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. 2014 Aug 29;111(37):E3860–E3869. doi: 10.1073/pnas.1322761111

Fig. 2.

Fig. 2.

PRESS. Coupling a slow binding reaction to a fast and transient response can expand the input dynamic range beyond equilibrium saturation. (A) Inset shows a toy model with a downstream response activated by the ligand-receptor complex computed in Fig. 1A. Occupied receptor activates effector X; then, X* converts into X^, which slowly converts back to X, closing the cycle (details are provided in SI Appendix, section 2). The plot shows X* vs. time for all of the concentrations of L included in Fig. 1A. (B) Shift and expansion of the input dynamic range are due to PRESS. L-receptor complex at equilibrium (Ceq, solid black line), as well as peak X* resulting from using slow (red dotted line) or fast (blue dashed line) binding/unbinding rates of L to R, vs. input L, are shown. The resulting input dynamic ranges (the fold change required in input to elicit a change from 10 to 90% of maximum output) are indicated. The two doses indicated, L1 = 55 Kd and L2 = 80 Kd, result in an 8.5% difference in peak X* for slow-fast coupling, and only a 0.75% difference for fast-fast coupling. (C) Graphical description of the expansion of the input dynamic range in the toy model. The plot shows L-receptor complex at equilibrium (Ceq, solid black line), or at the indicated times before equilibrium (C(t), solid gray line), as well as peak X* (solid red line), all as a function of input L. Note, as shown in A, that peak X* occurs at different times for different concentrations of input L. Therefore, the values of C at the time when X* peaks (Ctmax, solid green line) correspond to different C(t) gray curves for each dose of L (green ○). The Ctmax curve is itself shifted to higher doses than Ceq, and it has a larger input dynamic range (less steep) than either Ceq or any C(t) curves [EC50 = 17.7 and sensitivity (nH) = 0.9]. In B and C, the x axis corresponds to L normalized by the Kd of the ligand-receptor reaction. All data correspond to simulations, done using the following parameters for the X cycle: r1 = 0.1, r2 = 0.08, r3 = 0.001, and Xtot = 10 (Xtot being the total amount of X). Binding/unbinding rates were k− = 0.001 1/s, k+ = 0.00019 (nM · s)−1 for slow binding (A, red line in B and C) and 100-fold those values for fast binding (blue line in B) (SI Appendix, Fig. S1).