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. Since it was not practically feasible to conduct experiments of bacterial colonization inside tumors, we used results from reference to simulate colonization in a thin spherical layer inside a solid tumor.

The COMSOL model helped us to extend our MATLAB model in the following ways:

Diffusion physics of AHL was included to extend the ODEs into PDEs

Our MATLAB model does not take into account diffusion of AHL, since in the viable lab experiments (in test-tubes), the only sink for AHL is its degradation. However, in a tumor as explained in reasoning, diffusion has much more significant contribution than degradation. Thus our model helped us gauge and verify the behavior of our tumor-sensing circuit in more real-life conditions pertaining to the intended application context. Using the results obtained from our simulations, we could check the behavior of the AND gate functioning in different conditions of d_cell 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.

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

Model Overview

This section presents a brief overview of the COMSOL model. For details go to the detailed description of the 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. Due to the spherical symmetry of the system, a 2D axisymmetric COMSOL model was used as shown in Figure 1. For more details go to the detailed description of the model.

Figure 1: Geometry of the COMSOL Model - 2D Axisymmetric (axes in mm); Tumor is a solid sphere of radius 20mm located at (0,0), Bacterial colonization is a spherical layer of thickness 0.5mm at a distance of 10mm from the center of the tumor.
Equations
Transport of Diluted Species physics was used in COMSOL to integrate diffusion into our model. The diffusion equation for a species C is:

\[\begin{aligned} [\frac{\delta_{[C]}}{\delta_{t}}} + \nabla \cdot (-D \nabla [C]) &= R_{C} \\ [\text{LuxR-AHL}] &= K_{LuxRAHL} [\text{LuxR}]^2 [\text{AHL}]^2 & \text{rapid binding equilibrium} \\ [\text{LuxR}] &= [\text{LuxR}]_0 - 2 [\text{LuxR-AHL}] & \text{mass conservation}\end{aligned}\]

…where R_i is the reaction rate ie d[X]/dt. The reaction rates of the species depends on the domain – tumor or bacterial layer. The domain-wise reaction rate for each species (AHL, LuxI and Azurin) is mentioned in detail here linkToDetails.
- Growth phase
- Sensing (AHL and LuxI)
- Azurin
Assumptions

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 by tuning our model to fit experimental data as explained in detail by the Functional Parameter Search.

Symbol	Description	Value	Reference
a_luxR		1x10² nMmin^-1
d_luxR		2.3x10^-2 min^-1

For details about the model go to the detailed description.

Results

Beautiful GIFs coming soon .... MUST REALLY SOON

CASE: Tumour colonization - High d_cell AND High Lactate
CASE: Healthy tissue colonization: High d_cell AND Low Lactate

Figure 1. Normalized concentration of AHL and Azurin, Cell density (as a ratio of its steady state value), P_luxlldR and Temperature (as a ratio of its steady state value 42°C).
CASE: Tumour not colonized: Low d_cell AND High Lactate
CASE: Healthy tissue not colonized: Low d_cell AND Low Lactate

Bacterial colonization patterns