- Further reading[[Student version, January 17, 2003]] 481
Moreover, ifV is maintained at some valueV^0 +vother than its quasisteady value, the
Ohmic hypothesis says we get a net currentjq=vgtot(see Your Turn 12a). The voltage-
gating hypothesis agrees with this prediction at smallv,but at larger depolarization instead
gives positive feedback (Figure 12.9).- Cable: Foracylindrical axon of radiusafilled with axoplasm of conductivityκ,with the
approximation that the resistance of the exterior fluid is zero, the membrane currentjq,rand
potentialVare related by (Equation 12.7)
πa^2 κd(^2) V
dx^2
=2πa
(
jq,r+CdV
dt)
.
HereCis the capacitance per area of the membrane. Takingjq,rto be given by one of the
three hypotheses above gives a closed equation (“cable equation”), which can in principle be
solved. In the Ohmic model this equation is essentially a diffusion equation. Adding voltage-
gating leads to a nonlinear traveling-wavesolution. The full Hodgkin–Huxley conductance
model gives a cable equation with a realistic, self-limiting, traveling-wavesolution.Further reading
Semipopular:
Historical: Hodgkin, 1992; Neher & Sakman, 1992.
Intermediate:
This chapter again follows the approach of Benedek & Villars, 2000c.
See also, for example, Dowling, 1992; Koch, 1999 and Katz’s classic book Katz, 1966.
General: Nicholls et al., 2001.
Computer modeling of electrophysiology: Hoppensteadt & Peskin, 2002.
Technical:
General: Kandel et al., 2000.
Membrane electrophysiology: Aidley, 1998.
Action potentials: Hodgkin & Huxley, 1952b; Keener & Sneyd, 1998.
Nonlinear waves in excitable media: Murray, 1993.
Ion channels: Hille, 2001.
Synapses: Cowan et al., 2001.