Читать книгу Neurobiology For Dummies - Frank Amthor - Страница 102

So, which way will potassium ions move if potassium channels are opened? The Nernst equation — developed from basic thermodynamic principles by the 19th-century German chemist Walter Nernst — gives us the answer. It gives the “balance point” (called the equilibrium potential) between the diffusion and voltage forces, expressed in terms of voltage. This equilibrium potential (sometimes called the Nernst potential, for obvious reasons) is the voltage (inside the cell versus outside) that would exactly balance the tendency of ions to diffuse down their concentration gradient. In other words, if the inside of the neuron is at the Nernst potential for an ion, no net movement of that ion will occur when the relevant channels are open.

A separate Nernst equation is written for each ion. The Nernst equation giving the equilibrium potential for sodium, E_Na, would be written as follows:

 ENa = 59.8 mV log10 ([Na+]outside/[Na+]inside)

The constant 59.8 mV comes from the evaluation of several other constants (RT/zF), where R = the universal gas constant, T = temperature in degrees Kelvin, F = Faraday’s constant, and z = the ion valence (for Na⁺ z = 1).

For a typical neuron frequently studied, like the squid axon, Na_inside might equal 50 mM (millimolar), whereas Na_outside is typically 440 mM.

This gives

 ENa = 59.8 mV log10 (440/50) = 56.5 mV

What this means is that the potential inside the neuron would have to be raised from its –60 millivolt (mV) resting potential to +56.5 mV to balance the tendency of sodium ions to rush into the neuron by diffusion due to the much higher concentration outside than inside.

For potassium, where the concentrations are about 400 mM inside versus 20 mM outside, E_K = 59.8 mV log₁₀ ([K⁺]_outside/[K⁺]_inside) = 59.8 mV log₁₀ (20/400) = –77.8 mV.

This means that the potential inside the cell would have to be made more negative than –77.8 mV to keep potassium from going outside the cell through a membrane permeable to potassium due to the much larger concentration of potassium inside the cell than outside.

For chloride, E_Cl = 59.8 mV log₁₀ ([Cl^–]_outside/[Cl^–]_inside) = –59.8 mV log₁₀ (560/52) = –61.7 mV.

Note that a minus sign (–) appears in front of the 59.8 constant because the valence, z, of chloride is negative (–1). The reversal potential for chloride is often near the resting potential because chloride leak channels (channels without gates) exist in most neurons. These channels are always open and allow chloride to move through the membrane until its equilibrium potential is reached.

The concentration of chloride ions is much higher outside the cell than inside for the equilibrium potential of about –60 mV, close to the resting potential of many cells. The negative charge inside the cell compared to outside repels negative chloride ions. Also, many organic ions exist inside a cell that are negatively charged.

Chloride channels may be inhibitory even if the reversal potential for chloride is slightly above the resting potential. That’s because opening chloride channels will oppose depolarization by opening nearby sodium channels. Moreover, the open chloride channels reduce the membrane resistance, and by Ohm’s law (V = I · R), reduce the depolarizing voltage produced by sodium currents.