Integrating Mechanistic Modeling and Machine Learning to Study CD4+/CD8+ CAR-T Cell Dynamics with Tumor Antigen Regulation

TL;DR

An extended mathematical framework of CAR-T cell dynamics that explicitly models CD4+ helper and CD8+ cytotoxic lineages and their interactions with tumor antigen burden is presented and it is demonstrated how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

Abstract

Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4+ and CD8+ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4+ helper and CD8+ cytotoxic lineages and their interactions with tumor antigen burden. Building on the Kirouac et al. (2023) model of antigen-regulated memory-effector-exhaustion transitions, our system of differential equations incorporates CD4-mediated modulation of CD8+ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8+ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naive baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

Figures (9)

• Figure 1: Fig. 1 Schematic diagram of our extension of the Kirouac et al. (2023) CAR-T cell model. CD8+ T cells (top layer) undergo antigen-driven transitions from memory (TM) to effector (TE1, TE2) to exhausted (TX) states, with TE2CD8 mediating tumor killing. CD4+ CAR-T cells (bottom layer) follow a similar differentiation pathway but do not kill the tumor directly. Instead, TE2CD4 cells exert helper functions by secreting cytokines (e.g., IFN-$\gamma$, IL-2) which enhance CD8+ T cell expansion, survival, and memory formation (blue arrow). Tumor cells (B) generate a transient antigen signal (BA) that regulates T cell responses (green and red arrows)
• Figure 2: Fig. 2 Relative local sensitivity analysis using the area under the curve (AUC) of tumor burden over 365 days. Bars represent the relative sensitivity of the AUC of $B(t)$ to a 1% perturbation in each parameter and initial condition in the model, with parameters with the greatest sensitivities displayed
• Figure 3: Fig. 3 Global sensitivity analysis using the area under the curve (AUC) of tumor burden over 365 days. Bars represent the partial rank correlation coefficients (PRCC) between each parameter and the AUC of tumor burden, indicating the direction and strength of monotonic relationships while controlling for other parameters. Parameters with the greatest sensitivities are displayed
• Figure 4: Fig. 4 Sobol global sensitivity analysis using the area under the curve (AUC) of tumor burden over 365 days. Bars represent the first-order ($S_i$) and total-order ($S_{Ti}$) Sobol sensitivity indices for each parameter, quantifying the proportion of variance in tumor burden attributable to each parameter alone and in interaction with others. Only parameters with the greatest sensitivities are displayed
• Figure 5: Fig. 5 Percentage of baseline non-responders rescued to complete response as a function of CD4 fraction in the CAR-T product. Results are shown for five independent trials of 5,000 virtual patients each, with newly generated virtual patient cohorts in every trial. Bars represent the mean rescue percentage, and error bars denote the standard deviation across trials