Delayed Differentiation Makes Many Models Compatible with Data for CD8+ T Cell Differentiation

Abstract

Upon antigen stimulation, naïve CD8+ T cells differentiate into short-lived effectors and longer-lived memory T cells. The kinetics of expansion of antigen-specific CD8+ T cells is highly reproducible at the population level, but the fate of individual naïve cells is stochastic, as individual naïve CD8+ T cells produce different numbers of effector and memory cells. Using mathematical models to analyse experimental data on tracing the fate of individual naïve T cells, it was previously shown that a linear model where naïve CD8+ T cells first differentiate into memory precursors that subsequently differentiate into effector cells describes the data best. However, this ‘memory first’ linear model assumed that the proliferation and differentiation events were distributed exponentially, whereas several studies indicate that differentiation of CD8+ T cell subsets need not follow an exponential distribution. Here we investigate the effect of delayed differentiation by adding intermediate compartments and use similar ordinary differential equations and Gillespie simulations to evaluate alternate models of CD8+ T cell differentiation. Models where a substantial fraction of the naïve CD8+ T cells directly differentiate into effector cells, without going through a memory phase, exhibit population dynamics that are very similar to the original ‘memory first’ linear model. Because alternate models with delayed differentiation perform better than those without a delay, we conclude that non-exponential forms of cellular differentiation need to be considered when comparing models. Hence the exact pathway for the differentiation of naïve CD8+ T cells into effector and memory T cells remains an open question.