Figure 6.

Inaccuracies of different calcium 1D diffusion models result in erroneous calcium levels. (A) Errors introduced by making the number of concentric shells independent of compartment diameter, for 4, 8, or 12 shells respectively. Two mechanisms are implemented: the standard NEURON scheme with variable depths for all shells (circles) and an FD scheme where the submembrane shell has a constant depth d₁ = 0.1 μm and the rest of the shells has variable depth (triangles). The DM_FD mechanism is used as reference. Note that for both mechanisms the errors become large for diameters beyond 2 μm if only four shells are used (as is the case in some NEURON models). (B) Ca²⁺ transients generated using a “ramp-like” voltage command in single compartments (see Figure 3C for details) comparing the responses of the DM and DM_FD models. Both models show very similar behavior with only small numerical differences. (C) Errors due to discretization of radial shells in DM, which may result in variable d₁ resulting in rapid changes of submembrane shell volume for increasing compartment diameter. The broken line with asterisks shows errors related to conversion of Ca²⁺ influx to Ca²⁺ concentration with variable depth d₁ of the submembrane shell (it varies between 0.075 and 0.125 μm due to discretization) as compared to fixed d₁ of 0.1 μm (DM_FD). The solid lines with diamonds shows the actual error in free Ca²⁺ in the submembrane shell for DM models for different sizes of Ca²⁺ influx as indicated. Note that these errors are much smaller than predicted by the Ca²⁺ influx conversion.