Stem cells are proposed to segregate chromosomes asymmetrically during self-renewing divisions so that older ('immortal') DNA strands are retained in daughter stem cells whereas newly synthesized strands segregate to differentiating cells. Stem cells are also proposed to retain DNA labels, such as 5-bromo-2-deoxyuridine (BrdU), either because they segregate chromosomes asymmetrically or because they divide slowly. However, the purity of stem cells among BrdU-label-retaining cells has not been documented in any tissue, and the 'immortal strand hypothesis' has not been tested in a system with definitive stem cell markers. Here we tested these hypotheses in haematopoietic stem cells (HSCs), which can be highly purified using well characterized markers. We administered BrdU to newborn mice, mice treated with cyclophosphamide and granulocyte colony-stimulating factor, and normal adult mice for 4 to 10 days, followed by 70 days without BrdU. In each case, less than 6% of HSCs retained BrdU and less than 0.5% of all BrdU-retaining haematopoietic cells were HSCs, revealing that BrdU has poor specificity and poor sensitivity as an HSC marker. Sequential administration of 5-chloro-2-deoxyuridine and 5-iodo-2-deoxyuridine indicated that all HSCs segregate their chromosomes randomly. Division of individual HSCs in culture revealed no asymmetric segregation of the label. Thus, HSCs cannot be identified on the basis of BrdU-label retention and do not retain older DNA strands during division, indicating that these are not general properties of stem cells.

Stem cells are thought to balance self-renewal and differentiation through asymmetric and symmetric divisions, but whether such divisions occur during hematopoietic development remains unknown. Using a Notch reporter mouse, in which GFP acts as a sensor for differentiation, we image hematopoietic precursors and show that they undergo both symmetric and asymmetric divisions. In addition we show that the balance between these divisions is not hardwired but responsive to extrinsic and intrinsic cues. Precursors in a prodifferentiation environment preferentially divide asymmetrically, whereas those in a prorenewal environment primarily divide symmetrically. Oncoproteins can also influence division pattern: although BCR-ABL predominantly alters the rate of division and death, NUP98-HOXA9 promotes symmetric division, suggesting that distinct oncogenes subvert different aspects of cellular function. These studies establish a system for tracking division of hematopoietic precursors and show that the balance of symmetric and asymmetric division can be influenced by the microenvironment and subverted by oncogenes.

Most adult tissues consist of stem cells, progenitors, and mature cells, and this hierarchical architecture may play an important role in the multistep process of carcinogenesis. Here, we develop and discuss the important predictions of a simple mathematical model of cancer initiation and early progression within a hierarchically structured tissue. This work presents a model that incorporates both the sequential acquisition of phenotype altering mutations and tissue hierarchy. The model simulates the progressive effect of accumulating mutations that lead to an increase in fitness or the induction of genetic instability. A novel aspect of the model is that symmetric self-renewal, asymmetric division, and differentiation are all incorporated, and this enables the quantitative study of the effect of mutations that deregulate the normal, homeostatic stem cell division pattern. The model is also capable of predicting changes in both tissue composition and in the progression of cells along their lineage at any given time and for various sequences of mutations. Simulations predict that the specific order in which mutations are acquired is crucial for determining the pace of cancer development. Interestingly, we find that the importance of genetic stability differs significantly depending on the physiological expression of mutations related to symmetric self-renewal and differentiation of stem and progenitor cells. In particular, mutations that lead to the alteration of the stem cell division pattern or the acquisition of some degree of immortality in committed progenitors lead to an early onset of cancer and diminish the impact of genetic instability.

Abstract. Most mammalian tissues are organized into a hierarchical structure of stem, progenitor, and differentiated cells. Tumors exhibit similar hierarchy, even if it is abnormal in comparison with healthy tissue. In particular, it is believed that a small population of cancer stem cells drives tumorigenesis in certain malignancies. These cancer stem cells are derived from transformed stem cells or mutated progenitors that have acquired stem-cell qualities, specifically the ability to selfrenew. Similar to their normal counterparts, cancer stem cells are long-lived, can self-renew and differentiate, albeit aberrantly, and are capable of generating tissue, resulting in tumor formation. Although identified and characterized in several forms of malignancy, the specific multi-step process that causes the formation of cancer stem cells is uncertain. Here, a maturity-structured mathematical model is developed to investigate the sequential order of mutations that causes the fastest emergence of cancer stem cells. Using model predictions, we discuss conditions for which genetic instability significantly speeds cancer onset and suggest that unbalanced stem-cell selfrenewal and inhibition of progenitor differentiation contribute to aggressive forms of cancer. To our knowledge, this is the first continuous maturity-structured mathematical model used to investigate mutation acquisition within hierarchical tissue in order to address implications of cancer stem cells in tumorigenesis.

There is increasing evidence for the "cancer stem cell hypothesis" which holds that cancers originate in tissue stem cells or progenitor cells. As a result of this, cancers are driven by a cellular subcomponent that retains stem cell properties. Among these properties are self-renewal and multi-lineage differentiation. The biological processes which account for stem cell properties are currently being elucidated. Cancer stem cells maintain many of the same characteristics of their normal counterparts. The combination of biological research with mathematical modeling may provide for a greater understanding of the complex picture of breast cancer stem cells and assist cancer biologists and clinical oncologists in designing and testing novel therapeutic strategies.