Stochastic Modeling of Early Hematopoiesis

Abstract

Hematopoiesis is the body's way of making the cellular constituents of blood. Oxygen transport, response to infections, and control of bleeding are among the functions of different mature blood cells. These specific functions are acquired as cells mature in the bone marrow. Stem cells are the “master cells” at the top of this pedigree, having within them the capacity to reconstitute the entire system. Although the latter stages of hematopoiesis are fairly well understood, the functioning of stem cells and other multipotential cells is currently a matter of intense research. This article presents a statistical analysis providing support for the clonal succession model of early hematopoiesis. J. L. Abkowitz and colleagues at the University of Washington have developed an experimental method for studying the kinetics of early hematopoiesis in a hybrid cat. The essence of the method is to analyze G6PD, an enzyme linked to the X chromosome. The G6PD type of a cell forms a binary marker that is passed down to all its descendant cells. Data record time series of proportions of one G6PD type in cells from the bone marrow, providing information about the number and lifetime of unobservable stem cells. Studies were performed after the autologous transplantation of G6PD heterozygous cats with limited numbers of hematopoietic stem cells. Preliminary analysis of the observed proportions indicates that under these circumstances, the proportion of cells with one type of G6PD is not constant over time. A simple stochastic model is used to quantify the relationship between observed proportions and unobserved stem cell populations. The model has a hidden Markov structure. We develop parameter estimates, confidence sets, and goodness-of-fit tests for this model. For our simple model, a recursive updating algorithm allows computation of the multimodal likelihood functions. A similar algorithm produces estimates of the realized Markov process. The parametric bootstrap is used to calibrate likelihood-based confidence sets and to perform simple goodness-of-fit tests. We address the question of whether stem cells have a constant proliferative potential between cats, and we discuss criticisms of the simple model.

Key Words:

• Clonal succession
• Glucose phosphate dehydrogenase
• Hidden Markov model
• Overdispersion
• Parametric bootstrap
• Recursive updating
• Stem cells