# Investigating Two Modes of Cancer-Associated Antigen Heterogeneity in an Agent-Based Model of Chimeric Antigen Receptor T-Cell Therapy

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

^{3}, while the vascular grid has the size of 500 × 500 × 500, where each voxel represents a space of 2 μm

^{3}. An initial tumor of 100 cancer cells (80 progenitor and 20 stem cells) is placed in a corner of the grid. The cancer cells cannot leave the boundary of the grid, simulating a small tumor growing on the surface of normal tissue. The vasculature is initialized by putting 8 capillaries on the YZ plane, where they remain fixed. Each capillary consists of individual segments and has the ability to branch and become a sprout. We also assume that there is normal vasculature on the XY plane providing oxygen to the tumor. This initial setup is adapted from a previous model; for more information see [33].

#### 2.1. Cancer Cell Module

#### 2.2. Vasculature Module

#### 2.3. CAR T—Cell Module

#### 2.4. Statistics

## 3. Results

#### 3.1. Both Models of CAR T-Cell Therapy Can Successfully Reduce the Size of Tumor

#### 3.2. The Distribution of Antigen Presenting Cells Effects the Rate of Tumor Reduction in Both Antigen Distribution Models

#### 3.2.1. Gradated Heterogeneity Antigen Model

#### 3.2.2. Binary Heterogeneity Antigen Model

#### 3.3. There Is a Positive Trend between the Number of Antigen Presenting Cells and the Growth of CAR T-Cells in Both Models

#### 3.4. There Is a Positive Trend between the Percentage of Antigen Expression and the Number of Cancer Cells Killed by CAR T-Cells throughout the Simulation in Both Models of Antigen Distribution

#### 3.4.1. Gradated Heterogeneity Antigen Model

#### 3.4.2. Binary Heterogeneity Antigen Model

#### 3.5. In Both Models, There Are Parameter Values in which Cancer Stem Cells Get Eliminated

#### 3.5.1. Gradated Heterogeneity Antigen Model

#### 3.5.2. Binary Heterogeneity Antigen Model

#### 3.6. In Both Models, Antigen Presenting Cells Can Form a Shield over Antigen Non-Presenting Cells That Blocks CAR T-Cells from Killing Vulnerable Cancer Cells

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**3D plots of tumors with gradated (

**a**) and binary (

**b**) heterogeneity plotted over time with 12.5-day intervals starting from day 12.5 and ending on day 75, the last day of our simulations. Tumor cells are plotted in blue, CAR T-cells are plotted in green, and the vasculature is plotted as red capillaries growing across the grid. The data in the gradated heterogeneity tumor progression (

**a**) is from a run with 12.5% mean antigen expression tumor cells. The data in the binary heterogeneity tumor progression (

**b**) is from a run with 75% antigen presenting tumor cells. CAR T-cells are introduced halfway through the simulation, on day 37.5.

**Figure 3.**Tumor metrics over time for gradated heterogeneity (

**A**) and binary heterogeneity (

**B**). In both cases, the metrics include total number of tumor cells over time (

**a**), total number of CAR T-cells (

**b**), total number of cancer cell deaths (

**c**), and total number of stem cells over time (

**d**). Each iteration represents 6 h of real time. For the gradated heterogeneity metrics, 0% mean antigen expression is plotted in yellow, 12.5% mean antigen expression is plotted in light blue, 25% mean antigen expression is plotted in red, and 50% mean antigen expression is plotted in dark blue. For the binary heterogeneity metrics, 25% antigen presentation is plotted in yellow, 50% antigen presentation is plotted in light blue, 75% antigen expression is plotted in red, and 98% antigen expression is plotted in dark blue. Note: the parameters in which the line does not reach day 75 indicate that one of the tumors died out at this point and no further data was collected.

**Figure 4.**3D plots of tumors on the last day of our simulation, day 75, with different antigen presentations. For tumor with gradated heterogeneity (

**a**), the data comes from 0%, 12.5%, 25%, and 50% mean antigen presentation (left to right). Vasculature is plotted as red capillaries growing across the plane. Tumor cells with 100% chance of presenting the antigen are plotted in yellow. Tumor cells with 0% chance of presenting the antigen are plotted in red. Every cell with a chance of antigen presentation between 0% and 100% is plotted on a gradient from red to yellow. CAR T-cells are plotted in green and are introduced on day 37.5 of the simulation. For the tumors with binary heterogeneity (

**b**), the data comes from runs with 25%, 50%, 75%, and 98% antigen presentation. Tumor cells with 100% antigen presentation are plotted in yellow; cells with 0% antigen presentation are plotted in red.

**Figure 5.**Examples of antigen shielding occurring in tumors with gradated heterogeneity (

**a**) and binary heterogeneity (

**b**). For gradated heterogeneity, the 3D plot shows tumor cells with 100% of antigen presentation in yellow, tumor cells with 0% antigen presentation in red, and tumor cells with intermediate probabilities of antigen presentation on a gradient. For binary heterogeneity, antigen-presenting tumor cells are plotted in yellow and antigen non-presenting tumor cells in red. In both cases, the figure shows a layer (shield) of antigen non/low-presenting cells forming a shield with high antigen-presenting cells. In both cases, such a shield makes it difficult for CAR T-cells to break through that layer, as the cells making up that layer are either fully or highly immune to CAR T-cell therapy.

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**MDPI and ACS Style**

Giorgadze, T.; Fischel, H.; Tessier, A.; Norton, K.-A.
Investigating Two Modes of Cancer-Associated Antigen Heterogeneity in an Agent-Based Model of Chimeric Antigen Receptor T-Cell Therapy. *Cells* **2022**, *11*, 3165.
https://doi.org/10.3390/cells11193165

**AMA Style**

Giorgadze T, Fischel H, Tessier A, Norton K-A.
Investigating Two Modes of Cancer-Associated Antigen Heterogeneity in an Agent-Based Model of Chimeric Antigen Receptor T-Cell Therapy. *Cells*. 2022; 11(19):3165.
https://doi.org/10.3390/cells11193165

**Chicago/Turabian Style**

Giorgadze, Tina, Henning Fischel, Ansel Tessier, and Kerri-Ann Norton.
2022. "Investigating Two Modes of Cancer-Associated Antigen Heterogeneity in an Agent-Based Model of Chimeric Antigen Receptor T-Cell Therapy" *Cells* 11, no. 19: 3165.
https://doi.org/10.3390/cells11193165