Modelling the spatio-temporal cell dynamics reveals novel insights on cell differentiation and proliferation in the small intestinal crypt

We developed a slow structural relaxation model to describe cellular dynamics in the crypt of the mouse small intestine. Cells are arranged in a three dimensional spiral the size of which dynamically changes according to cell production demands of adjacent villi. Cell differentiation and proliferation is regulated through Wnt and Notch signals, the strength of which depends on the local cell composition. The highest level of Wnt activity is associated with maintaining equipotent stem cells (SC), Paneth cells and common goblet-Paneth cell progenitors (CGPCPs) intermingling at the crypt bottom. Low levels of Wnt signalling area are associated with stem cells giving rise to secretory cells (CGPCPs, enteroendocrine or Tuft cells) and proliferative absorptive progenitors. Deciding between these two fates, secretory and stem/absorptive cells, depends on Notch signalling. Our model predicts that Notch signalling inhibits secretory fate if more than 50% of cells they are in contact with belong to the secretory lineage. CGPCPs under high Wnt signalling will differentiate into Paneth cells while those migrating out from the crypt bottom differentiate into goblet cells. We have assumed that mature Paneth cells migrating upwards undergo anoikis. Structural relaxation explains the localisation of Paneth cells to the crypt bottom in the absence of active forces. The predicted crypt generation time from one SC is 4-5 days with 10-12 days needed to reach a structural steady state. Our predictions are consistent with experimental observations made under altered Wnt and Notch signalling. Mutations affecting stem cells located at the crypt floor have a 50% chance of being propagated throughout the crypt while mutations in cells above are rarely propagated. The predicted recovery time of an injured crypt losing half of its cells is approximately 2 days.     

A model of the control of cellular regeneration in the intestinal crypt after perturbation based solely on local stem cell regulation

Abstract. The control mechanisms involved in regeneration of murine intestinal crypts after perturbations are presently not well understood. The existence of some feedback signals from the cells on the villus to the cells in the crypt has been suggested. However, some recent experimental data point to the fact that regeneration in the crypt starts very early after perturbation, at a time when the villus cell population has hardly changed. In particular, this early cell proliferative activity is seen specifically at the bottom of the crypt, i.e. in the presumed stem cell zone and furthest from the villus.
The objective of this study was to investigate whether a new concept of regulation operating solely at the stem cell level could explain the present mass of accumulated data on the post-irradiation recovery, which is an extensively studied perturbation from the experimental point of view. In order to check its validity, the new concept was formalized as a mathematical simulation model thus enabling comparison with experimental data. The model describes the cellular development from stem cells to the mature villus cells. As a basic feature it is assumed that the self-maintenance and the cell cycle activity of the stem cells are controlled by the number of these cells in an autoregulatory fashion. The essential features of the experimental data (i.e. the recovery with time and the consistency between different types of measurements) can be very well reproduced by simulations using a range of model parameters. Thus, we conclude that stem cell autoregulation is a valid concept which could replace the villus crypt feedback concept in explaining the early changes after irradiation when the damage primarily affects the crypt. The question of the detailed nature of the control process requires further investigation.     

A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt

We present a development of a model [Tomlinson, I.P.M., Bodmer, W.F., 1995. Failure of programmed cell death and differentiation as causes of tumors: Some simple mathematical models. Proc. Natl. Acad. Sci. USA 92, 11130-11134.] of the relationship between cells in three compartments of the intestinal crypt: stem cells, semi-differentiated cells and fully differentiated cells. Stem and semi-differentiated cells may divide to self-renew, undergo programmed death or progress to semi-differentiated and fully differentiated cells, respectively. The probabilities of each of these events provide the most important parameters of the model. Fully differentiated cells do not divide, but a proportion undergoes programmed death in each generation. Our previous models showed that failure of programmed death--for example, in tumorigenesis--could lead either to exponential growth in cell numbers or to growth to some plateau. Our new models incorporate plausible fluctuation in the parameters of the model and introduce nonlinearity by assuming that the parameters depend on the numbers of cells in each state of differentiation. We present detailed analysis of the equilibrium conditions for various forms of these models and, where appropriate, simulate the changes in cell numbers. We find that the model is characterized by bifurcation between increase in cell numbers to stable equilibrium or explosive exponential growth; in a restricted number of cases, there may be multiple stable equilibria. Fluctuation in cell numbers undergoing programmed death, for example caused by tissue damage, generally makes exponential growth more likely, as long as the size of the fluctuation exceeds a certain critical value for a sufficiently long period of time. In most cases, once exponential growth has started, this process is irreversible. In some circumstances, exponential growth is preceded by a long plateau phase, of variable duration, mimicking equilibrium: thus apparently self-limiting lesions may not be so in practice and the duration of growth of a tumor may be impossible to predict on the basis of its size.     

A PDMP model of the epithelial cell turn-over in the intestinal crypt including microbiota-derived regulations

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. That is, whether parameters can be uniquely determined from perfect or realistic data in theory and practice. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

     

Intestinal cell proliferation. I. A comprehensive model of steady-state proliferation in the crypt

Cell replacement in the crypt of the murine small intestine has been studied and modelled mathematically under steady-state conditions. A great deal of information is available for this system, e.g. cell cycle times, S phase durations, the rate of daily cell production, the Paneth cell distribution etc. The purpose of the present work was to consider simultaneously as much of these data as possible and to formulate a model based upon the behaviour of individual cells which adequately accounted for them. A simple mathematical representation of the crypt has been developed. This consists of sixteen stem cells per crypt (TC = 16 hr, TS = 9 hr), and four subsequent transit cell divisions (TC = 11 to 12 hr, TS = 8 hr) before maturation. Experimental data considered to test the modelling were LI and data on the number of vertical runs of similarly labelled cells. All data were obtained from the ileum after 25 microCi [3H]TdR given at 09:00 hours. A number of alternative assumptions have been considered and either accepted or rejected. Two alternative model concepts of cell displacement explain the data equally well. One is dependent upon strong local cell generation age determinance while the other could accommodate any weak local cell displacement process in conjunction with an environmental cut-off determinant at the middle of the crypt. Both models provide new interpretations of the data, e.g. certain rates of lateral cell exchange between neighbouring columns (250 to 350 per crypt per day out of a total of 420 cell divisions per day) can be concluded from run data, while LI data provide information about the mechanisms involved in maintaining a position-related age order in the crypt.     

Stem cell self-renewal in intestinal crypt

As a rapidly cycling tissue capable of fast repair and regeneration, the intestinal epithelium has emerged as a favored model system to explore the principles of adult stem cell biology. However, until recently, the identity and characteristics of the stem cell population in both the small intestine and colon has remained the subject of debate. Recent studies based on targeted lineage tracing strategies, combined with the development of an organotypic culture system, have identified the crypt base columnar cell as the intestinal stem cell, and have unveiled the strategy by which the balance between proliferation and differentiation is maintained. These results show that intestinal stem cells operate in a dynamic environment in which frequent and stochastic stem cell loss is compensated by the proliferation of neighboring stem cells. We review the basis of these experimental findings and the insights they offer into the mechanisms of homeostatic stem cell regulation.     

Graded BMP signaling within intestinal crypt architecture directs self-organization of the Wnt-secreting stem cell niche

1. Download : Download high-res image (245KB)
2. Download : Download full-size image

     

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

A number of mechano-regulation theories have been proposed that relate the differentiation pathway of mesenchymal stem cells (MSCs) to their local biomechanical environment. During spontaneous repair processes in skeletal tissues, the organisation of the extracellular matrix is a key determinant of its mechanical fitness. In this paper, we extend the mechano-regulation theory proposed by Prendergast et al. (J Biomech 30(6):539–548, 1997) to include the role of the mechanical environment on the collagen architecture in regenerating soft tissues. A large strain anisotropic poroelastic material model is used in a simulation of tissue differentiation in a fracture subject to cyclic bending (Cullinane et al. in J Orthop Res 20(3):579–586, 2002). The model predicts non-union with cartilage and fibrous tissue formation in the defect. Predicted collagen fibre angles, as determined by the principal decomposition of strain- and stress-type tensors, are similar to the architecture seen in native articular cartilage and neoarthroses induced by bending of mid-femoral defects in rats. Both stress and strain-based remodelling stimuli successfully predicted the general patterns of collagen fibre organisation observed in vivo. This provides further evidence that collagen organisation during tissue differentiation is determined by the mechanical environment. It is envisioned that such predictive models can play a key role in optimising MSC-based skeletal repair therapies where recapitulation of the normal tissue architecture is critical to successful repair.     

The highest labelled cell in the intestinal crypt column

A formula is given, and proved, for the expected position of the highest labelled cell in an individual crypt column, if the labelling index distribution is known.     

The highest labelled cell in the intestinal crypt colum

Abstract A formula is given, and proved, for the expected position of the highest labelled cell in an individual crypt column, if the labelling index distribution is known.     

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.     

Variation in crypt size and its influence on the analysis of epithelial cell proliferation in the intestinal crypt.

The standard model of epithelial cell renewal in the intestine proposes a gradual transition between the region of the crypt containing actively proliferating cells and that containing solely terminally differentiating cells (Cairnie, Lamerton and Steel, 1965 a, b). The experimental justification for this conclusion was the gradual decrease towards the crypt top of the measured labeling and mitotic indices. Recently, however, we have proposed that intestinal crypts normally undergo a replicative cycle so that at any time in any region of the intestine, crypts will be found to have a wide range of sizes. We show here that if this intrinsic size variation is taken into account, then a sharp transition between the proliferative and nonproliferative compartments of individual intestinal crypts is consistent with the labeling and mitotic index distributions of mouse and rat jejunal crypts. Thus there is no need to invoke the region of gradual transition from proliferating to nonproliferating cells as is done in the standard model. The position of this sharp transition is estimated for both the mouse and rat. Experiments to further test our model are suggested and the significance of the results discussed.     

Cell migration and organization in the intestinal crypt using a lattice-free model

We present a novel class of spatial models of cell movement and arrangement applied to the two-dimensional cellular organization of the intestinal crypt. The model differs from earlier approaches in using a dynamic movement on a lattice-free cylindrical surface. Cell movement is a consequence of mitotic activity. Cells interact by viscoelastic forces. Voronoi tessellation permits simulations of individual cell boundaries. Simulations can be compared with experimental data obtained from cell scoring in sections. Simulation studies show that the model is consistent with the experimental results for the spatial distribution of labelling indices, mitotic indices and other observed phenomena using a fixed number of stem cells and a fixed number of transit cell divisions.     

Fluorescent labelling of intestinal epithelial cells reveals independent long-lived intestinal stem cells in a crypt

Background and aims

The dynamics of intestinal stem cells are crucial for regulation of intestinal function and maintenance. Although crypt stem cells have been identified in the intestine by genetic marking methods, identification of plural crypt stem cells has not yet been achieved as they are visualised in the same colour.

Methods

Intestinal organoids were transferred into Matrigel® mixed with lentivirus encoding mCherry. The dynamics of mCherry-positive cells was analysed using time-lapse imaging, and the localisation of mCherry-positive cells was analysed using 3D immunofluorescence.

Results

We established an original method for the introduction of a transgene into an organoid generated from mouse small intestine that resulted in continuous fluorescence of the mCherry protein in a portion of organoid cells. Three-dimensional analysis using confocal microscopy showed a single mCherry-positive cell in an organoid crypt that had been cultured for >1 year, which suggested the presence of long-lived mCherry-positive and -negative stem cells in the same crypt. Moreover, a single mCherry-positive stem cell in a crypt gave rise to both crypt base columnar cells and transit amplifying cells. Each mCherry-positive and -negative cell contributed to the generation of organoids.

Conclusions

The use of our original lentiviral transgene system to mark individual organoid crypt stem cells showed that long-lived plural crypt stem cells might independently serve as intestinal epithelial cells, resulting in the formation of a completely functional villus.     

Evidence for cell generation controlled proliferation in the small intestinal crypt

In this paper we discuss the hypothesis that cell proliferation is controlled by the number of generations after leaving an 'eternal' stem cell. The theory is based on a simulation of the kinetic behaviour of cells in the intestinal crypts. There is evidence of three, four and five generations of cells which are allowed to enter mitosis in the lower and upper part of the normal intestinal tract, and in some disease states, respectively. We suggest an internal proliferation control: some kind of knowledge that cells carry from generation to generation. It is an open question what sets and changes the generation counter: internal genetic information or external influences such as growth factors or chalones. The geometric shape of the epithelial tissue in the intestinal tract can be understood as the steady state of a highly dynamic process. Age and death are determined from the beginning; cell-cell interaction or communication is not necessary and can be neglected. Our theory will be illustrated using the intestinal crypts as they are easily accessible, of a simple structure and completely described in the literature.     

Colon stem cell and crypt dynamics exposed by cell lineage reconstruction

Stem cell dynamics in vivo are often being studied by lineage tracing methods. Our laboratory has previously developed a retrospective method for reconstructing cell lineage trees from somatic mutations accumulated in microsatellites. This method was applied here to explore different aspects of stem cell dynamics in the mouse colon without the use of stem cell markers. We first demonstrated the reliability of our method for the study of stem cells by confirming previously established facts, and then we addressed open questions. Our findings confirmed that colon crypts are monoclonal and that, throughout adulthood, the process of monoclonal conversion plays a major role in the maintenance of crypts. The absence of immortal strand mechanism in crypts stem cells was validated by the age-dependent accumulation of microsatellite mutations. In addition, we confirmed the positive correlation between physical and lineage proximity of crypts, by showing that the colon is separated into small domains that share a common ancestor. We gained new data demonstrating that colon epithelium is clustered separately from hematopoietic and other cell types, indicating that the colon is constituted of few progenitors and ruling out significant renewal of colonic epithelium from hematopoietic cells during adulthood. Overall, our study demonstrates the reliability of cell lineage reconstruction for the study of stem cell dynamics, and it further addresses open questions in colon stem cells. In addition, this method can be applied to study stem cell dynamics in other systems.     

Tales from the crypt: the expanding role of slow cycling intestinal stem cells

Similar to other highly self-renewing tissues, the intestinal epithelium contains both slowly and rapidly cycling progenitor/stem cells, though their relationship has been largely unexplored. Two recent reports in Nature (Tian et al., 2011) and Science (Takeda et al., 2011) shed new light on their dynamic interplay.