Lecture 10

Question 1

Rinp (Input Resistance)

Answer 1

When an electrode is inserted into a cell…

Rinp is the input resistance, which includes the resistance through the cytoplasm (Rcyt) and through the membrane (Rm)

Rinp = Rcty + Rm

Question 2

Where does injected current go first, Cm or Rinp?

Answer 2

• At first, Cm presents the path of least resistance, so current first goes to Cm
• As Cm accumulates voltage, more and more current goes through Rinp
• When Cm is fully charged, all of the current goes through Rinp
• When the current is shut off, the capacitor discharges through Rinp

Question 3

What will be the voltage increase across Cm and Rinp?

Answer 3

• Since there is no resistance between Cm and Rinp, they see the same increasing voltage

Question 4

If Rinp is creating a “leaky plug” that directs current to Cm, why does increasing Rinp slow down the charging of Cm?

Answer 4

Charging of Cm slows down because the effective voltage across Rinp (and hence Cm) increases with higher Rinp

Question 5

Specific capacitance (Csm)

Answer 5

Capacitance of 1 cm2 of membrane

• A typical value for Csm is 1 μF/cm2

Question 6

Capacitance of a cylindrical section of axon (Cm)

Answer 6

Cm = Csm x 2πrh (SA of a cylinder)

Increasing r or h increases Cm

Question 7

Specific resistance (Rsm)

Answer 7

Resistance of 1 cm2 of membrane

Quite variable depending on the number of active channels at the membrane

Typical values for Rsm range from 1,000 Ωcm2 (lots of channels) to 50,000 Ωcm2 (few channels)

Question 8

Resistance of a spherical cell (Rm)

Answer 8

• Rm=Rsm ÷4πr2

* Increasing r decreases Rm

Question 9

Resistance of a cylindrical section of axon (Rm)

Answer 9

• Rm=Rsm ÷2πrh

* Increasing r or h decreases Rm

Question 10

Specific axial or cytoplasmic resistance (Rsa)

Answer 10

As current travels through an axon, it meets resistance through the axoplasm

Question 11

Rsa is dependent on ion concentrations

What effect does [Na+] have on Rsa?

Answer 11

Increasing [Na+] decreases Rsa
Decreasing [Na+] increases Rsa

• Squid (high salt conc.) ~ 30 Ωcm at 20oC
• Mammals (low salt conc.) ~ 125 Ωcm at 27oC
• Frogs (even lower salt conc.) ~ 250 Ωcm at 20oC

Question 12

Axial resistance of a cylindrical section of axon (Ra)

Answer 12

• Ra=(Rsa xh)÷πr2

• Increasing h increases Ra
• Increasing r decreases Ra

Question 13

If you inject current into the center of an axon…

If the resistance along the axoplasm is ____, current is more likely to go through the membrane close to the site of injection

Answer 13

If the resistance along the axoplasm is high, current is more likely to go through the membrane close to the site of injection

Question 14

If you inject current into the center of an axon…

Current travels further if there is ____ axial resistance

Answer 14

current travels further if there is low axial resistance

Question 15

If you inject current into the center of an axon…

If the resistance of the membrane is high, current will travel ______ along the axon

Answer 15

If the resistance of the membrane is high, current will travel further along the axon

Question 16

If you inject current into the center of an axon…

______ membrane resistance will direct current through the membrane close to the site of injection, and hence it will not travel as far

Answer 16

low membrane resistance will direct current through the membrane close to the site of injection, and hence it will not travel as far

Question 17

As we move along the axon in the x direction…

• There is a continual ________ in ΔV (i.e. across Cm)

Answer 17

As we move along the axon in the x direction…

• There is a continual decrease in ΔV (i.e. across Cm)

Question 18

V0 is the maximal voltage resulting from current injection site at x= _______

Answer 18

V0 is the maximal voltage resulting from current injection site at x=0

Question 19

The input resistance Rinp is dependent on both the _______ resistance R_ and the _____ resistance R_

Answer 19

The input resistance Rinp is dependent on both the membrane resistance Rm and the axial resistance Ra

Question 20

λ is the length constant of the finer

• ↑ λ: current (and hence depolarization)
travels ______ along the axon
• ↓ λ: current/depolarization travels _______

Answer 20

• ↑ λ: current (and hence depolarization)
travels further along the axon
• ↓ λ: current/depolarization travels less far

Question 21

How would you increase the distance that current travels along an axon?

Answer 21

• Decrease Ra

* Increase Rm

Question 22

What effect does increasing the radius of the axon have on speed of current?

Answer 22

current/depolarization travels more effectively and quickly

Question 23

What allows the squid to escape predators?

Answer 23

The giant axon allows the squid brain to quickly tell muscles in the mantle to contract (for escaping danger)

Question 24

Why do electrical signals travel faster through thicker axons?

Answer 24

• When axonal Nav channels open, they create a local “current injection”
• λ determines how far the resulting depolarization will extend along the axon to activate new Nav channels
• Thus, with ↑λ, threshold is reached more quickly further along the axon

Question 25

There is also a time delay in ΔV along the axon

Answer 25

• At first, most of the current is consumed by the capacitor closest to
the current injection site
• As it charges, more and more current is directed to distal capacitors, each of which also initially consume most incoming current before passing it further along
• Thus, charging more distal capacitors takes longer and longer, depending on how far they are from the site of current injection

Question 26

Synaptic Potentials:

Small diameter dendrites experience a ____ local voltage change due to EPSPs

But they are ______ effective at transmitting current to the soma/axon than are large diameter dendrites

Answer 26

Small diameter dendrites experience a higher local voltage change due to EPSPs

But they are less effective at transmitting current to the soma/axon than are large diameter dendrites

Question 27

An optimal cable has:

Answer 27

More insulation (lower Cm and increase Rm) and lower axial resistance (decrease Ra)

Question 28

How do you speed up an action potential?

Answer 28

Increase the membrane resistance (Rm)
Decrease the axial resistance (Ra)
Decrease the membrane capacitance (Cm) - (takes less time to charge the capacitors)

Question 29

Myelination - Glial/Schwann cells

Answer 29

Insulate axons from extracellular saline

Decreases Cm while increasing Rm, both of which promote faster signal propagation

Question 30

Nodes of Ranvier

Answer 30

Interrupt Myelin sheaths

• Packed with Na and K channels
• The nodes boost the AP as it travels along the neuron

Question 31

Saltatory Conduction

Answer 31

Signals “jump” from node to node

Question 32

Geometry and conduction block

Answer 32

If current/depolarization traveling through a tiny dendrite opens up into a vast cellular space with lots of membrane, it can be consumed by the large membrane capacitance, greatly attenuating the signal
• Could bring depolarization below threshold for initiating an action potential

If an axon branches, its current gets divided into the branches, so an AP might fail if the front of depolarization does not reach threshold

Question 33

Back-propagating action potentials and dendritic excitability

Answer 33

Dendrites also have ion channels, and can thus generate their own Action Potentials