Fig. 1.

Multicompartment model for synthetic biomarkers. Synthetic biomarkers sense tumor protease activity to produce detection signals in urine. After i.v. administration, synthetic biomarkers diffuse into the tumor ($k_{tumor}^{NP}$) and are cleaved by tumor-associated proteases (e.g., MMP9) according to Michaelis−Menten kinetics ($k_{cat}^{MMP9}$, $K_M^{MMP9}$). The cleaved reporters then diffuse back into blood, where they combine with reporters produced from nonspecific proteases ($k_{cat}^{blood}$, $K_M^{blood}$, and $E_{n.s.}^{blood}$) and secreted tumor-associated proteases ($E_{tumor}^{blood}$). A fraction of the reporters are reabsorbed by the kidneys ($k_{absorb}$) before clearance into urine ($k_{urine}^{reporter}$). See SI Text for derivation of model equations.