Introduction
Scientific research frequently employs mathematical models to reinforce experimental efforts in collaboration with established theories. Utilizing these models to simulate experiments can yield fresh perspectives and guide the formulation of new experimental inquiries. Consequently, this approach can reduce the overall number of experiments required, enhancing the prospects for obtaining valuable outcomes. Substituting specific experiments with simulations offers several advantages, including increased safety, precise control via parameter adjustments, the capability to explore more extreme conditions than possible in a laboratory setting, cost-effectiveness, and the ability to observe intricate processes that defy easy observation through traditional experimentation, such as the evolution of a pathway.
What Syncova is aiming for is to create a new detection method for ovarian cancer that will open the possibility to detect the cancer in an early stage before it becomes deadly and irreversible. Yet this is not the only goal Syncova is trying to accomplish but also looking to create a solution to attack the tumor cells using CAR-T therapy.
Syncova is a 2 year project, and so we decided to start modeling the CAR-T cells from the first year so we can further improve it in our second year. The modeling we are working on is an overview on how CAR-T cells will interact with tumor cells once injected inside a host, it'll be taking into consideration different parameters concerning both the CAR-T cells and Tumor cells. Since we are working with both protein CD44 and CD117, it means we are looking to create two CAR-T cells at the moment CAR-T44 and CAR-T117 and studying their effectiveness against the tumor cells to conclude which one is more potent than the other.
The primary objective of this model is to provide invaluable support for upcoming laboratory research endeavors. Its key functions include predicting experimental results and identifying the parameters that are particularly sensitive and relevant within the laboratory context. In essence, the model acts as a virtual laboratory assistant, allowing researchers to explore different scenarios and configurations without the need for physically conducting each experiment.
One of the key advantages of this model is its flexibility. By adjusting the parameters within the model, researchers can simulate various experimental conditions and scenarios. This capability proves highly advantageous in the context of enhancing the effectiveness of CAR-T cells, a critical area of research in immunotherapy. Researchers can manipulate parameters related to CAR-T cell behavior and interactions with tumor cells, thereby gaining insights into optimal configurations and strategies.
Moreover this model provides the wet lab with the ability to modify a wide range of variables, including time of injection and the initial concentrations of CAR-T cells and tumor cells. This flexibility opens up a new world of possibilities, as researchers can explore a vast array of experimental conditions without the need for manual execution. This not only saves a substantial amount of time but also conserves valuable resources.
In essence, the model serves as a bridge between computational simulations and real-world laboratory work. It leverages the power of predictive modeling to guide experiments in a more focused and efficient manner. By offering the ability to test countless scenarios in silico, it enhances the wet lab's capabilities, accelerating the pace of research and potentially leading to breakthroughs in the field of CAR-T cell therapy.
Methods
The Ordinary Differential Equation (ODE) model was created in both MATLAB and PYTHON and solved using ODE45.
We started working in MATLAB to get the initial code for the simulation up and working, and to make sure that we're getting correct results with fast computational time, and the we migrated to PYTHON since we were aiming to create a more user friendly interface where we will create a GUI later on to make it easier for the wet lab to change whatever parameters they like and proceed with complete control in the experiment they want.
The Dry Lab team got their inspiration from the research paper "CARTmath—A Mathematical Model of CAR-T Immunotherapy in Preclinical Studies of Hematological Cancers" which was really helpful in explaining how CAR-T cells react against Tumor cells and the creation of memory CAR-T cells.
The modeling for the research paper and our simulation takes into consideration the host as immunodeficient mouse model of hematological cancers and it investigates the interplay between tumor cells, effector and memory CAR-T cells.
For the time being we decided to go with this model since it is simple to use and to explain. It's an easy way to study how the CAR-T cells act in a simplified system and it shows the core basics of how the process is being done.
We would also like to mention that the parameters used in this model are the parameters for the following CAR-T19 and CAR-T123 as these parameters were used in the research paper and were already provided. As for CAR-T44 and CAR-T117 there isn't much research done on them yet, which forced us to work on simulating the same CAR-T cells used in the research paper.
Model Construction
The model consists of three ordinary differential equations that describe the relations between effector CAR-T cells, Memory CAR-T cells and Tumor cells. The equations have been slightly modified to incorporate the interplay of two different CAR-T cells inside against Tumor cells inside the same host.
Equations
Parameters
Since we are working with two different CAR-T cells this allows us to create and model three different scenarios:
- The interplay between CAR-T117 and tumor cells.
- The interplay between CAR-T44 and tumor cells.
- The interplay between CAR-T44 + CAR-T117 and tumor cells.
Improvements
- Studying the effect of CAR-T cells on each other, meaning doing experiments to check if the coexistence of both CAR-T44 and CAR-T117 inside the same host will render one of the CAR-T cells ineffective or more effective against tumor cells.
- Adding a fourth equation for CAR-T cells : the fourth equation would represent both proteins CD44 and CD117 on the same CAR-T instead of them being injected separately. In other words the equation would target a bivalent CAR-T cell.
- Model the effect of a bivalent CAR-T cell on tumor cells.
- Using a more complex modeling system that would take into consideration the following options:
- Exhaustion of CAR-T cells.
- CAR-T cells getting attached to Tumor cells but not succeeding in killing them.
Results
Since we divided our modeling into three scenarios we were able to get three separate graphs that describe the interplay between effector CAR-T cells, Memory CAR-T cells and Tumor cells.
Scenario Car-T A
Scenario Car-T B
Scenario Dual Car-T
We also implemented a function that allows the user to study the change of tumor cells on a specific day after changing a certain parameter in a certain range. If we wanted to change the parameter in the range of -10 to 10% of it's initial value, the simulation can create a graph showing how it’ll affect the tumor cells and show you if at any case of this change the tumor cell will go below their default value at that time, which gives the wet lab the option to play and engineer the parameters as they like to achieve a better outcome in killing the tumor cells.