Effect of Dedifferentiation on Time to Mutation Acquisition in Stem Cell-Driven Cancers

Citation: Jilkine A, Gutenkunst RN ( Effect of Dedifferentiation on Time to Mutation Acquisition in Stem Cell-Driven Cancers Alexandra Jilkine 0 Ryan N. Gutenkunst 0 Edwin Wang, National Research Council of Canada, Canada 0 1 Department of Molecular and Cellular Biology, University of Arizona, Tucson, Arizona, United States of America, 2 Department of Applied and Computational Mathematics and Statistics, University of Notre Dame , Notre Dame, Indiana , United States of America Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated longlived cancer stem cells. It is unclear, however, whether cancer stem cells originate from normal stem cells or from dedifferentiated progenitor cells. To address this, we mathematically modeled the effect of dedifferentiation on carcinogenesis. We considered a hybrid stochastic-deterministic model of mutation accumulation in both stem cells and progenitors, including dedifferentiation of progenitor cells to a stem cell-like state. We performed exact computer simulations of the emergence of tumor subpopulations with two mutations, and we derived semi-analytical estimates for the waiting time distribution to fixation. Our results suggest that dedifferentiation may play an important role in carcinogenesis, depending on how stem cell homeostasis is maintained. If the stem cell population size is held strictly constant (due to all divisions being asymmetric), we found that dedifferentiation acts like a positive selective force in the stem cell population and thus speeds carcinogenesis. If the stem cell population size is allowed to vary stochastically with density-dependent reproduction rates (allowing both symmetric and asymmetric divisions), we found that dedifferentiation beyond a critical threshold leads to exponential growth of the stem cell population. Thus, dedifferentiation may play a crucial role, the common modeling assumption of constant stem cell population size may not be adequate, and further progress in understanding carcinogenesis demands a more detailed mechanistic understanding of stem cell homeostasis. - Funding: This work was funded by NSF Grant DEB-1146074 and University of Arizona startup funds. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Most tissues consist of three classes of cells: stem cells, transitamplifying progenitor cells, and differentiated cells. Multicellular organisms require a tight control of cell division to ensure a proper balance between these different cell populations. The cancer stem cell (CSC) hypothesis states that tumors are also hierarchically organized, with a small sub-population of cancer cells driving cancer growth [1]. Individual cell tracing studies of tumor development strongly support the cancer stem cell hypothesis in many (but not all) types of cancer [2,3], and identifying these cells in tissues is an ongoing goal in cancer research. Lineage studies find that malignant tumors contain more cancer stem cells compared to benign tumors and that cancers gradually lose their tissue-like hierarchical organization as they evolve from benign to malignant [2]. Cells escape proliferation control after acquiring a series of mutations in a multi-step process [4]. While some cancers may require only a few mutations [5], the number of required (driver) mutations in solid cancers is larger, with up to twenty driver mutations being required [6]. In order to accumulate this critical number of mutations during a lifetime, cells either have to be longlived or the mutation rate has to be large [7]. Stem cells have been proposed to be likely candidates for the initial cell of mutation due to their long lifetime and sustained self-renewal capacity [1]. In addition to their long life span, stem cells are able to generate full lineages of differentiated cells, thereby perpetuating mutations through clonal expansion. Given known division and mutation rates, theoretical studies have argued that the necessary number of mutations for carcinogenesis cannot be obtained in the stem cell population on a reasonable time scale without assuming either significant selective advantage or elevated mutation rates [4,7]. However, there is conflicting evidence as to how early in tumor development cancers acquire an elevated mutation rate [8,9] and several cancer genome sequencing studies have estimated mutation rates during cancer initiation to be normal for some types of cancer [1012]. Although a stem cell may sustain the first oncogenic hit, subsequent alterations required for development of CSCs can occur in descendent progenitor cells [13]. Dysregulation of pathways involved in stem cell self-renewal may lead to progenitor cells acquiring a stem cell-like phenotype. It remains an open question whether cancer stem cells originate from stem cells that escape homeostasis or from dedifferentiated progenitor cells that acquire infinite proliferating potential [14]. There is significant evidence that dedifferentiation can play a role in establishment of certain cancers [1517]. For example, cell sorting has demonstrated that stem-like cells can arise de novo from non-stem-like cancer cells in in vitro breast cancer cell lines [18,19]. In the hematopoietic system, it has been shown that leukemic stem cells Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of immortal stem cells that divide indefinitely to produce many differentiated cells. Cancer stem cells may come directly from mutation of normal stem cells, but this route demands high mutation rates, because there are few normal stem cells. There are, however, many differentiated cells, and mutations can cause such cells to dedifferentiate into a stem-like state. We used mathematical modeling to study the effects of dedifferentiation on the time to cancer onset. We found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset. can be generated from committed progenitor cells that acquire stem cell-like behavior [20]. It has been suggested that acute myeloid leukemia (AML) is a progenitor disease, where (...truncated)