Figure 6.

Supra-additive effects of intracellular and extracellular-surface CA activities on kinetics of pH changes, as predicted by mathematical modeling. The insets to Figure 4 show the protocol of the physiological experiment: the addition of CO₂/HCO₃⁻ to the extracellular fluid causes: (a) a quasi-exponential decrease of intracellular pH (pH_i); and (b) a rapid increase in the pH at the extracellular surface (pH_S), followed by a quasi-exponential decay. (A) The maximal rate of the pH_i decrease—(dpH_i/dt)_max—for 12 simulations, 6 varying the intracellular CA acceleration factor (A_i) at a fixed extracellular-surface CA acceleration factor (A_S) of 150 (diamonds), and 6 varying A_i at a fixed A_S of 10,000 (squares). (B) The maximal shift in pH_S—(ΔpH_S)_max—for the same 12 simulations in (A). Each of the 12 simulations models a hypothetical oocyte exposed to a bulk solution containing 1.5% CO₂/10 mM HCO₃⁻ at pH 7.50. (A) Dependence of (dpH_i/dt)_max on A_i, for each of the two different values of A_S. (B) Dependence of (ΔpH_S)_max on A_i, for each of the two different values of A_S. In each panel, the six diamonds represent an isopleth for A_S = 150, whereas the six squares represent an isopleth for A_S = 10,000. In each panel, the diamond labeled “~Ctrl” (i.e., A_i = 5, A_S = 150) represents a “control” oocyte that is, an oocyte not expressing or injected with any heterologous protein. For “~Ctrl”, the (dpH_i/dt)_max value in (A) and the (ΔpH_S)_max value in (B) approximately match the mean data for physiological experiments, indicated by the horizontal dashed gray lines. In each panel, the square labeled “CA IV” (i.e., A_i = 40, A_S = 10,000) represents an oocyte expressing CA IV, with (dpH_i/dt)_max and (ΔpH_S)_max values approximately matching the mean data for physiological experiments, indicated by the horizontal dashed green lines. In each panel, the square labeled “CA_S” (i.e., A_i = 5, A_S = 10,000) represents a hypothetical oocyte that—compared to “~Ctrl”—has an isolated increase in A_S. Note that the (dpH_i/dt)_max and (ΔpH_S)_max values for this hypothetical “CA_S” increase by amounts (red vector) that are far smaller than those actually observed for real oocytes expressing CA IV (i.e., vertical distances between horizontal dashed green and grey lines). The only way for the simulations to explain the physiological data is if CA IV expression not only raises A_S from 150 to 10,000 but also raises A_i from 5 to 40 (green vector). Indeed, physiological evidence indicates that A_i must indeed increase. In each panel, the diamond labeled “CA_i” (i.e., A_i = 40, A_S = 150) represents a hypothetical oocyte with a cytosolic CA activity that is the same as that postulated for an oocyte actually expressing CA IV (blue vector). The sum of the red vector (increase A_S only) and the blue vector (increase A_i only) is the point labeled “*” (dashed golden vector). Notice that the green vector predicts that CA IV expression (combined increases in A_S and A_i) produces much larger increases in (dpH_i/dt)_max and (ΔpH_S)_max than the dashed golden vector (the sum of isolated increases in A_S and A_i). In other words, the effects of simultaneously increasing A_S and A_i are supra-additive. Modified from Figure 13 in [79].