Cancer stem cells are controlled by developmental networks that are often topologically indistinguishable from normal, healthy stem cells. The question is why cancer stem cells can be both phenotypically distinct and have morphological effects so different from normal stem cells. The difference between cancer stem cells and normal stem cells lies not in differences their network architecture, but rather in the spatial-temporal locality of their activation in the genome and the resulting expression in the body. The metastatic potential cancer stem cells is not based primarily on their network divergence from normal stem cells, but on non-network based genetic changes that enable the evolution of gene-based phenotypic properties of the cell that permit its escape and travel to other parts of the body. Stem cell network theory allows the precise prediction of stem cell behavioral dynamics and a mathematical description of stem cell proliferation for both normal and cancer stem cells. It indicates that the best therapeutic approach is to tackle the highest order stem cells first, otherwise spontaneous remission of so called cured cancers will always be a danger. Stem cell networks poin
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 bu
Cycling tissues such as the intestinal epithelium, germ line, and hair follicles, require a constant flux of differentiated cells. These tissues are maintained by a population of stem cells, which generate differentiated progenies and self-renew. Asymmetric division of each stem cell into one stem cell and one differentiated cell can accomplish both tasks. However, in mammalian cycling tissues, some stem cells divide symmetrically into two differentiated cells and are replaced by a neighbor that divides symmetrically into two stem cells. Besides this heterogeneity in fate (population asymmetry), stem cells also exhibit heterogenous proliferation-rates; in the long run, however, all stem cells proliferate at the same average rate (equipotency). We construct and simulate a mathematical model based on these experimental observations. We show that the complex steady-state dynamics of population-asymmetric stem cells reduces the rate of replicative aging of the tissue --potentially lowering the incidence of somatic mutations and genetics diseases such as cancer. Essentially, slow-dividing stem cells proliferate and purge the population of the fast-dividing --older-- cells which had unde
Stem cell regeneration is a vital biological process in self-renewing tissues, governing development and tissue homeostasis. Gene regulatory network dynamics are pivotal in controlling stem cell regeneration and cell type transitions. However, integrating the quantitative dynamics of gene regulatory networks at the single-cell level with stem cell regeneration at the population level poses significant challenges. This study presents a computational framework connecting gene regulatory network dynamics with stem cell regeneration through a data-driven formulation of the inheritance function. The inheritance function captures epigenetic state transitions during cell division in heterogeneous stem cell populations. Our scheme allows the derivation of the inheritance function based on a hybrid model of cross-cell-cycle gene regulation network dynamics. The proposed scheme enables us to derive the inheritance function based on the hybrid model of cross-cell-cycle gene regulation network dynamics. By explicitly incorporating gene regulatory network structure, it replicates cross-cell-cycling gene regulation dynamics through individual-cell-based modeling. The numerical scheme holds the p
We present a general computational theory of stem cell networks and their developmental dynamics. Stem cell networks are special cases of developmental control networks. Our theory generates a natural classification of all possible stem cell networks based on their network architecture. Each stem cell network has a unique topology and semantics and developmental dynamics that result in distinct phenotypes. We show that the ideal growth dynamics of multicellular systems generated by stem cell networks have mathematical properties related to the coefficients of Pascal's Triangle. The relationship to cancer stem cells and their control networks is indicated. The theory lays the foundation for a new research paradigm for understanding and investigating stem cells. The theory of stem cell networks implies that new methods for generating and controlling stem cells will become possible.
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein expression networks consisting of two genes under cell--cell interactions mediated by the diffusion of a protein. Networks that show cell differentiation are extracted and two forms of symmetric differentiation based on Turing's mechanism and asymmetric differentiation are identified. In the latter network, the intracellular protein levels show oscillatory dynamics at a single-cell level, while cell-to-cell synchronicity of the oscillation is lost with an increase in the number of cells. Differentiation to a fixed-point type behavior follows with a further increase in the number of cells. The cell type with oscillatory dynamics corresponds to a stem cell that can both proliferate and differentiate, while the latter fixed-point type only proliferates. This differentiation is analyzed as a saddle-node bifurcation on an invariant circle, while the number ratio of each cell type is shown to be robust against perturbations due to self-consistent deter
Stem cells can precisely and robustly undergo cellular differentiation and lineage commitment, referred to as stemness. However, how the gene network underlying stemness regulation reliably specifies cell fates is not well understood. To address this question, we applied a recently developed computational method, Random Circuit Perturbation (RACIPE), to a nine-component gene regulatory network (GRN) governing stemness, from which we identified fifteen robust gene states. Among them, four out of the five most probable gene states exhibit gene expression patterns observed in single mouse embryonic cells at 32-cell and 64-cell stages. These gene states can be robustly predicted by the stemness GRN but not by randomized versions of the stemness GRN. Strikingly, we found a hierarchical structure of the GRN with the Oct4/Cdx2 motif functioning as the first decision-making module followed by Gata6/Nanog. We propose that stem cell populations, instead of being viewed as all having a specific cellular state, can be regarded as a heterogeneous mixture including cells in various states. Upon perturbations by external signals, stem cells lose the capacity to access certain cellular states, the
Induced pluripotent stem cells (iPSCs) provide a great model to study the process of reprogramming and differentiation of stem cells. Single-cell RNA sequencing (scRNA-seq) enables us to investigate the reprogramming process at single-cell level. Here, we introduce single-cell entropy (scEntropy) as a macroscopic variable to quantify the cellular transcriptome from scRNA-seq data during reprogramming and differentiation of iPSCs. scEntropy measures the relative order parameter of genomic transcriptions at single cell level during the cell fate change process, which shows increasing during differentiation, and decreasing upon reprogramming. Moreover, based on the scEntropy dynamics, we construct a phenomenological stochastic differential equation model and the corresponding Fokker-Plank equation for cell state transitions during iPSC differentiation, which provide insights to infer cell fates changes and stem cell differentiation. This study is the first to introduce the novel concept of scEntropy to the biological process of iPSC, and suggests that the scEntropy can provide a suitable quantify to describe cell fate transition in differentiation and reprogramming of stem cells.
Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the interactions between stem and non-stem cancer cell populations we develop a two-population mathematical model, which is suitable to describe tumorsphere growth. Both interspecific and intraspecific interactions, mediated by the microenvironment, are included. We show that there is a tipping point, characterized by a transcritical bifurcation, where a purely non-stem cell attractor is replaced by a new attractor that contains both stem and differentiated cancer cells. The model is then applied to describe the outcome of a recent experiment. This description reveals that, while the intraspecific interactions are inhibitory, the interspecific interactions stimulate growth. This can be understood in terms of stem cells needing differentiated cells to reinforce their niches, and phenotypic plasticity favoring the de-differentiation of differentiated cells into cancer stem cells. We posit that this is a consequence of the deregulation of the quorum sensing that
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment. The current prominence of high-resolution and live-cell imaging data provides an unprecedented opportunity to study the spatiotemporal dynamics of these cells within their stem cell niche and learn more about aberrant, but also unperturbed, normal hematopoiesis. However, this requires careful quantitative statistical analysis of the spatial and temporal behavior of cells and the interaction with their microenvironment. Moreover, such quantification is a prerequisite for the construction of hypothesis-driven mathematical models that can provide mechanistic explanations by generating spatiotemporal dynamics that can be directly compared to experimental observations. Here, we provide a brief overview of statistical methods in analyzing spatial distribution of cells, cell motility, cell shapes and cellular genealogies. We also describe cell- based modeling formalisms that allow researchers to simulate emergent behavior in a multicellular system based
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, and short-lived bimodal or unimodal distributions. In all cases, we approximate solutions to the vBD master equation using a renormalised system-size expansion
The question of what guides lineage segregation is central to development, where cellular differentiation leads to segregated cell populations destined for specialized functions. Here, using optical tweezers measurements of mouse embryonic stem cells (mESCs), we reveal a mechanical mechanism based on differential elasticity in the second lineage segregation of the embryonic inner cell mass into epiblast (EPI) cells - that will develop into the fetus - and primitive endoderm (PrE) - which will form extraembryonic structures such as the yolk sac. Remarkably, we find that these mechanical differences already occur during priming and not just after a cell has committed to differentiation. Specifically, we show that the mESCs are highly elastic compared to any other reported cell type and that the PrE cells are significantly more elastic than EPI-primed cells. Using a model of two cell types differing only in elasticity we show that differential elasticity alone can lead to segregation between cell types, suggesting that the mechanical attributes of the cells contribute to the segregation process. Our findings present differential elasticity as a previously unknown mechanical contributo
The shape that stem cells reach at the end of adhesion process influences their differentiation. Rearrangement of cytoskeleton and modification of intracellular tension may activate mechanotransduction pathways controlling cell commitment. In the present study, the mechanical signals involved in cell adhesion were computed in in vitro stem cells of different shapes using a single cell model, the so-called Cytoskeleton Divided Medium (CDM) model. In the CDM model, the filamentous cytoskeleton and nucleoskeleton networks were represented as a mechanical system of multiple tensile and compressive interactions between the nodes of a divided medium. The results showed that intracellular tonus, focal adhesion forces as well as nuclear deformation increased with cell spreading. The cell model was also implemented to simulate the adhesion process of a cell that spreads on protein-coated substrate by emitting filopodia and creating new distant focal adhesion points. As a result, the cell model predicted cytoskeleton reorganisation and reinforcement during cell spreading. The present model quantitatively computed the evolution of certain elements of mechanotransduction and may be a powerful
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 l
The crawling motility of many eukaryotic cells is driven by filamentous actin (F-actin), and regulated by a network of signaling proteins and lipids (including small GTPases). The tangle of positive and negative feedback loops gives rise to various experimentally observed dynamic patterns (``actin waves''). Here we consider a recent prototypical model for actin waves in which F-actin exerts negative feedback onto a GTPase. Guided by recent numerical PDE bifurcation analysis in Hughes (2025) and Hughes et al (2026), we explore cell shapes and motility associated with polar, oscillatory, and traveling waves solutions of a mass-conserved partial differential equation (PDE) model. We use Morpheus (cellular Potts) simulations to investigate the implications of such regimes of behavior on the shapes and motion of cells, and on transitions between modes of behavior. The model demonstrates various cell states, including resting (spatially uniform GTPase), polar cells (static ``zones'' of GTPase), and traveling waves along the cell edge. In some parameter regimes, such states can coexist, so that cells can transition from one behavior to another in response to noisy stimuli.
Cell-cell communication is essential for tissue development, regeneration and function, and its disruption can lead to diseases and developmental abnormalities. The revolution of single-cell genomics technologies offers unprecedented insights into cellular identities, opening new avenues to resolve the intricate cellular interactions present in tissue niches. CellPhoneDB is a bioinformatics toolkit designed to infer cell-cell communication by combining a curated repository of bona fide ligand-receptor interactions with a set of computational and statistical methods to integrate them with single-cell genomics data. Importantly, CellPhoneDB captures the multimeric nature of molecular complexes, thus representing cell-cell communication biology faithfully. Here we present CellPhoneDB v5, an updated version of the tool, which offers several new features. Firstly, the repository has been expanded by one-third with the addition of new interactions. These encompass interactions mediated by non-protein ligands such as endocrine hormones and GPCR ligands. Secondly, it includes a differentially expression-based methodology for more tailored interaction queries. Thirdly, it incorporates novel
Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: A
Stem cell heterogeneity is essential for the homeostasis in tissue development. This paper established a general formulation for understanding the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The model generalizes the classical G0 cell cycle model, and incorporates the epigenetic states of stem cells that are represented by a continuous multidimensional variable and the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, that are dependent on their epigenetic states. Moreover, the random transition of epigenetic states is represented by an inheritance probability that can be described as a conditional beta distribution. This model can be extended to investigate gene mutation-induced tumor development. The proposed formula is a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.
In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article, we provide a general theoretical framework to study mixtures of dividing and actively migrating particles, which we apply to biological tissues. We show in particular that the interplay between the stresses arising from active cell migration and stem cell division give rise to robust stem cell patterns. The instability of the tissue leads to spatial patterns which are either steady or oscillating in time. The wavelength of the instability has an order of magnitude consistent with the biological observations. We also discuss the implications of these results for future in vitro and in vivo experiments.
Stem cells maintain tissues by generating differentiated cell types while simultaneously self-renewing their own population. The mechanisms that allow stem cell populations to function collectively to control their density, maintain robust homeostasis and recover from injury remain elusive. Motivated by recent experimental advances, here we develop a generic and robust mechanism of stem cell self-renewal based on competition for diffusible fate determinants, which exert fate control. Using both analytical methods and stochastic simulations, we show that the mechanism is characterized by signature dynamic and statistical properties, from stem cell density fluctuations and transient large-scale oscillation dynamics during recovery, to scaling clonal dynamics, front-like boundary propagation and features of dynamical 'quantization' of self-renewal zones in localized domains. Based on these findings, we suggest that competition for fate determinants provides a generic and robust mechanism by which stem cells can self-organize to achieve density homeostasis in an open (or 'facultative') niche environment.