Cell lineages and the logic of proliferative control

Tradeoff Between Speed and Robustness in Primordium Initiation Mediated by Auxin-CUC1 Interaction

Robustness is the reproducible development of a phenotype despite stochastic noise. It often involves tradeoffs with other performance metrics, but the mechanisms underlying such tradeoffs were largely unknown. An Arabidopsis flower robustly develops four sepals from four precisely positioned auxin maxima. The development related myb-like 1 (drmy1) mutant generates noise in auxin signaling that disrupts robustness in sepal initiation. Here, we found that increased expression of CUP-SHAPED COTYLEDON1 (CUC1), a boundary specification transcription factor, in drmy1 underlies this loss of robustness. CUC1 surrounds and amplifies stochastic auxin noise in drmy1 to form variably positioned auxin maxima and sepal primordia. Removing CUC1 from drmy1 provides time for noisy auxin signaling to resolve into four precisely positioned auxin maxima, restoring robust sepal initiation. However, removing CUC1 decreases auxin maxima intensity and slows down sepal initiation. Thus, CUC1 increases morphogenesis speed but impairs robustness against auxin noise. Further, using a computational model, we found that the observed phenotype can be explained by the effect of CUC1 in repolarizing PIN FORMED1 (PIN1), a polar auxin transporter. Lastly, our model predicts that reducing global growth rate improves developmental robustness, which we validated experimentally. Thus, our study illustrates a tradeoff between speed and robustness during development.

Homeostatic regulation of renewing tissue cell populations via crowding control: stability, robustness and quasi-dedifferentiation

To maintain renewing epithelial tissues in a healthy, homeostatic state, cell divisions and differentiation need to be tightly regulated. Mechanisms of homeostatic regulation often rely on crowding feedback control: cells are able to sense the cell density in their environment, via various molecular and mechanosensing pathways, and respond by adjusting division, differentiation, and cell state transitions appropriately. Here, we determine, via a mathematically rigorous framework, which general conditions for the crowding feedback regulation (i) must be minimally met, and (ii) are sufficient, to allow the maintenance of homeostasis in renewing tissues. We show that those conditions naturally allow for a degree of robustness toward disruption of regulation. Furthermore, intrinsic to this feedback regulation is that stem cell identity is established collectively by the cell population, not by individual cells, which implies the possibility of 'quasi-dedifferentiation', in which cells committed to differentiation may reacquire stem cell properties upon depletion of the stem cell pool. These findings can guide future experimental campaigns to identify specific crowding feedback mechanisms.

A model about regulation on three division modes of stem cell

We construct a multi-stage cell lineage model for cell division, apoptosis and movement. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the stem cell divisions (including self-renewal, asymmetrical cell division (ACD) and differentiation). The densities of cells and molecules are described by coupled reaction-diffusion partial differential equations, and the plane wavefront propagation speeds can be obtained analytically and verified numerically. It is found that with ACD the population and propagation of stem cells can be promoted but the negative regulation on self-renewal and differentiation will work slowly. Regulatory inhibition on differentiation will inversely increase stem cells but not affect the population and wave propagation of the cell lineage. While negative regulation on self-renewal and ACD will decrease the population of stem cells and slow down the propagation, and even drive stem cells to extinction. Moreover we find that inhibition on self-renewal has a strength advantage while inhibition on ACD has a range advantage to kill stem cells. Possible relations to model cancer development and therapy are also discussed.

A synthetic differentiation circuit in Escherichia coli for suppressing mutant takeover

Differentiation is crucial for multicellularity. However, it is inherently susceptible to mutant cells that fail to differentiate. These mutants outcompete normal cells by excessive self-renewal. It remains unclear what mechanisms can resist such mutant expansion. Here, we demonstrate a solution by engineering a synthetic differentiation circuit in Escherichia coli that selects against these mutants via a biphasic fitness strategy. The circuit provides tunable production of synthetic analogs of stem, progenitor, and differentiated cells. It resists mutations by coupling differentiation to the production of an essential enzyme, thereby disadvantaging non-differentiating mutants. The circuit selected for and maintained a positive differentiation rate in long-term evolution. Surprisingly, this rate remained constant across vast changes in growth conditions. We found that transit-amplifying cells (fast-growing progenitors) underlie this environmental robustness. Our results provide insight into the stability of differentiation and demonstrate a powerful method for engineering evolutionarily stable multicellular consortia.

The inherent fragility of collective proliferative control

Tissues achieve and maintain their sizes through active feedback, whereby cells collectively regulate proliferation and differentiation so as to facilitate homeostasis and the ability to respond to disturbances. One of the best understood feedback mechanisms-renewal control-achieves remarkable feats of robustness in determining and maintaining desired sizes. Yet in a variety of biologically relevant situations, we show that stochastic effects should cause rare but catastrophic failures of renewal control. We define the circumstances under which this occurs and raise the possibility such events account for important non-genetic steps in the development of cancer. We further suggest that the spontaneous stochastic reversal of these events could explain cases of cancer normalization or dormancy following treatment. Indeed, we show that the kinetics of post-treatment recurrence for many cancers are often better fit by a model of stochastic re-emergence due to loss of collective proliferative control, than by deterministic models of cancer relapse.

Feedback control of organ size precision is mediated by BMP2-regulated apoptosis in the Drosophila eye

Biological processes are intrinsically noisy, and yet, the result of development-like the species-specific size and shape of organs-is usually remarkably precise. This precision suggests the existence of mechanisms of feedback control that ensure that deviations from a target size are minimized. Still, we have very limited understanding of how these mechanisms operate. Here, we investigate the problem of organ size precision using the Drosophila eye. The size of the adult eye depends on the rates at which eye progenitor cells grow and differentiate. We first find that the progenitor net growth rate results from the balance between their proliferation and apoptosis, with this latter contributing to determining both final eye size and its variability. In turn, apoptosis of progenitor cells is hampered by Dpp, a BMP2/4 signaling molecule transiently produced by early differentiating retinal cells. Our genetic and computational experiments show how the status of retinal differentiation is communicated to progenitors through the differentiation-dependent production of Dpp, which, by adjusting the rate of apoptosis, exerts a feedback control over the net growth of progenitors to reduce final eye size variability.

Self-Regulated Symmetry Breaking Model for Stem Cell Differentiation

In conventional disorder-order phase transitions, a system shifts from a highly symmetric state, where all states are equally accessible (disorder) to a less symmetric state with a limited number of available states (order). This transition may occur by varying a control parameter that represents the intrinsic noise of the system. It has been suggested that stem cell differentiation can be considered as a sequence of such symmetry-breaking events. Pluripotent stem cells, with their capacity to develop into any specialized cell type, are considered highly symmetric systems. In contrast, differentiated cells have lower symmetry, as they can only carry out a limited number of functions. For this hypothesis to be valid, differentiation should emerge collectively in stem cell populations. Additionally, such populations must have the ability to self-regulate intrinsic noise and navigate through a critical point where spontaneous symmetry breaking (differentiation) occurs. This study presents a mean-field model for stem cell populations that considers the interplay of cell-cell cooperativity, cell-to-cell variability, and finite-size effects. By introducing a feedback mechanism to control intrinsic noise, the model can self-tune through different bifurcation points, facilitating spontaneous symmetry breaking. Standard stability analysis showed that the system can potentially differentiate into several cell types mathematically expressed as stable nodes and limit cycles. The existence of a Hopf bifurcation in our model is discussed in light of stem cell differentiation.

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

Chronic myeloid leukemia (CML) is a blood cancer characterized by dysregulated production of maturing myeloid cells driven by the product of the Philadelphia chromosome, the BCR-ABL1 tyrosine kinase. Tyrosine kinase inhibitors (TKIs) have proved effective in treating CML, but there is still a cohort of patients who do not respond to TKI therapy even in the absence of mutations in the BCR-ABL1 kinase domain that mediate drug resistance. To discover novel strategies to improve TKI therapy in CML, we developed a nonlinear mathematical model of CML hematopoiesis that incorporates feedback control and lineage branching. Cell-cell interactions were constrained using an automated model selection method together with previous observations and new in vivo data from a chimeric BCR-ABL1 transgenic mouse model of CML. The resulting quantitative model captures the dynamics of normal and CML cells at various stages of the disease and exhibits variable responses to TKI treatment, consistent with those of CML patients. The model predicts that an increase in the proportion of CML stem cells in the bone marrow would decrease the tendency of the disease to respond to TKI therapy, in concordance with clinical data and confirmed experimentally in mice. The model further suggests that, under our assumed similarities between normal and leukemic cells, a key predictor of refractory response to TKI treatment is an increased maximum probability of self-renewal of normal hematopoietic stem cells. We use these insights to develop a clinical prognostic criterion to predict the efficacy of TKI treatment and design strategies to improve treatment response. The model predicts that stimulating the differentiation of leukemic stem cells while applying TKI therapy can significantly improve treatment outcomes.

Phenotypic and genotypic infidelity in B-lineage neoplasms, including transdifferentiation following targeted therapy: Report from the 2021 SH/EAHP Workshop

OBJECTIVES

Session 2 of the 2021 Society for Hematopathology and European Association for Haematopathology Workshop collected examples of lineage infidelity and transdifferentiation in B-lineage neoplasms, including after targeted therapy.

METHODS

Twenty cases were submitted. Whole-exome sequencing and genome-wide RNA expression analysis were available on a limited subsample.

RESULTS

A diagnosis of B-cell acute lymphoblastic leukemia (B-ALL) was rendered on at least 1 biopsy from 13 patients. There was 1 case of acute myeloid leukemia (AML); the remaining 6 cases were mature B-cell neoplasms. Targeted therapy was administered in 7 cases of B-ALL and 4 cases of mature B-cell neoplasms. Six cases of B-ALL underwent lineage switch to AML or mixed-phenotype acute leukemia at relapse, 5 of which had rearranged KMT2A. Changes in maturational state without lineage switch were observed in 2 cases. Examples of de novo aberrant T-cell antigen expression (n = 2) were seen among the mature B-cell lymphoma cohort, and their presence correlated with alterations in tumor cell gene expression patterns.

CONCLUSIONS

This cohort of cases enabled us to illustrate, discuss, and review current concepts of lineage switch and aberrant antigen expression in a variety of B-cell neoplasms and draw attention to the role targeted therapies may have in predisposing neoplasms to transdifferentiation as well as other, less expected changes in maturational status.

A cell model about symmetric and asymmetric stem cell division

We construct a multi-stage cell lineage model including self-renewal, apoptosis, cell movement and the symmetrical/asymmetrical division of stem cells. The evolution of cell populations can be described by coupled reaction-diffusion partial differential equations, and the propagating wavefront speeds can be obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effect of symmetric/asymmetric division of stem cells on the population and propagating dynamics of cell lineage. It is found that stem cells' asymmetric cell division (ACD) can move the phase boundary of the homogenous solution of the system. The population of the cell lineage will be promoted in presence of ACD. The concentration of stem cells increases with ACD but that of differentiated daughter cells decreases with ACD. In addition, it is found that the propagating speed of the stem cells can be evaluated with ACD. When the daughter cells move fast to a new space, stem cells can catch them up through increasing ACD. Our results may suggest a mechanism of collective migration of cell lineage through cooperation between ACD of stem cells and fast diffusion of the daughter cells.

Systemic GDF11 attenuates depression-like phenotype in aged mice via stimulation of neuronal autophagy

Cognitive decline and mood disorders increase in frequency with age. Many efforts are focused on the identification of molecules and pathways to treat these conditions. Here, we demonstrate that systemic administration of growth differentiation factor 11 (GDF11) in aged mice improves memory and alleviates senescence and depression-like symptoms in a neurogenesis-independent manner. Mechanistically, GDF11 acts directly on hippocampal neurons to enhance neuronal activity via stimulation of autophagy. Transcriptomic and biochemical analyses of these neurons reveal that GDF11 reduces the activity of mammalian target of rapamycin (mTOR), a master regulator of autophagy. Using a murine model of corticosterone-induced depression-like phenotype, we also show that GDF11 attenuates the depressive-like behavior of young mice. Analysis of sera from young adults with major depressive disorder (MDD) reveals reduced GDF11 levels. These findings identify mechanistic pathways related to GDF11 action in the brain and uncover an unknown role for GDF11 as an antidepressant candidate and biomarker.

Stability analysis of a multiscale model of cell cycle dynamics coupled with quiescent and proliferating cell populations

In this paper, we perform a mathematical analysis of our proposed nonlinear, multiscale mathematical model of physiologically structured quiescent and proliferating cell populations at the macroscale and cell-cycle proteins at the microscale. Cell cycle dynamics (microscale) are driven by growth factors derived from the total cell population of quiescent and proliferating cells. Cell-cycle protein concentrations, on the other hand, determine the rates of transition between the two subpopulations. Our model demonstrates the underlying impact of cell cycle dynamics on the evolution of cell population in a tissue. We study the model's well-posedness, derive steady-state solutions, and find sufficient conditions for the stability of steady-state solutions using semigroup and spectral theory. Finally, we performed numerical simulations to see how the parameters affect the model's nonlinear dynamics.

Modeling of ionizing radiation induced hair follicle regenerative dynamics

Hair follicles (HFs) are stem-cell-rich mammalian mini-organs that can undergo cyclic regenerations over the life span of the organism. The cycle of a HF consists of three consecutive phases: anagen-the active proliferation phase, catagen-the degeneration phase, and telogen-the resting phase. While HFs undergo irreversible degeneration during catagen, recent experimental research on mice shows that when anagen HFs are subject to ionizing radiation (IR), they undergo a transient degeneration, followed by a nearly full regeneration that makes the HFs return to homeostatic state. The mechanisms underlying these IR-induced HF regenerative dynamics and the catagen degenerative dynamics, remain unknown. In this work, we develop an ODE type cell differentiation population model to study the control mechanisms of HF regeneration. The model is built based on current theoretical knowledge in biology and mathematically formulated using feedback mechanisms. Model parameters are calibrated to IR experimental data, and we then provide modeling results with both deterministic ODE simulations and corresponding stochastic simulations. We perform stability and bifurcation analyses on the ODE model, which reveal that for anagen HFs, a low spontaneous apoptosis rate secures the stability of the HF homeostatic steady state, allowing the HF to regenerate even when subject to strong IR. On the other hand, the irreversible degeneration during catagen results from both strong spontaneous apoptosis rate and strong apoptosis feedback. Lastly, we perform sensitivity analysis to identify key parameters in the model to validate these hypotheses.

Mother cells control daughter cell proliferation in intestinal organoids to minimize proliferation fluctuations

During renewal of the intestine, cells are continuously generated by proliferation. Proliferation and differentiation must be tightly balanced, as any bias toward proliferation results in uncontrolled exponential growth. Yet, the inherently stochastic nature of cells raises the question how such fluctuations are limited. We used time-lapse microscopy to track all cells in crypts of growing mouse intestinal organoids for multiple generations, allowing full reconstruction of the underlying lineage dynamics in space and time. Proliferative behavior was highly symmetric between sister cells, with both sisters either jointly ceasing or continuing proliferation. Simulations revealed that such symmetric proliferative behavior minimizes cell number fluctuations, explaining our observation that proliferating cell number remained constant even as crypts increased in size considerably. Proliferative symmetry did not reflect positional symmetry but rather lineage control through the mother cell. Our results indicate a concrete mechanism to balance proliferation and differentiation with minimal fluctuations that may be broadly relevant for other tissues.

Effects of spatial variation in dose delivery: what can we learn from radon-related lung cancer studies?

Exposure to radon progeny results in heterogeneous dose distributions in many different spatial scales. The aim of this review is to provide an overview on the state of the art in epidemiology, clinical observations, cell biology, dosimetry, and modelling related to radon exposure and its association with lung cancer, along with priorities for future research. Particular attention is paid on the effects of spatial variation in dose delivery within the organs, a factor not considered in radiation protection. It is concluded that a multidisciplinary approach is required to improve risk assessment and mechanistic understanding of carcinogenesis related to radon exposure. To achieve these goals, important steps would be to clarify whether radon can cause other diseases than lung cancer, and to investigate radon-related health risks in children or persons at young ages. Also, a better understanding of the combined effects of radon and smoking is needed, which can be achieved by integrating epidemiological, clinical, pathological, and molecular oncology data to obtain a radon-associated signature. While in vitro models derived from primary human bronchial epithelial cells can help to identify new and corroborate existing biomarkers, they also allow to study the effects of heterogeneous dose distributions including the effects of locally high doses. These novel approaches can provide valuable input and validation data for mathematical models for risk assessment. These models can be applied to quantitatively translate the knowledge obtained from radon exposure to other exposures resulting in heterogeneous dose distributions within an organ to support radiation protection in general.

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

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.

DURIAN: an integrative deconvolution and imputation method for robust signaling analysis of single-cell transcriptomics data

Single-cell RNA sequencing trades read-depth for dimensionality, often leading to loss of critical signaling gene information that is typically present in bulk data sets. We introduce DURIAN (Deconvolution and mUltitask-Regression-based ImputAtioN), an integrative method for recovery of gene expression in single-cell data. Through systematic benchmarking, we demonstrate the accuracy, robustness and empirical convergence of DURIAN using both synthetic and published data sets. We show that use of DURIAN improves single-cell clustering, low-dimensional embedding, and recovery of intercellular signaling networks. Our study resolves several inconsistent results of cell-cell communication analysis using single-cell or bulk data independently. The method has broad application in biomarker discovery and cell signaling analysis using single-cell transcriptomics data sets.

Emerging mechanisms of telomerase reactivation in cancer

Mutations in the promoter of human telomerase reverse transcriptase (hTERT) result in hyperactivation of hTERT. Notably, all mutations are G>A transitions, frequently found in a wide range of cancer types, and causally associated with cancer progression. Initially, the mutations were understood to reactivate hTERT by generating novel E26 transformation-specific (ETS) binding sites. Recent work reveals the role of DNA secondary structure G-quadruplexes, telomere binding factor(s), and chromatin looping in hTERT regulation. Here, we discuss these emerging findings in relation to the clinically significant promoter mutations to provide a broader understanding of the context-dependent outcomes that result in hTERT activation in normal and pathogenic conditions.

Effect of dedifferentiation on noise propagation in cellular hierarchy

Many fast renewing tissues have a hierarchical structure. Tissue-specific stem cells are at the root of this cellular hierarchy, which give rive to a whole range of specialized cells via cellular differentiation. However, increasing evidence shows that the hierarchical structure can be broken due to cellular dedifferentiation in which cells at differentiated stages can revert to the stem cell stage. Dedifferentiation has significant impacts on many aspects of hierarchical tissues. Here we investigate the effect of dedifferentiation on noise propagation by developing a stochastic model composed of different cell types. The moment equations are derived, via which we systematically investigate how the noise in the cell number is changed by dedifferentiation. Our results suggest that dedifferentiation have different effects on the noises in the numbers of stem cells and nonstem cells. Specifically, the noise in the number of stem cells is significantly reduced by increasing dedifferentiation probability. Due to the dual effect of dedifferentiation on nonstem cells, however, more complex changes could happen to the noise in the number of nonstem cells by increasing dedifferentiation probability. Furthermore, it is found that even though dedifferentiation could turn part of the noise propagation process into a noise-amplifying step, it is very unlikely to turn the entire process into a noise-amplifying cascade.

Spatial dynamics of feedback and feedforward regulation in cell lineages

Feedback mechanisms within cell lineages are thought to be important for maintaining tissue homeostasis. Mathematical models that assume well-mixed cell populations, together with experimental data, have suggested that negative feedback from differentiated cells on the stem cell self-renewal probability can maintain a stable equilibrium and hence homeostasis. Cell lineage dynamics, however, are characterized by spatial structure, which can lead to different properties. Here, we investigate these dynamics using spatially explicit computational models, including cell division, differentiation, death, and migration / diffusion processes. According to these models, the negative feedback loop on stem cell self-renewal fails to maintain homeostasis, both under the assumption of strong spatial restrictions and fast migration / diffusion. Although homeostasis cannot be maintained, this feedback can regulate cell density and promote the formation of spatial structures in the model. Tissue homeostasis, however, can be achieved if spatially restricted negative feedback on self-renewal is combined with an experimentally documented spatial feedforward loop, in which stem cells regulate the fate of transit amplifying cells. This indicates that the dynamics of feedback regulation in tissue cell lineages are more complex than previously thought, and that combinations of spatially explicit control mechanisms are likely instrumental.

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations.

Distinguishing between multiple mathematical models of neural stem cell quiescence and activation during age-related neural stem cell decline in neurogenesis

Stem cells are required for tissue maintenance and homeostasis during an organism's lifetime. Neural stem cells (NSCs) can be in an actively dividing state or in a quiescent state. The balance between stem cell quiescence and cycling activity determines the rate of neurogenesis. With age, more NSCs enter the quiescent state, while the total number of NSCs decreases. Here we reconsider an existing mathematical model of how neural stem cells switch between active and quiescent states from the point of view of control theory by considering the activation rate, self-renewal probability, and division rate as control parameters rather than as pre-defined functions. Our goal is to test whether those modifications to the basic model could explain the observed decline of neural stem cells with age better than Gomerzian time-dependent parameters, and compare the output from different model variants to experimental data from mice using AIC. We find that time-dependent activation rate provides the best fit to the activated cell fraction (ACF) of NSCs over time, but that other model variants with constant parameter values can better fit the total number of NSCs over time. We also consider an alternate model for NSCs with nonlinear feedback from progenitor cells that affect NSC parameters, and compare all models to experimental stem cell and progenitor data. However, all of the feedback models considered provide a worse fit to the experimental data. This suggests that when switching between active and quiescent stem cells is considered, a time-dependent linear model outperforms the integral feedback mechanism considered by other models of stem cell lineages. Fitting progenitor data for both the time varying models and feedback models indicates that four or five intermediate transit amplifying progenitor states are necessary. Our modeling suggests that in order to determine whether an increase in age-related neural stem cell quiescence is determined by by a decreasing stem cell activation rate or an increased stem cell depletion rate, additional experiments should be designed to explore whether or not depletion of the stem cell pool is occurring, and that a higher resolution time series for activated cell fraction (ACF) would be best to resolve this issue.

Eph/Ephrin-Based Protein Complexes: The Importance of cis Interactions in Guiding Cellular Processes

Although intracellular signal transduction is generally represented as a linear process that transmits stimuli from the exterior of a cell to the interior via a transmembrane receptor, interactions with additional membrane-associated proteins are often critical to its success. These molecules play a pivotal role in mediating signaling via the formation of complexes in cis (within the same membrane) with primary effectors, particularly in the context of tumorigenesis. Such secondary effectors may act to promote successful signaling by mediating receptor-ligand binding, recruitment of molecular partners for the formation of multiprotein complexes, or differential signaling outcomes. One signaling family whose contact-mediated activity is frequently modulated by lateral interactions at the cell surface is Eph/ephrin (EphA and EphB receptor tyrosine kinases and their ligands ephrin-As and ephrin-Bs). Through heterotypic interactions in cis, these molecules can promote a diverse range of cellular activities, including some that are mutually exclusive (cell proliferation and cell differentiation, or adhesion and migration). Due to their broad expression in most tissues and their promiscuous binding within and across classes, the cellular response to Eph:ephrin interaction is highly variable between cell types and is dependent on the cellular context in which binding occurs. In this review, we will discuss interactions between molecules in cis at the cell membrane, with emphasis on their role in modulating Eph/ephrin signaling.

Cell Lineage Infidelity in PDAC Progression and Therapy Resistance

Infidelity to cell fate occurs when differentiated cells lose their original identity and either revert to a more multipotent state or transdifferentiate into a different cell type, either within the same embryonic lineage or in an entirely different one. Whilst in certain circumstances, such as in wound repair, this process is beneficial, it can be hijacked by cancer cells to drive disease initiation and progression. Cell phenotype switching has been shown to also serve as a mechanism of drug resistance in some epithelial cancers. In pancreatic ductal adenocarcinoma (PDAC), the role of lineage infidelity and phenotype switching is still unclear. Two consensus molecular subtypes of PDAC have been proposed that mainly reflect the existence of cell lineages with different degrees of fidelity to pancreatic endodermal precursors. Indeed, the classical subtype of PDAC is characterised by the expression of endodermal lineage specifying transcription factors, while the more aggressive basal-like/squamous subtype is defined by epigenetic downregulation of endodermal genes and alterations in chromatin modifiers. Here, we summarise the current knowledge of mechanisms (genetic and epigenetic) of cell fate switching in PDAC and discuss how pancreatic organoids might help increase our understanding of both cell-intrinsic and cell-extrinsic factors governing lineage infidelity during the distinct phases of PDAC evolution.

Regulatory feedback effects on tissue growth dynamics in a two-stage cell lineage model

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signaling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the nontrivial fixed point and the trivial fixed point, respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic timescales for these two growth modes are also derived. Remarkably, the trivial and nontrivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bistable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic.

GDF11 expressed in the adult brain negatively regulates hippocampal neurogenesis

Growth differentiation factor 11 (GDF11) is a transforming factor-β superfamily member that functions as a negative regulator of neurogenesis during embryonic development. However, when recombinant GDF11 (rGDF11) is administered systemically in aged mice, it promotes neurogenesis, the opposite of its role during development. The goal of the present study was to reconcile this apparent discrepancy by performing the first detailed investigation into the expression of endogenous GDF11 in the adult brain and its effects on neurogenesis. Using quantitative histological analysis, we observed that Gdf11 is most highly expressed in adult neurogenic niches and non-neurogenic regions within the hippocampus, choroid plexus, thalamus, habenula, and cerebellum. To investigate the role of endogenous GDF11 during adult hippocampal neurogenesis, we generated a tamoxifen inducible mouse that allowed us to reduce GDF11 levels. Depletion of Gdf11 during adulthood increased proliferation of neural progenitors and decreased the number of newborn neurons in the hippocampus, suggesting that endogenous GDF11 remains a negative regulator of hippocampal neurogenesis in adult mice. These findings further support the idea that circulating systemic GDF11 and endogenously expressed GDF11 in the adult brain have different target cells or mechanisms of action. Our data describe a role for GDF11-dependent signaling in adult neurogenesis that has implications for how GDF11 may be used to treat CNS disease.

Evolution of cancer stem cell lineage involving feedback regulation

Tumor emergence and progression is a complex phenomenon that assumes special molecular and cellular interactions. The hierarchical structuring and communication via feedback signaling of different cell types, which are categorized as the stem, progenitor, and differentiated cells in dependence of their maturity level, plays an important role. Under healthy conditions, these cells build a dynamical system that is responsible for facilitating the homeostatic regulation of the tissue. Generally, in this hierarchical setting, stem and progenitor cells are yet likely to undergo a mutation, when a cell divides into two daughter cells. This may lead to the development of abnormal characteristics, i.e. mutation in the cell, yielding an unrestrained number of cells. Therefore, the regulation of a stem cell’s proliferation and differentiation rate is crucial for maintaining the balance in the overall cell population. In this paper, a maturity based mathematical model with feedback regulation is formulated for healthy and mutated cell lineages. It is given in the form of coupled ordinary and partial differential equations. The focus is laid on the dynamical effects resulting from acquiring a mutation in the hierarchical structure of stem, progenitor and fully differentiated cells. Additionally, the effects of nonlinear feedback regulation from mature cells into both stem and progenitor cell populations have been inspected. The steady-state solutions of the model are derived analytically. Numerical simulations and results based on a finite volume scheme underpin various expected behavioral patterns of the homeostatic regulation and cancer evolution. For instance, it has been found that the mutated cells can experience significant growth even with a single somatic mutation, but under homeostatic regulation acquire a steady-state and thus, ensuing healthy cell population to either a steady-state or a lower cell concentration. Furthermore, the model behavior has been validated with different experimentally measured tumor values from the literature.

Spatiotemporal control of cell cycle acceleration during axolotl spinal cord regeneration

Axolotls are uniquely able to resolve spinal cord injuries, but little is known about the mechanisms underlying spinal cord regeneration. We previously found that tail amputation leads to reactivation of a developmental-like program in spinal cord ependymal cells (Rodrigo Albors et al., 2015), characterized by a high-proliferation zone emerging 4 days post-amputation (Rost et al., 2016). What underlies this spatiotemporal pattern of cell proliferation, however, remained unknown. Here, we use modeling, tightly linked to experimental data, to demonstrate that this regenerative response is consistent with a signal that recruits ependymal cells during ~85 hours after amputation within ~830 μm of the injury. We adapted Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) technology to axolotls (AxFUCCI) to visualize cell cycles in vivo. AxFUCCI axolotls confirmed the predicted appearance time and size of the injury-induced recruitment zone and revealed cell cycle synchrony between ependymal cells. Our modeling and imaging move us closer to understanding bona fide spinal cord regeneration.

Potential Osteoinductive Effects of Hydroxyapatite Nanoparticles on Mesenchymal Stem Cells by Endothelial Cell Interaction

Nano-hydroxyapatite (nano-HA) has attracted substantial attention in the field of regenerative medicine. Endothelial cell (EC)-mesenchymal stem cell (MSC) interactions are necessary for bone reconstruction, but the manner in which nano-HA interacts in this process remains unknown. Herein, we investigated the cytotoxicity and osteoinductive effects of HA nanoparticles (HANPs) on MSCs using an indirect co-culture model mediated by ECs and highlighted the underlying mechanisms. It was found that at a subcytotoxic dose, HANPs increased the viability and expression of osteoblast genes, as well as mineralized nodules and alkaline phosphatase production of MSCs. These phenomena relied on HIF-1α secreted by ECs, which triggered the ERK1/2 signaling cascade. In addition, a two-stage cell-lineage mathematical model was established to quantitatively analyze the impact of HIF-1α on the osteogenic differentiation of MSCs. It demonstrated that HIF-1α exerted a dose-dependent stimulatory effect on the osteogenic differentiation rate of MSCs up to 1500 pg/mL, which was in agreement with the above results. Our data implied that cooperative interactions between HANPs, ECs, and MSCs likely serve to stimulate bone regeneration. Furthermore, the two-stage cell-lineage model is helpful in vitro system for assessing the potential influence of effector molecules in bone tissue engineering.

Dynamic spatiotemporal coordination of neural stem cell fate decisions occurs through local feedback in the adult vertebrate brain

Neural stem cell (NSC) populations persist in the adult vertebrate brain over a lifetime, and their homeostasis is controlled at the population level through unknown mechanisms. Here, we combine dynamic imaging of entire NSC populations in their in vivo niche over several weeks with pharmacological manipulations, mathematical modeling, and spatial statistics and demonstrate that NSCs use spatiotemporally resolved local feedback signals to coordinate their decision to divide in adult zebrafish brains. These involve Notch-mediated short-range inhibition from transient neural progenitors and a dispersion effect from the dividing NSCs themselves exerted with a delay of 9–12 days. Simulations from a stochastic NSC lattice model capturing these interactions demonstrate that these signals are linked by lineage progression and control the spatiotemporal distribution of output neurons. These results highlight how local and temporally delayed interactions occurring between brain germinal cells generate self-propagating dynamics that maintain NSC population homeostasis and coordinate specific spatiotemporal correlations.

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NSC activation events are spatiotemporally coordinated within adult NSC populations

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This involves inhibition by neural progenitors (relying on Notch) and by dividing NSCs

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A dynamic lattice model shows that these interactions are linked by lineage progression

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NSCs dynamics generate an intrinsic niche that maintains the NSC population long-term

Senescent cells and the incidence of age-related diseases

Age-related diseases such as cancer, cardiovascular disease, kidney failure, and osteoarthritis have universal features: Their incidence rises exponentially with age with a slope of 6-8% per year and decreases at very old ages. There is no conceptual model which explains these features in so many diverse diseases in terms of a single shared biological factor. Here, we develop such a model, and test it using a nationwide medical record dataset on the incidence of nearly 1000 diseases over 50 million life-years, which we provide as a resource. The model explains incidence using the accumulation of senescent cells, damaged cells that cause inflammation and reduce regeneration, whose level rise stochastically with age. The exponential rise and late drop in incidence are captured by two parameters for each disease: the susceptible fraction of the population and the threshold concentration of senescent cells that causes disease onset. We propose a physiological mechanism for the threshold concentration for several disease classes, including an etiology for diseases of unknown origin such as idiopathic pulmonary fibrosis and osteoarthritis. The model can be used to design optimal treatments that remove senescent cells, suggeting that treatment starting at old age can sharply reduce the incidence of all age-related diseases, and thus increase the healthspan.

CELLULAR FEEDBACK NETWORKS AND THEIR RESILIENCE AGAINST MUTATIONS

Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth or reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.

Transit-Amplifying Cells Coordinate Changes in Intestinal Epithelial Cell-Type Composition

Renewing tissues have the remarkable ability to continually produce both proliferative progenitor and specialized differentiated cell types. How are complex milieus of microenvironmental signals interpreted to coordinate tissue-cell-type composition? Here, we investigate the responses of intestinal epithelium to individual and paired perturbations across eight epithelial signaling pathways. Using a high-throughput approach that combines enteroid monolayers and quantitative imaging, we identified conditions that enrich for specific cell types as well as interactions between pathways. Importantly, we found that modulation of transit-amplifying cell proliferation changes the ratio of differentiated secretory to absorptive cell types. These observations highlight an underappreciated role for transit-amplifying cells in the tuning of differentiated cell-type composition.

What determines organ size during development and regeneration?

The sizes of living organisms span over 20 orders of magnitude or so. This daunting observation could intimidate researchers aiming to understand the general mechanisms controlling growth. However, recent progress suggests the existence of principles common to organisms as diverse as fruit flies, mice and humans. As we review here, these studies have provided insights into both autonomous and non-autonomous mechanisms controlling organ growth as well as some of the principles underlying growth coordination between organs and across bilaterally symmetrical organisms. This research tackles several aspects of developmental biology and integrates inputs from physics, mathematical modelling and evolutionary biology. Although many open questions remain, this work also helps to shed light on medically related conditions such as tissue and limb regeneration, as well as metabolic homeostasis and cancer.

Inference of Intercellular Communications and Multilayer Gene-Regulations of Epithelial-Mesenchymal Transition From Single-Cell Transcriptomic Data

Epithelial-to-mesenchymal transition (EMT) plays an important role in many biological processes during development and cancer. The advent of single-cell transcriptome sequencing techniques allows the dissection of dynamical details underlying EMT with unprecedented resolution. Despite several single-cell data analysis on EMT, how cell communicates and regulates dynamics along the EMT trajectory remains elusive. Using single-cell transcriptomic datasets, here we infer the cell-cell communications and the multilayer gene-gene regulation networks to analyze and visualize the complex cellular crosstalk and the underlying gene regulatory dynamics along EMT. Combining with trajectory analysis, our approach reveals the existence of multiple intermediate cell states (ICSs) with hybrid epithelial and mesenchymal features. Analyses on the time-series datasets from cancer cell lines with different inducing factors show that the induced EMTs are context-specific: the EMT induced by transforming growth factor B1 (TGFB1) is synchronous, whereas the EMTs induced by epidermal growth factor and tumor necrosis factor are asynchronous, and the responses of TGF-β pathway in terms of gene expression regulations are heterogeneous under different treatments or among various cell states. Meanwhile, network topology analysis suggests that the ICSs during EMT serve as the signaling in cellular communication under different conditions. Interestingly, our analysis of a mouse skin squamous cell carcinoma dataset also suggests regardless of the significant discrepancy in concrete genes between in vitro and in vivo EMT systems, the ICSs play dominant role in the TGF-β signaling crosstalk. Overall, our approach reveals the multiscale mechanisms coupling cell-cell communications and gene-gene regulations responsible for complex cell-state transitions.

Variability of an Early Developmental Cell Population Underlies Stochastic Laterality Defects

Embryonic development seemingly proceeds with almost perfect precision. However, it is largely unknown how much underlying microscopic variability is compatible with normal development. Here, we quantify embryo-to-embryo variability in vertebrate development by studying cell number variation in the zebrafish endoderm. We notice that the size of a sub-population of the endoderm, the dorsal forerunner cells (DFCs, which later form the left-right organizer), exhibits significantly more embryo-to-embryo variation than the rest of the endoderm. We find that, with incubation of the embryos at elevated temperature, the frequency of left-right laterality defects is increased drastically in embryos with a low number of DFCs. Furthermore, we observe that these fluctuations have a large stochastic component among fish of the same genetic background. Hence, a stochastic variation in early development leads to a remarkably strong macroscopic phenotype. These fluctuations appear to be associated with maternal effects in the specification of the DFCs.

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High embryo-to-embryo variability of dorsal forerunner cell numbers

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Fluctuations of dorsal forerunner cells have a large stochastic component

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Embryos with fewer dorsal forerunner cells frequently develop laterality defects

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Variability of dorsal forerunner cell numbers is associated to maternal effects

Optimal experimental design for mathematical models of haematopoiesis

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

Neural stem cell pools in the vertebrate adult brain: Homeostasis from cell-autonomous decisions or community rules?

Adult stem cell populations must coordinate their own maintenance with the generation of differentiated cell types to sustain organ physiology, in a spatially controlled manner and over long periods. Quantitative analyses of clonal dynamics have revealed that, in epithelia, homeostasis is achieved at the population rather than at the single stem cell level, suggesting that feedback mechanisms coordinate stem cell maintenance and progeny generation. In the central nervous system, however, little is known of the possible community processes underlying neural stem cell maintenance. Recent work, in part based on intravital imaging made possible in the adult zebrafish, conclusively highlights that homeostasis in neural stem cell pools may rely on population asymmetry and long-term spatiotemporal coordination of neural stem cell states and fates. These results suggest that neural stem cell assemblies in the vertebrate brain behave as self-organized systems, such that the stem cells themselves generate their own intrinsic niche.

Effect of feedback regulation on stem cell fractions in tissues and tumors: Understanding chemoresistance in cancer

While resistance mutations are often implicated in the failure of cancer therapy, lack of response also occurs without such mutants. In bladder cancer mouse xenografts, repeated chemotherapy cycles have resulted in cancer stem cell (CSC) enrichment, and consequent loss of therapy response due to the reduced susceptibility of CSCs to drugs. A particular feedback loop present in the xenografts has been shown to promote CSC enrichment in this system. Yet, many other regulatory loops might also be operational and might promote CSC enrichment. Their identification is central to improving therapy response. Here, we perform a comprehensive mathematical analysis to define what types of regulatory feedback loops can and cannot contribute to CSC enrichment, providing guidance to the experimental identification of feedback molecules. We derive a formula that reveals whether or not the cell population experiences CSC enrichment over time, based on the properties of the feedback. We find that negative feedback on the CSC division rate or positive feedback on differentiated cell death rate can lead to CSC enrichment. Further, the feedback mediators that achieve CSC enrichment can be secreted by either CSCs or by more differentiated cells. The extent of enrichment is determined by the CSC death rate, the CSC self-renewal probability, and by feedback strength. Defining these general characteristics of feedback loops can guide the experimental screening for and identification of feedback mediators that can promote CSC enrichment in bladder cancer and potentially other tumors. This can help understand and overcome the phenomenon of CSC-based therapy resistance.

Dynamics of nevus development implicate cell cooperation in the growth arrest of transformed melanocytes

Mutational activation of the BRAF proto-oncogene in melanocytes reliably produces benign nevi (pigmented 'moles'), yet the same change is the most common driver mutation in melanoma. The reason nevi stop growing, and do not progress to melanoma, is widely attributed to a cell-autonomous process of 'oncogene-induced senescence'. Using a mouse model of Braf-driven nevus formation, analyzing both proliferative dynamics and single-cell gene expression, we found no evidence that nevus cells are senescent, either compared with other skin cells, or other melanocytes. We also found that nevus size distributions could not be fit by any simple cell-autonomous model of growth arrest, yet were easily fit by models based on collective cell behavior, for example in which arresting cells release an arrest-promoting factor. We suggest that nevus growth arrest is more likely related to the cell interactions that mediate size control in normal tissues, than to any cell-autonomous, 'oncogene-induced' program of senescence.

Mathematical Model of Muscle Wasting in Cancer Cachexia

Cancer cachexia is a debilitating condition characterized by an extreme loss of skeletal muscle mass, which negatively impacts patients' quality of life, reduces their ability to sustain anti-cancer therapies, and increases the risk of mortality. Recent discoveries have identified the myostatin/activin A/ActRIIB pathway as critical to muscle wasting by inducing satellite cell quiescence and increasing muscle-specific ubiquitin ligases responsible for atrophy. Remarkably, pharmacological blockade of the ActRIIB pathway has been shown to reverse muscle wasting and prolong the survival time of tumor-bearing animals. To explore the implications of this signaling pathway and potential therapeutic targets in cachexia, we construct a novel mathematical model of muscle tissue subjected to tumor-derived cachectic factors. The model formulation tracks the intercellular interactions between cancer cell, satellite cell, and muscle cell populations. The model is parameterized by fitting to colon-26 mouse model data, and the analysis provides insight into tissue growth in healthy, cancerous, and post-cachexia treatment conditions. Model predictions suggest that cachexia fundamentally alters muscle tissue health, as measured by the stem cell ratio, and this is only partially recovered by anti-cachexia treatment. Our mathematical findings suggest that after blocking the myostatin/activin A pathway, partial recovery of cancer-induced muscle loss requires the activation and proliferation of the satellite cell compartment with a functional differentiation program.

'Rinse and Replace': Boosting T Cell Turnover To Reduce HIV-1 Reservoirs

Latent HIV-1 persists indefinitely during antiretroviral therapy (ART) as an integrated silent genome in long-lived memory CD4+ T cells. In untreated infections, immune activation increases the turnover of intrinsically long-lived provirus-containing CD4+ T cells. Those are 'washed out' as a result of their activation, which when coupled to viral protein expression can facilitate local inflammation and recruitment of uninfected cells to activation sites, causing latently infected cells to compete for survival. De novo infection can counter this washout. During ART, inflammation and CD4+ T cell activation wane, resulting in reduced cell turnover and a persistent reservoir. We propose accelerating reservoir washout during ART by triggering sequential waves of polyclonal CD4+ T cell activation while simultaneously enhancing virus protein expression. Reservoir reduction as an adjunct to other therapies might achieve lifelong viral control.

Regulation of size and scale in vertebrate spinal cord development

All vertebrates have a spinal cord with dimensions and shape specific to their species. Yet how species‐specific organ size and shape are achieved is a fundamental unresolved question in biology. The formation and sculpting of organs begins during embryonic development. As it develops, the spinal cord extends in anterior–posterior direction in synchrony with the overall growth of the body. The dorsoventral (DV) and apicobasal lengths of the spinal cord neuroepithelium also change, while at the same time a characteristic pattern of neural progenitor subtypes along the DV axis is established and elaborated. At the basis of these changes in tissue size and shape are biophysical determinants, such as the change in cell number, cell size and shape, and anisotropic tissue growth. These processes are controlled by global tissue‐scale regulators, such as morphogen signaling gradients as well as mechanical forces. Current challenges in the field are to uncover how these tissue‐scale regulatory mechanisms are translated to the cellular and molecular level, and how regulation of distinct cellular processes gives rise to an overall defined size. Addressing these questions will help not only to achieve a better understanding of how size is controlled, but also of how tissue size is coordinated with the specification of pattern.

This article is categorized under:

Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing

Signaling Pathways > Global Signaling Mechanisms

Nervous System Development > Vertebrates: General Principles

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.

Modelling stem cell ageing: a multi-compartment continuum approach

Stem cells are important to generate all specialized tissues at an early life stage, and in some systems, they also have repair functions to replenish the adult tissues. Repeated cell divisions lead to the accumulation of molecular damage in stem cells, which are commonly recognized as drivers of ageing. In this paper, a novel model is proposed to integrate stem cell proliferation and differentiation with damage accumulation in the stem cell ageing process. A system of two structured PDEs is used to model the population densities of stem cells (including all multiple progenitors) and terminally differentiated (TD) cells. In this system, cell cycle progression and damage accumulation are modelled by continuous dynamics, and damage segregation between daughter cells is considered at each division. Analysis and numerical simulations are conducted to study the steady-state populations and stem cell damage distributions under different damage segregation strategies. Our simulations suggest that equal distribution of the damaging substance between stem cells in a symmetric renewal and less damage retention in stem cells in the asymmetric division are favourable strategies, which reduce the death rate of the stem cells and increase the TD cell populations. Moreover, asymmetric damage segregation in stem cells leads to less concentrated damage distribution in the stem cell population, which may be more robust to the stochastic changes in the damage. The feedback regulation from stem cells can reduce oscillations and population overshoot in the process, and improve the fitness of stem cells by increasing the percentage of cells with less damage in the stem cell population.

Purinergic signalling selectively modulates maintenance but not repair neurogenesis in the zebrafish olfactory epithelium

Olfactory sensory neurons (OSNs) of the vertebrate olfactory epithelium (OE) undergo continuous turnover but also regenerate efficiently when the OE is acutely damaged by traumatic injury. Two distinct pools of neuronal stem/progenitor cells, the globose (GBCs), and horizontal basal cells (HBCs) have been shown to selectively contribute to intrinsic OSN turnover and damage-induced OE regeneration, respectively. For both types of progenitors, their rate of cell divisions and OSN production must match the actual loss of cells to maintain or to re-establish sensory function. However, signals that communicate between neurons or glia cells of the OE and resident neurogenic progenitors remain largely elusive. Here, we investigate the effect of purinergic signaling on cell proliferation and OSN neurogenesis in the zebrafish OE. Purine stimulation elicits transient Ca²⁺ signals in OSNs and distinct non-neuronal cell populations, which are located exclusively in the basal OE and stain positive for the neuronal stem cell marker Sox2. The more apical population of Sox2-positive cells comprises evenly distributed glia-like sustentacular cells (SCs) and spatially restricted GBC-like cells, whereas the more basal population expresses the HBC markers keratin 5 and tumor protein 63 and lines the entire sensory OE. Importantly, exogenous purine stimulation promotes P2 receptor-dependent mitotic activity and OSN generation from sites where GBCs are located but not from HBCs. We hypothesize that purine compounds released from dying OSNs modulate GBC progenitor cell cycling in a dose-dependent manner that is proportional to the number of dying OSNs and, thereby, ensures a constant pool of sensory neurons over time.

Immunological Paradigms, Mechanisms, and Models: Conceptual Understanding Is a Prerequisite to Effective Modeling

Most mathematical models that describe the individual or collective actions of cells aim at creating faithful representations of limited sets of data in a self-consistent manner. Consistency with relevant physiological rules pertaining to the greater picture is rarely imposed. By themselves, such models have limited predictive or even explanatory value, contrary to standard claims. Here I try to show that a more critical examination of currently held paradigms is necessary and could potentially lead to models that pass the test of time. In considering the evolution of paradigms over the past decades I focus on the “smart surveillance” theory of how T cells can respond differentially, individually and collectively, to both self- and foreign antigens depending on various “contextual” parameters. The overall perspective is that physiological messages to cells are encoded not only in the biochemical connections of signaling molecules to the cellular machinery but also in the magnitude, kinetics, and in the time- and space-contingencies, of sets of stimuli. By rationalizing the feasibility of subthreshold interactions, the “dynamic tuning hypothesis,” a central component of the theory, set the ground for further theoretical and experimental explorations of dynamically regulated immune tolerance, homeostasis and diversity, and of the notion that lymphocytes participate in nonclassical physiological functions. Some of these efforts are reviewed. Another focus of this review is the concomitant regulation of immune activation and homeostasis through the operation of a feedback mechanism controlling the balance between renewal and differentiation of activated cells. Different perspectives on the nature and regulation of chronic immune activation in HIV infection have led to conflicting models of HIV pathogenesis—a major area of research for theoretical immunologists over almost three decades—and can have profound impact on ongoing HIV cure strategies. Altogether, this critical review is intended to constructively influence the outlook of prospective model builders and of interested immunologists on the state of the art and to encourage conceptual work.