chapter 18: neurons at rest

What is an Ion?

The next three chapters will contain information on the cell membrane and cell transport. Our focus will be on charged solutes called ions. Ions are atoms that have lost or gained one or more electrons. Cations are atoms that have lost electrons and have a positive charge. Anions are ions that have gained electrons and have a negative charge. The number of electrons an ion has gained or lost determines its value. For example, Ca²⁺ represents a calcium ion that has lost two electrons.

Ions can only enter and leave a cell through channel proteins. (The charge of ions makes them water-soluble, so they cannot diffuse through the hydrophobic center of a cell’s membrane.) Our focus will be on the movement of ions across a neuron’s axonal membrane. The moment of the ions is what initiates and propagates a nerve impulse. (I recommend you reread chapter 8. Pay particular attention to the different types of channel proteins and diffusion.)

What is the Resting Membrane Potential?

The voltage in a neuron’s intracellular fluid differs from that in the surrounding extracellular fluid. The voltage difference is the membrane potential. The distribution of sodium ions(Na⁺), potassium ions (K⁺), and other anions and cations determine a neuron’s membrane potential.  

The resting membrane potential, or resting potential, is the neuron’s membrane potential when it is not firing an impulse. At resting potential, the intracellular fluid has a negative charge, and the extracellular fluid has a positive charge. The negative and positive solutes ratio determines the charge inside and outside the neuron. A resting neuron has more negative than positive solutes in the intracellular fluid. The extracellular fluid surrounding the neuron has more positive than negative solutes.
Therefore, the resting membrane potential has a negative change. 

 

The resting potential depends on sodium ions (Na⁺), potassium ions (K⁺), and chloride ions (Cl^–) concentrations and their matching channel proteins. However, we will only focus on the cations Na⁺ and K+ and group all anions as A^–.

Almost no ion channel proteins are open within the neural membrane when a neuron is at rest. More K⁺ and negatively charged solutes exist in a neuron’s intracellular fluid than in the extracellular fluid. The extracellular fluid contains more Na⁺ and fewer negatively charged solutes than the intracellular fluid. This unequal distribution of ions causes an electrochemical gradient.  

The chemical potential is the diffusion of a solute down its concentration gradient. The electrical potential is the diffusion of a solute down its electrical gradient. The chemical and voltage potential are opposing forces forming the electrochemical gradient. Since the cell contains more negative solutes than positive K⁺, the intracellular fluid has a negative charge between -60 millivolts (mV) and -70 mV at resting potential. The extracellular fluid has a positive charge because it has more Na⁺ than negative solutes, so Na⁺ wants to move down its electrochemical gradient by entering the cell but can’t because there are no open Na⁺ channel proteins. The movement of K⁺ is different. During resting potential, the K⁺ chemical potential and K⁺ electrical potential are of equal opposing forces.

The equilibrium potential occurs when the two opposite forces across a cell membrane are of the same strength. At resting potential, the K⁺ chemical potential equals its electrical potential. Therefore, K⁺ is at its equilibrium potential.

A few K⁺ channel proteins are open during resting potential, and a small amount of K⁺ diffuses out of the cell down its chemical gradient. However, once K⁺ is outside the cell, the voltage potential pulls it in the opposite direction. K⁺ is then pulled back into the cell via its equilibrium potential. (The sodium-potassium pump pumps some K⁺ back inside too.)

The movement of K⁺ during resting potential is like the myth of Sisyphus. Sisyphus was a Greek king who tricked the gods one too many times. His punishment is to push a boulder up to the top of a hill because of his trickery. But there is a catch. Every time the stone almost reaches the top of the hill, it rolls back to the bottom. Sisyphus returns to the bottom of the hill and starts pushing the rock back up. He will repeat this process until eternity.

At resting potential, K⁺ is like Sisyphus in the following ways:

1. K⁺ diffuses out of the neuron down its concentration gradient – i.e., Sisyphus pushing the boulder up the hill
2. K⁺ moving back into the cell via its electrical potential – i.e., the boulder rolling back down the hill
3. And the process repeats over and over – i.e., the equilibrium potential

The equilibrium potential occurs when the concentration gradient equals the voltage gradient. The concentration of intracellular K⁺ is at its equilibrium potential when a neuron is at rest, but Na⁺ is not. 

Even though most Na⁺ channel proteins are not open during resting potential, a few act like leaky faucets and ions diffuse inside the axon. The sodium-potassium pump pumps the leaked Na⁺ back into the extracellular fluid. Therefore, there is no net movement of Na⁺ during resting potential.

Calculating the Equilibrium Potential

The equilibrium potential is dependent on the following:

1. The number of cations and anions in the intracellular fluid and extracellular fluid
2. The concentration of ion species in the intracellular fluid and extracellular fluid
3. The permeability of an ion species through a cell membrane

Resting Potential Math Part 1: Addition and Subtraction

When a neuron is at resting potential, the inside of the neuron has a negative charge because there are more negative solutes than positive solutes. The extracellular fluid has a positive charge because there are more positive solutes than negative solutes. This is a simple explanation of resting potential. Let’s do a little math to see the difference in charge along the axon.

Resting Potential Math Part 2: Calculating the Equilibrium Potential of a Single Ion

Now, there is a lot of chemistry behind the resting potential. This chapter will skip most of the chemistry and focus on why the resting potential is between -65 mV and -70 mV. At resting potential, the K⁺ concentration gradient equals the voltage gradient. This electrochemical equilibrium is the equilibrium potential. The Nernst equation calculates each ion species’ equilibrium potential.

If the intracellular fluid is less than -91 mV, then the K⁺ voltage gradient is stronger than the K⁺ concentration gradient, and K⁺ will not leave the neuron even when all K⁺ channel proteins are open. However, if the voltage exceeds -91 mV, the K⁺ concentration gradient is stronger than the K⁺ voltage gradient, and K⁺ will exit the neuron when K⁺ channel proteins open.

Sodium has the opposite effect. If the intracellular fluid is greater than 71 mV, then the Na⁺ electrical gradient is stronger than the Na⁺ concentration gradient, and Na⁺ will not enter the neuron even when all Na⁺ channel proteins are open. However, if the voltage is less than 71 mV, the Na⁺ concentration gradient is stronger than the Na+ voltage gradient, and Na⁺ will enter the neuron when Na+ channel proteins open.

Resting Potential Math Part 3: Calculating the Equilibrium Potential of Multiple Ions

Wait. If the equilibrium potential for K⁺ is -91 mV, then shouldn’t there be a net movement of K⁺ at resting potential? 

Well, this is where things get a little more complicated. Since the voltage of a neuron’s intracellular fluid at resting potential is less than equilibrium potential, there should be a net movement in K+ during resting potential. This would be true if K⁺ were the only ion in the intracellular fluid and K⁺ channel proteins were the only channel proteins in the neuron’s axonal membrane. However, many different intracellular and extracellular ion species exist, each with a channel protein.  

The two ions and their channel proteins that have the greatest effect on resting potential are Na⁺ and K⁺. The combined equilibrium potential of Na⁺ and K⁺ affects each ion species type; therefore, the voltage of the resting potential. However, not all ions affect the resting potential equally. Ions with a higher concentration of leaky channel proteins will have greater permeability and affect the resting potential. K⁺ has the most significant impact on resting membrane potential because its channel proteins are a hundred times more permeable than Na⁺ channel proteins. Therefore, K⁺ has the most significant effect on resting membrane potential. 

Let’s use a leaky faucet as an example. Assume a leaky K⁺ faucet leaks one drop per minute. A Na⁺ faucet leaks one drop every 100 minutes. We’ll assume that each drop averages 1 ml of water. After 24 hours, the K⁺ faucet will leak 1400 ml of water while the Na⁺ faucet leaks 14 ml.

Now, let’s do some math to explain the former paragraph. The Goldman-Hodgkin-Katz equation, or the GHK, uses multiple ion species to calculate resting membrane potential.

The Sodium-Potassium Pump

The sodium-potassium (Na⁺/K⁺) pump‘s primary function is maintaining resting potential. When sodium leaks into the resting neuron, the inside of the cell becomes more positive, and the outside becomes less positive. This changes the equilibrium potential for K⁺ and Na⁺. As the inside of the cell becomes more positive, the K⁺ electrical gradient becomes weaker than its concentration gradient. The difference in the electrochemical gradient means that K⁺ will leave the cell AND stay in the extracellular fluid. As K⁺ leaves the cell, the inside becomes more negative, causing more Na+ to leak into the cell. The leaking of Na⁺ and K⁺ creates a positive feedback loop, with more and more sodium entering the cell and more and more potassium leaving the cell. The feedback loop will continue until both ions are at their equilibrium potential, which is not good. When Na⁺ and K⁺ are at their equilibrium potentials, the neuron will not fire an impulse. 

The Na⁺/K⁺ pump’s job is to prevent Na⁺ and K⁺ from simultaneously reaching their equilibrium potential. The Na⁺/K⁺ pump works via active transport since it takes energy to pump ions against their concentration gradient. When Na⁺ leaks into the neuron, the Na⁺/K⁺ pump forces it back out. When K⁺ leaves the cell, the Na⁺/K⁺ pump propels it back inside.

Chapter Summary

So, each ion species wants to move down its electrochemical gradient to reach its equilibrium potential. However, ion channel proteins and sodium-potassium pumps prevent equilibrium from happening. If all ion species can meet their equilibrium potential, neurotransmission will stop.

1. When a neuron is at rest, the inside of the neuron is negatively charged, and the outside is positively charged. 
2. This polarity is caused by the fact that there are more positive ions than negative ions outside the axon and more negative ions than positive ions inside the neuron.
3. Sodium (Na⁺) is at its highest concentration outside the axon, and potassium (K⁺) is at its highest concentration inside the axon.
4. Na+ wants to enter the cell but can’t because the Na+ voltage transport proteins are closed.  K+ wants to leave the cell but can’t because the K⁺ voltage transport proteins are closed.
5. An analogy for resting potential is sprinkling salt on a banana.  The Na⁺ is on the surface of the banana (outside the axon), and the K⁺ is in the fruit of the banana (inside the axon)
6. Another analogy is “a lonely ball of potassium in a sodium-soaked world.”  (See Figure below)