Passive Electrical Properties of Neurons

Three passive properties of neuronal membranes

Membrane resistance (Rm/rm)

Axial/internal resistance (Ra/ra)

Membrane/input capacitance (Cm/Cin)

What is the time course of local graded potentials?

The time course of local graded potentials refers to how these potentials change over time.

What is the amplitude of local graded potentials?

The amplitude of local graded potentials is the measure of their strength or intensity.

What affects the speed of propagation of local graded and action potentials?

The speed of propagation of local graded and action potentials is influenced by factors such as axon diameter and myelination.

Ideal levels for fast signal propagation

High membrane resistance, low axial resistance, and low capacitance.

Local Graded Potentials

Passive, small amplitude (0.1-10 mV), and variable duration (ms-min).

Action Potentials

Active, large amplitude (70-110 mV), and brief duration (1-10 ms).

Total membrane current equation

Im equals the sum of ionic current (Ii) and capacitive current (Ic).

Membrane Time Constant (τ) equation

The product of input resistance and membrane capacitance (Rin * Cin).

Significance of one time constant (τ)

The time when potential change reaches 63% of its final value.

Effect of Membrane Capacitance

Slows down the rate of change in membrane potential in response to current.

Neuronal size and membrane resistance

The larger the neuronal cell body, the smaller the membrane resistance.

Length Constant (λ) Definition

Distance where potential decays to 1/e or 37% of its original value.

Voltage decay along an axon formula

V(x) = V0 * e^(-x/λ)

What does a large length constant mean?

Depolarization can spread over a longer distance before substantially decreasing.

What happens to the length constant when membrane resistance increases?

λ increases.

λ=r_m/r_a

What happens to the length constant when axial resistance decreases?

λ increases. Lower r_a → larger λ.

What are the two ways to increase length constant?

Increase membrane resistance r_m

Decrease axial resistance r_a

What happens to capacitance as membrane area increases?

Capacitance increases.

More membrane area provides greater capacity to store charge.

What happens to capacitance as neuronal cell-body size increases?

Capacitance increases.

Specific Membrane Resistance (Rm) formula

rm * 2πa (where a is the axon radius).

Specific Axial Resistance (Ra) formula

ra * π * a² (where a is the axon radius).

What is axial resistance?

The resistance to current flow through the cytoplasm along the length of the axon

Should axial resistance be high or low for fast signaling?

Low.

What happens to axial resistance when axon diameter increases?

Axial resistance decreases. A larger axon provides more area for current to flow through

Why does increasing axon diameter increase action-potential velocity?

Increasing axon diameter decreases internal/axial resistance, allowing current to spread more rapidly along the axon

How to increase conduction velocity

Increase the length constant or decrease the time constant.

What happens when you reverse the current flow?

The membrane hyperpolarizes.

What equation describes the relationship between injected current and membrane potential change?

ΔV=I×Rin

where:

ΔV = change in membrane potential

I = injected current

Rin = input resistance.

What does Ohm's law tell us about current, voltage, and resistance?

I=V/R, V=IR

Current is proportional to voltage when resistance is constant.

What happens to the membrane potential change when input resistance increases?

The membrane potential changes more for the same injected current.

ΔV=I(R_in)

So, higher R_{in} → larger voltage change.

What is specific membrane resistance (Rm)?

Membrane resistance normalized for membrane area, allowing comparison between neurons of different sizes.

For a spherical cell body:

Rm=Rin(4πa^2)

What effect does increased membrane capacitance have on membrane potential?

It slows the rate of membrane potential change.

What are the two types of current through the membrane in the electrical model?

Ionic current (I_i) + Capacitive current (I_c)

What happens to the time constant when capacitance increases?

τ increases, meaning the membrane potential changes more slowly.

What combination of passive properties produces faster electrical signaling?

Membrane resistance↑ High

Axial resistance↓ Low

Membrane capacitance↓ Low

What happens when a signal travels down an axon without regeneration?

Because of membrane leakiness, the action-potential peak would decrease with distance. It is regenerated by opening new voltage-gated Na⁺ channels farther along the axon.

During depolarization, what happens to the membrane currents?

An initial brief capacitive current

A rapidly rising inward ionic current

A slower, delayed outward current.

What does "inward current" mean in this lecture?

A positive charge entering the cell—for example, cations entering or anions leaving.

What evidence demonstrates that the early inward current is caused by Na⁺?

Reducing external Na⁺ eliminates the early inward current.

TTX blocks voltage-gated Na⁺ channels.

The Na⁺ current reverses near E_Na ≈ +55 mV

What evidence demonstrates that the late outward current is caused by K⁺?

Replacing intracellular K⁺ with Cs⁺ eliminates the outward current.

TEA blocks voltage-gated K⁺ channels.

What happens to Na⁺ and K⁺ conductances as the neuron depolarizes?

Both g_{Na} and g_K increase progressively as the neuron is depolarized.

Why does Na⁺ influx cause positive feedback?

Depolarization → increased g_{Na} → more Na⁺ enters → further depolarization.

Why does K⁺ efflux produce negative feedback?

Depolarization → increased g_K → K⁺ exits → repolarization → decreased g_K

Why does Na⁺-mediated depolarization eventually slow down?A: Three factors:

The driving force for Na⁺ decreases.

Na⁺ channels become inactivated.

K⁺ channels open and promote repolarization.

How does increasing axon diameter affect AP velocity?

It increases AP velocity by decreasing axial resistance.

How does increasing membrane resistance affect AP velocity?

It increases AP velocity because less signal is lost through membrane leakage

How does myelination increase AP velocity?

Myelination increases membrane resistance, reducing current leakage and increasing conduction velocity.

Where are voltage-gated Na⁺ and K⁺ channels concentrated in myelinated axons?

They are concentrated around the nodes/paranodes, with voltage-gated Na⁺ channels particularly concentrated at nodes.

Why don't dendrites and cell bodies generally generate action potentials?

They generally have a low density of voltage-gated Na⁺ channels.

What does TTX block?

Voltage-gated Na⁺ channels.

What does TEA block?

Voltage-gated K⁺ channels.