1. Cable Properties
Properties of the nerve, axon, cell body and dendrite affect the distance and speed of membrane potential
Passive conduction properties = cable properties
Signal becomes reduced over distance depending on the cable properties
Current (I) – amount of charge moving past a point at a given time
A function of the drop in voltage (V) across the circuit and the resistance (R) of the circuit
Voltage – energy carried by a unit charge
Resistance – force opposing the flow of electrical current
Ohm’s law: V = IR

2. Passive flow of current
A current traveling down a copper wire

3. Voltage Decreases With Distance
Conduction with decrement
Due to resistance
Intracellular fluid: high resistance   decrement
Extracellular fluid: high resistance   decrement
Membrane: high resistance   decrement
K+ leak channels (always open): some + charge leaks out   current
Few K+ leak channels   + charge leak out  high membrane resistance

4. Cable Properties Each area of axon consists of an electrical circuit
Three resisters: extracellular fluid (Re), the membrane (Rm), and the cytoplasm (Rc)
A capacitor (Cm) – stores electrical charge; two conducting materials (ICF and ECF) and an insulating layer (phospholipids)

5. Cable Properties
Loss of current across membrane (through rest channels)
loss of current across membrane results in membrane potential dropping with distance
dependent on the internal resistance (ri) and the membrane resistance (rm)
the length or space constant (λ) describes this property
λ = distance (mm) at which V = 1/e V0 or the distance at which V has decreased to 37%
the relationship between the voltage at any distance (x) from the applied (or original) voltage is :  
Vx = Vo e-x/λ

6. Cable Properties
2. Loss of current (charge) due to capacitance properties of the membrane
cell membrane acts as a capacitor
2 conducting sheets separated by an insulating material
- the closer the sheets the better the capacitor
lipid bilayer is 7 nm thick therefore = excellent capacitor
it takes time and current (charge) to charge the membrane capacitor
as current drops over the length of the nerve takes longer and longer to charge the capacitor
the time constant describes this effect
τ is the time it takes to reach 63% of the final voltage (msec)
τ = Rm x Cm
the smaller the capacitance properties the less the current
loss and the faster the nerve impulse travels
the larger the capacitance properties the more current loss and the slower the nerve impulse
time constants range from 1 to 20 msec.  

7. Length Constant (l)
Distance over which change in membrane potential will decrease by 37% (1/e) where e = 2.718
dependent on the internal (ri) and membrane resistance (rm) 
l is largest when rm is high and ri is low
ro is usually low and constant
λ = square root of (rm/ri)
if the membrane resistance is large then the longer the impulse will travel along the nerve before reaching 37% of original
if the internal resistance is large then the shorter the impulse will travel along the nerve before reaching 37% of original
giant axon of squid (1mm diameter) λ = 13 mm
mammalian nerve fiber (1 micron diameter)
λ = 0.2 mm

8. Conduction Speed
rm is inversely proportional to surface area:  diameter   surface area   leak channels   resistance
ri is inversely proportional to volume:  diameter   volume   resistance
Effect of resistance
 rm   l   conduction speed
 ri   l   conduction speed
Do not cancel each other out: rm is proportional to radius, ri is proportional to radius2
Therefore, net effect of increasing radius of the axon is to increase the speed of conduction

9. Conduction Speed
Figure 5.25

10. Speed of Conduction and Capacitance
Capacitance – quantity of charge needed to create a potential difference between two surfaces of a capacitor
Depends on three features of the capacitor
Material properties: generally the same in cells
Area of the two conducting surfaces:  area   capacitance
Thickness of the insulating layer:  thickness   capacitance

11. Speed of Conduction and Capacitance
Time constant (t) - time needed to charge the capacitor; t = rmcm
Low rm or cm  low t  capacitor becomes full faster  faster depolarization  faster conduction

12. Conduction Speed
Two ways to increase speed: myelin and increasing the diameter of the axon
Table 5.3

13. Axon diameter
increased axon diameter in axons increases action potential velocity - i.e. giant axon of squid = 1 mm diameter = huge!
why does increasing the diameter of an axon increase the speed of an action potential?  
rm, ri and cm are all related to the radius of a fiber
rm ~ ½ π radius
ri ~ 1/π radius2
cm ~ radius - increase diameter of a fiber rm and ri decrease, but ri decreases faster, therefore benefit as the internal resistance decreases faster relative to the membrane resistance - therefore the distance the membrane potential can travel is increased by an increased diameter  

14. Axon diameter, cont….
the length constant is increased - giant axon of squid (1 mm dia.) λ = 13mm - mammalian nerve fiber (1 micron dia.) λ  = 0.2mm
- increase in fiber diameter also increases cm, but this increase is proportional to the increase in the radius while the decrease in ri is proportional to the radius2 - therefore internal resistance decreases faster than the capacitance of the membrane - the decrease in ri speeds up the current transfer to the next region of the nerve and threshold is reached sooner

15. Giant Axons Easily visible to the naked eye Not present in mammals
Figure 5.24

16. Myelin Increases Conduction Speed
 membrane resistance: act as insulators   current loss through leak channels   membrane resistance   l
 capacitance:  thickness of insulating layer   capacitance   time to constant of membrane   conduction speed
Nodes of Ranvier are needed to boost depolarization

17. Myelin Increases Conduction Speed
passive spread of the depolarizing current between the nodes is the rate limiting step on an action potential
depends on how much current is lost due the three cable properties
1. if the internal membrane resistance (ri) is high - current spread is not as far, speed of the action potential is slower
2. if the membrane resistance (rm) is low- current is lost and so current spread is slower and the action potential slows down
myelin increases rm so that little current is lost, passive spread of the current is further
3. if the membrane capacitance (cm) is high - the longer and more charge it takes to charge the capacitor and the slower the action potential
myelin decreases cm so that less current is lost in charging the capacitor and more is available to spread down the axon