The name is absent

130

where [Λ∕g²⁺]₀ is the concentration of magnesium outside the cell (Destexhe et al.,
1998). If the Γb_s,nmda(0 term were not there, this would be a straightforward DEIM
reduction, treating B(,(υ) just like a gating variable. But this term is coupled to
t⅛,nmda(0> which so far cannot be reduced because it is a synaptic input that is local
to each compartment. Since we cannot reduce this term, we focus our attention on
extracting the Bb(υ) term.

After discretizing the morphology, applying the POD reduction to the NMDA
synaptic input term yields

Inmda (O = U^rG^rNMDArNMDA (t)B(Uv)(Uv — Enmda) ∙          (5.5)

The product r(t)B(Uv) is actually a pointwise multiplication, and this is what allows
us to extract B and reduce it. We first approximate B via the DEIM as

B(Uv) ≈ RgB(U(:, Zβ)v),

where Zβ are the interpolation points. We can then use pointwise multiplication to
write

Inmda(0 ≈ GnmdaCbB(u(:, z^)v)∙U^tγnmda(^) (Uv — Enmda),      (5.6)

where Cb = U^τRβ.

With this derivation in place, reduced order models using receptor kinetics can
now be simulated. Perhaps the most pressing issue for further study is determining

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