Team:ETH Zurich/Model/In Vivo

Modelling the Behavior of CATE inside Tumor

We developed a model to gauge the behavior of our sensing circuit in the real life conditions of solid tumor colonization.

Model Overview

This section presents a brief overview of the COMSOL model.

Geometry

As mentioned in system specifications, the tumour has been chosen as a solid sphere of radius 20mm and the bactierial colonization pattern as a homogenous distribution in a spherical shell-shaped 0.5mm thick layer in the tumour at a distance of 10mm from the centre of the tumor, as shown in Figure 1. For more details go to the detailed description of the model.

Geometry of tumor and bacterial colony
Figure 1: Geometry of the tumor and bacteria colony (green area: colonized by E. coli Nissle)

Equations

Transport of Diluted Species physics was used in COMSOL to integrate diffusion into our model. The partial differential equation for diffusion of a species C with reaction source rate RC is \[\frac{\partial \text{[C]}}{\partial t} + \nabla \cdot (-D_{\text{C}} \nabla \text{[C]})= R_{\text{C}}\]. The reaction rates of the species depends on the domain – tumor (no production and only extracellular degradation) or bacterial layer (production and intracellular degradation). Read here about the details of the domain-wise reaction rates for each species (AHL, LuxI and Azurin) and equations used.

Parameters

The parameters that were used in the COMSOL model were obtained partly from literature, partly from characterizations of previous iGEM teams and finally the most important ones were estimated by fitting our experimental data and tuning the fitted-results in the context of the intended applciation, as explained in detail by the Functional Parameter Search. Check out details about the model to read more about the different parameter values used.

For more details about the model go to the detailed description and Functional Parameter Search.

Strengths

We could simulate for a geometry of the system closer to the real-life tumor conditions

Since it was not practically feasible to conduct experiments of bacterial colonization inside tumors, we simulated the bacterial colonization in a thin spherical layer inside a solid tumor considering the simplifications and assumptions as mentioned in the system specifications. This helped us to test our tumour sensing AND-Gate switch functionality in all the possible real-life scenarios that CATE might encounter in context of the intended application.

Exact diffusion physics of AHL was included witout any simplifications

Our MATLAB model uses a simplified AHL diffusion model with the assumption of negligible degradation inside the layer and and not taking into consideration the diffusion of AHL far from the source. Extending the diffusion physics ordinary differential equations into partial differential equations using the COMSOL model helped us gauge and verify the behavior of our tumor-sensing circuit in more real-life conditions pertaining to the intended application context of a solid spherical tumor. Using the results obtained from our simulations, we could check the behavior of the AND Gate Switching in different conditions of dcell and lactate.

Diffusion physics of Azurin was included to simulate the effect of lysis

To simulate the effect of lysis, our COMSOL model stops the production of Azurin and starts its diffusion when temperature reaches 42°C. This simulates the effect of increase in temperature with FUS to cause cell lysis. Using data obtained from such a simulation, we could also find the temporal-maximum concentrations of Azurin at each point in the tumor, effectively helping us to estimate the killing area and the time-scale of the treatment.

Simulation of different colonization patterns

Using our model, we also tried a few other colonization patterns to show our system works as expected inside a tumor while stays dormant in healthy tissue. We simulated the following patterns:

  • Homogeneous distribution in a Single spherical-shell-shaped layer in Tumor

  • Heterogeneous distribution in a Single spherical-shell-shaped layer in Tumor

  • Heterogeneous distribution in Double spherical-shell-shaped layer in Tumor

  • Homogeneous distribution in Healthy tissue

Limitations

Our model has some limitations. We do not model protein E production and cell lysis caused by it. Instead lysis is just simulated in effect as the end of production of AHL and Azurin and start of diffusion of Azurin. Moreover, a step signal is used as a trigger for the lysis. As mentioned in the parameters description, Azurin production is taken to be 10 times proportional to LuxI production. Also, killing mechanism of Azurin has not been modelled since that was not necessary to demonstrate the working of our project CATE in the scope of iGEM.

Tools used