Passive Cable Properties of Neurons

This set of flashcards covers the passive and active electrical properties of neurons, including key mathematical constants such as the time and space constants, and the mechanisms of synaptic integration.

According to the lecture, how are passive electrical properties defined?

These are electrical properties that are constant and do not change with voltage or intracellular $[Ca^{2+}]$.

What characterizes active electrical properties in neurons?

Membrane conductances (ion channels) that change with voltage, time, or intracellular concentrations of $[Ca^{2+}]$ or $[Na^{+}]$.

What is the mathematical formula for the membrane time constant $\tau_m$?

$$\tau_m = R_m C_m$$

What is the formula for the space or length constant $\lambda$?

$$\lambda = \sqrt{\frac{R_m d}{4 R_i}}$$

Through what biophysical mechanism do temporal and spatial summation actually occur?

Integration works via charge piling up on the membrane capacitance.

How does the membrane time constant $\tau_m$ influence temporal summation?

A long time constant results in much temporal summation, whereas a short time constant results in little temporal summation.

What is the relationship between the time constant $\tau$ and the half-life of a decaying voltage?

Half-life is approximately $0.69 \times \tau$, and the time constant is approximately $1.44 \times \text{half-life}$.

What is the equation for the exponential decay of voltage along a passive cable over distance $x$?

$$V = V_0 e^{-\frac{x}{\lambda}}$$

Over a distance of one space constant ($\lambda$), how much does the voltage fall in a passive electrical cable?

The voltage falls to $1/e$ (approximately $0.37$) of the value at the starting position.

Why is the Excitatory Post-Synaptic Potential (EPSP) typically much smaller at the soma than at the dendritic input site?

The attenuation is mainly due to the charge spreading and being \u201cdiluted\u201d over the entire membrane capacitance of the tree, which is much larger than at the input site.