Table 1.

Model equations

Equation type	Equation	Equation number
Membrane potential equation
Membrane potential	ψ = (RT/F) ln[(α + [K+]e)/(β +[K+]a)]	1
Flux equations
Potassium flux	JKa = PK(ψF/RT)([K+]a − [K+]eexp(−ψF/RT))/(1 − exp(-ψF/RT)) − JKapump	2
Potassium pump flux	JKapump = 2JKapump(0) [1 + [K+]e(0)/(Δ[K+] − Δ[K+](0) − 2[K+]e(0))]	3
Water flux	JVa = PfvW(Φe − Φa)	4
Differential equations for volume and concentration
ECS volume	d(de)/dt = JVa	5
Astrocyte volume	d(da)/dt = −JVa	6
ECS [K+]	d[K+]e/dt + (Jva/de)[K+] = JKa/de	7
Astrocyte [K+]	d[K+]a/dt − (Jva/da)[K+] = −JKa/da	8
Integral equations for osmolarity
ECS osmolarity	Φe = Φe(0)/de + 2(∫JKadt)/de	9
Astrocyte osmolarity	Φa = Φa(0)/da-2(∫JKadt)/da	10
Non-K+ osmolarity	[non-K+]a = Φa(t + Δt) − 2[K+]a	11
Diffusion equations
K+ diffusion	∂[K+]/∂t = Da ∂2[K+]/∂x2	12
Non-K+ diffusion	∂[non-K+]/∂t = Da ∂2[non-K+]/∂x2	13
Equation for flux through the moving membrane
Flux boundary condition	∂[K+]a/∂t = −JKa /δ	14