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Bioinformatics, Computational and Systems Biology

Bioinformatics, Computational and Systems Biology - Poster Session C & D

S26 - A System-Level PDE Model of T-Cell Immune Response Integrating Multi-Compartment Geometry and Convective Transport

Friday, October 10, 2025

10:00 AM - 11:00 AM PDT

Location: Exhibit Hall F, G & H

Presenting Author(s)

Howard Wang

Researcher
Swarthmore College, United States

Last Author(s)

Howard Wang

Researcher
Swarthmore College, United States

Primary Investigator(s)

Ryan Zurakowski

Professor and Interim Chair
University of Delaware
Newark, Delaware, United States

Co-Author(s)

Michael Piovoso

Professor
University of Delaware
Newark, Delaware, United States

Moderator(s)

Michael Piovoso

Professor
University of Delaware
Newark, Delaware, United States

Introduction: : One fundamental question in immunology is how the complex three-dimensional architecture of a lymph node (LN) shapes the course of an immune response. Although it is known that T cell activation is a spatially organized process, traditional non-spatial models treat the LN as a "well-mixed" bag of cells, precluding any investigation into the role of physical location. This work proposes to answer a central question: "How does the specific site of initial T-cell proliferation affect both the local cellular environment and the total systemic T-cell population?"

To address this, we developed a spatially explicit partial differential equation (PDE) model that simulates the dynamics of T cells within a realistic 3D LN geometry. Specifically, we compare T cell concentrations in the proliferative follicle region versus the inactive periphery. Our simulations reveal that the specific site of proliferation drives major concentration gradients between the proliferative region and the quiescent periphery. These physiologically sensible results demonstrate the model's robustness and its power to further uncover spatial dynamics of the LN.

Materials and

Methods: : Our analysis is based on a PDE framework that governs the concentration of activated T cells (u_A) and memory (u_M) T cells across a multi-compartment 3D mesh composed of the LN lobule, blood, and lymphatic systems.

du_A/dt = div(D_u * grad(u_A) - vu_A) + rhoS(t)u_A - (delta_A + alpha(t))u_A - ru_A
du_M/dt = div(D_u * grad(u_M) - vu_M) + ru_A - delta_Mu_M

Cell migration is modeled by both diffusion (Du) and a transverse flux term representing convective fluid flow (v). Biological reactions are controlled by smooth logistic functions, with proliferation (ρ) modulated by a temporal switch S(t) and contraction driven by an additional death rate, α(t) = α ⋅ (1 + tanh(kdeath(t−Tpeak)))/2, ensuring a gradual transition around the peak response time, Tpeak. The model was parameterized by fitting its output to experimental data from a CD4+ T cell response using Bayesian Optimization.

To investigate spatial dynamics, we performed a computational experiment to analyze local concentration gradients by tracking T-cell density over time in two representative tetrahedrons: one inside the proliferative follicle and one in the distant periphery.

Results, Conclusions, and Discussions:: A primary achievement of the spatial PDE framework is its improved ability to replicate experimental data compared to a non-spatial ODE model, as shown in Figure 1. The ODE model, while capturing the basic timeline, produces an artificially sharp peak because it assumes that all cells transition from proliferation to contraction instantaneously. In contrast, our PDE model naturally produces the characteristic "rounded peak" of the T-cell response. This is an emergent property of the spatial system: by localizing proliferation and modeling cell transport, the transition to a system-wide contraction phase becomes asynchronous, smoothing the macroscopic dynamics to better match physiological observations.

This spatial context is also critical for interpreting the model's biological parameters. As shown in Figure 2, there is a vast, multi-order-of-magnitude difference in cell density between the proliferative follicle "hot zone" and the quiescent periphery. To accurately capture these dynamics, the model was carefully parameterized using Bayesian Optimization. The best-fit parameters indicate that the response initiates from a small precursor pool (A0 = 56 cells) which then undergoes rapid proliferation (ρ = 3.1/day). This proliferation rate ramps up over the first 8 days of the response, reflecting a gradual recruitment and activation process. For the model to match experimental data, proliferation must be extremely intense within these localized follicular regions to produce enough T-cells to populate the entire lymph node and generate the observed systemic average. Furthermore, the model incorporates a sharp, switch-like onset of the contraction phase death rate (kdeath = 8), which is critical for replicating the rapid decline in T-cell numbers following the peak response at day 7.5.

In conclusion, this work demonstrates that a spatially explicit modeling approach provides a more mechanistic interpretation of the T-cell immune response. By moving beyond non-spatial models, we have shown that the response is defined by extreme concentration gradients at the local level, a phenomenon masked when observing the system as a whole. The model serves as a powerful quantitative framework for investigating these spatial dynamics, which are otherwise challenging to measure directly.

Acknowledgements and/or References (Optional): : Acknowledgements
We gratefully acknowledge the valuable guidance and support of Professor Ryan Zurakowski and Professor Michael Piovoso, as well as the insightful discussions with Sobia Anam, from the University of Delaware.

References
De Boer, R. J., Oprea, M., Antia, R., Murali-Krishna, K., Ahmed, R., & Perelson, A. S. (2003). Different Dynamics of CD4+ and CD8+ T Cell Responses During and After Acute Lymphocytic Choriomeningitis Virus Infection. The Journal of Immunology, 171(8), 3928–3935. https://doi.org/10.4049/jimmunol.171.8.3928

Hawkins, E. D., Hommel, M., & Hodgkin, P. D. (2009). Quantal and analog control of lymphocyte fate and function. Immunology and Cell Biology, 87(4), 276–282. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2819428/