Individual Neurons - Computational Explorations in Cognitive Neuroscience - page 43

Parameter ( 0 ￿ 1 )

level models. For example, our computations are sen-
sitive to the projection-level organization of inputs, and
they allow for the differential scaling of distal versus
proximal inputs. Furthermore, we use time averaging
to simulate the sluggishness of real neurons. Neverthe-
less, we are still ignoring a number of known properties
of dendritic integration in real neurons.
For example, we now know that dendrites have a
number of active voltage-gated channels that can po-
tentially dramatically affect the way that information is
integrated (e.g., Cauller & Connors, 1994). One re-
sult of these channels might be that weak, distal signals
might be amplified and thus equalized to stronger, prox-
imal inputs, which could be easily handled in our com-
putation of the inputs. However, these channels may
also impose thresholds and other nonlinearities that are
not included in our simple model. These active chan-
nels may also communicate the output spikes produced
at the axon hillock all the way back into the dendrites,
which could be useful for learning based on the overall
activity of the postsynaptic neuron (Amitai, Friedman,
Connors, & Gutnick, 1993; Stuart & Sakmann, 1994).
Some researchers have emphasized the complex, log-
iclike interactions that can occur between inputs on
the dendritic spines (where most excitatory inputs oc-
cur) and other branching aspects of the dendrites (e.g.,
Shepherd & Brayton, 1987). If these played a dominant
role in the integration of inputs, our averaging model
could be substantially inaccurate. However, these ef-
fects have not been well demonstrated in actual neurons,
and may actually be mitigated by the presence of active
channels. Furthermore, some detailed analyses of den-
dritic integration support the point neuron approxima-
tion, at least for some dendritic configurations (Jaffe &
Carnevale, 1999). See section 2.8 for more discussion
of the relative advantages and disadvantages of this kind
of logiclike processing.

a (K + )

-90 0.00 0.50

l (K + ,Na + )

-70 0.15 0.10

-70 0.15 —

i (Cl ￿ )

-70 0.15 1.00

-55 0.25 —

(Na + ) +55 1.00 1.00

h (Ca ++ ) y

+100 1.00 0.10

Tab le 2 . 1 : Reversal potentials (in mV and 0 ￿ 1 normalized
values) and maximum conductance values for the channels
simulated in Leabra, together with other biologically based
constants including the resting potential V rest and the nom-
inal firing threshold ￿ ( thr in the simulator). E a and E h
are the accommodation and hysteresis currents discussed in
greater detail in section 2.9. y Note that this value is clipped
to 1.0 range based on -90 to +55.

malized biologically based values. The normalized val-
ues are easier to visualize on a common axis, are more
intuitively meaningful, and can be related more easily
to probability-like values (see section 2.7). Table 2.1
shows a table of all the basic parameters used in our
simulations (including some that will be introduced in
subsequent sections), with both the biological and nor-
malized values. Normalization was performed by sub-
tracting the minimum ( ￿90 ) and dividing by the range
( 55 to ￿90 ), and rounding to the nearest .05. Also, we
note that the dt vm parameter in equation 2.8 is called
dt_vm in the simulator, with a typical value of .2.

2.5.3 The Discrete Spiking Output Function

After updating the membrane potential, we need to
compute an output value as a function of this potential.
In this section we describe one of the two options for
computing this output — the more biologically realistic
discrete spiking output. The next section then discusses
the other option, which is the continuous, real-valued
rate code approximation to discrete spiking.
Recall that in a real neuron, spiking is caused by the
action of two opposing types of voltage-gated channels,
one that excites the membrane potential (by letting in
Na + ions), and another that counters this excitement
and restores the negative resting potential (by letting out

2.5.2 Point Neuron Parameter Values

The next step in the activation function after the in-
put conductances are computed is to apply the mem-
brane potential update equation (equation 2.8). We lit-
erally use this equation, but we typically use parame-
ter values that range between 0 and 1, based on nor-