Modeling of experimental observations of altered K⁺ dynamics in AQP4 deficiency. (A) Single neuron firing (Δt_n = 0.1 ms). Time course of [K⁺]_e modeled for wild type (WT) mice (P_f = 0.04 cm/s) and AQP4 knockout mice (AQP4^−/−, P_f = 0.001 cm/s, d_e = 2 or 2.4 µm) for well-mixed model (WMM, left) and diffusion-limited model (DLM, D_a = 10⁻⁹ cm²/s, center). Parameters: P_K^a = 1.2 × 10⁻⁵ cm/s, J_Kⁿ_o = 3.5 × 10⁻⁷ mol/cm²/s, and Δt_n = 0.1 ms. (right) Relative increase [K⁺]_e after neuroexcitation in WT vs. AQP4 knockout mice (Δ[K⁺]_e^−/−/Δ[K⁺]_e^+/+). (B) Repetitive pulsed neuronal excitation. (left and center) [K⁺]_e in response to 20 Hz stimulation (Δt_n = 0.1 ms firing) for 10 s. Parameters: P_K^a = 1.2 × 10⁻⁵ cm/s and J_Kⁿ_o = 2.1 × 10⁻⁷ mol/cm²/s. (right) [K⁺]_e at 20 s (broken line) after neuroexcitation and relative half-times for return of [K⁺]_e to baseline (t_1/2^−/−/t_1/2^+/+). (inset) P_f dependence of t_1/2 in the DLM (at fixed d_e of 2 µm), shown on a normalized y scale (denoted <t_1/2>). A similar P_f dependence was seen for [K⁺]_e (not depicted). (C) Prolonged neuronal firing. (left and center) [K⁺]_e responses to 20 Hz stimulation for 30 s. Parameters: P_K^a = 1.2 × 10⁻⁵ cm/s and J_Kⁿ_o = 3.45 × 10⁻⁷ mol/cm²/s. (right) Summary of t_1/2^−/−/t_1/2^+/+. (inset) P_f dependence of <t_1/2> in the DLM (at fixed d_e of 2 µm), shown on a normalized y scale.