Multi-variate model of T cell clonotype competition and homeostasis
Published in Submitted to: Scientific Reports, 2022
The diversity of the naive T cell receptor repertoire is maintained by competition for homeostatic proliferation stimuli. We make use of a pre- viously defined bi-variate competition model to propose a multi-variate model to study the dynamics of $\eta$ different competing T cell clonotypes for stimuli provided by self-peptides bound to major histocompatibility complexes (self-pMHCs). We characterise the late time behaviour of the system by analysing: (i) its dynamics before extinction of the first clonotype, making use of the quasi-stationary probability distribution, (ii) the time to the first extinction event, (iii) the probability of extinction for each clonotype, and (iv) the size of the surviving clonotypes when the first extinction event takes place. Additionally we define and study the probability distribution of the number of divisions undergone by a clonotype before its extinction. Our results indicate that the mean size of a new clonotype at quasi-steady state increases as the total self-pMHC stimulus available to it increases, or as the fraction of self-pMHC stimuli shared with other clonotypes decreases. Furthermore, the competition experi- enced by a a new clonotype entering the homeostatic distribution of naive T cell clonotypes and its initial size are the most significant parameters since they determine its probability of extinction in the periphery.
Recommended citation: Daniel Luque Duque, Martín López García, Jessica A. Gaevert, Grant Lythe, Paul G. Thomas, and Carmen Molina-París. Multi-variate model of T cell clonotype competition and homeostasis. Submitted to: Scientific Reports, 2022