Lecture 10 Flashcards
Rinp (Input Resistance)
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
Where does injected current go first, Cm or Rinp?
- 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
What will be the voltage increase across Cm and Rinp?
• Since there is no resistance between Cm and Rinp, they see the same increasing voltage
If Rinp is creating a “leaky plug” that directs current to Cm, why does increasing Rinp slow down the charging of Cm?
Charging of Cm slows down because the effective voltage across Rinp (and hence Cm) increases with higher Rinp
Specific capacitance (Csm)
Capacitance of 1 cm2 of membrane
• A typical value for Csm is 1 μF/cm2
Capacitance of a cylindrical section of axon (Cm)
Cm = Csm x 2πrh (SA of a cylinder)
Increasing r or h increases Cm
Specific resistance (Rsm)
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)
Resistance of a spherical cell (Rm)
- Rm=Rsm ÷4πr2
* Increasing r decreases Rm
Resistance of a cylindrical section of axon (Rm)
- Rm=Rsm ÷2πrh
* Increasing r or h decreases Rm
Specific axial or cytoplasmic resistance (Rsa)
As current travels through an axon, it meets resistance through the axoplasm
Rsa is dependent on ion concentrations
What effect does [Na+] have on Rsa?
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
Axial resistance of a cylindrical section of axon (Ra)
• Ra=(Rsa xh)÷πr2
- Increasing h increases Ra
- Increasing r decreases Ra
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
If the resistance along the axoplasm is high, current is more likely to go through the membrane close to the site of injection
If you inject current into the center of an axon…
Current travels further if there is ____ axial resistance
current travels further if there is low axial resistance
If you inject current into the center of an axon…
If the resistance of the membrane is high, current will travel ______ along the axon
If the resistance of the membrane is high, current will travel further along the axon
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
low membrane resistance will direct current through the membrane close to the site of injection, and hence it will not travel as far
As we move along the axon in the x direction…
• There is a continual ________ in ΔV (i.e. across Cm)
As we move along the axon in the x direction…
• There is a continual decrease in ΔV (i.e. across Cm)
V0 is the maximal voltage resulting from current injection site at x= _______
V0 is the maximal voltage resulting from current injection site at x=0
The input resistance Rinp is dependent on both the _______ resistance R_ and the _____ resistance R_
The input resistance Rinp is dependent on both the membrane resistance Rm and the axial resistance Ra
λ is the length constant of the finer
• ↑ λ: current (and hence depolarization)
travels ______ along the axon
• ↓ λ: current/depolarization travels _______
• ↑ λ: current (and hence depolarization)
travels further along the axon
• ↓ λ: current/depolarization travels less far
How would you increase the distance that current travels along an axon?
- Decrease Ra
* Increase Rm
What effect does increasing the radius of the axon have on speed of current?
current/depolarization travels more effectively and quickly
What allows the squid to escape predators?
The giant axon allows the squid brain to quickly tell muscles in the mantle to contract (for escaping danger)
Why do electrical signals travel faster through thicker axons?
- 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
There is also a time delay in ΔV along the axon
• 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
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
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
An optimal cable has:
More insulation (lower Cm and increase Rm) and lower axial resistance (decrease Ra)
How do you speed up an action potential?
Increase the membrane resistance (Rm)
Decrease the axial resistance (Ra)
Decrease the membrane capacitance (Cm) - (takes less time to charge the capacitors)
Myelination - Glial/Schwann cells
Insulate axons from extracellular saline
Decreases Cm while increasing Rm, both of which promote faster signal propagation
Nodes of Ranvier
Interrupt Myelin sheaths
- Packed with Na and K channels
- The nodes boost the AP as it travels along the neuron
Saltatory Conduction
Signals “jump” from node to node
Geometry and conduction block
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
Back-propagating action potentials and dendritic excitability
Dendrites also have ion channels, and can thus generate their own Action Potentials
