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Cable Properties

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

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Cable Properties

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  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, riis proportional toradius2 • 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 πradius • 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

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