Mechanics and fate stochasticity shape stem cell distribution in tissues

  1. Johannes C Krämer
  2. Edouard Hannezo
  3. Jens Elgeti

  • Curated by eLife

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    eLife Assessment

    This is a useful and clearly presented study showing how simple feedback between cell crowding and cell growth can maintain tissue balance and lead to the spontaneous formation of stem-cell clusters. The evidence supporting the behavior of the model is solid, but the significance of the clustering result would be strengthened by relating the emphasizing the differences to prior studies, and potentially relating the clustering mechanism to properties of critical birth-death processes in two dimensions.

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Abstract

Balancing cellular loss in tissues requires fine balance of cell proliferation and differentiation. In differentiated tissues consisting of a single cell type, a mechanical regulation of proliferation has been proposed to underlie growth-control and homeostatic steady-states. Yet, how tissues containing different cell types with distinct proliferation rates, mechanical interactions, and spatial self-organization retain robust homeostasis of cell proportions remains poorly understood. Here, we combine particle-based mechanical models of proliferative tissues with a classical hierarchy of stem, progenitor, and differentiated cells, undergoing stochastic fate choices, and show that mechanical feedback alone is sufficient to stabilize populations. We derive analytically and computationally a phase diagram of possible stable states, in particular those maintained either via slow and rare stem cells with short-lived progenitors or no stem cells and long-lived progenitors. Our simulations uncover that mechanical control of growth is sufficient, in the absence of any codes of adhesion or extrinsic niche signals, to cause stable spatial structures, with small stem cell clusters forming and maintaining dynamical renewal units. Our results demonstrate how complex spatial structures can emerge in minimal stochastic and mechanical simulations with impact to understand the homeostasis of multi-cellular systems.

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  1. eLife

    eLife Assessment

    This is a useful and clearly presented study showing how simple feedback between cell crowding and cell growth can maintain tissue balance and lead to the spontaneous formation of stem-cell clusters. The evidence supporting the behavior of the model is solid, but the significance of the clustering result would be strengthened by relating the emphasizing the differences to prior studies, and potentially relating the clustering mechanism to properties of critical birth-death processes in two dimensions.

  2. eLife

    Reviewer #1 (Public review):

    Summary:

    This theoretical study of a simple system of stem, transient progenitors and fully differentiated cells provides interesting results about how tissues can reach homeostasis with different proportions of these cell types. The key ingredient is the feedback due to pressure, which regulates the proliferation rate. The study shows that by varying the rates at which stem cells switch to progenitor cells, and progenitor cells to differentiated cells, the final composition of the tissue can be tuned. In addition, the model shows that clusters of stem cells can arise in this model due to their effective immobilization and therefore that stem-cell niches can arise even in the absence of specific adhesion between different cell types.

    The model is calculated using both cell-based simulations and continuum dynamics, and is thoroughly analyzed in its spatial and temporal characteristics.

    Strengths:

    The model is simple, yet leads to very rich results. The authors demonstrate the results of the model using both particle-based simulations and a continuum model, thereby enhancing our understanding of this complex system.

    Weaknesses:

    The origin of the stem cell niche is not so clearly explained.

  3. eLife

    Reviewer #2 (Public review):

    Summary:

    This is a theory/computational paper that explores a model of a two-dimensional tissue undergoing homeostatic turnover. The motivation is to explore how the rates of cell division and cell loss in a tissue can be precisely balanced to maintain tissue integrity. It is already well appreciated that this can be achieved by a feedback mechanism whereby cells tune their division or loss rate in response to a change in cell density relative to a homeostatic set point (e.g. PMID 30269903 and other papers cited in the introduction to this new manuscript). Cell density can be sensed locally by mechanical pressure.

    Here, the question asked is whether pressure-dependent homeostatic control can maintain not only cell density (as previously known) but also cell type proportions when a tissue has a proliferative hierarchy. The specific example considered is a 3-tier hierarchy with stem cells (S) that give rise to transit-amplifying cells (T) that give rise to terminally differentiated cells (D), which are then lost. Next, the authors notice in simulations that in such a model of density-dependent cell division, stem cells undergo spontaneous clustering without any need for cell adhesion. Thus, the key result of the paper is that a simple pressure-based homeostatic feedback control leads to spontaneous formation of stem cell clusters, which the authors call "niche-like". They characterize these clusters numerically.

    Overall, the work is elegant and presented in a pedagogical manner. But I think its central result has already been previously described (DOI 10.1103/PhysRevE.77.031907), albeit without the use of terms such as "niche-like" that increase the relevance of the work, and using a different detailed choice of model. Essentially, clustering is the outcome of a log-divergence of the density of random walkers undergoing a critical birth-death process in two dimensions, as discussed in the 2008 paper. Essentially, once stem cell division is coupled to total density (rather than just stem cell density), then the stem cells follow a critical birth-death process in 2D, and the clustering is an inevitable outcome. This is the precise point of the previous paper. As such, my review will focus on novelty compared to prior work.

    Strengths:

    The first strength of the paper is that it gives a clear and biologically oriented presentation of how pressure-dependent (or more simply, density-dependent) feedback can be sufficient to maintain steady-state homeostasis with defined proportions of stem, transit-amplifying, and differentiated cells. The authors scan parameters in numerical simulations using an established agent-based model of cells under mechanical tension, and show that tissue can be maintained provided that stem cell division rates are able to match loss rates. This is not very surprising, but I believe it has not been laid out before in this way, and it is clearly presented.

    A second strength is that the paper may make a useful contribution by drawing attention to the connection between mechanical homeostatic feedback and the spatial organization of stem/progenitor cells. Even though there is a precedent for this point (see overview above), the work is more biologically oriented than the prior paper, and may therefore be useful to readers interested in how simple local rules can shape tissue organization. The current paper uses a more biophysically informed particle-based model for simulations than the prior work, and it provides a useful framework for studying the interaction between mechanical feedback, tissue homeostasis, and cell-type hierarchy that could be generalized. The simulations are well motivated, and the results are presented in a pedagogical manner. More on the comparison to the 2008 paper below.

    Weaknesses (or rather, comparison to prior work):

    The main weakness is that the central result of the paper appears to have already been previously described, albeit using different terminology and a different detailed choice of model. I will describe the similarities and differences between the two papers below.

    The 2008 paper...

    • ...is motivated by asking how a critical birth-death process can maintain uniform density in 2D. This is different from the current paper, which asks whether a birth-death process can be tuned by total density and still maintain cell type proportions. As such, the questions motivating the work are subtly different, although both worry about how homeostasis is maintained.

    • ...considers a 2-tier model consisting of progenitor and differentiated cells (A->B->0). This is different from the current paper, which considers a 3-tier model (S->T->D->0). But the current paper is aiming to be general rather than specific, and I would propose that complexifying the model from a 2-tier hierarchy to a 3-tier hierarchy doesn't make the new paper qualitatively different.

    • ...shows that "the population of progenitor cells should cluster over time" (quoted from the paper). This is shown for A cells in the 2008 paper, and is shown for stem (S) cells in this new paper. As such, the prior paper already shows the key result of this new paper.

    • ...uses slightly different rules, which are clunkier: it allows for symmetric and asymmetric division of A cells, does not allow direct A cell differentiation (no A->B allowed), and it uses a hard-core lattice-based model with hole-diffusion to model density-dependent cell division. By contrast, the current paper uses a more biophysically informed two-particle agent-based model for simulations, and it only considers symmetric divisions and direct differentiation. As such, the current paper is a more realistic treatment than a lattice-based model, and simply different (not more or less realistic) in terms of ignoring epigenetic heritable sister cell correlations. But since clustering is a large-scale phenomenon, as is often the case in statistical physics, the microscopic implementations should not be important. As such, I would not expect the difference in rules to be important to the clustering.

    • ...derives a long-term asymptotic form for the clustering dynamics of progenitor cells (Equation 15 of that paper, and the unnumbered equation at the top of column 2 of page 7 of the paper). This goes beyond the new paper, which only describes the phenomenon numerically. The 2008 paper also explains the phenomenon in terms of prior work on random walkers undergoing birth-death processes, which better links the phenomenon to prior statistical literature.

    • ...shows experimental evidence for clustering of progenitors in mouse epidermis. This goes substantially beyond the current paper, which is entirely computational. That said, despite the excellent fit of data to the theory, I am myself not convinced that the clustering seen in epidermis is the result of this phenomenon alone.

    • ...studies clonal dynamics and shows that it is consistent with a voter-model-like behavior, with clone size growing as t/log(t). The scaling law is different from that reported in the current paper.
    Thus, the key result that progenitor cells undergo clustering seems to have been mathematically described in the 2008 paper and even shown in that paper to be consistent with experimental data in one tissue.

    That said, I do think that this new paper may make a useful contribution. It is certainly more biologically oriented (despite lacking experimental data, which the prior paper has). And it may be that the quantitative dynamics of clustering and clonal competition are subtly different in this model. So, with certain revisions, I am supportive of this work.

    Specific suggestions:

    (1) The new paper should appropriately cite precedent. The paper should avoid making claims that progenitor clustering in this model of birth-death with spatial density control is a major novel discovery. This was a key result of the previous paper. The new paper should also cite the 2008 paper for evidence that clustering of this type has been proposed to be seen experimentally. The differences between the papers discussed above could be used as needed in highlighting the contribution of the new work.

    (2) There is still a question about whether microscopic details of the simulation may alter the asymptotic dynamics of the clusters and clones. The authors could compare the dynamics of clustering between their simulations and the 2008 lattice-based result (Equation 15 of that paper, the "1/log(t)" behavior of the density radial correlation function) derived in the original paper, and similarly compare clonal dynamics in that paper to this new paper. Whatever they find is interesting: if they confirm that the same dynamic behaviours occur, it will reinforce the results of the prior work, rephrase the problem in more relevant terms, and help make it accessible to a broader audience. If they show that their model leads to different quantitative dynamics, they could explore (in a supplement perhaps?) what is the origin of the difference, given that the models are superficially similar.

  4. eLife

    Reviewer #3 (Public review):

    Summary:

    The manuscript studies a minimal model of tissue homeostasis in which stem (S), progenitor/transit-amplifying (T), and differentiated (D) cells interact through stochastic fate decisions and mechanically regulated proliferation. Combining a compartment-level analytical description with particle-based simulations, the authors show that pressure-dependent growth can stabilise cell populations and maintain tissue homeostasis over a broad parameter range. They derive homeostatic cell fractions and identify distinct regimes, including tissues maintained by rare stem cells or by long-lived progenitors. Most notably, the simulations reveal the spontaneous emergence of persistent stem-cell clusters and renewal-unit-like structures in the absence of explicit niche signals or differential adhesion. The authors further analyse spatial correlations, cluster statistics, lineage dynamics and neighbourhood compositions, and argue that stochastic fate decisions qualitatively alter the spatial organisation of mechanically regulated tissues. Based on the annotated manuscript, several of these central claims concern the emergence and stability of stem-cell clusters and their interpretation as self-organised structures.

    Strengths:

    The manuscript is clearly written, technically competent, and combines analytical calculations with large-scale agent-based simulations in an elegant way. The systematic analysis of spatial observables, including pair correlations, cluster-size distributions, void statistics, neighbourhood composition, and lineage tracing, provides a rich characterisation of tissue organisation. The comparison with the authors' previous work on deterministic stem-cell hierarchies is particularly interesting, as it demonstrates that altering the fate-choice scheme can qualitatively change the resulting tissue architecture from stem-cell repulsion to stem-cell clustering. The study therefore generates a number of experimentally testable predictions regarding stem-cell spatial organisation and lineage dynamics. I also found the attempt to connect microscopic fate decisions to mesoscopic tissue-level organisation valuable, as this remains a relatively underexplored area at the interface of stem-cell biology and tissue mechanics.

    Weaknesses:

    My main concern relates to novelty and positioning within the existing literature. The manuscript frequently presents mechanical feedback as a mechanism capable of generating tissue homeostasis and robust cell-type proportions. However, the idea that crowding- or pressure-dependent feedback can robustly stabilise renewing tissues is already well established, both in mechanical homeostasis models and in more general feedback-based theories of tissue regulation. Consequently, the homeostasis aspect of the present manuscript appears more as an application of existing principles to a particular mechanical framework than as a fundamentally new conceptual advance. The authors should position their work more clearly with respect to these studies and explain more explicitly what genuinely new biological or mathematical insights are provided beyond the existence of homeostatic steady states.

    The manuscript therefore derives its novelty primarily from the spatial phenomena emerging from the coupling of stochastic fate decisions and mechanical interactions. While the observed stem-cell clustering is intriguing, the mechanistic explanation remains incomplete. The authors attribute clustering to stochastic symmetric divisions combined with mechanical control, yet it remains unclear whether the observed structures genuinely arise from a new self-organised mechanical mechanism or simply reflect local genealogical correlations generated by repeated symmetric divisions. Several of the strongest conclusions, including long-range order, renewal-unit formation, and stable niche-like organisation, require more rigorous support. In particular, the manuscript currently lacks appropriate control models that would disentangle the effects of mechanics, stochasticity, and daughter-cell placement. Furthermore, the definition of clusters via a specific distance threshold appears somewhat arbitrary and may itself influence the inferred cluster sizes and conclusions regarding finite renewal units. It would be important to demonstrate robustness with respect to this choice.

    I also have concerns regarding the simulation methodology and interpretation of the spatial statistics. Large tissues are assembled from smaller pre-equilibrated patches. While this may be computationally convenient, it raises concerns about whether long-range structures can emerge naturally and whether the reported spatial organisation could be affected by the construction procedure. Given that one of the central claims concerns spatial ordering over large scales, it would be important to demonstrate explicitly that the patching procedure does not influence the results. Similarly, the manuscript interprets pair-correlation and void statistics as evidence for long-range ordering of stem-cell clusters, but does not sufficiently exclude alternative explanations arising from finite system size, patch construction, or simple genealogical clustering.

    Conclusion:

    Overall, I find the manuscript interesting, whilst I also believe it should have a major revision. The most valuable contribution of the study is not the demonstration that mechanical feedback can maintain homeostasis, but rather the suggestion that stochastic fate decisions can qualitatively reshape the spatial organisation produced by mechanically regulated tissues. For a broad-interest journal, however, the authors should sharpen the positioning of the work relative to prior homeostasis theory, establish more clearly the mechanistic origin of the reported stem-cell clustering, and provide additional evidence that the observed structures are genuine emergent features of the model rather than artefacts of modelling assumptions or analysis choices.

  5. eLife

    Author response:

    Thank you for providing detailed and positive feedback. This will help us to improve manuscript and its accessibility for a broad audience.

    We first want to highlight what we believe is the main aspect, and therefore novelty, of our work: Combining cell-cell mechanics, mechanical regulation of growth and stochastic cell fate decisions leads to a stable population of stem cells in a stable balance with more differentiated cells, avoiding neutral drift, extinction or overgrowth. Furthermore, this combination leads to stable clusters, i.e. without further coarsening. We call these structures “niche-like”, as we believe stability is fundamental for biological function.

    As the referees point out, this work builds on previous works in the literature, and highlighting the differences and advances will benefit the manuscript. As referee 3 points out, homeostatic regulation by mechanics, in particular pressure, has been discussed intensively in the literature, by us and many others. The novelty in our work is that we apply this regulatory mechanism to a multi-component tissue, and there can stabilize not only the total number of cells, but also their relative composition. In particular, we derive analytical equations relating composition to differentiation rates, and demonstrate their validity in agent-based simulations. In the revised manuscript we will highlight more clearly that this is an application of previous works on a novel system.

    Referee 2 points to Klein et al. (2008). We do agree that their model also shows clustering, and therefore that we should have compared and contrasted our model more thoroughly with this work. However, as we will show more clearly in a revised manuscript, our results differ crucially from this form of clustering without detailed mechanical interactions. As also discussed in the original work by Klein et al., the mechanism therein results in clusters which are not stable, but continue to grow indefinitely over time (although at a slow rate). We show that our simulations display stable clusters which do not grow further, even when simulating for very long time scales, and that these clusters are well-defined, by structurally different correlation functions showing clear inter-cluster separation. In the revision, we will demonstrate that even when starting from a perfect cluster, the stem cells separate, resulting in finite stable clustering. Thus, our clusters are true “fix points” of the stem cell dynamics. Referee 3 rightfully recommends that we should identify more clearly which mechanism is responsible for the stable niche-like structures. To this end, we will compare more closely to Klein2008 as a model without mechanics leading to log(t) coarsening, and our earlier work (Krämer et al., 2024) where stem cells were immortal. There, we had found that mechanics alone produces the reverse result, i.e. leads to enhanced separation of stem cells, which anti-cluster and are dispersed as single cells. We will add new simulations as an additional control that contain cell-cell mechanics, but no mechanical regulation of growth. This combination will allow us to disentangle how the combination of cell mechanics, mechanical feedback on growth and stochastic differentiation results in the formation of stable niche-like structures.

    Note that neither Klein2008 nor Krämer2024 have a physical mechanism that maintains the overall stem cell population number stable. Krämer2024 simply fixes the number of stem cells, whereas the model in Klein 2008 results in stochastic drift in stem cell number.

    Evidentially, we will also address the more technical weaknesses of the manuscript identified by the referees. In particular, we will demonstrate more clearly that the observed structures are genuine emergent features of the model rather than artefacts of modelling assumptions or analysis choices, especially with respect to the patching technique used to obtain large simulations.

  6. Version published to 10.7554/elife.111984.1 on eLife
  7. Version published to 10.7554/elife.111984 on eLife
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    Mechanics and fate stochasticity shape stem cell distribution in tissues https://www.biorxiv.org/content/10.64898/2026.06.10.731353v1

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    Mechanics and fate stochasticity shape stem cell distribution in tissues https://www.biorxiv.org/content/10.64898/2026.06.10.731353v1

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