Minimizing the risk of cancer: tissue architecture and cellular replication limits

Constrained optimization of divisional load in hierarchically organized tissues during homeostasis

It has been hypothesized that the structure of tissues and the hierarchy of differentiation from stem cell to terminally differentiated cell play a significant role in reducing the incidence of cancer in that tissue. One specific mechanism by which this risk can be reduced is by minimizing the number of divisions—and hence the mutational risk—that cells accumulate as they divide to maintain tissue homeostasis. Here, we investigate a mathematical model of cell division in a hierarchical tissue, calculating and minimizing the divisional load while constraining parameters such that homeostasis is maintained. We show that the minimal divisional load is achieved by binary division trees with progenitor cells incapable of self-renewal. Contrary to the protection hypothesis, we find that an increased stem cell turnover can lead to lower divisional load. Furthermore, we find that the optimal tissue structure depends on the time horizon of the duration of homeostasis, with faster stem cell division favoured in short-lived organisms and more progenitor compartments favoured in longer-lived organisms.

Differentiation of leukemic blasts is not completely blocked in acute myeloid leukemia

Hematopoiesis, the formation of blood cells, involves the hierarchical differentiation of immature blast cells into mature, functional cell types and lineages of the immune system. Hematopoietic stem cells precisely regulate self-renewal versus differentiation to balance the production of blood cells and maintenance of the stem cell pool. The canonical view of acute myeloid leukemia (AML) is that it results from a combination of molecular events in a hematopoietic stem cell that block differentiation and drive proliferation. These events result in the accumulation of primitive hematopoietic blast cells in the blood and bone marrow. We used mathematical modeling to determine the impact of varying differentiation rates on myeloblastic accumulation. Our model shows that, instead of the commonly held belief that AML results from a complete block of differentiation of the hematopoietic stem cell, even a slight skewing of the fraction of cells that differentiate would produce an accumulation of blasts. We confirmed this model by interphase fluorescent in situ hybridization (FISH) and sequencing of purified cell populations from patients with AML, which showed that different leukemia-causing molecular abnormalities typically thought to block differentiation were consistently present in mature myeloid cells such as neutrophils and monocytes at similar levels to those in immature myeloid cells. These findings suggest reduced or skewed, rather than blocked, differentiation is responsible for the development of AML. Approaches that restore normal regulation of hematopoiesis could be effective treatment strategies.

The invasion of de-differentiating cancer cells into hierarchical tissues

Many fast renewing tissues are characterized by a hierarchical cellular architecture, with tissue specific stem cells at the root of the cellular hierarchy, differentiating into a whole range of specialized cells. There is increasing evidence that tumors are structured in a very similar way, mirroring the hierarchical structure of the host tissue. In some tissues, differentiated cells can also revert to the stem cell phenotype, which increases the risk that mutant cells lead to long lasting clones in the tissue. However, it is unclear under which circumstances de-differentiating cells will invade a tissue. To address this, we developed mathematical models to investigate how de-differentiation is selected as an adaptive mechanism in the context of cellular hierarchies. We derive thresholds for which de-differentiation is expected to emerge, and it is shown that the selection of de-differentiation is a result of the combination of the properties of cellular hierarchy and de-differentiation patterns. Our results suggest that de-differentiation is most likely to be favored provided stem cells having the largest effective self-renewal rate. Moreover, jumpwise de-differentiation provides a wider range of favorable conditions than stepwise de-differentiation. Finally, the effect of de-differentiation on the redistribution of self-renewal and differentiation probabilities also greatly influences the selection for de-differentiation.

How can a tissue such as the blood system or the skin, which constantly produces a huge number of cells, avoids that errors accumulate in the cells over time? Such tissues are typically organized in cellular hierarchies, which induce a directional relation between different stages of cellular differentiation, minimizing the risk of retention of mutations. However, recent evidence also shows that some differentiated cells can de-differentiate into the stem cell phenotype. Why does de-differentiation arise in some tumors, but not in others? We developed a mathematical model to study the growth competition between de-differentiating mutant cell populations and non de-differentiating resident cell population. Our results suggest that the invasion of de-differentiation is jointly influenced by the cellular hierarchy (e.g. number of cell compartments, inherent cell division pattern) and the de-differentiation pattern, i.e. how exactly cells acquire their stem-cell like properties.

COMPUTATIONAL MODELING OF LOW DOSE HYPER-RADIOSENSITIVITY AND INDUCED RADIORESISTANCE APPLYING THE PRINCIPLE OF MINIMUM MUTATION LOAD

Low dose hyper-radiosensitivity (HRS) and induced radioresistance (IRR) can be observed in the dose dependence of survival of many different cell lines. While surviving fraction decreases exponentially in a large-scale view, a local minimum can be found at around 0.5 Gy. Although, there is evidence that the regulation of apoptosis and DNA repair are involved in HRS and IRR, the fundamental causes of the phenomena remain unclear. The objective of the present study is to test whether the principle of minimum mutation load can provide an explanation for both low dose HRS and IRR. For this purpose, a mathematical model was elaborated considering radiation induced mutagenic DNA lesions as well as cell divisions as sources of mutations. It was presumed that cell number is in dynamic equilibrium in the tissue, the number of mutations follows Poisson distribution, and its average is proportional to absorbed dose. For each value of absorbed dose, the minimum number of mutations were computed for different surviving fractions. Then that surviving fraction was plotted that results in the lowest number of mutations. One minimum or multiple minima can be seen in the dose dependence of surviving fractions with reasonable values for the model parameters: spontaneous and radiation induced mutation rate. Although the mechanisms remain unclear, the principle of minimum mutation load provides a potential explanation for low dose HRS and IRR and for the fact that they are mostly observed in cell lines with defected DNA repair.

The role of telomere shortening in carcinogenesis: A hybrid stochastic-deterministic approach

Genome instability is a characteristic of most cancers, contributing to the acquisition of genetic alterations that drive tumor progression. One important source of genome instability is linked to telomere dysfunction in cells with critically short telomeres that lack p53-mediated surveillance of genomic integrity. Here we research the probability that cancer emerges through an evolutionary pathway that includes a telomere-induced phase of genome instability. To implement our models we use a hybrid stochastic-deterministic approach, which allows us to perform large numbers of simulations using biologically realistic population sizes and mutation rates, circumventing the traditional limitations of fully stochastic algorithms. The hybrid methodology should be easily adaptable to a wide range of evolutionary problems. In particular, we model telomere shortening and the acquisition of two mutations: Telomerase activation and p53 inactivation. We find that the death rate of unstable cells, and the number of cell divisions that p53 mutants can sustain beyond the normal senescence setpoint determine the likelihood that the first double mutant originates in a cell with telomere-induced instability. The model has applications to an influential telomerase-null mouse model and p16 silenced human cells. We end by discussing algorithmic performance and a measure for the accuracy of the hybrid approximation.

Variation of mutational burden in healthy human tissues suggests non-random strand segregation and allows measuring somatic mutation rates

The immortal strand hypothesis poses that stem cells could produce differentiated progeny while conserving the original template strand, thus avoiding accumulating somatic mutations. However, quantitating the extent of non-random DNA strand segregation in human stem cells remains difficult in vivo. Here we show that the change of the mean and variance of the mutational burden with age in healthy human tissues allows estimating strand segregation probabilities and somatic mutation rates. We analysed deep sequencing data from healthy human colon, small intestine, liver, skin and brain. We found highly effective non-random DNA strand segregation in all adult tissues (mean strand segregation probability: 0.98, standard error bounds (0.97,0.99)). In contrast, non-random strand segregation efficiency is reduced to 0.87 (0.78,0.88) in neural tissue during early development, suggesting stem cell pool expansions due to symmetric self-renewal. Healthy somatic mutation rates differed across tissue types, ranging from 3.5 × 10-9/bp/division in small intestine to 1.6 × 10-7/bp/division in skin.

Optimizing homeostatic cell renewal in hierarchical tissues

In order to maintain homeostasis, mature cells removed from the top compartment of hierarchical tissues have to be replenished by means of differentiation and self-renewal events happening in the more primitive compartments. As each cell division is associated with a risk of mutation, cell division patterns have to be optimized, in order to minimize or delay the risk of malignancy generation. Here we study this optimization problem, focusing on the role of division tree length, that is, the number of layers of cells activated in response to the loss of terminally differentiated cells, which is related to the balance between differentiation and self-renewal events in the compartments. Using both analytical methods and stochastic simulations in a metapopulation-style model, we find that shorter division trees are advantageous if the objective is to minimize the total number of one-hit mutants in the cell population. Longer division trees on the other hand minimize the accumulation of two-hit mutants, which is a more likely evolutionary goal given the key role played by tumor suppressor genes in cancer initiation. While division tree length is the most important property determining mutant accumulation, we also find that increasing the size of primitive compartments helps to delay two-hit mutant generation.

Cells in multicellular organisms are organized hierarchically. A stem cell gives rise to a chain of dividing and progressively differentiating offspring. At the end of this chain (called a lineage) are terminally differentiated cells that perform their function and undergo programmed cell death, to be replaced by new divisions of less differentiated cells. Here we are interested in the design of such lineages. At one extreme, one can imagine that a loss of terminally differentiated cells only results in divisions of cells in close hierarchical proximity to them, giving rise to very short division trees. On the other hand, it is possible that a long chain of increasingly primitive cells gets activated in response to the loss of differentiated cells. We expect that an important type of selection pressure acting upon tissue design is the minimization of mutations that happen in the course of everyday tissue maintenance (homeostasis). For example, tumor suppressor gene inactivation (two consecutive mutations) is an early rate-limiting step in many cancers. Using mathematical and computational methods, we find that the length of division trees is anti-correlated with the likelihood of double mutations, and lengthening the trees may provide an evolutionary advantage to the organism by delaying the onset of cancer.

Adaptive self-organization in the embryo: its importance to adult anatomy and to tissue engineering

The anatomy of healthy humans shows much minor variation, and twin‐studies reveal at least some of this variation cannot be explained genetically. A plausible explanation is that fine‐scale anatomy is not specified directly in a genetic programme, but emerges from self‐organizing behaviours of cells that, for example, place a new capillary where it happens to be needed to prevent local hypoxia. Self‐organizing behaviour can be identified by manipulating growing tissues (e.g. putting them under a spatial constraint) and observing an adaptive change that conserves the character of the normal tissue while altering its precise anatomy. Self‐organization can be practically useful in tissue engineering but it is limited; generally, it is good for producing realistic small‐scale anatomy but large‐scale features will be missing. This is because self‐organizing organoids miss critical symmetry‐breaking influences present in the embryo: simulating these artificially, for example, with local signal sources, makes anatomy realistic even at large scales. A growing understanding of the mechanisms of self‐organization is now allowing synthetic biologists to take their first tentative steps towards constructing artificial multicellular systems that spontaneously organize themselves into patterns, which may soon be extended into three‐dimensional shapes.

Clonal dominance and transplantation dynamics in hematopoietic stem cell compartments

Hematopoietic stem cells in mammals are known to reside mostly in the bone marrow, but also transitively passage in small numbers in the blood. Experimental findings have suggested that they exist in a dynamic equilibrium, continuously migrating between these two compartments. Here we construct an individual-based mathematical model of this process, which is parametrised using existing empirical findings from mice. This approach allows us to quantify the amount of migration between the bone marrow niches and the peripheral blood. We use this model to investigate clonal hematopoiesis, which is a significant risk factor for hematologic cancers. We also analyse the engraftment of donor stem cells into non-conditioned and conditioned hosts, quantifying the impact of different treatment scenarios. The simplicity of the model permits a thorough mathematical analysis, providing deeper insights into the dynamics of both the model and of the real-world system. We predict the time taken for mutant clones to expand within a host, as well as chimerism levels that can be expected following transplantation therapy, and the probability that a preconditioned host is reconstituted by donor cells.

Clonal hematopoiesis—where mature myeloid cells in the blood deriving from a single stem cell are over-represented—is a major risk factor for overt hematologic malignancies. To quantify how likely this phenomena is, we combine existing observations with a novel stochastic model and extensive mathematical analysis. This approach allows us to observe the hidden dynamics of the hematopoietic system. We conclude that for a clone to be detectable within the lifetime of a mouse, it requires a selective advantage. I.e. the clonal expansion cannot be explained by neutral drift alone. Furthermore, we use our model to describe the dynamics of hematopoiesis after stem cell transplantation. In agreement with earlier findings, we observe that niche-space saturation decreases engraftment efficiency. We further discuss the implications of our findings for human hematopoiesis where the quantity and role of stem cells is frequently debated.

Should tissue structure suppress or amplify selection to minimize cancer risk?

Background

It has been frequently argued that tissues evolved to suppress the accumulation of growth enhancing cancer inducing mutations. A prominent example is the hierarchical structure of tissues with high cell turnover, where a small number of tissue specific stem cells produces a large number of specialized progeny during multiple differentiation steps. Another well known mechanism is the spatial organization of stem cell populations and it is thought that this organization suppresses fitness enhancing mutations. However, in small populations the suppression of advantageous mutations typically also implies an increased accumulation of deleterious mutations. Thus, it becomes an important question whether the suppression of potentially few advantageous mutations outweighs the combined effects of many deleterious mutations.

Results

We argue that the distribution of mutant fitness effects, e.g. the probability to hit a strong driver compared to many deleterious mutations, is crucial for the optimal organization of a cancer suppressing tissue architecture and should be taken into account in arguments for the evolution of such tissues.

Conclusion

We show that for systems that are composed of few cells reflecting the typical organization of a stem cell niche, amplification or suppression of selection can arise from subtle changes in the architecture. Moreover, we discuss special tissue structures that can suppress most types of non-neutral mutations simultaneously.

Reviewers

This article was reviewed by Benjamin Allen, Andreas Deutsch and Ignacio Rodriguez-Brenes. For the full reviews, please go to the Reviewers’ comments section.

A morphospace for synthetic organs and organoids: the possible and the actual

Efforts in evolutionary developmental biology have shed light on how organs are developed and why evolution has selected some structures instead of others. These advances in the understanding of organogenesis along with the most recent techniques of organotypic cultures, tissue bioprinting and synthetic biology provide the tools to hack the physical and genetic constraints in organ development, thus opening new avenues for research in the form of completely designed or merely altered settings. Here we propose a unifying framework that connects the concept of morphospace (i.e. the space of possible structures) with synthetic biology and tissue engineering. We aim for a synthesis that incorporates our understanding of both evolutionary and architectural constraints and can be used as a guide for exploring alternative design principles to build artificial organs and organoids. We present a three-dimensional morphospace incorporating three key features associated to organ and organoid complexity. The axes of this space include the degree of complexity introduced by developmental mechanisms required to build the structure, its potential to store and react to information and the underlying physical state. We suggest that a large fraction of this space is empty, and that the void might offer clues for alternative ways of designing and even inventing new organs.

The Cancer Stem Cell Fraction in Hierarchically Organized Tumors Can Be Estimated Using Mathematical Modeling and Patient-Specific Treatment Trajectories

Many tumors are hierarchically organized and driven by a subpopulation of tumor-initiating cells (TIC), or cancer stem cells. TICs are uniquely capable of recapitulating the tumor and are thought to be highly resistant to radio- and chemotherapy. Macroscopic patterns of tumor expansion before treatment and tumor regression during treatment are tied to the dynamics of TICs. Until now, the quantitative information about the fraction of TICs from macroscopic tumor burden trajectories could not be inferred. In this study, we generated a quantitative method based on a mathematical model that describes hierarchically organized tumor dynamics and patient-derived tumor burden information. The method identifies two characteristic equilibrium TIC regimes during expansion and regression. We show that tumor expansion and regression curves can be leveraged to infer estimates of the TIC fraction in individual patients at detection and after continued therapy. Furthermore, our method is parameter-free; it solely requires the knowledge of a patient's tumor burden over multiple time points to reveal microscopic properties of the malignancy. We demonstrate proof of concept in the case of chronic myeloid leukemia (CML), wherein our model recapitulated the clinical history of the disease in two independent patient cohorts. On the basis of patient-specific treatment responses in CML, we predict that after one year of targeted treatment, the fraction of TICs increases 100-fold and continues to increase up to 1,000-fold after 5 years of treatment. Our novel framework may significantly influence the implementation of personalized treatment strategies and has the potential for rapid translation into the clinic. Cancer Res; 76(7); 1705-13. ©2016 AACR.

Wide-field tissue polarimetry allows efficient localized mass spectrometry imaging of biological tissues

While mass spectrometers can detect chemical signatures within milliseconds of data acquisition time, the non-targeted nature of mass spectrometry imaging (MSI) necessitates probing the entire surface of the sample to reveal molecular composition even if the information is only sought from a sample subsection. This leads to long analysis times. Here, we used polarimetry to identify, within a biological tissue, areas of polarimetric heterogeneity indicative of cancer. We were then able to target our MS analysis using polarimetry results to either the cancer region itself or to the cancer margin. A tandem of polarimetry and Desorption Electrospray Ionization Mass Spectrometry Imaging (DESI-MSI) enables fast (10 fold compared to non-targeted imaging), and accurate pathology assessment (cancer typification in less than 2 minutes compared to 30 minutes for histopathology) of ex vivo tissue slices, without additional sample preparation. This workflow reduces the overall analysis time of MSI as a research tool.

Quantifying replicative senescence as a tumor suppressor pathway and a target for cancer therapy

To study quantitatively replicative senescence as a tumor suppressor mechanism, we investigate the distribution of a growing clonal cell population restricted by Hayflick’s limit. We find that in the biologically relevant range of parameters, if the imbalance between cell division and death is moderate or low (high death-to-birth ratio), senescence offers significant protection against cancer by halting abnormal cell proliferation at early pre-diagnostic stages of tumor development. We also find that by the time tumors are typically detected, there is a high probability that telomerase is activated, even if the cell of origin was telomerase negative. Hence, the fact that most cancers are positive for telomerase is not necessarily an indication that cancer originated in a telomerase positive cell. Finally, we discuss how the population dynamics of cells can determine the outcomes of anti-telomerase cancer therapies, and provide guidelines on how the model could potentially be applied to develop clinically useful tools to predict the response to treatment by telomerase inhibitors in individual patients.

Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions

We investigate the in vivo patterns of stem cell divisions in the human hematopoietic system throughout life. In particular, we analyze the shape of telomere length distributions underlying stem cell behavior within individuals. Our mathematical model shows that these distributions contain a fingerprint of the progressive telomere loss and the fraction of symmetric cell proliferations. Our predictions are tested against measured telomere length distributions in humans across all ages, collected from lymphocyte and granulocyte sorted telomere length data of 356 healthy individuals, including 47 cord blood and 28 bone marrow samples. We find an increasing stem cell pool during childhood and adolescence and an approximately maintained stem cell population in adults. Furthermore, our method is able to detect individual differences from a single tissue sample, i.e. a single snapshot. Prospectively, this allows us to compare cell proliferation between individuals and identify abnormal stem cell dynamics, which affects the risk of stem cell related diseases.

Toward an evolutionary model of cancer: Considering the mechanisms that govern the fate of somatic mutations

Our understanding of cancer has greatly advanced since Nordling [Nordling CO (1953) Br J Cancer 7(1):68-72] and Armitage and Doll [Armitage P, Doll R (1954) Br J Cancer 8(1):1-12] put forth the multistage model of carcinogenesis. However, a number of observations remain poorly understood from the standpoint of this paradigm in its contemporary state. These observations include the similar age-dependent exponential rise in incidence of cancers originating from stem/progenitor pools differing drastically in size, age-dependent cell division profiles, and compartmentalization. This common incidence pattern is characteristic of cancers requiring different numbers of oncogenic mutations, and it scales to very divergent life spans of mammalian species. Also, bigger mammals with larger underlying stem cell pools are not proportionally more prone to cancer, an observation known as Peto's paradox. Here, we present a number of factors beyond the occurrence of oncogenic mutations that are unaccounted for in the current model of cancer development but should have significant impacts on cancer incidence. Furthermore, we propose a revision of the current understanding for how oncogenic and other functional somatic mutations affect cellular fitness. We present evidence, substantiated by evolutionary theory, demonstrating that fitness is a dynamic environment-dependent property of a phenotype and that oncogenic mutations should have vastly different fitness effects on somatic cells dependent on the tissue microenvironment in an age-dependent manner. Combined, this evidence provides a firm basis for understanding the age-dependent incidence of cancers as driven by age-altered systemic processes regulated above the cell level.

Characterizing inhibited tumor growth in stem-cell-driven non-spatial cancers

Healthy human tissue is highly regulated to maintain homeostasis. Secreted negative feedback factors that inhibit stem cell division and stem cell self-renewal play a fundamental role in establishing this control. The appearance of abnormal cancerous growth requires an escape from these regulatory mechanisms. In a previous study we found that for non-solid tumors if feedback inhibition on stem cell self-renewal is lost, but the feedback on the division rate is still intact, then the tumor dynamics are characterized by a relatively slow sub-exponential growth that we called inhibited growth. Here we characterize the cell dynamics of inhibited cancer growth by modeling feedback inhibition using Hill equations. We find asymptotic approximations for the growth rates of the stem cell and differentiated cell populations in terms of the strength of the inhibitory signal: stem cells grow as a power law t(1/k+1),and the differentiated cells grow as t(1/k), where k is the Hill coefficient in the feedback law regulating cell divisions. It follows that as the tumor grows, undifferentiated cells take up an increasingly large fraction of the population. Implications of these results for specific cancers including CML are discussed. Understanding how the regulatory mechanisms that continue to operate in cancer affect the rate of disease progression can provide important insights relevant to chronic or other slow progressing types of cancer.

Preventing clonal evolutionary processes in cancer: Insights from mathematical models

Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.

Organismal stress, telomeres and life histories

Most organisms, including ourselves, are exposed to environmental stressors at various points during life, and responses to such stressors have been optimised by evolution to give the best fitness outcomes. It is expected that environmental change will substantially increase long-term stress exposure in many animal groups in the coming decades. A major challenge for biologists is to understand and predict how this will influence individuals, populations and ecosystems, and over what time scale such effects will occur. This requires a multi-disciplinary approach, combining studies of mechanisms with studies of fitness consequences for individuals and their descendants. In this review, I discuss the positive and negative fitness consequences of responses to stressful environments, particularly during early life, and with an emphasis on studies in birds. As many of the mechanisms underlying stress responses are highly conserved across the vertebrate groups, the findings from these studies have general applicability when interpreted in a life history context. One important route that has recently been identified whereby chronic stress exposure can affect health and longevity over long time frames is via effects on telomere dynamics. Much of this work has so far been done on humans, and is correlational in nature, but studies on other taxa, and experimental work, are increasing. I summarise the relevant aspects of vertebrate telomere biology and critically appraise our current knowledge with a view to pointing out important future research directions for our understanding of how stress exposure influences life histories.

A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis--a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division--we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.

Robustness of differentiation cascades with symmetric stem cell division

Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.

Cancer-associated mutations in healthy individuals: assessing the risk of carcinogenesis

Mutations associated with hematopoietic malignancies have been repeatedly identified in healthy individuals. For certain cases, such as the t(14;18) translocation and monoclonal B-cell lymphocytosis, no clear link between the presence of aberrant cells and the later development of cancer has been established. Intriguingly, longitudinal studies suggest that these abnormalities persist for long periods of time in some individuals, but in others are transient in which they disappear completely. Here, we present a mathematical model, based on cellular replication limits, that provides a possible explanation for these seemingly contradictory findings. It proposes that the transient and persistent nature of the phenotypes depends on the stage in the differentiation pathway of a given lineage in which the mutation originates. Our work suggests that cellular replication limits may not only prevent cancer by aborting clonal expansion of cells, but also by influencing the fate of altered but nonneoplastic cells in healthy tissue.