The name is absent

128

open receptors of a given type:

uT

= MΓ](O(¹~^r(^f)) -k-r,                  (5.1)

where [T] is the concentration (in mM) of neurotransmitter, k₊ is the forward rate
constant in (mM ms)^-1, and k_ is the backward rate constant in (ms)^-1 (Destexhe
et al., 1998).

To include these types of inputs in the reduced models is rather straightforward,
but these ODE’s must be solved at each compartment. When [T] has the form of a
step function, (5.1) can be solved analytically (Destexhe et al., 1994), but for more
general dosage functions time-stepping schemes must be used. Due to this computa-
tional cost, efficient numerical methods must be applied if the reduced systems are
to yield fast simulations. One technique is to implement a shutoff mechanism like
that of §3.5 so that (5.1) is only solved for compartments where r is not close to
zero. However, this shutoff mechanism is likely to be more effective for fast synapses
(primarily excitatory ones) than for slow synapses.

Receptors fall into two categories, excitatory and inhibitory, depending on the
type of neurotransmitter which activates them. AMPA and NMDA receptors are
excitatory and are activated by glutamate, while GABA_yl and GABA_β receptors are
inhibitory and are activated by GABA (Destexhe et al., 1998). AMPA and GABA_j4
operate on much faster timescales than NMDA and GABAβ do. For now, we ignore
GABAβ because it requires second-order kinetics. Translating the receptor kinetics

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