The growth threshold conjecture: a theoretical framework for understanding T-cell tolerance
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Updated: Mar 30, 2026

In Vitro and In Vivo Assessment of T, B and Myeloid Cells Suppressive Activity and Humoral Responses from Transplant Recipients
Published on: August 12, 2017
Clemente F Arias1, Miguel A Herrero2, José A Cuesta3
1Departamento de Matemática Aplicada, and , Universidad Complutense de Madrid , Madrid, Spain ; Departamento de Ecología , Universidad Complutense de Madrid , Madrid, Spain.
Abstract:
Adaptive immune responses depend on the capacity of T cells to target specific antigens. As similar antigens can be expressed by pathogens and host cells, the question naturally arises of how can T cells discriminate friends from foes. In this work, we suggest that T cells tolerate cells whose proliferation rates remain below a permitted threshold. Our proposal relies on well-established facts about T-cell dynamics during acute infections: T-cell populations are elastic (they expand and contract) and they display inertia (contraction is delayed relative to antigen removal). By modelling inertia and elasticity, we show that tolerance to slow-growing populations can emerge as a population-scale feature of T cells. This result suggests a theoretical framework to understand immune tolerance that goes beyond the self versus non-self dichotomy. It also accounts for currently unexplained observations, such as the paradoxical tolerance to slow-growing pathogens or the presence of self-reactive T cells in the organism.
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