Article Figures & Data
Figures
- Figure 1.
Model overview. The tissue is represented as a 1D domain of length 10 mm including neurons, ECS, and glial cells. Within each compartment, the model describes the dynamics of the volume fraction (α), the Na+, K+, Cl– and glutamate concentrations (
- Figure 2.
Simulated CSD wave in the WT model (A) triggered by excitatory fluxes. The upper panels display a snapshot in time (plot of the respective field vs spatial coordinate x) of ECS glutamate (A), ECS ion concentrations (B), potentials (C), and change in volume fractions (D) at 60 s. The lower panels display time evolution of ECS glutamate (E), ECS ion concentrations (F), potentials (G), and change in volume fractions (H) at x = 2.0 mm.
- Figure 3.
Comparison of Model A (solid) and Model B (stippled) CSD wave. The upper panels display snapshots (plot of field vs spatial coordinate x) of ECS glutamate (A), ECS ion concentrations (B), potentials (C), and change in volume fractions (D) at 60 s. The lower panels display time evolution of ECS glutamate (E), ECS ion concentrations (F), potentials (G) and change in volume fractions (H) evaluated at x = 2.0 mm.
- Figure 4.
Comparison of electrical potentials during simulated CSD where the glial gap junction factor χg is reduced by 0% (Model A), 25%, 50%, 75%, and 100% (Model B). The panels display neuronal potentials (A), glial potentials (B), and ECS potentials (C) evaluated at x = 2.0 mm.
- Figure 5.
Comparison of Model A (solid) and Model C (stippled) CSD wave. The upper panels display snapshots (plot of field vs spatial coordinate x) of ECS glutamate (A), ECS ion concentrations (B), potentials (C), and change in volume fractions (D) at 60 s. The lower panels display time evolution of ECS glutamate (E), ECS ion concentrations (F), potentials (G), and change in volume fractions (H) evaluated at x = 2.0 mm.
- Figure 6.
Comparison of simulated CSD where the neuronal and glia membrane area-to-volume factors γne and γge are reduced by 0% (Model A), 25%, 50%, and 75% (Model C). The panels display ECS glutamate concentrations (A), ECS potassium concentrations (B), ECS potentials (C), change in ECS volume fractions (D), neuronal potentials (E), glial potentials (F), change in neuronal volume fractions (G), and change in glial volume fractions (H) evaluated at x = 2.0 mm.
- Figure 7.
Comparison of intervals (boxes) and min/max-ranges (whiskers) for experimentally and computationally measured values for relevant quantities in WT mice. Red lines indicate median values, and open circles denote outliers. The panels display the mean wave propagation speed (A), amplitude (B), and duration (C) of the DC shift, amplitude of elevated extracellular potassium (D), duration of elevated extracellular glutamate concentration (E), amplitude (F), and duration (G) of neuronal swelling, and amplitude of extracellular shrinkage (H).
- Figure 8.
Comparison of changes in volume fractions during simulated CSD where the glial water permeability ηge is reduced by 0% (Model A), 25%, 50%, 75%, and 100% (Model D). The panel displays the largest (over time) change in neuronal, glial, and ECS volume fractions relative to baseline at x = 2 mm for each of the reductions.
- Figure 9.
Comparison of Model A (solid) and Model E (stippled) CSD wave. The upper panels display snapshots in time of ECS glutamate (A), ECS ion concentrations (B), potentials (C), and change in volume fractions (D) at 60 s. The lower panels display time evolution of ECS glutamate (E), ECS ion concentrations (F), potentials (G), and change in volume fractions (H) evaluated at x = 2.0 mm.
- Figure 10.
Comparison of glial dynamics without stimuli (A) and during induced CSD (B, C) where the Kir 4.1 expression is reduced by 0% (Model A), 10%, 20%, and 30% (Model E), 40%, 50%, 60%, 70%, and 80%. The panels display the resting glial potential (A), the glial potential during simulated CSD (B), and the change in glial volume fractions during simulated CSD (C) evaluated at x = 2.0 mm. Asterisks (*) indicate that CSD could not be induced successfully in the computational models.
Tables
- Table 1
Overview of the computational models with parameter values: χg: glial gap junction factor, γne: neuronal membrane area-to-volume, γge: glial membrane area-to-volume, ηge: glial membrane water permeability,
Model χg γne (m– 1) γge (m– 1) ηge (m4/(mol s)) A 0.05 5.38 × 105 6.38 × 105 5.40 × 10– 10 1.30 B 0 – – – – C – 1.35 × 105 1.6 × 105 – – D – – – 0 – E – – – – 0.91 Model A corresponds to the default parameters (given in Extended Data 1, only three significant digits included here). The dash (–) indicates no change from the default values.
- Table 2
Summary of computational quantities of interest for different models (A, B, C, D, E)
Quantity of interest A B C D E Mean wave propagation speed (mm/min) 5.84 5.52 3.19 5.83 5.27 DC shift (mV) 11.02 3.80 10.18 11.02 10.16 DC shift duration (s) 32 50 86 32 36 Neuronal swelling (%) 11.69 11.67 5.69 14.93 11.81 Glial swelling (%) 7.13 7.05 3.74 0 6.73 ECS shrinkage (%) 39.79 39.56 19.32 37.33 39.60 Neuronal swelling duration (s) 109 111 183 115 100 Glial swelling duration (s) 103 101 181 0 148 ECS shrinkage duration (s) 135 135 185 136 141 ECS K+ elevation (mm) 76.39 76.46 54.40 75.39 76.60 ECS Glu elevation (mm) 1.38 1.38 0.20 1.37 1.39 ECS Cl– elevation (mm) 21.12 20.88 7.43 23.12 20.81 ECS K+ elevation duration (s) 26 26 60 26 27 ECS Glu elevation duration (s) 20 19 25 20 20 ECS Cl– elevation duration (s) 84 84 178 87 90 Neuronal membrane potential (mV) 63.36 63.38 51.51 63.32 64.53 Glial membrane potential (mV) 55.14 55.77 46.52 54.24 48.23 Neuronal membrane potential duration (s) 79 79 158 83 69 Glial membrane potential duration (s) 45 40 96 42 160 Numerical errors are <1.5%.
- Table 3
Summary and overview of experimentally reported propagation speeds, DC shift amplitudes (DC) and their duration (DC dur.), peak in extracellular K+ levels (Peak
Speed DC DC dur. Peak Δαn Δαn dur. Δαe (mm/min) (mV) (s) (mm) (s) (%) (min) (%) Study (WT) M Lauritzen and Hansen (1992) IV 3.8 ± 0.9 23 ± 6 Theis et al. (2003) S 3.8 ± 0.4 16.8 ± 1.1 58 ± 15 38.6 ± 3 – – 4.4 ± 0.3 Padmawar et al. (2005) IV 4.4 ± 0.5 Takano et al. (2007) IV 66 ± 4 37.1 ± 0.1 8 – 10 Chang et al. (2010) IV 18.5 68 Zhou et al. (2010) S 1.56 ± 0.24† 11.0 ± 0.9§ 5 – 7 Thrane et al. (2013) IV 18.71 ± 2.11 75.54 ± 1.86 Enger et al. (2015) IV 3.34 ± 0.1 66.4 ± 3.8 18.6 ± 1.7 Yao et al. (2015) IV 3.70 ± 0.1 22 ± 1.8 31 ± 2.4* 34.3 ± 0.8 70.6** – – 48 ± 4.8* Enger et al. (2017) IV 4.60 ± 0.2 66.7 ± 10.1 19.5 ± 1.3 Kucharz et al. (2017) IV 12.44 ± 0.65 Study (AQP4– /–) M Thrane et al. (2013) IV 12.80 ± 1.16 64.49 ± 1.73 Yao et al. (2015) IV 2.90 ± 0.1 19.6 ± 1.4 38 ± 3.6* 35.5 ± 0.7 72.6** – – 58 ± 2.4* Enger et al. (2017) IV 4.60 ± 0.2 86.0 ± 13.3 15.7 ± 1.2 * Duration measured at half-maximum amplitude; † speed reported in experiments with TTX, indicated to be 50% of the CSD wave speed without TTX; § deviation from baseline of high
Extended Data 1
Supplementary material. Download Extended Data 1, TEX file.
Extended Data 2
Code. Download Extended Data 2, ZIP file.
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