Figure 3.

Errors introduced by incorrect submembrane volumes of single pool models. (A) Comparison between cylindrical dendritic compartments with diameters of 1 μm (left) and 0.5 μm (right) with submembrane shells with a depth of 0.1 μm. A correct implementation of the volume of the submembrane shell representing the single Ca²⁺ pool (SP_new mechanism) results in a SVR that depends on the compartment diameter. (B) For the same compartments using the SP_old mechanism results in volumes that are too large and have a constant SVR. The cross-sectional area of each compartment (black disks shown in A) is unfolded and drawn to show that the actual volume of the submembrane shell (SP_new) is smaller than the volume used in the SP_old mechanism. The red triangles represent extra cross-sectional area included in the volume of SP_old. (C) Ca²⁺ transients generated using a “ramp-like” voltage command in single compartments with diameters ranging from 0.2 to 6 μm in steps of 0.1 μm. P-type Ca²⁺ channel with P_max of 5.2 × 10⁻⁵ cm/s was used for Ca²⁺ influx. Inset: comparison of peak amplitudes of Ca²⁺ transients using SP_old and SP_new show that the first mechanism causes exactly the same transient in all compartments, whereas, SP_new causes transients with varying peak Ca²⁺ amplitudes. (D) Error in peak Ca²⁺ levels caused by using the SP_old mechanism [error = (max([Ca²⁺]_{SP_old}) − max([Ca²⁺]_{SP_new})/max([Ca²⁺]_{SP_new}))]. Pool models used β-values of 0.02, 6.86, and 10 ms⁻¹; and depth (d) values of 0.05, 0.1, 0.15, 0.2, and 0.25 μm. The lower edge of shaded areas of each color shows error in peak calcium for β-value of 10 ms⁻¹, whereas, the upper edge of shaded areas of each color show error for β-value of 0.02 ms⁻¹. The colored asterisks show corresponding error for β-value (used to model PC dendrites) of 6.86 ms⁻¹. Inset highlights large errors for branches with small diameters (diam ≤ 1 μm).