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A Mathematical Model to Assess the Effectiveness and Side Effects of CAR T-Cell Therapy

08.08.2024

The Laboratory for Mathematical Modeling of Biological Processes of the NMRC for Hematology has derived an equation that makes it possible to compare newly created immunotherapies based on cellular technologies according to their degree of specificity. The article was published in the Journal Biophysical Reports

Doctors have long searched for medicines capable of neutralizing malignantly transformed cells in the human body. With the development of new bioengineering technologies, ideas of using the capabilities of the human immune system for anti-cancer therapy are actively being discussed. Among the numerous attempts to implement such ideas, technologies related to the use of chimeric antigen receptors (CAR technologies) have begun to attract increasing attention. From a conceptual point of view, everything looks quite simple. Each transformed (cancer) cell carries a unique antigenic structure on its surface. As soon as technologies for the biosynthesis of highly sensitive receptors for critical antigenic structures appeared, promising opportunities for so-called "targeted" antitumor therapy immediately opened up. During such therapy, the patient's own T lymphocytes are "retrofitted" with chimeric receptors capable of effectively recognizing and binding to tumor cells. 

After a number of successful examples of using CAR-T, when scientists found a way to modify a person's own T lymphocytes so that they could detect (recognize) and destroy malignant cells with high sensitivity, the well-known "dizziness of success" began. Numerous experiments have shown that T lymphocytes equipped with chimeric antigen receptors (abbreviated as CAR-T) really do have increased sensitivity to cancer target cells. Moreover, molecular biology methods have made it possible to obtain CAR T-cells with extremely high sensitivity. Despite the fact that CAR technology is expensive and complex, it has aroused unprecedented enthusiasm around the world. It has been found that drugs based on CAR T-cells are able to work effectively when nothing else helps. 

However, it quickly became clear that in addition to enhancing the direct damaging effect on target cells, CAR T-cells have a certain toxic effect on healthy tissues, which can lead to serious side effects. The question arose about the degree of specificity of CAR T-cells. At the same time, it turned out that the relationship between the degree of sensitivity of CAR T-cells and specificity is, figuratively speaking, inversely proportional - the higher the sensitivity, the lower the specificity. That is, the more likely it is not the "target cells" that will be affected, but the cells of healthy tissues. 

202408081.jpgIt has become clear that it is impossible to set the task of creating the most sensitive CAR T-cells, while possessing the highest (absolute) specificity. In this regard, the question arose about the creation of CAR technologies that would make it possible to find and then neutralize target cells as efficiently as possible with minimal damage to healthy tissues. In modern science such tasks are commonly called minimax search tasks. When solving such problems, it is customary to rely on a well-developed mathematical apparatus. However, in relation to onco-hematology, so far the problem of the relationship between sensitivity and specificity has not been formulated. The work performed at the NMRC for Hematology by two graduates of the Department of Physics of Living Systems of MIPT is devoted to its formulation and analysis. 

"It is not surprising that chimeric antigenic receptors fit like “keys to locks" to antigenic macromolecular structures located on the surface of cancer cells. Such receptors are manufactured according to the patterns of the latter. This ensures an increased sensitivity of CAR T-cells compared to unmodified T lymphocytes. If we compare the immune system with a highly sensitive barrier line, then with increased sensitivity it will work not only on "regular violators", but also on smaller objects and disturbances. That is, the higher the sensitivity of the detection system, the lower the specificity. If, under some circumstances, the sensitivity threshold turns to zero, then there is no need to talk about any specificity. The system will be triggered at any arbitrarily small disturbances. In relation to the discussion of the problems of recognizing target cells in the human body, this means that the higher the sensitivity of the drug, the more, generally speaking, it is capable of causing more toxic side effects. Continuing the analogy with the barrier line, the researcher needs to find a method to find in the lines of drugs offered for CAR-T therapy those that will have increased, but not maximum, sensitivity, combined with sufficient specificity," said Georgy Guria, co—author of the study, head of the Laboratory for Mathematical Modeling of Biological Processes at the NMRC for Hematology and professor of the Department of Physics of Living Systems at MIPT. 

202408082.jpgIdeally, the CAR product being developed should have not only high sensitivity to target cells, but also low sensitivity to healthy tissue cells. In other words, it must be highly specific, that is, "sharpened" in relation to target cells. As a rule, the issue of specificity is clarified a posteriori when the drug has already been created and is being tested on animals. At the same time, the assessment of side effects at the prebiological stages could further reduce the cost of developing CAR systems by an order of magnitude. The authors set the task to assess the probability of nonspecific damage to healthy tissue cells at the earliest stages. 

The secret of the specificity of future CAR T therapies, as it turns out, is related to the ability of receptors to combine on the cell surface into groups or clusters. The main factor that makes it possible to distinguish target cells from non-target cells is the critical size of the receptor cluster on the surface of CAR T-cells. The authors derived mathematical expressions to evaluate the specificity of CAR T-cells. These expressions establish a relationship between the parameters of the CAR system and the probability of cytotoxicity of CAR-T for target tissues and for non-specifically affected healthy tissues. This will make it possible to obtain CAR T-cells with a given specificity in the early stages of development. 

Based on the developed approach, the authors formulated recommendations for bioengineers developing CAR T-cell therapy drugs. 

Article: https://www.cell.com/biophysreports/fulltext/S2667-0747(24)00031-4?_returnURL=https%3A%2F%2Flinkingh...

 https://doi.org/10.1016/j.bpr.2024.100172

 Figure 1. Targeted-critical pair configurations

 Figure 2. Target and critical tissue heterogeneity

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