Modeling

Overview

Our system consists of a signalling chain, with a lactate sensor triggering the amplification of AHL production which is sensed my neighboring cells. When AHL becomes sufficiently concentrated, it triggers the production of a fluorescent signal. Our model was divided into the modules pictured below.

Figure 1. The genetic design of the MicroBeacon system.

These were modeled and tested independently before being merged into a single model of the whole system. Each module was first evaluated and characterized at the single cell level in MATLAB in order to evaluate their initial states, steady states, and to study their dynamics. Then, each module was implemented in COMSOL Multiphysics to characterize their spatial and temporal behavior, and to implement additional biological properties of our system.

The final result is a model providing a reasonable approximation of the behavior of our system under our test conditions. In addition, our characterization of the lactate module is a significant contribution to the understanding of this system.

Lactate module

The lactate sensor is a fold-change sensor with the topology of an incoherent feed-forward loop. As shown in the figure, LuxR production is repressed by both LacI and LldR (the feed-forward), but LacI is produced when LldR binds lactate and is no longer a repressor. When a delay in the activation of LacI is present, the action of lactate produces LuxR until LacI becomes active, thus producing a pulse whose amplitude depends on the lactate production rate.

AHL module

Combined model

GFP concentration over time in four cases: A) Cancer cell, bound E. coli B)Cancer cell, unbound E. coli C) Normal cell, bound E. coli D) Normal cell, unbound E. coli

Conclusions

We characterized our system by simulating its modules separately and together through a series of increasingly-complex models. We show that under certain parameters, our lactate module is able to produce LuxR such that the lactate production input signal is amplified. Simulation of the AHL module with a simplified compartment model and with a more accurate reaction-diffusion model show that degradation of AHL by the E. coli does not significantly delay the self-activation of our LuxI and AHL production feedback loop. Instead, riboregulation of the LuxR promoter to prevent leaky expression of LuxI is sufficient to prevent this self-activation within the timescale of our experiment. This demonstrates the viability of our system as a specific CTC detection system utilizing these two general cancer markers.