Fig 1.
A compartmental schematic of our model showing how the neurons and glia communicate with the extracellular space.
Table 1.
Glutamate-Glutamine cycle parameters.
Table 2.
NMDA receptor parameters.
Fig 2.
The time course of all variables with PNMDA = 1 × 10−5cm/s and PNaP = 2 × 10−5cm/s. For a 0.5cm domain Δx = 0.0156cm with Δt = 0.01s. The time course is from the third grid point from the left end of the domain.
Fig 3.
Duration and velocity of spreading depression.
Varied over a range of PNaP and PNMDA. Details on the calculation of duration and velocity are provided in S2 Text.
Fig 4.
Velocity of spreading depression without glutamate diffusion.
Varied over a range of PNaP and PNMDA.
Fig 5.
NMDA receptor feedback mechanism.
Summary of CSD dynamics of our model. Initiation due to NMDA receptor with propagation caused by the combination of interstitial glutamate and potassium diffusion. Neuronal swelling causes prolonged activation of NMDA receptors.
Fig 6.
Persistent sodium feedback scheme.
Summary of Initiation and Propagation due to the persistent sodium channel activation and interstitial potassium diffusion.
Fig 7.
Different time profiles of neuronal membrane voltage and extracellular volume.
Each panel shows time courses from four different levels of NMDAR and NaP. For neuronal membrane voltage, as NMDAR permeability increases a secondary bump appears. It appears for even smaller levels of NMDAR, barely visible on the dashed line. The volume graph shows the large reduction in extracellular space.
Fig 8.
Time profiles with extracellular voltage.
The figure on the top shows voltage traces for a sampling of NMDAR and NaP permeability. The figure on the bottom is the contour plot for the time course for extracellular voltage for different values of NMDAR permeability. Note that the overshoot is prominent for intermediate values of NMDAR permeability.
Fig 9.
Influence of cell swelling on extracellular voltage.
We vary NMDAR permeability between 4.5 − 6 × 10−5cm/s along the y-axis. Each panel has a different value for hydraulic permeability (water flux). The top and bottom panel have a minimum extracellular space of 2.5% and 10% respectively. For small enough hydraulic permeability, the wave looks no different than a NaP driven wave with no/little NMDA receptor activity.
Fig 10.
Effect of varying hydraulic permeability on extracellular glutamate.
This shows the difference between the amount of glutamate(concentration times volume) and just concentration.
Fig 11.
Plot of major variables during a spiral.
All spiral simulations done with Δx = Δy = 0.0156cm and Δt = 0.01s.
Fig 12.
Velocity and period of the wave at each point.
Speed of wave is calculated at each point in the domain (edges excluded due to edge effects, details provided in S2 Text). Period is calculated as the time between each depolarization for each point in the domain.
Fig 13.
Dependence of velocity and duration on NMDAR and NaP during a spiral.
Calculated by finding the average value over the whole domain. The zero sections are regions where the spiral dies off due to a lack of propagation. Beyond the NMDAR level shown in the above graphs, the duration becomes too long preventing the spiral from recurring.
Fig 14.
Work done by ion pumps as a function of distance from center.
Top: Maximum and time average of the work done by ion pumps (note the two different y-axis scales), in both neurons and glia (over 3 minute duration), as measured by averaging over concentric circles around on the spiral center. Region closer to the center of the spiral does significantly more work. Bottom: Increasing NMDA receptor expression causes much more work to be done near the center, with a smaller increase seen away from the center.