  Single-cell lineage tracking strategies enabled by recent experimental
technologies have produced significant insights into cell fate decisions, but
lack the quantitative framework necessary for rigorous statistical analysis of
mechanistic models describing cell division and differentiation. In this paper,
we develop such a framework with corresponding moment-based parameter
estimation techniques for continuous-time, multi-type branching processes. Such
processes provide a probabilistic model of how cells divide and differentiate,
and we apply our method to study hematopoiesis, the mechanism of blood cell
production. We derive closed-form expressions for higher moments in a general
class of such models. These analytical results allow us to efficiently estimate
parameters of much richer statistical models of hematopoiesis than those used
in previous statistical studies. After validating the methodology in simulation
studies, we apply our estimator to hematopoietic lineage tracking data from
rhesus macaques. Our analysis provides a more complete understanding of cell
fate decisions during hematopoiesis in non-human primates, which may be more
relevant to human biology and clinical strategies than previous findings from
murine studies. For example, in addition to previously estimated hematopoietic
stem cell self-renewal rate, we are able to estimate fate decision
probabilities and to compare structurally distinct models of hematopoiesis
using cross validation. These estimates of fate decision probabilities and our
model selection results should help biologists compare competing hypotheses
about how progenitor cells differentiate. The methodology is transferrable to a
large class of stochastic compartmental models and multi-type branching models,
commonly used in studies of cancer progression, epidemiology, and many other
fields.
