Electrical neural signalling typically takes place at the time-scale of
milliseconds, and is typically modeled using the cable equation. This is a good
approximation for processes when ionic concentrations vary little during the
time course of a simulation. During periods of intense neural signalling,
however, the local extracellular K+ concentration may increase by several
millimolars. Clearance of excess K+ likely depends partly on diffusion in the
extracellular space, partly on local uptake by- and intracellular transport
within astrocytes. This process takes place at the time scale of seconds, and
can not be modeled accurately without accounting for the spatiotemporal
variations in ion concentrations. The work presented here consists of two main
parts: First, we developed a general electrodiffusive formalism for modeling
ion concentration dynamics in a one-dimensional geometry, including both an
intra- and extracellular domain. The formalism was based on the Nernst-Planck
equations. It ensures (i) consistency between the membrane potential and ion
concentrations, (ii) global particle/charge conservation, and (iii) accounts
for diffusion and concentration dependent variations in resistivities. Second,
we applied the formalism to model how astrocytes exchange ions with the ECS,
and identified the key astrocytic mechanisms involved in K+ removal from high
concentration regions. We found that a local increase in extracellular
K\textsuperscript{+} evoked a local depolarization of the astrocyte membrane,
which at the same time (i) increased the local astrocytic uptake of
K\textsuperscript{+}, (ii) suppressed extracellular transport of K+, (iii)
increased transport of K+ within astrocytes, and (iv) facilitated astrocytic
relase of K+ in extracellular low concentration regions. In summary, these
mechanisms seem optimal for shielding the extracellular space from excess K+.Comment: 19 pages, 5 figures, 1 table (Equations 37 & 38 and the two first
equations in Figure 2 were corrected May 30th 2013
