Mathematical model of AND-gated protease sensors identifies strategies to achieve earlier detection of small tumors

Introduction: Early detection of cancer can improve patient outcomes, yet radiographic imaging and blood biomarkers are only available for a subset of indications and are limited in sensitivity. The challenge of early detection necessitates substantial improvements in signal-to-noise to enable detection of small lesions without excessive false positives. Compared to endogenous biomarkers, activity-based diagnostics have been shown to achieve lower limits of detection by producing synthetic reporters in response to enzymatic activity. For example, several classes of synthetic biomarkers make use of linear peptides to detect tumor-associated proteases and produce amplified reporters in biofluids like blood and urine. However, background signals from proteases expressed in blood and healthy organs narrow the detection threshold. Moreover, proteases are promiscuous and multiple proteases can catalyze the same amino acid sequence. Multi-input sensor designs, such as AND-gates, have been proposed to address these specificity barriers. For example, sensors have been designed that require cleavage by multiple target proteases for detection, such as “hub-and-spoke” peptides that require cleavage of multiple quenchers for fluorescence and tandem-activatable molecular probes that are sequentially cleaved by an endoprotease and an exoprotease. Despite the potential of these approaches to increase specificity, there is a lack of computational tools to guide target protease and substrate selection to maximize signal-to-noise ratios. Here we develop a mathematical model of AND-gated activity by protease pairs to predict substrate design regimes in which AND-gated sensors provide improvements to specificity compared to conventional single-input sensors.

Materials and

Methods: We developed a mass action model for a single-input activity-based sensor in which either a target protease or a noise protease can bind to and catalyze cleavage of a substrate (Fig. 1a). We included kinetic rate constants for binding (kon), unbinding (koff), and catalysis (kcat) for both proteases. We expanded this model to AND-gated sensors in which the first cleavage produces an intermediary that must also be cleaved for product formation (Fig. 1b). We simulated “noise only” (target concentration ET=0) and “target and noise” (ET>0) conditions, then calculated signal over noise by calculating the area between the two kinetic curves. Given that systemic sensors experience blood proteases that contribute “noise” prior to tumor trafficking, we initialized the model parameters to simulate proteases in tumor (e.g., matrix metalloproteinases (MMPs)) and blood compartments, then varied these values. For example, blood proteases like coagulation and complement factors are found at micromolar concentrations in circulation but are primarily zymogens or inactivated by inhibitors. By contrast, tumor-associated proteases like MMPs are overexpressed at high nanomolar concentrations, ~one order of magnitude higher than in healthy tissue, and substrates are selected with high on-target activity. The experimental result was generated using a linear single-input peptide or a cyclic peptide with two substrates for granzyme B (GzmB), each of which had a fluorophore and quencher pair to monitor cleavage by fluorimetry. Peptides were incubated with media conditioned by MC38 cancer cells as “noise” and/or recombinant GzmB.

Results, Conclusions, and Discussions: Recent reports have demonstrated the use of mass action models to predict the behavior of protease-based networks such as inducible switches and autodigestion cascades. We therefore developed a mass action model of competitive binding and cleavage of a single-input protease substrate by a target or noise protease (Fig. 1a). We extended this model to simulate AND-gated sensors representing cyclic peptides in which two substrates must be cleaved for reporter release (Fig. 1b). We first assessed whether the model predicts improvements to specificity for AND-gated sensors versus single-input sensors by simulating noise from coagulation proteases in high concentration (1 μM, kcat/Km=320 M-1s-1) compared to target tumor protease MMP9 (100 nM, kcat/Km=1.6×104 M-1s-1). The model predicted a ~1.9-fold increase in signal over noise – i.e., the increase in signal induced by MMP9 compared to background levels from noise only – for AND-gated sensors compared to single-input sensors (Fig. 1c). To experimentally assess the predictive value of the model, we incubated a single-input GzmB sensor and a cyclic peptide AND-gated sensor bearing two GzmB substrates with recombinant GzmB and “noise” from media conditioned by MC38 cancer cells. The cyclic peptide had higher signal over noise than the single-input sensor, leading to significant detection of GzmB activity within 10 minutes compared to 50 minutes for the single-input sensor (Fig. 1d). This result supports the model’s value in predicting improvements to specificity. We next evaluated whether tuning system parameters could further increase signal over background. We first simulated various target protease concentrations. As expected, the model predicted that higher target concentrations lead to higher signal over noise (Fig. 1e). Moreover, at low target protease concentrations, the model predicted that AND-gated sensors increase the detection window compared to single-input sensors. Finally, as cancers induce a hypercoagulable state leading to activation of coagulation factors, we varied the rate constants for noise protease kinetics. The model predicted that AND-gated sensors have higher specificity than single-input sensors in high noise conditions (high kcat,N, low koff,N). Collectively, our results indicate that AND-gated sensors can improve signal-to-noise ratios and our mathematical model can predict substrate designs that maximize detection specificity.

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