Mathematical models and computational approaches in CAR-T therapeutics

Abstract

Background: The field of synthetic biology aims to engineer living organisms for specific therapeutic applications, with CAR-T cell therapy emerging as a groundbreaking approach in cancer treatment due to its potential for flexibility, specificity, predictability, and controllability. CAR-T cell therapies involve the genetic modification of T cells to target tumor-specific antigens. However, challenges persist because the limited spatio-temporal resolution in current models hinders the therapy's safety, cost-effectiveness, and overall potential, particularly for solid tumors.

Main body: This manuscript explores how mathematical models and computational techniques can enhance CAR-T therapy design and predict therapeutic outcomes, focusing on critical factors such as antigen receptor functionality, treatment efficacy, and potential adverse effects. We examine CAR-T cell dynamics and the impact of antigen binding, addressing strategies to overcome antigen escape, cytokine release syndrome, and relapse.

Conclusion: We propose a comprehensive framework for using these models to advance CAR-T cell therapy, bridging the gap between existing therapeutic methods and the full potential of CAR-T engineering and its clinical application.

Keywords: CAR-T cells; T cell engineering; biological system modeling; computational immunotherapy; mathematical modeling; synthetic biology; therapeutic optimization.

Figure 1

Structural comparison of five generations of Chimeric Antigen Receptor (CAR) designs. All generations contain an ScFv domain for antigen recognition and a transmembrane domain. Each subsequent generation introduces additional components: CD3ζ signaling domain (1st gen), costimulatory domain (2nd gen), multiple costimulatory domains (3rd gen), IL-12 inducer (4th gen), and IL-2Rβ with JAK/STAT3/5 signaling (5th gen). The figure depicts key functional domains and their roles in CAR-T cell activation and anti-tumor response.

Figure 2

The computational modeling cycle in CAR-T development. This figure illustrates the iterative cycle of computational modeling in CAR-T cell therapy development. Four interconnected stages are represented: “Computational Modeling” (blue, top) featuring ODE models, agent-based models, and machine learning; “Experimental Design” (red, right) encompassing in vitro studies, animal models, and CAR engineering; “Clinical Application” (green, bottom) focusing on dosing optimization, toxicity management, and combination therapies; and “Data Collection & Analysis” (purple, left) incorporating patient outcomes and model validation. The central “Key Outcomes” highlight the ultimate goals: improved efficacy, reduced toxicity, enhanced persistence, and expanded applications. These models generate testable hypotheses about CAR-T mechanisms and therapeutic responses, which are then validated through experimental and clinical studies that continuously refine model accuracy. Bidirectional arrows indicate how each stage both informs and is informed by the others, with experimental and clinical data continuously feeding back into computational modeling for iterative hypothesis generation, testing, and model refinement.

Figure 3

Schematic representation of CAR-T cell therapy modeling pipeline from disease state to recovery. The workflow progresses through six interconnected stages: antigen receptors, treatment specificity, combination therapy, time and dosage, cell dynamics, and treatment efficacy. Each stage includes specific modeling considerations depicted by icons and detailed subpoints below. The pathway flows from initial patient condition to healthy outcome, with a timeline emphasizing continuous data collection throughout the treatment process. The figure highlights both molecular-level considerations (such as antigen receptor engineering) and systemic responses (like cytokine release syndrome), demonstrating the comprehensive nature of CAR-T therapy modeling.

Figure 4

Comprehensive illustration of key side effects and challenges in CAR-T cell therapy. The central tumor mass (middle) expresses both tumor-specific antigens (TSA) and tumor-associated antigens (TAA), and is surrounded by four major therapeutic challenges: (1) Cytokine release syndrome (bottom left) - depicted by the cytokine storm and activated immune cells that contribute to systemic inflammation; (2) On-target/off-target effects (top left) - where CAR-T cells recognize antigens on non-tumor cells; (3) Tumor response mechanisms (bottom right) - including growth suppressors and resistance pathways; and (4) Potential relapse (top right) - showing tumor cells that have escaped immune surveillance. While these challenges can occur independently, they often interact—for example, tumor resistance can lead to relapse, while excessive CAR-T activation can cause both cytokine release syndrome and off-target toxicity. The figure also highlights cancer-associated fibroblasts (CAF) and their expression of fibroblast activation protein-α (FAP) in the tumor microenvironment, which can serve as both potential targets and obstacles for CAR-T therapy by modulating the tumor microenvironment and influencing CAR-T cell infiltration and function.

Figure 5

CAR-T Computational modeling: matrix selection framework. This figure presents a decision matrix for selecting appropriate computational modeling approaches based on specific CAR-T research objectives. The matrix categorizes six modeling methodologies (rows: ODE Systems, Agent-Based Models, Machine Learning, Bayesian Methods, Control Theory, and Sensitivity Analysis) against four research question types (columns: Mechanistic Understanding, Outcome Prediction, Parameter Estimation, and System Optimization). Each intersection is rated with plus signs (+, ++, or +++) indicating relative effectiveness and includes concise descriptions of strengths or limitations. This framework guides researchers in selecting optimal modeling approaches for their specific CAR-T research questions, highlighting that ODE systems excel in signaling pathway analysis, agent-based models in spatial tumor-immune interactions, machine learning in pattern recognition, Bayesian methods in uncertainty quantification, control theory in optimization, and sensitivity analysis in parameter ranking.

Figure 6

Comprehensive framework showing the evolution of computational modeling for CAR-T cell therapy. The left panel outlines current research objectives organized under four foundational principles: (1) ‘Accuracy is power’ emphasizes the importance of patient-specific parameters and clinically relevant outcomes in models; (2) ‘Less is often more’ advocates for focused modeling approaches that prioritize essential interactions over comprehensive but unwieldy systems; (3) ‘Variety leads to veracity’ highlights how diverse modeling techniques (from deterministic to stochastic approaches) provide complementary insights into complex biological processes; and (4) ‘Unity is strength’ underscores the value of integrating multiple therapeutic approaches and recognizing nonlinear effects in combination therapies. The right panel illustrates how these current approaches are evolving toward three transformative future opportunities: generative models that can synthesize and analyze multiple data types simultaneously; biomarker development for precise prediction of patient-specific therapy responses and toxicities; and safe, continuously improving treatment strategies through predictive control methods. The connecting arrow represents the natural progression from current modeling goals to more advanced computational approaches, demonstrating how today’s foundational principles will enable tomorrow’s precision medicine applications in CAR-T therapy.