Stem Cell Population Dynamics Research Articles

Regulation of stem cell dynamics through volume exclusion

The maintenance and regeneration of adult tissues rely on the self-renewal of stem cells. Regeneration without over-proliferation requires precise regulation of the stem cell proliferation and differentiation rates. The nature of such regulatory mechanisms in different tissues, and how to incorporate them in models of stem cell population dynamics, is incompletely understood. The critical birth-death (CBD) process is widely used to model stem cell populations, capturing key phenomena, such as scaling laws in clone size distributions. However, the CBD process neglects regulatory mechanisms. Here, we propose the birth-death process with volume exclusion (vBD), a variation of the birth-death process that considers crowding effects, such as may arise due to limited space in a stem cell niche. While the deterministic rate equations predict a single non-trivial attracting steady state, the master equation predicts extinction and transient distributions of stem cell numbers with three possible behaviours: long-lived quasi-steady state (QSS), and short-lived bimodal or unimodal distributions. In all cases, we approximate solutions to the vBD master equation using a renormalized system-size expansion, QSS approximation and the Wentzel–Kramers–Brillouin method. Our study suggests that the size distribution of a stem cell population bears signatures that are useful to detect negative feedback mediated via volume exclusion.

Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network

<abstract><p>In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity $ \mathcal{R}_{0} $ to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely $ (i) $ free equilibrium points, $ (ii) $ absence of stem and progenitor cells, and $ (iii) $ endemic equilibrium points are investigated in this study. The model is first formulated in non-fractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.</p></abstract>

Computational tools for assessing gene therapy under branching process models of mutation.

Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical interest as insertional mutagenesis carries the potential threat of leukemogenesis following gene therapy with autologous stem cell transplantation. In this paper, we develop a three-type branching process model describing accumulations of mutations in a population of stem cells distinguished by their ability for long-term self-renewal. Our outcome of interest is the appearance of a double-mutant cell, which carries a high potential for leukemic transformation. In our model, a single-hit mutation carries a slight proliferative advantage over a wild-type stem cells. We compute marginalized transition probabilities that allow us to capture important quantitative aspects of our model, including the probability of observing a double-hit mutant and relevant moments of a single-hit mutation population over time. We thoroughly explore the model behavior numerically, varying birth rates across the initial sizes and populations of wild type stem cells and single-hit mutants, and compare the probability of observing a double-hit mutant under these conditions. We find that increasing the number of single-mutants over wild-type particles initially present has a large effect on the occurrence of a double-mutant, and that it is relatively safe for single-mutants to be quite proliferative, provided the lentiviral gene addition avoids creating single mutants in the original insertion process. Our approach is broadly applicable to an important set of questions in cancer modeling and other population processes involving multiple stages, compartments, or types.

Fractional model of stem cell population dynamics

Abstract We develop the fractional model of stem cell population dynamics with state-dependent and time-dependent delays. In this model, the stem cell division rate and self-renewal rate are controlled by an external signal, depending on the effects of the environment’s heterogeneity. We quantify a relationship between the fractional derivative order, which shows the effects of the environment’s heterogeneity and stem cell division and stem cell self-renewal rate. We consider a general form of the fractional neutral delay differential equations with state-dependent and time-dependent delay to study this relationship. First, we show the solution’s existence and uniqueness using the fixed point theorem on the Banach space. We define a completely continuous operator on the non-empty closed convex set to use the fixed point theorem on the Banach space and show this operator has a uniquely defined fixed point. Also, we proof the Ulam–Hyers stability to make sure a close exact solution could be reached using the numerical approximation. Then, we develop a new numerical method based on Jacobi polynomials for solving the fractional neutral delay differential equations with state-dependent and time-dependent delay. We use the least-squares approximation of the candidate function to reduce the solution of fractional neutral delay differential equations to a set of algebraic equations and compare the results obtained by using different collocation points. We evaluate the accuracy of the numerical method, theoretically and numerically. We have used the numerical method to evaluate the fractional model’s behavior of stem cell population dynamics and quantify the relationship between the effects of the environment’s heterogeneity and the rate of stem cell division and stem cell self-renewal.

Epidermal structure and differentiation.

In this Primer, Moreci and Lechler follow the lifetime of an epidermal cell from its birth to its ultimate death, and detail how this journey is necessary for epidermal function.

Assessment of iron oxide nanoparticle ecotoxicity on regeneration and homeostasis in the replacement model system Schmidtea mediterranea_suppl

Iron oxide nanoparticles (IONs) are used in a number of applications from food to cosmetics and from medical applications to magnetic storage. In spite of the 550 tons produced each year in Europe alone, no effective dose limit recommendations are established and the overall risks connected to IONs are still debated. The incorporation of IONs in daily life raises a concern about their effects on the environment, on living organisms, and on human health. In this study, we used freshwater planarians to assess the nanoecotoxicity of IONs. Planarians are free-living invertebrates known for their astonishing regenerative ability. Because of their sensitivity to toxicants, they are often used to determine the effects of toxic, genotoxic, and carcinogenic environmental compounds with an approach in line with the 3Rs (Reduce, Refine, Replace) principle. Planarians were exposed to IONs at concentrations up to 1 mg/ml and their effects were evaluated at the behavioral, morphofunctional, and molecular levels, with a special emphasis on the regeneration process. Our results indicate that IONs did not affect the stem cell population dynamics, nor did they induce substantial changes in either homeostatic or regenerating planarians. As positive controls, gold nanoparticles coated with the pro-apoptotic anti-cancer drug hexadecylmethylammonium bromide and highly concentrated polystyrene nanoparticles were used; these all elicited toxic effects. Therefore, we conclude that IONs at environmental concen­trations are safe for planarians, and that the planarian is a powerful model system that can replace vertebrate animal models in nanoecotoxicology research and for nanoecotoxicology studies.

Assessment of iron oxide nanoparticle ecotoxicity on regeneration and homeostasis in the replacement model system Schmidtea mediterranea.

Iron oxide nanoparticles (IONs) are used in a number of applications, from food to cosmetics, from medical applications to magnetic storage. In spite of the 550 tons produced each year in Europe alone, no effective dose limit recommendations are established and the overall risks connected to IONs are still debated. The incorporation of IONs in daily life raises a concern about their effects on the environment, on living organisms, and on human health. In this study, we used freshwater planarians to assess the nanoecotoxicity of IONs. Planarians are free-living invertebrates known for their astonishing regenerative ability. Because of their sensitivity to toxicants, they are often used to determine the effects of toxic, genotoxic and carcinogenic environmental compounds with an approach in line with the 3Rs (Reduce, Refine, Replace) principle. Planarians were exposed to IONs at concentrations up to 1 mg/mL and their effects were evaluated at the behavioral, morphofunctional and molecular levels, with a special emphasis on the regeneration process. Our results indicate that IONs did not affect the stem cell population dynamics, nor did they induce substantial changes in either homeostatic or regenerating planarians. As positive controls, gold nanoparticles coated with the pro-apoptotic anti-cancer drug hexadecylmethylammonium bromide, silver nanoparticles and highly concentrated polystyrene nanoparticles were used. These all elicited toxic effects. Therefore, we conclude that IONs at environmental concentrations are safe for planarians, and that the planarian is a powerful model system that can replace vertebrate animal models in nanoecotoxicology research and for nanoecotoxicology studies.

FZD4 Marks Lateral Plate Mesoderm and Signals with NORRIN to Increase Cardiomyocyte Induction from Pluripotent Stem Cell-Derived Cardiac Progenitors.

SummaryThe identification of cell surface proteins on stem cells or stem cell derivatives is a key strategy for the functional characterization, isolation, and understanding of stem cell population dynamics. Here, using an integrated mass spectrometry- and microarray-based approach, we analyzed the surface proteome and transcriptome of cardiac progenitor cells (CPCs) generated from the stage-specific differentiation of mouse and human pluripotent stem cells. Through bioinformatics analysis, we have identified and characterized FZD4 as a marker for lateral plate mesoderm. Additionally, we utilized FZD4, in conjunction with FLK1 and PDGFRA, to further purify CPCs and increase cardiomyocyte (CM) enrichment in both mouse and human systems. Moreover, we have shown that NORRIN presented to FZD4 further increases CM output via proliferation through the canonical WNT pathway. Taken together, these findings demonstrate a role for FZD4 in mammalian cardiac development.

Modeling mechanical control of spindle orientation of intestinal crypt stem cells

Tissue development requires a control over the sequence of symmetric and asymmetric stem cell divisions to obtain the specific numbers of differentiated cells populating the tissue and stem cells residing in the niche. A good experimental model to study this process is the mouse intestinal crypt development, where it has been shown that stem cells follow an optimal strategy in which asymmetric division occurs only after all symmetric divisions have taken place to reach a fixed number of cells in the niche in the shortest time. Here we introduce a model of stem cell division that is able to explain the experimentally observed stem cell population dynamics by the effect of mechanical forces acting on the spindle. We also observe that the mechanically induced strategy for development is sub-optimal and crucially depends on the stiffness of the spindle. These findings highlight the crucial importance of mechanical forces for the development and maintenance of the intestinal crypt.

Single-cell gene expression analysis reveals diversity among human spermatogonia.

Is the molecular profile of human spermatogonia homogeneous or heterogeneous when analysed at the single-cell level? Heterogeneous expression profiles may be a key characteristic of human spermatogonia, supporting the existence of a heterogeneous stem cell population. Despite the fact that many studies have sought to identify specific markers for human spermatogonia, the molecular fingerprint of these cells remains hitherto unknown. Testicular tissues from patients with spermatogonial arrest (arrest, n = 1) and with qualitatively normal spermatogenesis (normal, n = 7) were selected from a pool of 179 consecutively obtained biopsies. Gene expression analyses of cell populations and single-cells (n = 105) were performed. Two OCT4-positive individual cells were selected for global transcriptional capture using shallow RNA-seq. Finally, expression of four candidate markers was assessed by immunohistochemistry. Histological analysis and blood hormone measurements for LH, FSH and testosterone were performed prior to testicular sample selection. Following enzymatic digestion of testicular tissues, differential plating and subsequent micromanipulation of individual cells was employed to enrich and isolate human spermatogonia, respectively. Endpoint analyses were qPCR analysis of cell populations and individual cells, shallow RNA-seq and immunohistochemical analyses. Unexpectedly, single-cell expression data from the arrest patient (20 cells) showed heterogeneous expression profiles. Also, from patients with normal spermatogenesis, heterogeneous expression patterns of undifferentiated (OCT4, UTF1 and MAGE A4) and differentiated marker genes (BOLL and PRM2) were obtained within each spermatogonia cluster (13 clusters with 85 cells). Shallow RNA-seq analysis of individual human spermatogonia was validated, and a spermatogonia-specific heterogeneous protein expression of selected candidate markers (DDX5, TSPY1, EEF1A1 and NGN3) was demonstrated. The heterogeneity of human spermatogonia at the RNA and protein levels is a snapshot. To further assess the functional meaning of this heterogeneity and the dynamics of stem cell populations, approaches need to be developed to facilitate the repeated analysis of individual cells. Our data suggest that heterogeneous expression profiles may be a key characteristic of human spermatogonia, supporting the model of a heterogeneous stem cell population. Future studies will assess the dynamics of spermatogonial populations in fertile and infertile patients. RNA-seq data is published in the GEO database: GSE91063. This work was supported by the Max Planck Society and the Deutsche Forschungsgemeinschaft DFG-Research Unit FOR 1041 Germ Cell Potential (grant numbers SCHO 340/7-1, SCHL394/11-2). The authors declare that there is no conflict of interest.

Maternal-fetal conflict, genomic imprinting and mammalian vulnerabilities to cancer.

Antagonistic coevolution between maternal and fetal genes, and between maternally and paternally derived genes may have increased mammalian vulnerability to cancer. Placental trophoblast has evolved to invade maternal tissues and evade structural and immunological constraints on its invasion. These adaptations can be co-opted by cancer in intrasomatic selection. Imprinted genes of maternal and paternal origin favour different degrees of proliferation of particular cell types in which they reside. As a result, the set of genes favouring greater proliferation will be selected to evade controls on cell-cycle progression imposed by the set of genes favouring lesser proliferation. The dynamics of stem cell populations will be a particular focus of this intragenomic conflict. Gene networks that are battlegrounds of intragenomic conflict are expected to be less robust than networks that evolve in the absence of conflict. By these processes, maternal-fetal and intragenomic conflicts may undermine evolved defences against cancer.

Analysis of stochastic stem cell models with control

Understanding the dynamics of stem cell lineages is of central importance both for healthy and cancerous tissues. We study stochastic population dynamics of stem cells and differentiated cells, where cell decisions, such as proliferation vs. differentiation decisions, or division and death decisions, are under regulation from surrounding cells. The goal is to understand how different types of control mechanisms affect the means and variances of cell numbers. We use the assumption of weak dependencies of the regulatory functions (the controls) on the cell populations near the equilibrium to formulate moment equations. We then study three different methods of closure, showing that they all lead to the same results for the highest order terms in the expressions for the moments. We derive simple explicit expressions for the means and the variances of stem cell and differentiated cell numbers. It turns out that the variance is expressed as an algebraic function of partial derivatives of the controls with respect to the population sizes at the equilibrium. We demonstrate that these findings are consistent with the results previously obtained in the context of particular systems, and also present two novel examples with negative and positive control of division and differentiation decisions. This methodology is formulated without any specific assumptions on the functional form of the controls, and thus can be used for any biological system.

Collective dynamics of stem cell populations

This year marks the 50th anniversary of the publication of a landmark paper in PNAS in which Till et al. proposed a remarkable model of stem cell proliferation (1). Their idea, based on assessment of colony-forming statistics in light of a mathematical model of a stochastic birth–death process, was that individual stem cell dynamics are inherently random. This surprising proposal quickly ignited a heated, and long-running, debate over stochastic and instructive models of stem cell behavior (2). In the intervening half century, many models of stem cell dynamics have been proposed, yet the mechanisms by which stem cell numbers and activity are regulated are still not completely understood. In PNAS, Lei et al. contribute an original idea to the ongoing discussion (3). Drawing on notions from evolutionary theory, they propose a general mathematical framework that views regulation of stem cell population activity as an optimization problem, which achieves best solution when there is cross-talk between genetic and epigenetic feedback mechanisms.

Two Discrete Stochastic Cellular Automata Models of Cancer Stem Cell Proliferation

 Abstract—Cancer stem cells (CSCs) are cancer cells that exhibit stem cell-like properties. They are immune to standard chemotherapy and are often implicated for relapse and metastasis. Modeling of CSC-caused relapse is difficult as organisms tend to die before the relapse can be studied, and thus in silico models are ideal but are in development. Two kinds of CSC-induced tumor growth were modeled mathematically and visually using the mass-action and spatial models. Mathematical models of population growth and a better understanding of cancer stem cell population dynamics and neural networks can be achieved by applying discrete stochastic models, automata theory, and cellular automaton. Due to its wide range of possibilities, cellular automata theory opens up new field of mathematical applications in cancer modeling and providing a bridge between bioinformatics and individualized cancer modeling.

A model of stem cell population dynamics: in silico analysis and in vivo validation

The proper renewal and maintenance of tissues by stem cell populations is simultaneously influenced by anatomical constraints, cell proliferation dynamics and cell fate specification. However, their relative influence is difficult to examine in vivo. To address this difficulty we built, as a test case, a cell-centered state-based computational model of key behaviors that govern germline development in C. elegans, and used it to drive simulations of cell population dynamics under a variety of perturbations. Our analysis provided unexpected possible explanations for laboratory observations, including certain ‘all-or-none’ phenotypes and complex differentiation patterns. The simulations also offered insights into niche-association dynamics and the interplay between cell cycle and cell fate. Subsequent experiments validated several predictions generated by the simulations. Notably, we found that early cell cycle defects influence later maintenance of the progenitor cell population. This general modeling approach is potentially applicable to other stem cell systems.

An insulin-like peptide regulates size and adult stem cells in planarians

Animal growth depends on nutritional intake during development. In many animals, nutritional status is uncoupled from moderation of adult stature after adult size is achieved. However, some long-lived animals continue to regulate adult size and fertility in a nutrition-dependent manner. For example, the regenerating flatworm Schmidtea mediterranea becomes smaller, or degrows, during periods of starvation. These animals provide an opportunity to readily observe adult stem cell population dynamics in response to nutritional cues. We explored the role of insulin signaling in S. mediterranea. We disrupted insulin signaling via RNA interference and showed that animals, despite eating, degrew similarly to starved animals. Utilizing in situ hybridization and immunofluorescence, we assessed cellular changes in proliferative populations including the planarian adult stem cell population (neoblasts) and the germline. Both impaired insulin signaling and nutritional deprivation correlated with decreased neoblast proliferation. Additionally, insulin signaling played a role in supporting spermatogenesis that was distinct from the effects of starvation. In sum, we have demonstrated that insulin signaling is responsible for regulation of adult animal size and tissue homeostasis in an organism with plastic adult size. Importantly, insulin signaling continued to affect stem cell and germline populations in a mature organism. Furthermore, we have shown that adult organisms can differentially regulate specific cell populations as a result of environmental challenges.

Stem Cell Niche Dynamics: From Homeostasis to Carcinogenesis

The stem cell microenvironment is involved in regulating the fate of the stem cell with respect to self-renewal, quiescence, and differentiation. Mathematical models are helpful in understanding how key pathways regulate the dynamics of stem cell maintenance and homeostasis. This tight regulation and maintenance of stem cell number is thought to break down during carcinogenesis. As a result, the stem cell niche has become a novel target of cancer therapeutics. Developing a quantitative understanding of the regulatory pathways that guide stem cell behavior will be vital to understanding how these systems change under conditions of stress, inflammation, and cancer initiation. Predictions from mathematical modeling can be used as a clinical tool to guide therapy design. We present a survey of mathematical models used to study stem cell population dynamics and stem cell niche regulation, both in the hematopoietic system and other tissues. Highlighting the quantitative aspects of stem cell biology, we describe compelling questions that can be addressed with modeling. Finally, we discuss experimental systems, most notably Drosophila, that can best be used to validate mathematical predictions.

A model of stem cell population dynamics: in silico analysis and in vivo validation

The proper renewal and maintenance of tissues by stem cell populations is simultaneously influenced by anatomical constraints, cell proliferation dynamics and cell fate specification. However, their relative influence is difficult to examine in vivo. To address this difficulty we built, as a test case, a cell-centered state-based computational model of key behaviors that govern germline development in C. elegans, and used it to drive simulations of cell population dynamics under a variety of perturbations. Our analysis provided unexpected possible explanations for laboratory observations, including certain 'all-or-none' phenotypes and complex differentiation patterns. The simulations also offered insights into niche-association dynamics and the interplay between cell cycle and cell fate. Subsequent experiments validated several predictions generated by the simulations. Notably, we found that early cell cycle defects influence later maintenance of the progenitor cell population. This general modeling approach is potentially applicable to other stem cell systems.

Stability analysis of multi-compartment models for cell production systems

We study two- and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result.

Abstract 4247: MicroRNA profile of the human colonic crypt base region is predictive of colon cancer

Abstract Dysregulation of crypt cell proliferation and differentiation has been implicated in the development of colorectal cancer (CRC). It is believed that human colonic crypt renewal involves programmed cellular proliferation initiated by a few (6-8) stem cells residing at or near the bottom of the crypt, and that stem cell (SC) overpopulation may be the key to CRC initiation. As part of our investigation of regulatory factors involved in the stem cell origin of CRC, we investigated the role that microRNAs (miRNAs) might play in colon carcinogenesis. miRNAs are RNAs 20-24 nucleotides long that were recently shown to modulate many cellular signaling pathways through post-transcriptional regulation of messenger RNA (mRNA) levels and thus protein synthesis. Our previous microarray analysis (368 gene chip) showed increased expression of 37 miRNAs in CRCs compared to normal colonic epithelium. Here we further evaluated miRNA expression in CRC versus purified colonic epithelium by quantitative PCR (QPCR). Total RNA was immediately isolated from tissue by the TrizolTM method. RNA was transcribed into first-strand complementary DNA (cDNA) through reverse transcription (RT). cDNA was then amplified through QPCR. Statistical analysis and plots of expression data for miRNAs were done to find miRNA genes that are differentially expressed. We found, using QPCR, five miRNAs to be differentially expressed in CRCs versus normal colonic epithelium including mir-25 and mir-198. Profiling of purified colonic crypt subregions showed that a distinct signature involving 16 differentially expressed miRNAs characterizes the crypt bottom. This miRNA signature of the crypt bottom was found to be predictive of CRC. Out of the sixteen, three miRNAs (mir-206, mir- 7 and mir-25) were independently capable to distinguish colorectal tissue from normal colonic epithelia (p<0.01). Because this subset of miRNAs is differentially expressed in the crypt bottom, where SC resides, they may be involved in regulating SC population dynamics and contribute to the SC origin of CRC. Further identification and characterization of miRNAs expressed specifically in SC and changes in their expression in CRCs will provide important information to help understand mechanisms of colon tumorigenesis. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 4247.