the concentration gradient for potassium and sodium.
Let’s focus on potassium, which has a concentration of 150 mMol/L on the inside of the cell and
about 5 mMol/L on the outside of the cell.
With so much potassium within the cell relative to outside the cell, there will be fairly
strong concentration gradient moving potassium ions out of the cell.
Although these ions can’t simply diffuse through the phospholipid bilayer membrane,
it turns out that potassium can get across the membrane using potassium leak channels
and inward rectifier channels that are scattered throughout the membrane.
So using those channels, the concentration gradient pushes potassium out of the cell,
and that potassium brings with it some positive charge and leaves behind unpaired anions which
carry negative charge because they aren’t able to go through the leak channels.
Over time as more potassium ions leave the cell, a negative charge builds up within the
cell and this starts to attract positively charged potassium ions back into the cell,
and this is called the electrostatic gradient.
This electrostatic gradient is established with the movement of relatively few ions,
so it doesn’t upset the overall concentration gradient that was already established.
For potassium, the exact point when the potassium moving out of the cell due to the concentration
gradient equals the potassium moving back into the cell due to the electrostatic gradient
is called the equilibrium potential or nernst potential for potassium, and it’s about
-92 mV.
In other words, -92 mV is the electric potential for attracting potassium into the cell that
is needed to balance the concentration gradient that is pushing potassium out of the cell.
So the equilibrium potential of an ion is dependent on two things: the concentration
gradient for the ion and the cell being permeable to that ion.
If we’re only dealing with a single ion, then the equilibrium potential for the ion
equals the resting membrane potential for the cell.
In reality, though, there are multiple ions that have concentration gradients and are
permeable across the cell membrane, each of which has it’s own equilibrium potential.
Now the formula that tells us the equilibrium potential for each ion called the Nernst equation,
and it’s Vm (for membrane) equals 61.5 times the log of the concentration of the ion outside
the cell, divided by the concentration of the ion inside the cell, for an ion with a
single charge like sodium, and Vm equals 30.75 times the log the concentration of the ion
outside divided by the concentration of the ion inside for an ion with a double charge
like calcium.
For the four main ions that affect the cell’s resting membrane potential, which are potassium,
sodium, chloride, and calcium, the concentrations are 150 mMol/L, 10 mMol/L, and 4 mMol/L, and
less than 1μMol/L on the inside of the cell, and 5 mMol/L, 142 mMol/L, and 103 mMol/L,
5 mMol/L on the outside of the cell.
Plugging those into the formula, we get equilibrium potentials of -92 mV, +67 mV, 86 mV, and +123
mV.
One thing to note, though, is that since chloride ion is negative, the equilibrium potential
actually gets flipped, so it’s actually -86 mV.
These all represent the charge in the cell needed to balance the movement of each of
these ions based on the concentration gradients, and to make it clear the concentration gradients
themselves are potassium moving out, calcium moving in, sodium moving in, and chloride
moving in, since remember there’s low concentration of potassium outside the cell, but high concentration
of calcium, sodium, and chloride outside the cell, and concentration gradients move from
high concentration to low concentration.
Alright, so the actual resting membrane potential of the cell will end up being somewhere in
between all these individual membrane potentials, depending on how much of each of these ions
is moving across the membrane at a given time.
This differs depending on the cell that we’re talking about, but in general potassium makes
up the biggest proportion of ions moving across the membrane, while the other three have way
less moving across at any given time.
Alright so of all the ions moving across the cell membrane through leak channels, let’s
say that 90% of them are potassium ions, whereas only 1% are calcium ions, 1% are sodium ions,
8% are chloride ions.
Now we can take these proportions and multiply them by the equilibrium potentials and then
add up the total to get the resting membrane potential of the cell.
In this case it works out to 90% of -90mV (-81 mV) plus 1% of 123 mV or 1.23 mV, plus
1% of 67 mV which is 0.67 mV, and plus 8% of -86mV which is -6.88mV, which gives a grand
total resting membrane potential of -86 mV.
Now this resting membrane potential is usually closest to whichever ion is most permeable
across the membrane, which in this case is potassium, right?
But by changing the cell’s permeability to ions by adding or removing ion channels,
a cell can actually change its resting membrane potential.
Okay, as a quick recap, an ion’s equilibrium potential is the point where its concentration
gradient equals its electrostatic gradient, and can be calculated using the Nernst equation.
The cell’s resting membrane potential is therefore a summation of each individual ion’s
equilibrium potential, depending on each ion’s relative permeability.
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