Figure 8. The need for a large front-end Ca⁺⁺-mediated gain severely constrains RecRK parameters

The relationship between R* lifetime gain change and the dissociation constant for the interaction between Ca⁺⁺-Rec complex and RK (i.e., K_D = q₄/q₃ in Eq. 8, A10). The gain change (ordinate) is defined as the ratio of τ_Rdark (theoretical value of τ_R when Ca⁺⁺ = c_dark = 0.3 μM) to τ_Rmin (τ_R when Ca⁺⁺ = c_min = 0.02 μM). The curves shown correspond to a family of K_Rec,Ca values ranging from 0.2 to 1.2 μM (from top to bottom, in 0.1 μM increments). The red curve is for K_Rec,Ca = 0.9 μM, a value obtained by Klenchin et al. [8]. The horizontal dashed line marks a gain of 10. See text for details.

Note that K_D must be very small if other RecRK- and Ca⁺⁺ parameters are set to values estimated in the literature. In this example, Rec_tot = 34 μM [8] and the Hill coefficient, w = 2 [8]. For K_Rec,Ca = ~0.9 μM (red curve) [8], K_D must be less than ~0.25 μM in order to get a gain change of 10x. This value for K_D is ~14 times less than the value estimated by Klenchin et al. (~3.4 μM; [8]). Analyses show that K_D will be even more severely constrained (to even smaller values) if it is assumed that the minimum physiological value for Ca⁺⁺ is greater than 0.02 μM, as estimated in some studies [33,63-65].

Not only is K_D restricted to small values, but, due to the steepness of the functions in the region of high gain values (10x or more), the overall range of permissible values is highly restricted. Hence, for a given K_Rec,Ca value, only a very restricted range of (small) values for K_D are permissible in order to achieve the empirically observed gain changes.