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. Thanks for watching, you can help support
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