When the neuron is at rest its charge inside relative to the outside is said to be

As covered in the previous chapter, at rest there is an uneven distribution of ions on either side of the membrane. The inside of the neuron is more negatively charged than the outside.

Permeability at Rest

How the ions are distributed across the membrane plays an important role in the generation of the resting membrane potential. When the cell is at rest, some non-gated, or leak, ion channels are actually open. Significantly more potassium channels are open than sodium channels, and this makes the membrane at rest more permeable to potassium than sodium.

Potassium Can Cross Membrane at Rest

Since the membrane is permeable to potassium at rest due to the open non-gated channels, potassium will be able to flow across the membrane. The electrochemical gradients at work will cause potassium to flow out of the cell in order to move the cell’s membrane potential toward potassium’s equilibrium potential of -80 mV.

https://openbooks.lib.msu.edu/app/uploads/sites/6/2021/01/PotassiumFlowAtRest.mp4

Animation 4.1. Electrochemical gradients drive potassium out of the cell, removing positive charge, making the cell’s membrane potential more negative, in the direction of potassium’s equilibrium potential. The dotted, blue channels represent sodium leak channels; the striped, green channels represent potassium leak channels; the solid yellow channels represent chloride leak channels. ‘Potassium Flow at Rest’ by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License. View static image of animation.

Resting Membrane Potential Value

You might ask, though, if the cell has these open non-gated ion channels, and ions are moving at rest, won’t the cell eventually reach potassium’s equilibrium potential if the membrane is only permeable to potassium?

If the only structural element involved in ion flow present in the cell membrane were the open non-gated potassium channels, the membrane potential would eventually reach potassium’s equilibrium potential. However, the membrane has other open non-gated ion channels as well. There are fewer of these channels compared to the potassium channels, though. The permeability of chloride is about half of that of potassium, and the permeability of sodium is about 25 to 40 times less than that of potassium. This leads to enough chloride and sodium ion movement to keep the neuron at a resting membrane potential that is slightly more positive than potassium’s equilibrium potential.

https://openbooks.lib.msu.edu/app/uploads/sites/6/2020/01/IonFlowAtRest.mp4

Animation 4.2. The membrane is most permeable to potassium at rest, and this leads to potassium efflux. However, the membrane is also permeable to chloride and sodium, and the flow of these ions keep the resting membrane potential more positive than potassium’s equilibrium potential. The dotted, blue channels represent sodium leak channels; the striped, green channels represent potassium leak channels; the solid yellow channels represent chloride leak channels. ‘Ion Flow at Rest’ by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License. View static image of animation.

Maintenance of Gradients

As ions move across the membrane both at rest and when the neuron is active, the concentrations of ions inside and outside of the cell would change. This would lead to changes in the electrochemical gradients that are driving ion movement. What, then, maintains the concentration and electrical gradients critical for the ion flow that allows the neuron to function properly?

The sodium-potassium pump is the key. The pump uses energy in the form of ATP to move three sodium ions out of the cell and two potassium ions in. This moves the ions against their electrochemical gradients, which is why it requires energy. The pump functions to keep the ionic concentrations at proper levels inside and outside the cell.

https://openbooks.lib.msu.edu/app/uploads/sites/6/2020/01/SodiumPotassiumPump.mp4

Animation 4.3. The sodium-potassium pump is embedded in the cell membrane and uses ATP to move sodium out of the cell and potassium into the cell, maintaining the electrochemical gradients necessary for proper neuron functioning. Three intracellular sodium ions enter the pump. ATP is converted to ADP, which leads to a conformational change of the protein, closing the intracellular side and opening the extracellular side. The sodium ions leave the pump while two extracellular potassium ions enter. The attached phosphate molecule then leaves, causing the pump to again open toward the inside of the neuron. The potassium ions leave, and the cycle begins again. ‘Sodium-Potassium Pump’ by by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License. View static image of animation.

Calculating Membrane Potential with Goldman Equation

It is possible to calculate the membrane potential of a cell if the concentrations and relative permeabilities of the ions are known. Recall from the last chapter, the Nernst equation is used to calculate one ion’s equilibrium potential. Knowing the equilibrium potential can help you predict which way one ion will move, and it also calculates the membrane potential value that the cell would reach if the membrane were only permeable to one ion. However, at rest, the membrane is permeable to potassium, chloride, and sodium. To calculate the membrane potential, the Goldman equation is needed.

The Goldman Equation

[latex]V_{m}=61 * \log \displaystyle \frac{P_{K}\left[K^{+}\right]_{\text {outside }}+P_{N a}\left[N a^{+}\right]_{\text {outside }}+P_{C l}\left[C l^{-}\right]_{\text {inside }}}{P_{K}\left[K^{+}\right]_{\text {inside }}+P_{N a}\left[N a^{+}\right]_{\text {inside }}+P_{C l}\left[C l^{-}\right]_{\text {outside }}}[/latex]

Like the Nernst equation, the constant 61 is calculated using values such as the universal gas constant and temperature of mammalian cells

Pion is the relative permeability of each ion

[Ion]inside is the intracellular concentration of each ion

[Ion]outside is the extracellular concentration of each ion

[latex]V_{m}=61 * \log \displaystyle \frac{P_{K}\left[K^{+}\right]_{\text {outside }}+P_{N a}\left[N a^{+}\right]_{\text {outside }}+P_{C l}\left[C l^{-}\right]_{\text {inside }}}{P_{K}\left[K^{+}\right]_{\text {inside }}+P_{N a}\left[N a^{+}\right]_{\text {inside }}+P_{C l}\left[C l^{-}\right]_{\text {outside }}}[/latex]

Table 4.1. Intra- and extracellular concentration and relative permeability values for a typical neuron at rest for sodium, potassium, and chloride.

[latex]V_{m}=61 * \log \displaystyle \frac{1[5]+0.04[145]+0.4[13]}{1[125]+0.04[15]+0.4[150]}= -65 mV[/latex] 

• Non-gated (leak) potassium channels are open at rest causing potassium to have the highest permeability at rest
• Other ion channels (chloride and sodium) are also open, but fewer are open than potassium
• The resting membrane potential of a typical neuron is relatively close to the equilibrium potential for potassium
• The sodium-potassium pump is responsible for maintaining the electrochemical gradients needed for neuron functioning

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