Mathematical Modeling: Telomeres open a window on stem cell division

  1. Ignacio A Rodriguez-Brenes
  2. Dominik Wodarz  Is a corresponding author
  1. University of California Irvine, United States

Stem cells are undifferentiated cells that can develop into more specialized cells. There are two kinds of stem cells: embryonic stem cells and adult stem cells. Embryonic stem cells are active during early development and give rise to all the different cell types in the body. Adult stem cells are specific to each tissue and give rise to all the specialized cells in a particular tissue or organ. When a stem cell divides, each new cell has the potential to either remain a stem cell or differentiate into a more specialized type of cell (Figure 1A). However, it can be difficult to analyze these division patterns in humans. Now, in eLife, Benjamin Werner, Fabian Beier, Arne Traulsen and colleagues have used a mathematical model to reconstruct the dynamics of blood stem cells from measurements of telomere length (Werner et al., 2015).

Patterns of stem cell division and the protective role of telomeres.

(A) Stem cells can divide asymmetrically to produce a new stem cell and a non-stem cell that can differentiate to replace other types of cells that are lost from the tissue because of cell death (top). Stem cells can also divide symmetrically, producing two daughter stem cells (symmetric self-renewal, middle) or two non-stem cells (symmetric differentiation, bottom). (B) Telomeres are the regions of DNA that cap and protect the ends of linear chromosomes. Each time a cell divides the telomeres get shorter. When telomeres become too short, cell division stops.

Telomeres are lengths of DNA that cap both ends of linear chromosomes (Figure 1B), and they protect the chromosomes by preventing their natural ends from being interpreted as breaks in the DNA. During cell division, the enzymes that duplicate DNA cannot copy the very ends of chromosomes; this ‘end-replication problem’ is part of the reason why the telomeres get shorter each time a cell divides (Martinez and Blasco, 2015). When telomeres become very short, they lose their protective properties and cell division stops. This process is known as ‘replicative senescence’ and is correlated with aging: put simply, telomeres get shorter as people get older.

Replicative senescence is believed to have evolved as a means to curb excessive cell division, which is a hallmark of cancer. However, human cancers find ways to bypass this process, typically by expressing an enzyme called telomerase that acts to lengthen the telomeres. Telomerase is highly active in embryonic stem cells, but it is not expressed in most normal cells.

Werner, Beier, Traulsen and colleagues – who are based at the Max Planck Institute for Evolutionary Biology, RWTH Aachen University Hospital, University Hospital Zürich and the Mayo Clinic – measured the average telomere lengths from blood samples taken from 356 individuals aged between 0 and 85 years old. Two alternative models of stem cell dynamics were then analyzed. The first model considered that the stem cells only divide asymmetrically, producing one stem cell and one non-stem cell. The second model included both asymmetric cell division and symmetric self-renewal (where a stem cell divides to form two daughter stem cells; Figure 1A). Werner, Beier et al. found that the first model predicted a linear relationship between average telomere length and the donor’s age, whereas the second model predicted a nonlinear decrease in telomere length. The data strongly favored the second model.

The findings suggest that symmetric self-renewal is more frequent during adolescence. Since symmetric self-renewal could promote the accumulation of mutations (Tomasetti and Vogelstein, 2015), this has implications for understanding how cancer emerges. A previous theoretical study argued that the high number of cell divisions that occur during fetal development puts us at risk of acquiring mutations even before birth (Frank and Nowak, 2003). The new results extend this argument into childhood and adolescence. That is, before adulthood is reached, there is possibly a relatively high risk of acquiring mutations that may predispose an individual to cancer – even if the onset of cancer typically occurs much later in life.

An important question that arises from this study concerns the exact nature of the cell divisions that ensure tissue maintenance in adulthood. In the model of Werner, Beier et al., tissues are maintained in adulthood through asymmetric cell divisions. However, as they point out, this model cannot be mathematically distinguished from an alternative mechanism that relies on a mixture of symmetric self-renewal and symmetric differentiation (i.e., when the stem cell divides to produce two non-stem cells). This is because tissues can also be maintained if the probabilities of symmetric self-renewal and differentiation are balanced and controlled through feedback loops (Lander et al., 2009); this latter model is supported by stem cell data from both humans and other animals (see Shahryiari and Komarova, 2013 for references). Some mathematical models suggest that the prevalence of mutations depends on the division patterns, so it may be possible to distinguish between them mathematically (Shahryiari and Komarova, 2013).

Using telomere length as an indicator of biological processes is not a new idea. Telomere length has previously been singled out as a marker to identify adult stem cells and their location in the body (Flores et al., 2008). From a modeling perspective, the length of telomeres has also been proposed as a signal to assess the risk posed by pre-cancerous mutations in healthy individuals (Rodriguez-Brenes et al., 2014). Telomere length might also help predict the success rate of cancer therapies, and studies of telomerase inhibitors predict better outcomes for patients with short telomere length (Chiappori et al., 2015). The work by Werner, Beier et al. adds an important contribution in this context, allowing us to use telomere lengths to gain insights into cell division patterns that occur in vivo.

References

Article and author information

Author details

  1. Ignacio A Rodriguez-Brenes

    Department of Mathematics and the Department of Ecology and Evolutionary Biology, University of California Irvine, Irvine, United States
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9117-6006
  2. Dominik Wodarz

    Department of Ecology and Evolutionary Biology and the Department of Mathematics, University of California Irvine, Irvine, United States
    For correspondence
    dwodarz@uci.edu
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-8017-3707

Publication history

  1. Version of Record published: January 25, 2016 (version 1)

Copyright

© 2016, Rodriguez-Brenes et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

Metrics

  • 1,742
    Page views
  • 295
    Downloads
  • 2
    Citations

Article citation count generated by polling the highest count across the following sources: Crossref, PubMed Central, Scopus.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

  1. Ignacio A Rodriguez-Brenes
  2. Dominik Wodarz
(2016)
Mathematical Modeling: Telomeres open a window on stem cell division
eLife 5:e12481.
https://doi.org/10.7554/eLife.12481

Further reading

    1. Computational and Systems Biology
    2. Physics of Living Systems
    Mario García-Navarrete, Merisa Avdovic ... Krzysztof Wabnik
    Research Article Updated

    Cells convert electrical signals into chemical outputs to facilitate the active transport of information across larger distances. This electrical-to-chemical conversion requires a tightly regulated expression of ion channels. Alterations of ion channel expression provide landmarks of numerous pathological diseases, such as cardiac arrhythmia, epilepsy, or cancer. Although the activity of ion channels can be locally regulated by external light or chemical stimulus, it remains challenging to coordinate the expression of ion channels on extended spatial–temporal scales. Here, we engineered yeast Saccharomyces cerevisiae to read and convert chemical concentrations into a dynamic potassium channel expression. A synthetic dual-feedback circuit controls the expression of engineered potassium channels through phytohormones auxin and salicylate to produce a macroscopically coordinated pulses of the plasma membrane potential. Our study provides a compact experimental model to control electrical activity through gene expression in eukaryotic cell populations setting grounds for various cellular engineering, synthetic biology, and potential therapeutic applications.

    1. Computational and Systems Biology
    2. Developmental Biology
    Feng Xian, Julia Regina Sondermann ... Manuela Schmidt
    Tools and Resources

    The age and sex of studied animals profoundly impact experimental outcomes in biomedical research. However, most preclinical studies in mice use a wide-spanning age range from 4 to 20 weeks and do not assess male and female mice in parallel. This raises concerns regarding reproducibility and neglects potentially relevant age and sex differences, which are largely unknown at the molecular level in naïve mice. Here, we employed an optimized quantitative proteomics workflow in order to deeply profile mouse paw skin and sciatic nerves (SCN) – two tissues implicated in nociception and pain as well as diseases linked to inflammation, injury, and demyelination. Remarkably, we uncovered significant differences when comparing male and female mice at adolescent (4 weeks) and adult (14 weeks) age. Our analysis deciphered protein subsets and networks that were correlated with the age and/or sex of mice. Notably, among these were proteins/biological pathways with known (patho)physiological relevance, e.g., homeostasis and epidermal signaling in skin, and, in SCN, multiple myelin proteins and regulators of neuronal development. Extensive comparisons with available databases revealed that various proteins associated with distinct skin diseases and pain exhibited significant abundance changes in dependence on age and/or sex. Taken together, our study uncovers hitherto unknown sex and age differences at the level of proteins and protein networks. Overall, we provide a unique proteome resource that facilitates mechanistic insights into somatosensory and skin biology, and integrates age and sex as biological variables – a prerequisite for successful preclinical studies in mouse disease models.