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. 2009 Jan;5(1):e1000272.
doi: 10.1371/journal.pcbi.1000272. Epub 2009 Jan 23.

Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space

Ivar Østby  1 , Leiv Øyehaug, Gaute T Einevoll, Erlend A Nagelhus, Erik Plahte, Thomas Zeuthen, Catherine M Lloyd, Ole P Ottersen, Stig W Omholt
Affiliations

Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space

Ivar Østby et al. PLoS Comput Biol. 2009 Jan.

Abstract

Neuronal stimulation causes approximately 30% shrinkage of the extracellular space (ECS) between neurons and surrounding astrocytes in grey and white matter under experimental conditions. Despite its possible implications for a proper understanding of basic aspects of potassium clearance and astrocyte function, the phenomenon remains unexplained. Here we present a dynamic model that accounts for current experimental data related to the shrinkage phenomenon in wild-type as well as in gene knockout individuals. We find that neuronal release of potassium and uptake of sodium during stimulation, astrocyte uptake of potassium, sodium, and chloride in passive channels, action of the Na/K/ATPase pump, and osmotically driven transport of water through the astrocyte membrane together seem sufficient for generating ECS shrinkage as such. However, when taking into account ECS and astrocyte ion concentrations observed in connection with neuronal stimulation, the actions of the Na(+)/K(+)/Cl(-) (NKCC1) and the Na(+)/HCO(3) (-) (NBC) cotransporters appear to be critical determinants for achieving observed quantitative levels of ECS shrinkage. Considering the current state of knowledge, the model framework appears sufficiently detailed and constrained to guide future key experiments and pave the way for more comprehensive astroglia-neuron interaction models for normal as well as pathophysiological situations.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Outline of basic model premises in baseline and excited states.
(A) In the baseline condition the neuron is assumed to be silent, i.e. there is no net exchange of ions across the neuronal membrane, cotransporters KCC1 and NBC are approximately in equilibrium and NKCC1 is assumed to be non-operative. (B) The neuron is treated as a black box, but in the excited state the neuron's contribution to the ECS shrinkage phenomenon is considered to be through its potassium efflux and a sodium influx (arrows) during high-frequency firing and through the reversal of these fluxes after the high rate of firing has abated. KCC1, NBC and NKCC1 are assumed to be operative in the excited state (arrows indicate the direction of ion flux, note that KCC1 may transfer ions both ways). Changes in font size and astrocyte size refer to the magnitude of changes from baseline to excited state.
Figure 2
Figure 2. Distribution of volume shrinkage and the potassium-volume shrinkage relation for different models.
Left panels: Normalised histograms of the distributions of relative ECS volume shrinkage (in %) for the five model configurations (mc1–mc5). The results were obtained by repeated numerical solution of steady state equations and only those parameter sets that satisfied the imposed ion concentrations constraints were used (see Methods). Right panels: Corresponding scatter plots of excited state relative shrinkage and potassium concentrations using the same data as in the left panels. Since the upper limit of the shown relative shrinkage and the lower limit of the shown [K+]o are set to 40% and 5 mM, respectively, some of the data are not displayed. Best linear fits are shown, and the corresponding slopes are 1.97, 1.70, 3.11, 2.74 and 4.08, respectively. Moreover, for reasons of visualization only 2% of the data are depicted.
Figure 3
Figure 3. Parameter sensitivities and robustness to simultaneous parameter perturbation.
(A–G) Normalised histograms of parameter values that satisfy both the imposed ion concentration constraints and an ECS shrinkage in the range of 25–35% for mc3, mc4 and mc5. (A) A/Vi (astrocyte area to volume ratio) for mc5 (mc3 and mc4 display roughly the same pattern), (B–D) V i/V o, (astrocyte volume to ECS volume ratio) for models mc3, mc4 and mc5, respectively, (E) k C (magnitude of neuronal potassium efflux/sodium influx) for mc5 (mc3 and mc4 display roughly the same pattern), (F,G) g Cl (chloride conductance) for models mc4 and mc5, respectively (mc3 displays a uniform pattern). (H) For each of 100 parameter sets randomly selected from the 5000 sets associated with H5 we sampled randomly 100 new parameter sets where all parameter values were within a given percentage range of the original value, and for each of these 10000 sets we estimated the remaining parameters by use of the steady state equations as described. The figure shows the percentage of the empirically consistent parameter sets (satisfying prequalification set 2) for mc5 that still satisfy all imposed constraints after having been perturbed by uniformly resampling of each directly estimated parameter value from the specified percentage range around the initial parameter value (percentages corresponding to mc3 and mc4 are similar). The horizontal lines within the boxes indicate median, boxes comprise data that lie within quartiles and full vertical lines (“whiskers”) indicate the spread of the data (all data are included).
Figure 4
Figure 4. Predicted dynamics of [TMA+]o and [K+]o in wild types and NKCC1 knockouts.
Predicted activity-dependent ECS volume dynamics in wild types (blue) and NKCC1 knockouts (or bumetanide-treated) (red) obtained by numerical solution of model equations (3) (see Methods) from t = 0 s to t = 100 s with enhanced neural activity for 10 s<t<30 s, using the parameter sets that satisfy all imposed constraints for (A) mc3, (B) mc4, (C) mc5. (D) Wild type and NKCC1 knockout of mc5 with active water transport through NKCC1 (in addition to AQP4-mediated passive water transport). In all plots, curves drawn with strong contrast are median values and the upper and lower curves drawn with weaker contrast define the boundaries between which 80% of all values in the used parameter sets fall. Lower insets show corresponding temporal evolution of the median ECS potassium level. (A) The upper inset displays the time-dependent potassium efflux (resp. sodium influx) rate profile (beta distribution with a = 2 and b = 16.0304) that is optimized for each model to yield potassium profiles in accordance with empirical observations (see Methods). The profiles corresponding to (B–D) resemble the one in (A) very closely (values for b are 15.18, 14.56 and 14.59, respectively). (D) The upper inset shows the AQP4-mediated water flux relative to zero. In mc3, NKCC1 is not included, hence NKCC1 knockout yields identical results as the wild type (A).
Figure 5
Figure 5. Predicted dynamics of [TMA+]o and [K+]o in wild type and AQP4 knockout.
Predicted activity-dependent ECS volume dynamics in wild type (blue) and AQP4 knockout (red) obtained by numerical solution of model equations (3) (see Methods) from t = 0 s to t = 100 s with enhanced neural activity for 10 s<t<30 s, using the parameter sets that satisfy all imposed empirical constraints for mc5 without (A) and with (B) active water transport through NKCC1. For figure details, see legend to Figure 4. In both plots, the upper insets show the AQP4-mediated water flux relative to zero, and lower insets display the dynamics of ECS potassium levels.
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