Figure 4. Analytical model of the system predicts log-linear relationships leading to receptor-based memory and relative sensing.

(a) Approximate log-linear dependence of the scaled steady-state surface receptor abundance ${\displaystyle [R{]}_T}$ on the normalized background ligand concentration ${\displaystyle u_0=[L{]}_0/K_{d1}}$, where ${\displaystyle K_{d1}}$ is the equilibrium dissociation constant of EGF binding to EGFR. (b) Approximate log-linear dependence of the maximal phosphorylation response on the normalized ligand stimulus ${\displaystyle u_1=[L{]}_1/K_{d1}}$. Dashed red lines represent the exact log-linear approximation.