Individual Neurons - Computational Explorations in Cognitive Neuroscience - page 65

Perhaps the most important source of what we have
termed self-regulatory dynamics in the neuron are volt-
age and calcium gated channels, of which a large num-
ber have been described (see Johnston & Wu, 1995 for
a textbook treatment). These channels open and close as
a function of the instantaneous activity (voltage-gated)
and averaged prior activity (calcium-gated, where inter-
nal calcium concentrations reflect prior activation his-
tory). Consistent with the need for simplification in
cognitive-level models, we summarize more compli-
cated biological mechanisms into two broad categories
of self-regulatory effects:

2.9.1 Implementation of Accommodation and

Hysteresis

As we stated, our implementation of self-regulatory dy-
namics represents a simplification of the underlying bi-
ological mechanisms. We use the same basic equations
for accommodation and hysteresis, with the different ef-
fects dictated by the parameters. The basic approach is
to capture the delayed effects of accommodation and
hysteresis by using a basis variable b that represents
the gradual accumulation of activation pressure for the
relevant channels (e.g., calcium concentration, or per-
sistently elevated membrane potential). The actual ac-
tivation of the channel is then a function of this basis
variable. Once the basis variable gets above an activa-
tion threshold value ￿ a , the conductance of the channel
begins to increase with a specified time constant ( dt g ).
Then, once the basis falls below a second (lower) deac-
tivation threshold value ￿ d , the conductance decreases
again with the same time constant.
First, we will go through the example of the com-
putation of the accommodation conductance g a (t) with
basis variable b a (t) , and then show how the same equa-
tions can be used for hysteresis. The gated nature of the
channel is captured by the following function:

accommodation and hys-

teresis .
We use the term accommodation to refer to any in-
hibitory current (typically a K + channel) that is typi-
cally opened by increasing calcium concentrations, re-
sulting in the subsequent inhibition of the neuron. The
longer acting GABA-B inhibitory synaptic channel may
also play a role in accommodation. Thus, a neuron that
has been active for a while will accommodate or fatigue
and become less and less active for the same amount of
excitatory input. In contrast, hysteresis refers to excita-
tory currents (mediated by Na + or Ca ++ ions) that are
typically opened by elevated membrane potentials, and
cause the neuron to remain active for some period of
time even if the excitatory input fades or disappears.
The opposition between the two forces of accommo-
dation and hysteresis, which would otherwise seem to
cancel each other out, is resolved by the fact that hys-
teresis appears to operate over a shorter time period
based on membrane potential values, whereas accom-
modation appears to operate over longer time periods
based on calcium concentrations. Thus, neurons that
have been active have a short-term tendency to remain
active (hysteresis), but then get fatigued if they stay
active longer (accommodation). Indeed, some of the
hysteresis-type channels are actually turned off by in-
creasing calcium concentrations. We will see in later
chapters that the longer-term accommodation results in
a tendency for the network to switch to a different inter-
pretation, or locus of attention, for a given input pattern.
The detailed implementation of these processes in the
simulator is spelled out in the following section.

if (b a (t) > ￿ a )

if (b a (t) < ￿ d )
(2.39)
This accommodation conductance g a (t) is then used in
a diffusion-corrected current equation:

(2.40)

which is then added together with the other standard
conductances (excitation, inhibition, and leak) to get
the net current (see equation 2.6). Note that accom-
modation has an inhibitory effect because E a is set to
be at the resting potential (as is appropriate for a K +
channel). Finally, the basis variable for accommoda-
tion, b a (t) , is updated as a function of the activation
value of the neuron:

(2.41)

where y j (t) is the activation value of the neuron. Thus,
the basis value is just a time average of the activation
state, with a time constant of dt ba .