The protective role of symmetric stem cell division on the accumulation of heritable damage

Asymmetric stem cell division maintains the genetic heterogeneity of tissue cells

Within a given tissue, the stem cell niche provides the microenvironment for stem cells suitable for their self-renewal. Conceptually, the niche space constrains the size of a stem-cell pool, as the cells sharing the niche compete for its space. It has been suggested that either neutral- or non-neutral-competition of stem cells changes the clone dynamics of stem cells. Theoretically, if the rate of asymmetric division is high, the stem cell competition is limited, thus suppressing clonal expansion. However, the effects of asymmetric division on clone dynamics have never been experimentally tested. Here, using the Drosophila germline stem cell (GSC) system, as a simple model of the in-vivo niche, we examine the effect of division modes (asymmetric or symmetric) on clonal dynamics by combining experimental approaches with mathematical modeling. Our experimental data and computational model both suggest that the rate of asymmetric division is proportional to the time a stem cell clone takes to expand. Taken together, our data suggests that asymmetric division is essential for maintaining the genetic variation of stem cells and thus serves as a critical mechanism for safeguarding fertility over the animal age or preventing multiple disorders caused by the clonal expansion of stem cells.

How mutation accumulation depends on the structure of the cell lineage tree

All the cells of a multicellular organism are the product of cell divisions that trace out a single binary tree, the so-called cell lineage tree. Because cell divisions are accompanied by replication errors, the shape of the cell lineage tree is a key determinant of how somatic evolution, which can potentially lead to cancer, proceeds. Carcinogenesis requires the accumulation of a certain number of driver mutations. By mapping the accumulation of mutations into a graph theoretical problem, we present an exact numerical method to calculate the probability of collecting a given number of mutations and show that for low mutation rates it can be approximated with a simple analytical formula, which depends only on the distribution of the lineage lengths, and is dominated by the longest lineages. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms and curtail somatic evolution.

Stochastic stem cell models with mutation: A comparison of asymmetric and symmetric divisions

In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell division on the lifetime risk of cancer, and report that symmetric division is more beneficial to delay the onset of cancer. The fate uncertainty of symmetric division is considered to be the reason for the cancer-delaying effect. In this paper we compare asymmetric and symmetric divisions of stem cells via studying stochastic stem cell models with mutation. Specially, by using rigorous mathematical analysis we find that both the asymmetric and symmetric models show the same statistical average, but the symmetric model shows higher fluctuation than the asymmetric model. We further show that the difference between the two models would be more remarkable for lower mutation rates. Our work quantifies the uncertainty of cell division and highlights the significance of stochasticity for distinguishing between different modes of stem cell division.

Does Shoot Apical Meristem Function as the Germline in Safeguarding Against Excess of Mutations?

A genetic continuity of living organisms relies on the germline which is a specialized cell lineage producing gametes. Essential in the germline functioning is the protection of genetic information that is subjected to spontaneous mutations. Due to indeterminate growth, late specification of the germline, and unique longevity, plants are expected to accumulate somatic mutations during their lifetime that leads to decrease in individual and population fitness. However, protective mechanisms, similar to those in animals, exist in plant shoot apical meristem (SAM) allowing plants to reduce the accumulation and transmission of mutations. This review describes cellular- and tissue-level mechanisms related to spatio-temporal distribution of cell divisions, organization of stem cell lineages, and cell fate specification to argue that the SAM functions analogous to animal germline.

Modelling stem cell ageing: a multi-compartment continuum approach

Stem cells are important to generate all specialized tissues at an early life stage, and in some systems, they also have repair functions to replenish the adult tissues. Repeated cell divisions lead to the accumulation of molecular damage in stem cells, which are commonly recognized as drivers of ageing. In this paper, a novel model is proposed to integrate stem cell proliferation and differentiation with damage accumulation in the stem cell ageing process. A system of two structured PDEs is used to model the population densities of stem cells (including all multiple progenitors) and terminally differentiated (TD) cells. In this system, cell cycle progression and damage accumulation are modelled by continuous dynamics, and damage segregation between daughter cells is considered at each division. Analysis and numerical simulations are conducted to study the steady-state populations and stem cell damage distributions under different damage segregation strategies. Our simulations suggest that equal distribution of the damaging substance between stem cells in a symmetric renewal and less damage retention in stem cells in the asymmetric division are favourable strategies, which reduce the death rate of the stem cells and increase the TD cell populations. Moreover, asymmetric damage segregation in stem cells leads to less concentrated damage distribution in the stem cell population, which may be more robust to the stochastic changes in the damage. The feedback regulation from stem cells can reduce oscillations and population overshoot in the process, and improve the fitness of stem cells by increasing the percentage of cells with less damage in the stem cell population.

Exploring immuno-regulatory mechanisms in the tumor microenvironment: Model and design of protocols for cancer remission

The tumor microenvironment comprising of the immune cells and cytokines acts as the ‘soil’ that nourishes a developing tumor. Lack of a comprehensive study of the interactions of this tumor microenvironment with the heterogeneous sub-population of tumor cells that arise from the differentiation of Cancer Stem Cells (CSC), i.e. the ‘seed’, has limited our understanding of the development of drug resistance and treatment failures in Cancer. Based on this seed and soil hypothesis, for the very first time, we have captured the concept of CSC differentiation and tumor-immune interaction into a generic model that has been validated with known experimental data. Using this model we report that as the CSC differentiation shifts from symmetric to asymmetric pattern, resistant cancer cells start accumulating in the tumor that makes it refractory to therapeutic interventions. Model analyses unveiled the presence of feedback loops that establish the dual role of M2 macrophages in regulating tumor proliferation. The study further revealed oscillations in the tumor sub-populations in the presence of T_H1 derived IFN-γ that eliminates CSC; and the role of IL10 feedback in the regulation of T_H1/T_H2 ratio. These analyses expose important observations that are indicative of Cancer prognosis. Further, the model has been used for testing known treatment protocols to explore the reasons of failure of conventional treatment strategies and propose an improvised protocol that shows promising results in suppressing the proliferation of all the cellular sub-populations of the tumor and restoring a healthy T_H1/T_H2 ratio that assures better Cancer remission.

Control of cell fraction and population recovery during tissue regeneration in stem cell lineages

Multicellular tissues are continually turning over, and homeostasis is maintained through regulated proliferation and differentiation of stem cells and progenitors. Following tissue injury, a dramatic increase in cell proliferation is commonly observed, resulting in rapid restoration of tissue size. This regulation is thought to occur via multiple feedback loops acting on cell self-renewal or differentiation. Models of ordinary differential equations have been widely used to study the cell lineage system. Prior modeling studies have suggested that loss of homeostasis and initiation of tumorigenesis can be contributed to the loss of control of these processes, and the rate of symmetric versus asymmetric division of the stem cells may also be altered. While most of the previous works focused on analysis of stability, existence and uniqueness of steady states of multistage cell lineage models, in this work we attempt to understand the cell lineage model from a different perspective. We compare three variants of hierarchical stem cell lineage tissue models with different combinations of negative feedbacks and use sensitivity analysis to examine the possible strategies for the cells to achieve certain performance objectives. Our results suggest that multiple negative feedback loops must be present in the stem cell lineage to keep the fractions of stem cells to differentiated cells in the total population as robust as possible to variations in cell division parameters, and to minimize the time for tissue recovery in a non-oscillatory manner.

Cell dynamics in tumour environment after treatments

Most cancer treatments cause necrotic cell deaths in the tumour microenvironment. Necrotic cells send signals to immune cells to start the wound healing process in the tissue. Therefore, we assume after stopping treatments there is a wound that needs to be healed. We develop a simple computational model to investigate cell dynamics during the wound healing process after treatments. The model predicts that the involvement of high-fitness cancer cells in the wound healing leads to fast relapse, and cancer cells outside of the wound can cause a slow recurrence of the tumour. Therefore, the absence of relapse after treatments may imply a slow-developing tumour that might not reach an observable size in the patients' lifetime. Additionally, the model indicates that the location of remaining cancer cells after treatments is an important factor in the recurrence time. The fastest recurrence happens when high-fitness cancer cells remain inside of the wound. However, the longest time to recurrence corresponds to cancer cells located outside of the wound. Note that this model is the first attempt to study cell dynamics in the wound healing process after cancer treatments, and it has some limitations that might influence the results. Experiments are needed to validate the results.

The role of backward cell migration in two-hit mutants' production in the stem cell niche

It has been discovered that there are two stem cell groups in the intestinal crypts: central stem cells (CeSCs), which are at the very bottom of the crypt, and border stem cells (BSCs), which are located between CeSCs and transit amplifying cells (TAs). Moreover, backward cell migration from BSCs to CeSCs has been observed. Recently, a bi-compartmental stochastic model, which includes CeSCs and BSCs, has been developed to investigate the probability of two-hit mutant production in the stem cell niche. In this project, we improve this stochastic model by adding the probability of backward cell migration to the model. The model suggests that the probability of two-hit mutant production increases when the frequency of backward cell migration increases. Furthermore, a small non-zero probability of backward cell migration leads to the largest range of optimal values for the frequency of symmetric divisions and the portion of divisions at each stem cell compartment in terms of delaying 2-hit mutant production. Moreover, the probability of two-hit mutant production is more sensitive to the probability of symmetric divisions than to the rate of backward cell migrations. The highest probability of two-hit mutant production corresponds to the case when all stem cell’s divisions are asymmetric.

Mathematical models of cell phenotype regulation and reprogramming: Make cancer cells sensitive again!

A cell's phenotype is the observable actualization of complex interactions between its genome, epigenome, and local environment. While traditional views in cancer have held that cellular and tumor phenotypes are largely functions of genomic instability, increasing attention has recently been given to epigenetic and microenvironmental influences. Such non-genetic factors allow cancer cells to experience intrinsic diversity and plasticity, and at the tumor level can result in phenotypic heterogeneity and treatment evasion. In 2006, Takahashi and Yamanaka exploited the epigenome's plasticity by "reprogramming" differentiated cells into a pluripotent state by inducing expression of a cocktail of four transcription factors. Recent advances in cancer biology have shown not only that cellular reprogramming is possible for malignant cells, but it may provide a foundation for future therapies. Nevertheless, cell reprogramming experiments are frequently plagued by low efficiency, activation of aberrant transcriptional programs, instability, and often rely on expertise gathered from systems which may not translate directly to cancer. Here, we review a theoretical framework tracing back to Waddington's epigenetic landscape which may be used to derive quantitative and qualitative understanding of cellular reprogramming. Implications for tumor heterogeneity, evolution and adaptation are discussed in the context of designing new treatments to re-sensitize recalcitrant tumors. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

Modeling dynamics of mutants in heterogeneous stem cell niche

Studying the stem cell (SC) niche architecture is a crucial step for investigating the process of oncogenesis and obtaining an effective stem cell therapy for various cancers. Recently, it has been observed that there are two groups of SCs in the SC niche collaborating with each other to maintain tissue homeostasis: border stem cells (BSCs), which are responsible in controlling the number of non-stem cells as well as stem cells, and central stem cells (CeSCs), which regulate the SC niche. Here, we develop a bi-compartmental stochastic model for the SC niche to study the spread of mutants within the niche. The analytic calculations and numeric simulations, which are in perfect agreement, reveal that in order to delay the spread of mutants in the SC niche, a small but non-zero number of SC proliferations must occur in the CeSC compartment. Moreover, the migration of BSCs to CeSCs delays the spread of mutants. Furthermore, the fixation probability of mutants in the SC niche is independent of types of SC division as long as all SCs do not divide fully asymmetrically. Additionally, the progeny of CeSCs have a much higher chance than the progeny of BSCs to take over the entire niche.

Mathematical models of tissue stem and transit target cell divisions and the risk of radiation- or smoking-associated cancer

There is compelling biological data to suggest that cancer arises from a series of mutations in single target cells, resulting in defects in cell renewal and differentiation processes which lead to malignancy. Because much mutagenic damage is expressed following cell division, more-rapidly renewing tissues could be at higher risk because of the larger number of cell replications. Cairns suggested that renewing tissues may reduce cancer risk by partitioning the dividing cell populations into lineages comprising infrequently-dividing long-lived stem cells and frequently-dividing short-lived daughter transit cells. We develop generalizations of three recent cancer-induction models that account for the joint maintenance and renewal of stem and transit cells, also competing processes of partially transformed cell proliferation and differentiation/apoptosis. We are particularly interested in using these models to separately assess the probabilities of mutation and development of cancer associated with "spontaneous" processes and with those linked to a specific environmental mutagen, specifically ionizing radiation or cigarette smoking. All three models demonstrate substantial variation in cancer risks, by at least 20 orders of magnitude, depending on the assumed number of critical mutations required for cancer, and the stem-cell and transition-cell mutation rates. However, in most cases the conditional probabilities of cancer being mutagen-induced range between 7-96%. The relative risks associated with mutagen exposure compared to background rates are also stable, ranging from 1.0-16.0. Very few cancers, generally <0.5%, arise from mutations occurring solely in stem cells rather than in a combination of stem and transit cells. However, for cancers with 2 or 3 critical mutations, a substantial proportion of cancers, in some cases 100%, have at least one mutation derived from a mutated stem cell. Little difference is made to relative risks if competing processes of proliferation and differentiation in the partially transformed stem and transit cell population are allowed for, nor is any difference made if one assumes that transit cells require an extra mutation to confer malignancy from the number required by stem cells. The probability of a cancer being mutagen-induced correlates across cancer sites with the estimated cumulative number of stem cell divisions in the associated tissue (p<0.05), although in some cases there is sensitivity of findings to removal of high-leverage outliers and in some cases only modest variation in probability, but these issues do not affect the validity of the findings. There are no significant correlations (p>0.3) between lifetime cancer-site specific radiation risk and the probability of that cancer being mutagen-induced. These results do not depend on the assumed critical number of mutations leading to cancer, or on the assumed mutagen-associated mutation rate, within the generally-accepted ranges tested. However, there are borderline significant negative correlations (p = 0.08) between the smoking-associated mortality rate difference (current vs former smokers) and the probability of cancer being mutagen-induced. This is only the case where values of the critical number of mutations leading to cancer, k, is 3 or 4 and not for smaller values (1 or 2), but does not strongly depend on the assumed mutagen-associated mutation rate.

A miR-34a-Numb Feedforward Loop Triggered by Inflammation Regulates Asymmetric Stem Cell Division in Intestine and Colon Cancer

Emerging evidence suggests that microRNAs can initiate asymmetric division, but whether microRNA and protein cell fate determinants coordinate with each other remains unclear. Here, we show that miR-34a directly suppresses Numb in early-stage colon cancer stem cells (CCSCs), forming an incoherent feedforward loop (IFFL) targeting Notch to separate stem and non-stem cell fates robustly. Perturbation of the IFFL leads to a new intermediate cell population with plastic and ambiguous identity. Lgr5+ mouse intestinal/colon stem cells (ISCs) predominantly undergo symmetric division but turn on asymmetric division to curb the number of ISCs when proinflammatory response causes excessive proliferation. Deletion of miR-34a inhibits asymmetric division and exacerbates Lgr5+ ISC proliferation under such stress. Collectively, our data indicate that microRNA and protein cell fate determinants coordinate to enhance robustness of cell fate decision, and they provide a safeguard mechanism against stem cell proliferation induced by inflammation or oncogenic mutation.

The role of cell location and spatial gradients in the evolutionary dynamics of colon and intestinal crypts

BACKGROUND

Colon and intestinal crypts serve as an important model system for adult stem cell proliferation and differentiation. We develop a spatial stochastic model to study the rate of somatic evolution in a normal crypt, focusing on the production of two-hit mutants that inactivate a tumor suppressor gene. We investigate the effect of cell division pattern along the crypt on mutant production, assuming that the division rate of each cell depends on its location.

RESULTS

We find that higher probability of division at the bottom of the crypt, where the stem cells are located, leads to a higher rate of double-hit mutant production. The optimal case for delaying mutations occurs when most of the cell divisions happen at the top of the crypt. We further consider an optimization problem where the "evolutionary" penalty for double-hit mutant generation is complemented with a "functional" penalty that assures that fully differentiated cells at the top of the crypt cannot divide.

CONCLUSION

The trade-off between the two types of objectives leads to the selection of an intermediate division pattern, where the cells in the middle of the crypt divide with the highest rate. This matches the pattern of cell divisions obtained experimentally in murine crypts.

REVIEWERS

This article was reviewed by David Axelrod (nominated by an Editorial Board member, Marek Kimmel), Yang Kuang and Anna Marciniak-Czochra. For the full reviews, please go to the Reviewers' comments section.

Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques

Background

How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10¹¹ mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages.

Results

While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs.

Conclusions

Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-015-0191-8) contains supplementary material, which is available to authorized users.

The role of the bi-compartmental stem cell niche in delaying cancer

In recent years, by using modern imaging techniques, scientists have found evidence of collaboration between different types of stem cells (SCs), and proposed a bi-compartmental organization of the SC niche. Here we create a class of stochastic models to simulate the dynamics of such a heterogeneous SC niche. We consider two SC groups: the border compartment, S1, is in direct contact with transit-amplifying (TA) cells, and the central compartment, S2, is hierarchically upstream from S1. The S1 SCs differentiate or divide asymmetrically when the tissue needs TA cells. Both groups proliferate when the tissue requires SCs (thus maintaining homeostasis). There is an influx of S2 cells into the border compartment, either by migration, or by proliferation. We examine this model in the context of double-hit mutant generation, which is a rate-limiting step in the development of many cancers. We discover that this type of a cooperative pattern in the stem niche with two compartments leads to a significantly smaller rate of double-hit mutant production compared with a homogeneous, one-compartmental SC niche. Furthermore, the minimum probability of double-hit mutant generation corresponds to purely symmetric division of SCs, consistent with the literature. Finally, the optimal architecture (which minimizes the rate of double-hit mutant production) requires a large proliferation rate of S1 cells along with a small, but non-zero, proliferation rate of S2 cells. This result is remarkably similar to the niche structure described recently by several authors, where one of the two SC compartments was found more actively engaged in tissue homeostasis and turnover, while the other was characterized by higher levels of quiescence (but contributed strongly to injury recovery). Both numerical and analytical results are presented.

Stem cell regulation: Implications when differentiated cells regulate symmetric stem cell division

We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting because stem cells are less sensitive than differentiated cells to environmental factors, such as medical therapy. Our result implies that stem cells can be manipulated indirectly by medical treatments that target the differentiated cells.

Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases

Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be quantified by their population at a corresponding node within a network of states. Their dynamics across the state-space network involve genotypic or phenotypic transitions that can occur upon cell division, such as during symmetric or asymmetric cell differentiation, or upon spontaneous mutation. Here, we use a general multi-type branching processes to study first passage time statistics for a single cell to appear in a specific state. Our approach readily allows for nonexponentially distributed waiting times between transitions, reflecting, e.g., the cell cycle. For simplicity, we restrict most of our detailed analysis to exponentially distributed waiting times (Poisson processes). We present results for a sequential evolutionary process in which L successive transitions propel a population from a "wild-type" state to a given "terminally differentiated," "resistant," or "cancerous" state. Analytic and numeric results are also found for first passage times across an evolutionary chain containing a node with increased death or proliferation rate, representing a desert/bottleneck or an oasis. Processes involving cell proliferation are shown to be "nonlinear" (even though mean-field equations for the expected particle numbers are linear) resulting in first passage time statistics that depend on the position of the bottleneck or oasis. Our results highlight the sensitivity of stochastic measures to cell division fate and quantify the limitations of using certain approximations (such as the fixed-population and mean-field assumptions) in evaluating fixation times.