Individual Neurons - Computational Explorations in Cognitive Neuroscience - page 31

+

tion! In brief, the opening and closing of membrane
channels determines the conductances ( G ) for each type
of ion as a function of the input it receives. The poten-
tial V is just the membrane potential that we discussed
previously. We will see below that this potential can be
updated by computing the current I using Ohm's law
(equation 2.2) — this will tell us how many charges
are moving into or out of the neuron, and thus how the
membrane potential will change. By iteratively (repeat-
edly) applying Ohm's law, we can compute the changes
in potential over time, resulting in a model of how the
neuron computes. Owing to the combined forces of
diffusion (explained below) and the electrical potential,
each ion will respond to a given membrane potential in
a different way. Thus, each ion makes a unique contri-
bution to the overall current.

V

−

+

−

G

I

Figure 2.6: Sketch of Ohm's law in action, where an imbal-
ance of charges leads to a potential V (with the difference in
charge in the two chambers represented by the height of the
line) that drives a current I through a channel with conduc-
tance G .

changes as a function of the current coming into that
area. This will play an important role in how the neuron
behaves when excited by incoming charges.
Usually, ions (like everything else) encounter resis-
tance when they move, caused by being stuck in a vis-
cous liquid, or by their path being blocked by a wall
(membrane) with only small channels or pores they can
pass through. The greater the resistance encountered
by the ions when they move, the greater amount of po-
tential required to get them there. Imagine an inclined
plane with a ball on the top and a bunch of junk lying
in its path. The more junk (resistance), the higher you
have to tilt the plane (potential) to get the ball (ion) to go
down the plane. This relationship is known as Ohm's
law (figure 2.6):

2.4.2 Diffusion

In addition to electrical potentials, the main other fac-
tor that causes ions to move into or out of the neuron
is a somewhat mysterious “force” called diffusion .Re-
call that electrical potentials are caused by imbalanced
concentrations of positive and negative ions in a given
location. Diffusion also comes into play when there
are imbalanced concentrations. Put simply, diffusion
causes particles of a given type to be evenly distributed
throughout space. Thus, any time there is a large con-
centration of some particle in one location, diffusion
acts to spread out ( diffuse ) this concentration as evenly
as possible.
Though diffusion may sound simple enough, the un-
derlying causes of it are somewhat more complicated.
Diffusion results from the fact that atoms in a liquid or
gas are constantly moving around, and this results in a
mixing process that tends (on average) to cause every-
thing to be evenly mixed. Thus, diffusion is not a direct
force like the electrical potential, but rather an indirect
effect of stuff bouncing around and thus tending to get
well mixed.
The key thing about diffusion is that each type of par-
ticle that can move independently gets evenly mixed, so
having a large concentration of one type of ion in one
place (e.g., Na + ) cannot be compensated for by having
an equally large concentration of another ion with the

(2.1)

where I is the current (amount of motion), V is the elec-
trical potential, and R is the resistance. This equation
can be expressed in a slightly more convenient form in
terms of the inverse of resistance, called conductance
( G = R ). Conductance G represents how easily ions
can be conducted from one place to the other. Ohm's
law written in these terms is just:

(2.2)

We will see that Ohm's law forms the basis for the
equation describing how the neuron integrates informa-