Figure 4.20b,c

Cable Properties of Axons

Voltage Decreases with Distance

• Change in membrane potential (voltage) during AP decreases over distance due to resistance– Conduction with decrement– Higher resistance of intracellular and extracellular

fluids causes greater decrease in voltage along axon

– Lower resistance of membrane causes greater decrease in voltage along axon

– K+ leak channels (always open)» Some + charge leaks out

– Number of K+ leak channels will affect current loss and voltage decrease along axon

)/( orrr im im rr /

Length Constant () of Axons• Distance over which membrane potential will

decrease to 37% (1/e) of its original value

• Variables affecting length constant:• Resistance of cell membrane (rm)

• Resistance of intracellular fluid (ri)

• Resistance of extracellular fluid (ro)

– ro is usually low and constant; and is often ignored

– is largest when rm is high and ri is low

Length Constant () of Axons)/( orrr im im rr /

Figure 4.21

and the Speed of Conduction• Axonal conduction is a combination of

electrotonic current flow and ions flowing through voltage-gated channels during AP– Electrotonic current flow much faster than

opening of voltage-gated channels– Electronic current flow decreases over distance

• Higher allows more electrotonic current flow and faster speed of conduction

Axon Membrane 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 (lipid bilayer)

– Area of two conducting surfaces• Larger area increases capacitance

– Thickness of insulating layer• Greater thickness decreases capacitance

Figure 4.20b and Figure 4.22

Axon Membrane Capacitance

Time Constant (t) • Time over which membrane potential will

decay to 37% of its maximal value• How well does the membrane “hold” its charge?

• Variables affecting time constant:• Resistance of cell membrane (rm)

• Capacitance of the cell membrane (cm)

= rmcm

– Low rm or cm result in low • Capacitor becomes full faster• Faster depolarization• Faster conduction

Figure

Time Constant (t)

Figure

Giant Axons– Easily visible to naked eye (up to 1 mm

diameter)– Not present in mammals

Giant Axons Have High Conduction Speed

– rm inversely proportional to surface area• Large diameter axons have greater surface area and more

leak channels; therefore low resistance

– ri inversely proportional to volume• Large diameter axons have greater volume; therefore low

resistance

• As axon diameter increases, rm and ri both decrease

im rr /

Giant Axons Have High Conduction Speed

– Low rm reduces the length constant and decreases conduction speed

– Low ri increases the length constant and increases conduction speed

– Do not cancel each other out: rm is proportional to radius, ri is proportional to radius2

• Net effect of increasing axon radius is to increase speed of conduction

Figure

Axon Diameter and the Length Constant

Myelinated Neurons in Vertebrates

• Disadvantage of large axons– Take up a lot of space which

• Limits number of neurons that can be packed into nervous system

– Large volume of cytoplasm makes them expensive to produce and maintain

• Myelin enables rapid signal conduction in compact space

Myelin Increases Conduction Speed

• Increased membrane resistance– Insulators decrease current loss through leak

channels, increasing the length constant

• Decreased membrane capacitance– Increased thickness of insulating layer reduces

capacitance, decreasing the time constant

• High length constant and low time constant increase conduction speed

• Nodes of Ranvier are needed to boost depolarization