Optimal structure of heterogeneous stem cell niche: The importance of cell migration in delaying tumorigenesis

Leili Shahriyari, Ali Mahdipour Shirayeh

doi: http://dx.doi.org/10.1101/082982

This article is a preprint and has not been peer-reviewed [what does this mean?].

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Abstract

Studying the stem cell 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 stem cells in the stem cell niche collaborating with each other to maintain tissue homeostasis. One group comprises the border stem cells, which is responsible to control the number of non-stem cells as well as stem cells. The other group, central stem cells, regulates the stem cell niche. In the present study, we develop a bi-compartmental stochastic model for the stem cell 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 stem cell niche, a small but non-zero number of stem cell proliferations must occur in the central stem cell compartment. Moreover, the migration of border stem cells to the central stem cell compartment delays the spread of mutants. Furthermore, the fixation probability of mutants in the stem cell niche is independent of types of stem cell division as long as all stem cells do not divide fully asymmetrically. Additionally, the progeny of central stem cells have a much higher chance than the progeny of border stem cells to take over the entire niche.

http://biorxiv.org/content/early/2016/10/24/082982

The Evolutionary Trade-off between Stem Cell Niche Size, Aging, and Tumorigenesis

Vincent L. Cannataro, Scott A. McKinley, Colette M. St. Mary

Abstract

Many epithelial tissues within large multicellular organisms are continually replenished by small independent populations of stem cells. These stem cells divide within their niches and differentiate into the constituent cell types of the tissue, and are largely responsible for maintaining tissue homeostasis. Mutations can accumulate in stem cell niches and change the rate of stem cell division and differentiation, contributing to both aging and tumorigenesis. Here, we create a mathematical model of the intestinal stem cell niche, crypt system, and epithelium. We calculate the expected effect of fixed mutations in stem cell niches and their expected effect on tissue homeostasis throughout the intestinal epithelium over the lifetime of an organism. We find that, due to the small population size of stem cell niches, fixed mutations are expected to accumulate via genetic drift and decrease stem cell fitness, leading to niche and tissue attrition, and contributing to organismal aging. We also explore mutation accumulation at various stem cell niche sizes, and demonstrate that an evolutionary trade-off exists between niche size, tissue aging, and the risk of tumorigenesis; where niches exist at a size that minimizes the probability of tumorigenesis, at the expense of accumulating deleterious mutations due to genetic drift. Finally, we show that the probability of tumorigenesis and the extent of aging trade-off differently depending on whether mutational effects confer a selective advantage, or not, in the stem cell niche.

http://dx.doi.org/10.1101/059279

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Daniel Nichol, Mark Robertson-Tessi, Peter Jeavons, Alexander RA Anderson

Abstract

For the last few decades modern biology has focused on quantifying, understanding and mapping the genetic characteristics of cells. This genotype-driven perspective has led to significant advances in our understanding and treatment of diseases such as cancer e.g. the discovery of driver mutations and the development of molecularly-targeted therapeutics. However, this perspective has largely ignored the functional outcome of genetic changes: the cellular phenotype. In part, this is simply because phenotypes are neither easy to define or measure as they critically depend on both genotype and context. Heterogeneity at the gene scale has been known for sometime, and there has been significant effort invested in trying to find patterns within it, but much less is understood about how this heterogeneity manifests itself in phenotypic change, i.e. the genotype-phenotype map (GP-map). This mapping is not one-to-one but many-to-many and is fundamentally the junction at which both genes and environment meet to produce phenotypes. Many genotypes produce similar phenotypes, and multiple phenotypes can emerge from a single genotype. To further complicate matters, genetically identical cells in uniform environments still exhibit phenotypic heterogeneity. Therefore a central open question in biology today is how can we connect the abundance of genomic data with cell phenotypic behaviour, this is especially pertinent to the issue of treatment resistance as many therapies act on cellular phenotypes. Our focus here is to tackle the GP-map question through the use of the simplest functional mapping we can define that also captures phenotypic heterogeneity: a molecular switch. Molecular switches are ubiquitous in biology, observed in many organisms and naturally map molecular components to decisions (i.e. phenotypes). Often stochastic in nature, such switches can be the difference between life or death in environments that fluctuate unpredictably, since they will ensure that at least some offspring are adapted to future environments. For convenience we use Chemical Reaction Networks (CRNs) to define the map of gene products to phenotypes, allowing us to investigate the impact of distinct mappings (CRNs) and perturbations to them. We observe that key biological properties naturally emerge, including both robustness and persistence. Robustness may explain why such bet hedging strategies are common in biology, and not readily destroyed through mutation. Whereas persistence may explain the apparent paradox of bet-hedging - why does phenotypic hedging exist in environments beneficial to only one of the phenotypes, when selection necessarily acts against it? The structure of the molecular switch, itself subject to selection, can slow the loss of hedging to ensure a survival mechanism even against environmental catastrophes which are very rare. Critically, these properties when taken together have profound and significant implications for the emergence of treatment resistance, since the timescale of extinction depends heavily on the underlying GP-map.

doi: http://dx.doi.org/10.1101/042424

A non-local model for cancer stem cells and the tumor growth paradox

Iacopo Borsi, Antonio Fasano, Mario Primicerio, Thomas Hillen

The "tumor growth paradox" refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSC) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumor selects for CSC, thereby increasing the fitness of the tumor. In this paper we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumor growth and tumor spread. Such a model has never been analysed, and we prove results on local and global existence of solutions, their uniqueness and their boundedness. We show numerically that this model exhibits the tumor growth paradox for all parameters tested. This effect becomes more relevant for small renewal rate of the CSC.

http://biorxiv.org/content/early/2015/05/21/019604

 

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

Xiufang Chen, Yue Wang, Tianquan Feng, Ming Yi, Xingan Zhang, Da Zhou

(Submitted on 16 Mar 2015)

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which challenges the cellular hierarchy proposed by the conventional cancer stem cell (CSC) theory. Since the validity of the reversible model versus the hierarchical model of cancer cells is still experimentally debated, it is worthwhile to theoretically explore the dynamic behavior characterizing the reversible model in comparison of the hierarchical model. By comparing the two models in predicting the cell-state dynamics observed in biological experiments, our results imply that the reversible model has advantages over the hierarchical model in predicting both long-term stable and short-term transient dynamics of cancer cells. In particular, it is found that i) the reversible model can predict the phenotypic equilibrium better than the hierarchical model, namely, the stability of the phenotypic mixture of cancer cells is more rooted in the reversible model; ii) the reversible model can perform various types of overshoot behavior, whereas the hierarchical model can never predict the overshoot of CSCs proportion. These also indicate that the phenotypic equilibrium and overshoot can be good candidates to characterize the models with the reversible phenotypic plasticity.

http://arxiv.org/abs/1503.04558

Replicator Dynamics of of Cancer Stem Cell; Selection in the Presence of Differentiation and Plasticity

Kamran Kaveh, Mohammad Kohandel, Siv Sivaloganathan

(Submitted on 5 Nov 2014)

Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either symmetrically or asymmetrically. The selection dynamics of a mutant cancer stem cell should be investigated in the light of a stem cell proliferation hierarchy and presence of a non-stem cell population. By constructing a three-compartment Moran-type model composed of normal stem cells, mutant (cancer) stem cells and differentiated cells, we derive the replicator dynamics of stem cell frequencies where asymmetric differentiation and differentiated cell death rates are included in the model. We determine how these new factors change the conditions for a successful mutant invasion and discuss the variation on the steady state fraction of the population as different model parameters are changed. By including the phenotypic plasticity/dedifferentiation, in which a progenitor/differentiated cell can transform back into a cancer stem cell, we show that the effective fitness of mutant stem cells is not only determined by their proliferation and death rates but also according to their dedifferentiation potential. By numerically solving the model we derive the phase diagram of the advantageous and disadvantageous phases of cancer stem cells in the space of proliferation and dedifferentiation potentials. The result shows that at high enough dedifferentiation rates even a previously disadvantageous mutant can take over the population of normal stem cells. This observation has implications in different areas of cancer research including experimental observations that imply metastatic cancer stem cell types might have lower proliferation potential than other stem cell phenotypes while showing much more phenotypic plasticity and can undergo clonal expansion.

link: http://arxiv.org/abs/1411.1399 

Tumour Control Probability in Cancer Stem Cells Hypothesis

Tumour Control Probability in Cancer Stem 

Cells Hypothesis

A. Dhawan, M. Kohandel, R. P. Hill, S. Sivaloganathan

(Submitted on 19 Dec 2013)

The tumour control probability (TCP) is a formalism derived to compare various treatment regimens of radiation therapy, defined as the probability that given a prescribed dose of radiation, a tumour has been eradicated or controlled. In the traditional view of cancer, all cells share the ability to divide without limit and thus have the potential to generate a malignant tumour. However, an emerging notion is that only a sub-population of cells, the so-called cancer stem cells (CSCs), are responsible for the initiation and maintenance of the tumour. A key implication of the CSC hypothesis is that these cells must be eradicated to achieve cures, thus we define TCP_S as the probability of eradicating CSCs for a given dose of radiation. A cell surface protein expression profile, such as CD44high/CD24low for breast cancer, is often used as a biomarker to monitor CSCs enrichment. However, it is increasingly recognized that not all cells bearing this expression profile are necessarily CSCs, and in particular early generations of progenitor cells may share the same phenotype. Thus, due to the lack of a perfect biomarker for CSCs, we also define a novel measurable TCP_CD+, that is the probability of eliminating or controlling biomarker positive cells. Based on these definitions, we use stochastic methods and numerical simulations to compare the theoretical TCP_S and the measurable TCP_CD+. We also use the measurable TCP to compare the effect of various radiation protocols.

link: http://arxiv.org/abs/1312.5582

Investigating the relation between stochastic differentiation and homeostasis in intestinal crypts via multiscale modeling

Alex Graudenzi, Giulio Caravagna, Giovanni De Matteis, Marco Antoniotti

doi: 10.1101/000927

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ABSTRACT

Colorectal tumors originate and develop within intestinal crypts. Even though some of the essential phenomena that characterize crypt structure and dynamics have been effectively described in the past, the relation between the differentiation process and the overall crypt homeostasis is still partially understood. We here investigate this relation and other important biological phenomena by introducing a novel multiscale model that combines a morphological description of the crypt with a gene regulation model: the emergent dynamical behavior of the underlying gene regulatory network drives cell growth and differentiation processes, linking the two distinct spatio-temporal levels. The model relies on a few a priori assumptions, yet accounting for several key processes related to crypt functioning, such as: dynamic gene activation patterns, stochastic differentiation, signaling pathways ruling cell adhesion properties, cell displacement, cell growth, mitosis, apoptosis and the presence of biological noise. We show that this modeling approach captures the major dynamical phenomena that characterize the regular physiology of crypts, such as cell sorting, coordinate migration, dynamic turnover, stem cell niche maintenance and clonal expansion. All in all, the model suggests that the process of stochastic differentiation might be sufficient to drive the crypt to homeostasis, under certain crypt configurations. Besides, our approach allows to make precise quantitative inferences that, when possible, were matched to the current biological knowledge and it permits to investigate the role of gene-level perturbations, with reference to cancer development. We also remark the theoretical framework is general and may applied to different tissues, organs or organisms.

link: http://www.biorxiv.org/content/early/2013/11/25/000927

A multi-phenotypic cancer model with cell plasticity

Da Zhou, Yue Wang, Bin Wu

(Submitted on 25 Nov 2013)

The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. Based on our model, we theoretically explain the universality of the phenotypic equilibrium phenomena reported in various cancer cell lines. By applying our model to concrete biological examples with real experimental data, we show that cancer cell plasticity plays an essential role in transient regulation of cancer heterogeneity. Our work may pave the way for modeling and analyzing the cell population dynamics with cell plasticity.

http://arxiv.org/abs/1311.6222

Moderate stem cell telomere shortening rate postpones cancer onset in stochastic model

Simon Holbek, Kristian Moss Bendtsen, Jeppe Juul

(Submitted on 18 May 2013)

Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and, when they reach a critical length, the cell will enter permanent cell cycle arrest - a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably.
Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer free life span before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favour a shorter than optimal average cancer free life span in order to postpone cancer onset until late in life.

 Link to the arXiv.

Symmetric vs asymmetric stem cell divisions: an adaptation against cancer?

Interesting paper on the effect of different division patterns on the accumulation of mutations in tissue cells. In particular, symmetric vs asymmetric divisions are compared, and it is found that symmetric cell divisions could delay the accumulation or carcinogenic mutations and thus the development of cancer. 

Symmetric vs asymmetric stem cell divisions: an adaptation against cancer?

Leili Shahriyari, Natalia L. Komarova

 

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a sequence of two consecutive "hits", and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more differentiated cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.

Preprint: http://arxiv.org/abs/1305.0100 

A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues

A nice follow on paper to their recent work in PLoS Computational Biology studying the deterministic dynamics of mutant clones in hierarchically structured (stem cell-driven) populations.  They derive closed form solutions describing the make up and diversity of tissues derived from this architecture and show specifically that that dynamics of a hierarchically structured tissue suppress the possibility of multiply mutated cells, and discuss the ramifications of this in regards to acute lymphoblastic leukemia of childhood.

A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues

B. Werner, D. Dingli, A. Traulsen

(Submitted on 14 May 2013)

We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single clones. Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters.