Primer
A Neuron in One Page
Written for physicists. A neuron is a cell wrapped in a thin insulating membrane, about 4 nm thick, that separates two salty solutions. Its signals are voltages across that membrane, and those voltages come from ions moving through protein pores called ion channels.
Unequal ion concentrations
Molecular pumps keep the inside rich in potassium (K⁺) and poor in sodium (Na⁺); outside, the reverse holds. Typical mammalian values:
| Ion | Inside (mM) | Outside (mM) |
|---|---|---|
| K⁺ | 140 | 5 |
| Na⁺ | 12 | 145 |
The Nernst potential
If a membrane lets only one ion species through, ions diffuse down their concentration gradient until the voltage they build up stops them. At equilibrium the Boltzmann distribution links the concentrations on the two sides to the energy difference zeΔV of one ion of charge ze:
\[ \frac{c_{\text{in}}}{c_{\text{out}}} = \exp\!\left(-\frac{z e\,(V_{\text{in}} - V_{\text{out}})}{k_B T}\right) \quad\Longrightarrow\quad E_{\text{ion}} = \frac{k_B T}{z e}\,\ln\frac{c_{\text{out}}}{c_{\text{in}}} \]
At body temperature (310 K), kBT/e ≈ 26.7 mV. For potassium, EK = 26.7 mV × ln(5/140) ≈ −89 mV; for sodium, ENa = 26.7 mV × ln(145/12) ≈ +67 mV.
The resting potential
At rest the membrane is mostly permeable to K⁺, with a small Na⁺ leak, so it settles near −70 mV: between the two Nernst potentials, but much closer to potassium's. This is Vrest in Part 3.
Why channelrhodopsin reverses near 0 mV
ChR2 lets Na⁺, K⁺ and H⁺ through almost indiscriminately. A pore that passes Na⁺ and K⁺ about equally has a reversal potential roughly halfway between +67 mV and −89 mV, close to 0 mV. Opening it therefore always pulls a resting neuron upward, toward firing — which is the whole reason the protein works as a switch.
The action potential
If the membrane is pushed about 15–20 mV above rest, voltage-gated sodium channels open, Na⁺ floods in, and the voltage shoots to about +30 mV within a millisecond before potassium channels restore it. This all-or-nothing spike is the neuron's output.
Optogenetics only has to supply the initial push; the cell's own machinery does the rest. Part 3 works out how much light that initial push costs.