Cable Properties

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
• Ohms 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 (?) describes this
  property
• ? 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/?

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
• t is the time it takes to reach 63 of the final
  voltage (msec)
• t 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
• ? 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) ? 13 mm
• mammalian nerve fiber (1 micron diameter)
• ? 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 p radius
• ri 1/p 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.) ? 13mm- mammalian nerve
  fiber (1 micron dia.) ?  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