Lecture 4: Signal Propagation and Cable Theory

Question 1

What are the characteristics of an iso-potential sphere?

Answer 1

• (Membrane) Potential is the same everywhere on the sphere
• Membrane resistance is constant
• When current is injected into such a sphere, it will rush to distribute itself around the whole sphere

Question 2

Define the convention for current in a neuron

Answer 2

• Outward Current – positive – expulsion/emigration of positive ions from within the cell to outside the cell.
• Inward Current – negative – positive ions coming from outside to inside the cell

Question 3

What is the time constant?

Answer 3

Time constant, tau, is defined as the time for the potential to fall from the resting to a fraction (1-1/e), or 63%, of its final value in the charging curve during the application of a small negative current pulse.
It is the product of the membrane resistance and membrane capacitance.

Question 4

What is the steady-state value of membrane potential?

Answer 4

If same amount of current is injected for a long time, the value of voltage saturates. This is called the steady-state value of the membrane potential

Question 5

What is the length constant?

Answer 5

Length constant is a measure of how far the voltage travels down the axon before it decays to zero.
If you have a length constant of 1 mm, that means at 1 mm away from the cell body in an axon, 37% of the voltage magnitude remains.

Question 6

Give the relationship between input resistance and surface area of a cell

Answer 6

Input resistance of a cell is inversely proportional to its surface area.
The bigger the cell, the lower the input resistance for any given membrane resistance native to the cell.

Question 7

How do small synaptic currents give rise to action potentials?

Answer 7

APs are triggered when summed currents exceed a threshold

• Temporal Summation: If synaptic currents induce synaptic potentials within close proximity in time, then depending on the time constant of the local system, these potentials can add up enough to exceed a threshold that triggers an action potential
• Spatial Summation: If two synaptic currents induce synaptic potentials and lie within the length constant of the local system, then these will add up and exceed the threshold, triggering an action potential

Question 8

Where is the threshold for AP believed to be the lowest?

Answer 8

Lowest at the start of the axon, known as the axon initial segment, which is the birthplace of the action potential