Editing Resting potential (section)

==Generation of the resting potential==

Cell membranes are typically permeable to only a subset of ions. These usually include potassium ions, chloride ions, bicarbonate ions, and others.  To simplify the description of the ionic basis of the resting membrane potential, it is most useful to consider only one ionic species at first, and consider the others later.  Since trans-plasma-membrane potentials are almost always determined primarily by potassium permeability, that is where to start.{{cn|date=May 2025}}

[[Image:Membrane potential development.jpg|thumb|400px|A diagram showing the progression in the development of a membrane potential from a concentration gradient (for potassium). <span style="color:#008000;">Green</span> arrows indicate net movement of K<sup>+</sup> down a concentration gradient. <span style="color:#ff0000;">Red</span> arrows indicate net movement of K<sup>+</sup> due to the membrane potential. The diagram is misleading in that while the concentration of potassium ions outside of the cell increases, only a small amount of K<sup>+</sup> needs to cross the membrane in order to produce a membrane potential with a magnitude large enough to counter the tendency of the potassium ions to move down the concentration gradient.]]

*Panel 1 of the diagram shows a diagrammatic representation of a simple cell where a concentration gradient has already been established.  This panel is drawn as if the membrane has no permeability to any ion.  There is no membrane potential because despite there being a concentration gradient for potassium, there is no net charge imbalance across the membrane.  If the membrane were to become permeable to a type of ion that is more concentrated on one side of the membrane, then that ion would contribute to membrane voltage because the permeant ions would move across the membrane with net movement of that ion type down the concentration gradient. There would be net movement from the side of the membrane with a higher concentration of the ion to the side with lower concentration. Such a movement of one ion across the membrane would result in a net imbalance of charge across the membrane and a membrane potential. This is a common mechanism by which many cells establish a membrane potential.{{cn|date=May 2025}}
*In panel 2 of the diagram, the cell membrane has been made permeable to potassium ions, but not the anions (An<sup>−</sup>) inside the cell. These anions are mostly contributed by protein.  There is energy stored in the potassium ion concentration gradient that can be converted into an electrical gradient when potassium (K<sup>+</sup>) ions move out of the cell.  Note that potassium ions can move across the membrane in both directions but by the purely statistical process that arises from the higher concentration of potassium ions inside the cell, there will be more potassium ions moving out of the cell.   Because there is a higher concentration of potassium ions inside the cells, their random molecular motion is more likely to encounter the permeability pore ([[ion channel]]) that is the case for the potassium ions that are outside and at a lower concentration. An internal K<sup>+</sup> is simply "more likely" to leave the cell than an extracellular K<sup>+</sup> is to enter it.  It is a  matter of [[diffusion]] doing work by dissipating the concentration gradient.  As potassium leaves the cell, it is leaving behind the anions.  Therefore, a charge separation is developing as K<sup>+</sup> leaves the cell.  This charge separation creates a transmembrane voltage.  This transmembrane voltage '''''is''''' the membrane potential.  As potassium continues to leave the cell, separating more charges, the membrane potential will continue to grow.  The length of the arrows (green indicating concentration gradient, red indicating voltage), represents the magnitude of potassium ion movement due to each form of energy. The direction of the arrow indicates the direction in which that particular force is applied.  Thus, the building membrane voltage is an increasing force that acts counter to the tendency for net movement of potassium ions down the potassium concentration gradient.{{cn|date=May 2025}}
*In Panel 3, the membrane voltage has grown to the extent that its "strength" now matches the concentration gradients.  Since these forces (which are applied to K<sup>+</sup>) are now the same strength and oriented in opposite directions, the system is now in [[Donnan equilibrium|equilibrium]]. Put another way, the tendency of potassium to leave the cell by running down its concentration gradient is now matched by the tendency of the membrane voltage to pull potassium ions back into the cell. K<sup>+</sup> continues to move across the membrane, but the rate at which it enters and leaves the cell are the same, thus, there is no '''net''' potassium current. Because the K<sup>+</sup> is at equilibrium, membrane potential is stable, or "resting" (E<sub>K</sub>).

The resting voltage is the result of several ion-translocating enzymes ([[uniporters]], [[cotransporter]]s, and [[ion transporter|pumps]]) in the plasma membrane, steadily operating in parallel, whereby  each ion-translocator has its characteristic [[electromotive force]] (= [[reversal potential]] = 'equilibrium voltage'), depending on the particular substrate concentrations inside and outside (internal [[Adenosine triphosphate|ATP]] included in case of some pumps). H<sup>+</sup> exporting [[ATPase]] render the membrane voltage in plants and fungi much more negative than in the more extensively investigated animal cells, where the resting voltage is mainly determined by selective ion channels.

In most neurons the resting potential has a value of approximately −70&nbsp;mV.  The resting potential is mostly determined by the concentrations of the [[ion]]s in the fluids on both sides of the [[cell membrane]] and the [[membrane transport|ion transport]] [[protein]]s that are in the cell membrane. How the concentrations of ions and the membrane transport proteins influence the value of the resting potential is outlined below.

The resting potential of a cell can be most thoroughly understood by thinking of it in terms of equilibrium potentials.  In the example diagram here, the model cell was given only one permeant ion (potassium).  In this case, the resting potential of this cell would be the same as the equilibrium potential for potassium.

However, a real cell is more complicated, having permeabilities to many ions, each of which contributes to the resting potential.  To understand better, consider a cell with only two permeant ions, potassium, and sodium.  Consider a case where these two ions have equal concentration gradients directed in opposite directions, and that the membrane permeabilities to both ions are equal.  K<sup>+</sup> leaving the cell will tend to drag the membrane potential toward ''E''<sub>K</sub>.  Na<sup>+</sup> entering the cell will tend to drag the membrane potential toward the reversal potential for sodium ''E''<sub>Na</sub>.  Since the permeabilities to both ions were set to be equal, the membrane potential will, at the end of the Na<sup>+</sup>/K<sup>+</sup> tug-of-war, end up halfway between ''E''<sub>Na</sub> and ''E''<sub>K</sub>.  As ''E''<sub>Na</sub> and ''E''<sub>K</sub> were equal but of opposite signs, halfway in between is zero, meaning that the membrane will rest at 0&nbsp;mV.<br />
  
Note that even though the membrane potential at 0&nbsp;mV is stable, it is not an equilibrium condition because neither of the contributing ions is in equilibrium.  Ions diffuse down their electrochemical gradients through ion channels, but the membrane potential is upheld by continual K<sup>+</sup> influx and Na<sup>+</sup> efflux via [[ion transporter]]s. Such situation with similar permeabilities for counter-acting ions, like potassium and sodium in animal cells, can be extremely costly for the cell if these permeabilities are relatively large, as it takes a lot of [[Adenosine triphosphate|ATP]] energy to pump the ions back. Because no real cell can afford such equal and large ionic permeabilities at rest, resting potential of animal cells is determined by predominant high permeability to potassium and adjusted to the required value by modulating sodium and chloride permeabilities and gradients.

In a healthy animal cell Na<sup>+</sup> permeability is about 5% of the K<sup>+</sup> permeability or even less, whereas the respective [[reversal potential]]s are +60&nbsp;mV for sodium (''E''<sub>Na</sub>)and −80&nbsp;mV for potassium (''E''<sub>K</sub>). Thus the membrane potential will not be right at ''E''<sub>K</sub>, but rather depolarized from ''E''<sub>K</sub> by an amount of approximately 5% of the 140&nbsp;mV difference between ''E''<sub>K</sub> and ''E''<sub>Na</sub>. Thus, the cell's resting potential will be about −73&nbsp;mV.

In a more formal notation, the membrane potential is the [[weighted mean|weighted average]] of each contributing ion's equilibrium potential.  The size of each weight is the relative conductance of each ion.  In the normal case, where three ions contribute to the membrane potential:
:<math>E_{m} = \frac{g_{K^+}} {g_{tot}} E_{K^+} + \frac{g_{Na^+}} {g_{tot}} E_{Na^+} + \frac{g_{Cl^-}} {g_{tot}} E_{Cl^-}</math>,
where 
*''E''<sub>m</sub> is the membrane potential, measured in volts
*''E''<sub>X</sub> is the equilibrium potential for ion X, also in volts
*''g''<sub>X</sub>/''g''<sub>tot</sub> is the relative conductance of ion X, which is dimensionless
*''g''<sub>tot</sub> is the total conductance of all permeant ions in arbitrary units (e.g. [[Siemens (unit)|siemens]] for electrical conductance), in this case ''g''<sub>K<sup>+</sup></sub> + ''g''<sub>Na<sup>+</sup></sub> + ''g''<sub>Cl<sup>−</sup></sub>