Figure 4.

Mechanistic Hill analysis of transporter mechanism HHHS (n = 3). Simulation of the double logarithmic plot of the Hill equation (bottom) and the first derivative (top). The Hill equation of the HHHS mechanism is $[y/(1-y)]=\{x^3/\left\{\right({\beta }_2{K}_D^S/(K_D^S+\left[S\right])\left)\right({\beta }_1+{\beta }_{1}x+x^2)\}.$ The affinity constant K_A/K_D^H is the value of [H]/K_D^H at the x-axis intercept in the bottom plot, and the mechanistic Hill coefficient n is the value of the first derivative in the top plot at K_A/K_D^H; β is the ratio of equilibrium constants for noninteracting co-ion binding sites, K_D^H is the binding constant for binding of co-ion H in successive steps, and K_D^S is the binding constant for binding of substrate S. Blue and green curves demonstrate the effect of changing the substrate concentration. Increasing the substrate concentration shifts the curves up by an amount of log(K_D^S + [S]), and consequently, the intercept with the ordinate K_A goes down and the Hill coefficient n goes up. The same holds for the difference between the gray and red curves. Comparison of blue and red curves (and similarly of green and gray curves) shows the effect of changing the q parameters (Table 4).