Week 5: Resistance 189
ions. As such there is a “rise time” required to charge up a neuron towhere it can fire, followed by
a sudden exponential drop in charge across the membrane when it does fire to create an electrical
pulse capable of triggering the next neuron(s) down the network. From nothing but this we can
deduce a number of important properties of biological neural networks: They have a maximum firing
rate (consider the charging/discharging curves, where one has to exceed some threshold in order to
be able to trigger downstream neurons upon depolarization). Theyconsume energy, as all of the
teensy biological batteries that charge them up deliver power to the circuit – the human brain, for
example, consumes around 1/4 of the metabolic energy used by theentire human body, some 25
watts (out of 100 watts total). Neurotoxins such astetrodotoxin^58 which block the sodium channel
effectively freeze the otherwise variable resistance of the capacitative membrane, locking each neuron
in the “charged” state and preventing the triggered discharge that is required for normal operation.
Various nervous system disorders are related to “short circuiting” this network (by e.g. altering the
resistance of the myelin sheaths that protect the axons of the neurons as they transport the current
pulse downstream to the next neural synapse. Other disorders or neurotoxins are associated with
the neurotransmitter-mediated transport across the synapticgaps themselves.
Basically, one cannot evenbeginto understand the biology of the nervous system of any organism
without at least a conceptual understanding of batteries, resistances, and capacitances, and asound
conceptual understanding is always based on having really gone through the whole thing and worked
it all out, in detail, at least one time in your life. So even if you don’t plan to become a physicist
and work on all of this (very cool) stuff for the rest of your life,pay attention and work hardon
it now, because if you do you will reap the rewards in your work inotherdisciplines, where you
will discover it lurking, time and again, to confound your understanding if you never worked hard
enough to master it now.
This concludes our treatment of electrostatics with our first electrodynamicmodel. It is time
to move on from the electrostatic field to the next major piece of the electromagnetic puzzle: The
magnetic field.
(^58) Wikipedia: http://www.wikipedia.org/wiki/tetrodotoxin. Found in pufferfish and blue-ringed octupi, for the
marine biology crowd.