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
Passive flow of current
A current traveling down a copper wire
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
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)
Cable Properties
1. 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
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.
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
l  rm /( ri  r )
o
l  rm / ri
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
l  rm / ri
•  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
Conduction Speed
Figure 5.25
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
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
Conduction Speed
Two ways to increase speed: myelin and
increasing the diameter of the axon
Table 5.3
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
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
Giant Axons
• Easily visible to the naked eye
• Not present in mammals
Figure 5.24
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
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