Stochastic Modeling of Early Hematopoiesis
Newton, Michael A., Guttorp, Peter, Catlin, Sandra, Assuncao, Renato, Abkowitz, Janis L., Journal of the American Statistical Association
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
1. HEMATOPOIESIS: THE PRODUCTION
OF BLOOD CELLS
The bone marrow of humans and other vertebrata contains a relatively small number of remarkable cells, the hematopoietic stem cells. Through replication and differentiation, these cells produce all the different kinds of blood cells: red cells, which transport oxygen throughout the body; white cells, which form the immune defense; and platelets, which initiate clotting. A human creates 3-10 billion platelets, red cells, and neutrophils (one kind of white cell) every hour, and in an emergency this rate of production can increase by an order of magnitude (Golde 1991). Neutrophils are active for 8 hours in humans, whereas platelets and red cells circulate for 7 days and 4 months. With stem cells at the source, hematopoiesis is the complex dynamic process that maintains this vast and varied blood cell population. (See Brecher, Beal, and Schneiderman 1993 or Lemischka 1992 for reviews.)
Although it has proven very difficult to isolate stem cells from bone marrow, stem cells must have certain functional properties. To maintain a reserve for the lifetime of the animal, it is essential that stem cells be able to self-replicate. Also, they must be able to supply cells for differentiation and development into mature blood cells. As cells progress along a pathway from stem cell to mature blood cell, there is a sequential loss of potential to become any one of the mature blood cell types. That is, cells become specialized as they divide and differentiate. Stem cells at the beginning of these pathways are totipotent cells; that is, they can produce all the different types of mature blood cells. …