Figure 9.

Computational model of sodium entry into and diffusion from a dendritic spine. A, Components of the model: spine head, spine neck, two dendritic segments. The starting dimensions are shown next to each component. Using the NEURON platform, the sodium conductance generating the EPSC was modeled as a point process on the spine head using g_AMPA(t) = g_A * [exp(−t/t₁) − exp(−t/t₂)], t₁ = 2 ms, t₂ = 0.5 ms (Grunditz et al., 2008); g_NMDA(t) = g_N * [1 − (1/[1+k/[Mg]])] * exp(−t/t₃) * [1 − exp(−t/t₄)], t₃ = 71 ms, t₄ = 13.2 ms, k = 1.07 * exp(0.057 * V), where V is voltage in mV and [Mg] = 2 mm (McCormick et al., 1993); temperature, 22°C. g_A and g_N are constants that were adjusted to give ∼5 mm peak [Na⁺]_i at the spine head. Resting [Na⁺]_i = 4 mm and E_Na = +40 mV. The only mechanisms affecting [Na⁺]_i were entry through AMPA and NMDA receptors and diffusion. The traces in the modeled concentrations were taken from the locations marked with a black dot; on the dendrite, this point was 3 μm from the neck. The time to half decay in the spine head was 15 ms. Removing the NMDA conductance (dashed black line) had almost no effect on the fast component of the response but decreased the slow component; the half-removal time was reduced by 2.4 ms. B, Variations in the half-decay time in models where only one of four parameters was varied; the other parameters were as in A. The arrows point to the starting values in A. Most of the models predicted half-decay times within the range of measured values with two exceptions: small spine-neck diameter and small diffusion constant.