What does the term membrane time constant mean in neuroscience?

Answer by Paul King:

The “membrane time constant” of a neuron is simply a way of measuring how quickly a neuron’s voltage level decays to its “resting state” after it receives an input signal.

In physics and engineering, a “time constant” is a way of describing how fast or slow a system reacts to something when the reaction can be described as an exponential decay.

Radioactive decay is a familiar example of a time constant. An element with a 100-year “half-life” will be 50% less radioactive after 100 years. The somewhat-less-intuitive “time constant” is how long something will take to get to 1/e of its original value. The mathematical constant “e” is around 2.7, and 1/e = 0.368, so a radioactive element with a time constant of 100 years will be at 37% of its original intensity after 100 years, assuming it is decaying to zero.

Neurons have time constants of around 5 – 20 milliseconds (ms), which means that after a neuron receives an input signal (or “spike”) from another neuron, it will be at 37% above its resting state voltage 5 – 20 ms later.

This image shows what an inbound neural spike looks like (top plot) and what the “EPSP” (excitatory postsynaptic potential) looks like (bottom plot). You can see that the EPSP rises quickly following the input spike, and decays to around 37% of its voltage after around 10 ms.

I did a Google search on “neuron membrane time constant”, and one of the top results was this plot of the membrane time constants of common neurons created by Quora contributor Shreejoy Tripathy: membrane time constant

Neurons can be modeled as miniature electrical circuits, and the time constant can be computed from the circuit values in the model. Although, it actually works the other way around… neuroscientists measure the time constant experimentally and infer the circuit values from from that. See Yohan John‘s answer for details.

What does the term membrane time constant mean in neuroscience?