A mathematical model of cancer stem cell driven tumor initiation: implications of niche size and loss of homeostatic regulatory mechanisms.

Hierarchical organized tissue structures, with stem cell driven cell differentiation, are critical to the homeostatic maintenance of most tissues, and this underlying cellular architecture is potentially a critical player in the development of a many cancers. Here, we develop a mathematical model of mutation acquisition to investigate how deregulation of the mechanisms preserving stem cell homeostasis contributes to tumor initiation. A novel feature of the model is the inclusion of both extrinsic and intrinsic chemical signaling and interaction with the niche to control stem cell self-renewal. We use the model to simulate the effects of a variety of types and sequences of mutations and then compare and contrast all mutation pathways in order to determine which ones generate cancer cells fastest. The model predicts that the sequence in which mutations occur significantly affects the pace of tumorigenesis. In addition, tumor composition varies for different mutation pathways, so that some sequences generate tumors that are dominated by cancerous cells with all possible mutations, while others are primarily comprised of cells that more closely resemble normal cells with only one or two mutations. We are also able to show that, under certain circumstances, healthy stem cells diminish due to the displacement by mutated cells that have a competitive advantage in the niche. Finally, in the event that all homeostatic regulation is lost, exponential growth of the cancer population occurs in addition to the depletion of normal cells. This model helps to advance our understanding of how mutation acquisition affects mechanisms that influence cell-fate decisions and leads to the initiation of cancers.

Phosphorylation of antiviral and endogenous nucleotides to di- and triphosphates by guanosine monophosphate kinase.

Many fraudulent nucleosides including the antivirals acyclovir (ACV) and ganciclovir (GCV) must be metabolized to triphosphates to be active. Cyclopropavir (CPV) is a newer, related guanosine nucleoside analog that is active against human cytomegalovirus (HCMV) in vitro and in vivo. We have previously demonstrated that CPV is phosphorylated to its monophosphate (CPV-MP) by the HCMV pUL97 kinase. Consequently, like other nucleoside analogs phosphorylated by viral kinases, CPV most likely must be converted to a triphosphate (CPV-TP) in order to elicit antiviral activity. Once formed by pUL97, we hypothesized that guanosine monophosphate kinase (GMPK) is the enzyme responsible for the conversion of CPV-MP to CPV-DP. Incubation of CPV-MP with GMPK resulted in the formation of CPV-DP and, surprisingly, CPV-TP. When CPV-DP was incubated with GMPK, a time-dependent increase in CPV-TP occurred corresponding to a decrease in CPV-DP thereby demonstrating that CPV-DP is a substrate for GMPK. Substrate specificity experiments revealed that GMP, dGMP, GDP, and dGDP are substrates for GMPK. In contrast, GMPK recognized only acyclovir and ganciclovir monophosphates as substrates, not their diphosphates. Kinetic studies demonstrated that CPV-DP has a K(M) value of 45±15µM. We were, however, unable to determine the K(M) value for CPV-MP directly, but a mathematical model of experimental data gave a theoretical K(M) value for CPV-MP of 332±60µM. We conclude that unlike many other antivirals, cyclopropavir can be converted to its active triphosphate by a single cellular enzyme once the monophosphate is formed by a virally encoded kinase.

Pathways to tumorigenesis--modeling mutation acquisition in stem cells and their progeny.

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.

Haematopoietic stem cells do not asymmetrically segregate chromosomes or retain BrdU.

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.