Figure 5.

Features of the allosteric kinetics in NMDAR-EPSP. A, Derivation of NMDAR-EPSPs by postspiking → prespiking. NMDAR-EPSPs (right) was derived by the subtraction of AP alone from the NMDAR-EPSP plus AP in the absence of AMPAR activation (left, solid line) in presence of CNQX, a specific AMPAR antagonist (Froemke et al., 2005) (left, dashed line). B, Time courses of NMDAR-EPSPs by postspiking → prespiking in experiment (T_post − T_pre = −10 ms, red; prespike-only as control, gray), in the no-allosteric model (−1, −2, −4,…, −256 ms) with rapid (τ₁ = τ₂ = 2.3 ms) and slow (τ₁ = τ₂ = 230 ms) suppression, and in the allosteric model (−1, −2, −4,…, −256 ms; τ₁ = 2.3 ms and τ₂ = 230 ms), as indicated. C–E, Peak amplitude (C), peak time (D), and decay amplitude (E) of NMDAR-EPSPs in the models (top) and the experiments (bottom). The responses were normalized by the control responses. The decay amplitude was taken at the time when three times longer than the largest peak time in each set. The responses of the no-allosteric model with rapid and slow suppression (blue and green, respectively) and the allosteric model (red) are plotted (top). The timing-dependent NMDAR-EPSPs in the experiments were fitted by a single exponential curve using the least square method (bottom). The apparent time constants of the responses of NMDAR-EPSPs versus the spike timing, τ_app, are indicated. F, Evaluation of goodness of fit of the no-allosteric and allosteric models with the experimental data. The time constant in the no-allosteric model was changed as indicated, and the measure S(θ, Σ) was plotted. S(θ, Σ) is a sum of variance and covariance of errors between experiment and simulation in peak amplitude, peak time, and decay amplitude, normalized by variance and covariance of residuals in the best-fit model. S(θ, Σ) is given by , where f (x_i, θ) is the fitting function, and θ is the parameter vector, Σ is the variance–covariance matrix of residuals of the best-fit model (τ₁ = 2.3 ms and τ₂ = 2.3 × 10⁴ ms), Y_i is a column vector of the peak amplitude, peak time, and decay amplitude of ith NMDAR-EPSP, and x_i is T_post − T_pre of the EPSP (Gallant, 1987). Note that the closer to 1 the S(θ, Σ) becomes, the better the model fits the experimental results. Arrowheads denote the time constants used in the no-allosteric and allosteric models. G, Goodness of fit against various time constant of Ca²⁺ · CaM binding to NMDARs, τ₂, in the allosteric model. The τ₂ was changed as indicated, and the S(θ, Σ) was measured. The arrowhead indicates τ₂ (230 ms) used in the allosteric model.