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I know the sodium-potassium pump pumps out 3 Na+ ions and pumps in 2 K+ ions per reaction so the negative charge in the axon increases. However, once the voltage (difference of charge inside and outside of the neuron) gets down to -70 mV, this stops going further below. Why?

I know that this is because of other transport proteins and the presence of anions and cations in the axon, but what are those proteins and ions precisely? There are always negatively charged proteins inside a cell, including a neuron, so I assume there must be a strong force which keeps the voltage from going down.

By the way, is the opening and closing of an ion channel triggered by the voltage of the neuron or the concentration of the ion?

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    $\begingroup$ Take a look at the wiki article for Resting Potential: en.wikipedia.org/wiki/Resting_potential. Essentially, you form a balance between the electrical force pushing ions through the channels and the force caused by an imbalance in chemical concentration in ions across the membrane. $\endgroup$ – Dylan Richard Muir Sep 23 '14 at 14:09
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The neuronal cell membrane is quite permeable to K+. Because the Na+,K+-ATPase pumps K+ inside of the cell, K+ tends to diffuse outward again, thereby taking positive charge outside the cell and making it negative inside (see Further Reading 1). This outward flow of K+ stops at a certain point, because the driving force of K+ diffusion out of the cell along with its concentration gradient, equals the charge gradient, which becomes more and more negative inside the cell as more K+ diffuses out (see Further Reading 2). Hence an equilibrium is reached which is close to the resting membrane potential of -70 mV. Other ions such as Cl- are also relatively permeable and affect the resting membrane potential (see Further Reading 1). Ions such as Na+ and Ca2+ are typically highly impermeable and do not substantially affect the resting potential.

As to your second sub-question:voltage-gated channels are gated through voltage differences (Purves et al., 2001), not ion concentration differences.

Further Readings
1. If the average resting potential of a neuron is -70 mV, why is there such a high ratio of K+ ions inside relative to out?
2. Why do negative ions flow into a cell in an inhibitory synapse, even though a neuron has a negative resting potential?

Reference
- Purves et al., Neuroscience (2001). 2nd ed. Sunderland (MA): Sinauer Associates

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