Circuit Elements Required for Neural Systems - Brain Theory from a Circuits and Systems Perspective - page 33

lightening in air (about 30 kV/cm breaks down air). So electrical stress is significant.
All molecules in a membrane are polarized to some extent and held by electrical
force in an elongated fixed position until triggered.

Pulses Brokered by a Membrane

To begin, the interior voltage of a neuron is at rest, 70 mV. A neural membrane

consists of a phospholipid bilayer of molecules that is profusely and randomly
textured with larger transmembrane proteins (they number about 10 10 /cm 2
roughly). One way to trigger a membrane is to impose a modest reduction in the
voltage across the membrane, from

55 mV. This will begin to unlock some
of the larger transmembrane proteins in the membrane and to open channels of
conduction. Thus begins a neural pulse.
Sodium ions from outside the neuron penetrate into the unlocked membrane,
capturing electrons, and resulting in positive charge accumulation inside. Particles
have been estimated to go into and through a membrane at about 10 15 particles/s/
cm 2

70 to

[ 1 ]. This converts to amperes by multiplying by the charge of one electron,

10 19 C, Coulomb/electron, and then multiplying by membrane area in
square centimeters. The resulting current charges membrane capacitance in a
positive direction.
Voltage is determined by a basic formula: Δ

1.6

V is the increase
in voltage in millivolts, I is charging current in microamperes, C is membrane
capacitance in microfarads, and

V ¼ I Δ t/C, where Δ

t is the amount of time used in milliseconds.
Voltage build up across a membrane depends largely on the duration of the current
pulse. Charging current has been observed to be fairly steady, as evidenced by
photographs of neural pulses, and also computerized simulations, more or less like
the curve in Fig. 3.1 , whose rising voltage increases at a constant rate of about
140 mV/ms. 1
Note that once triggered, the pulse goes smoothly up to its peak and then
smoothly down to its undershoot value. Subsequently it slowly drifts back to a
resting potential. All occurs within a few milliseconds; this simulation indicates a
risetime of about 1 ms; a slightly longer falltime, perhaps 1.5 ms; and a longer
recovery time of perhaps 2 ms. This recovery time and other variables define a
refractory period during which a neuron, if triggered, will not give a full output.
Relevant to explaining a neural pulse is that charging current is maintained until
internal voltage reaches about +40 mV. At this point the electric field applied to the
molecules in the membrane is strongly reversed. The molecules now change
orientation so that the sodium current begins to cut off. Once sodium charging is

Δ

1 Note that slower positive ions in a channel would be stopped and reversed by the repelling
internal positive electric field, blocking the channel. But experimentally the average rise in current
is steady. This indicates capturing of electrons from the interior, allowing the pulse to maintain a
steady rise.