FIGURE 2.

Exact Ca²⁺ transients and their approximation. Time-dependent Ca²⁺ concentration profiles obtained by numerical integration of reaction-diffusion system using the Crank-Nicolson algorithm (dotted curves) are approximated by the analytical solution for the logarithmic diffusion (solid curves). The diffusion coefficients were D_Ca = 200 μm²/s, d_Buffer = 20 μm²/s, the on- and off-rate constants were k_on = 10⁸ M⁻¹s⁻¹ and k_off = 100 s⁻¹ (K_d = 1 μM), and the total buffer concentration B_o = 1 mM. For the logarithmic diffusion the apparent diffusion coefficient Δ was 40 μm²/s. In panel b the amplitude of instantaneous Ca²⁺ source was seven times bigger than in panel a. Note a close correspondence between the two solutions (a) and underestimation of the large amplitude transients in the case of the logarithmic diffusion (b).