Dynamics and turnover of memory CD8 T cell responses following yellow fever vaccination

Immunological memory, generated in response to infection or vaccination, may provide complete or partial protection from antigenically similar infections for the lifetime. Memory CD8 T cells are important players in protection from secondary viral infections but quantitative understanding of their dynamics in humans is limited. We analyze data from two studies where immunization with the yellow fever virus vaccine (YFV-17D) generates a mild acute infection and long-term memory. We find that: (i) the division rate of YFV-17D-specific CD8 T cells drops and stabilizes at similar to 0.1% per day during the first year following vaccination whereas the death rate declines more gradually, and (ii) the number of these cells declines approximately in accordance with a power law (proportional to time(-0.75)) for at least several decades following vaccination. Understanding how immunological memory lasts a lifetime requires quantifying changes in the number of memory cells as well as how their division and death rates change over time. We address these questions by using a statistically powerful mixed-effects differential equations framework to analyze data from two human studies that follow CD8 T cell responses to the yellow fever vaccine (YFV-17D). Models were first fit to the frequency of YFV-specific memory CD8 T cells and deuterium enrichment in those cells 42 days to 1 year post-vaccination. A different dataset, on the loss of YFV-specific CD8 T cells over three decades, was used to assess out of sample predictions of our models. The commonly used exponential and bi-exponential decline models performed relatively poorly. Models with the cell loss following a power law (exactly or approximately) were most predictive. Notably, using only the first year of data, these models accurately predicted T cell frequencies up to 30 years post-vaccination. Our analyses suggest that division rates of these cells drop and plateau at a low level (0.1% per day, similar to double the estimated values for naive T cells) within one year following vaccination, whereas death rates continue to decline for much longer. Our results show that power laws can be predictive for T cell memory, a finding that may be useful for vaccine evaluation and epidemiological modeling. Moreover, since power laws asymptotically decline more slowly than any exponential decline, our results help explain the longevity of immune memory phenomenologically.