Aquaporin-4-dependent K(+) and water transport modeled in brain extracellular space following neuroexcitation - PubMed (original) (raw)

Aquaporin-4-dependent K(+) and water transport modeled in brain extracellular space following neuroexcitation

Byung-Ju Jin et al. J Gen Physiol. 2013 Jan.

Abstract

Potassium (K(+)) ions released into brain extracellular space (ECS) during neuroexcitation are efficiently taken up by astrocytes. Deletion of astrocyte water channel aquaporin-4 (AQP4) in mice alters neuroexcitation by reducing ECS [K(+)] accumulation and slowing K(+) reuptake. These effects could involve AQP4-dependent: (a) K(+) permeability, (b) resting ECS volume, (c) ECS contraction during K(+) reuptake, and (d) diffusion-limited water/K(+) transport coupling. To investigate the role of these mechanisms, we compared experimental data to predictions of a model of K(+) and water uptake into astrocytes after neuronal release of K(+) into the ECS. The model computed the kinetics of ECS [K(+)] and volume, with input parameters including initial ECS volume, astrocyte K(+) conductance and water permeability, and diffusion in astrocyte cytoplasm. Numerical methods were developed to compute transport and diffusion for a nonstationary astrocyte-ECS interface. The modeling showed that mechanisms b-d, together, can predict experimentally observed impairment in K(+) reuptake from the ECS in AQP4 deficiency, as well as altered K(+) accumulation in the ECS after neuroexcitation, provided that astrocyte water permeability is sufficiently reduced in AQP4 deficiency and that solute diffusion in astrocyte cytoplasm is sufficiently low. The modeling thus provides a potential explanation for AQP4-dependent K(+)/water coupling in the ECS without requiring AQP4-dependent astrocyte K(+) permeability. Our model links the physical and ion/water transport properties of brain cells with the dynamics of neuroexcitation, and supports the conclusion that reduced AQP4-dependent water transport is responsible for defective neuroexcitation in AQP4 deficiency.

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Figures

Figure 1.

Figure 1.

Model of K+ and water transport in brain ECS. (A) Diagram showing neurons and astrocytes in brain surrounded by an ECS. (B) Schematic of mathematical model. Neuronal, ECS, and astrocytic compartments are shown, along with key transport mechanisms including neuronal K+ release (JKn), K+ uptake by astrocytes (JKa), and osmotic water transport into astrocytes (JVa).

Figure 2.

Figure 2.

Computational approach. See the Model computations section for description.

Figure 3.

Figure 3.

Predictions of the well-mixed model. (A) Schematic of well-mixed model showing neuronal K+ release into ECS, and astrocytic uptake of K+ and water causing ECS shrinkage. (B) Time course of ECS potassium concentration ([K+]e) and volume (de), astrocyte membrane potential (ψ), and astrocyte K+ and water flux (JKa, JVa) after neuronal excitation causing [K+]e increase from 5 to 10 mM. Parameters: Pf = 0.04 cm/s, JKno = 10−8 mol/cm2/s, Δtn = 0.1 s, da = 10 µm, de = 2 µm, with the indicated PK. (C) Computations as in B for PK = 1.2 × 10−5 cm/s with the indicated Pf. (D) Computations as in B for PK = 1.2 × 10−5 cm/s, with the indicated de. JKno was adjusted to increase [K+]e from 5 to 10 mM. (E) Effect of magnitude of neuroexcitation. Computations as in B, with PK = 1.5 × 10−5 cm/s and JKno = 5 × 10−8 mol/cm2/s, with the indicated Pf. (F) The effect of duration of neuroexcitation. Computations as in B, with PK = 1.3 × 10−5 cm/s, JKno = 8 × 10−10 mol/cm2/s, and Δtn = 10 s, with the indicated Pf.

Figure 4.

Figure 4.

Predictions of the diffusion-limited model for high astrocyte water permeability. Pf = 0.04 cm/s for computations in this figure. (A) Schematic showing nonlinear and newly added mesh elements in astrocyte cytoplasm used for numerical solution of the diffusion equation. See text for explanation. (B) Time course of [K+]e, de, ψ, JKa, and JVa after neuroexcitation for the indicated cytoplasmic diffusion coefficients, Da. Parameters: PK = 1.2 × 10−5 cm/s, JKno = 10−8 mol/cm2/s, Δtn = 0.1 s, da = 10 µm, and de = 2 µm. (C and D) Astrocyte spatial distribution of [K+]a and [non-K+]a at the indicated times, with parameters as in B, for Da = 10−8 cm2/s (C) and t = 5 s (D). (E) Effect of duration of neuroexcitation. Computations as in B, with PK = 1.3 × 10−5 cm/s, JKno = 8 × 10−10 mol/cm2/s, and Δtn = 10 s.

Figure 5.

Figure 5.

Water permeability effects in the diffusion-limited model. (A) Time course of [K+]e and de for the indicated Pf and Da. Parameters: PK = 1.2 × 10−5 cm/s, JKno = 10−8 mol/cm2/s, Δtn = 0.1 s, da = 10 µm, and de = 2 µm. (B) Effect of magnitude of neuroexcitation. Computations as in B, but with JKno = 5 × 10−8 mol/cm2/s to increase [K+]e from 5 to 30 mM. (C) Effect of duration of neuroexcitation. Computations as in C, with PK = 1.3 × 10−5 cm/s, JKno = 8 × 10−10 mol/cm2/s, and Δtn = 10 s. (D) Spatial distributions of [K+]a and osmolarity (Φa) in astrocyte cytoplasm for the indicated Pf and Da, with parameters as in C.

Figure 6.

Figure 6.

Modeling of experimental observations of altered K+ dynamics in AQP4 deficiency. (A) Single neuron firing (Δtn = 0.1 ms). Time course of [K+]e modeled for wild type (WT) mice (Pf = 0.04 cm/s) and AQP4 knockout mice (AQP4−/−, Pf = 0.001 cm/s, de = 2 or 2.4 µm) for well-mixed model (WMM, left) and diffusion-limited model (DLM, Da = 10−9 cm2/s, center). Parameters: PKa = 1.2 × 10−5 cm/s, JKno = 3.5 × 10−7 mol/cm2/s, and Δtn = 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 (Δtn = 0.1 ms firing) for 10 s. Parameters: PKa = 1.2 × 10−5 cm/s and JKno = 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 (t1/2−/−/t1/2+/+). (inset) Pf dependence of t1/2 in the DLM (at fixed de of 2 µm), shown on a normalized y scale (denoted <t1/2>). A similar Pf 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: PKa = 1.2 × 10−5 cm/s and JKno = 3.45 × 10−7 mol/cm2/s. (right) Summary of t1/2−/−/t1/2+/+. (inset) Pf dependence of <t1/2> in the DLM (at fixed de of 2 µm), shown on a normalized y scale.

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