5.5: The electrochemical gradient

Without ion channels, ions do not cross the cell membrane and therefore stay either outside or inside the cell. But when an ion channel is present and open, ions can move across the cell membrane, depending on the specific conditions inside and outside the neuron. There are two different forces that act on ions once an ion channel is open: the electrical gradient and the chemical gradient.

1. Electrical gradient

The electrical gradient refers to the electrical forces acting on charged molecules, “pulling” opposite charges together while also “pushing” like charges away from one another - just like the polarity of magnets.

At rest, the interior of the cell has a negative charge, about -70 mV. Because of these negative charges inside the cell, the electrical gradient causes positively charged ions to be attracted to the inside of the cell. At the same time, negatively charged ions will be repelled out of the cell.

The voltage of the neuron (V_m ) can deviate significantly from -70 mV, reaching potentials as high as +40 mV. When the V_m changes, the force exerted by the electrical gradient changes as well. If the cell now has a positive potential instead of a negative potential, movement of charged ions will change as well. In this case, the electrical gradient now attracts negatively charged ions into the cell while pushing positively charged ions out of the cell.

Figure 4.4 The electrical gradient describes the forces acting on ions as they follow the rules of magnetism in physics - “opposites attract, and similar charges repel.”

2. Chemical gradient

The chemical gradient refers to the natural process by which a high concentration of a substance, given enough time, will eventually diffuse to a lower concentration and settle evenly over the space.

Figure 4.5 The chemical gradient describes the same forces acting on ions as diffusion, where ions move from areas of high concentration to low concentration.

You can think of the chemical gradient as similar to the way people behave when they exit a full elevator. People don’t want to be so close to each other inside a cramped space. Once the doors open, people scatter quickly, going to where they can have more personal space. They move from an area of high concentration to low concentration. Molecules behave the same way.

Unlike the electrical gradient, the chemical gradient is unaffected by biological movement of ions. In other words, the distribution of ions across the membrane does not change significantly. The number of ions that flow across the cell membrane is so minute that the relative distribution of ions across the cell membrane essentially does not change.

These two forces are collectively called the electrochemical gradient. In order to accurately predict the forces acting on a given ion, you need to know 1) the charge of the ion and 2) the relative concentrations of ions across the membrane.

1. Sodium (Na+) movement across the membrane

Consider the positively-charged ion, sodium (Na⁺). Because it has a positive charge, it is electrically attracted to the inside of the cell, which has a negative charge at rest. Therefore, when a sodium-permeable ion channel opens and Na⁺ is now able to pass across the cell membrane, the electrical gradient causes the sodium to move into the cell.

We also know that the concentration of sodium outside the cell (written as [Na⁺]_o , where the brackets indicate concentration and the “o” refers to “outside”) is high compared to the concentration of sodium inside the cell (written as [Na⁺]_i ) by roughly an order of magnitude. Therefore, when that sodium-permeable ion channel opens, Na⁺ will move from the area of high concentration to low concentration, causing Na⁺ to move into the cell.

Given that both the electrical and chemical gradients are in favor of moving Na+ into the cell, opening a sodium channel causes a net flow of Na⁺ ions into the cell.

Figure 4.6 When a sodium channel opens (purple), sodium ions (orange) are acted on by two forces. They have a positive charge, which is attracted to the negatively-charged inside of the cell (electrical gradient). They are at a higher concentration outside the cell, which causes them to move to the inside of the cell with the lower concentration (chemical gradient).

2. Potassium (K⁺) movement across the membrane

Just like with sodium, we can use our knowledge of potassium’s charge and the distribution of K⁺ ions across the membrane in order to predict the forces acting on K+ ions when a potassium channel is open.

We know that the inside of the cell is negative and K⁺ has a positive charge, so the electrical gradient causes K⁺ to be attracted into the cell. We also know that the inside of the cell has a relatively high concentration of K⁺ ions compared to the outside of the cell; therefore the chemical gradient pushes K⁺ out of the cell.

Since the ion concentrations across the membrane do not change significantly, but the membrane voltage can, you could imagine there exists some V_m where the flow of ions moving in are exactly equal to the flow of ions moving out. In this case, the two forces acting on the ion oppose one another perfectly, resulting in a dynamic equilibrium (This process is called “dynamic” because there is a constant movement of ions going in and going out, and yet it is at an “equilibrium” because there is no net movement of charge: the charge moving in is balanced by the charge moving out.) This exact value of the Vm is called the equilibrium potential for the ion, which is also abbreviated E_x where x is the ion of interest. The equilibrium potential differs for each ion, and is described in Table 4.8.

Figure 4.7 When a potassium channel opens (blue), potassium ions (green) are acted on by two opposing forces. They have a positive charge, which is attracted to the negatively-charged inside of the cell (electrical gradient). At the same time, they are at a higher concentration inside the cell, which causes them to want to move outside of the cell (chemical gradient). This process is at equilibium.

Table 4.8 Charged ions are unequally distributed across the cell membrane. Typical concentrations of ions in a mammalian neuron and their respective equilibrium potentials.

Ion	Abbreviation	Concentration outside [X]o	Concentration inside [X]i	Equilibrium potential Ex
Sodium	Na^+	140 mM	15 mM	60 mV
Potassium	K^+	5 mM	150 mM	-91 mV
Chloride	Cl^-	120 mM	10 mM	-66 mV
Calcium	Ca^2^+	1 mM	100 nM = 0.1 µM	123 mV
Magnesium	Mg^2^+	2 mM	0.5 mM	19 mV
Miscellaneous anions	A^-	20 mM	100 mM