The growth and life of a monoclonal crypt

A computer simulation of a highly dynamic model for the birth, growth and adult life of a monoclonal crypt in the intestine was developed starting with a single precursor stem cell. The intestinal epithelial system was studied and observed in analogy to 'in vivo' experiments. The model output, e.g. the geometric shape of a crypt, mitotic index, labelling index and the crypt length distribution in adult state, was compared with experimental data. There was evidence from the simulation that a certain steady state in the adult life could be reached regardless of some harmless influences in post-natal life, e.g. the influence of being weaned or non-weaned. The model is based on our hypothesis of the generation-controlled proliferation mechanism and at the same time is a confirmation of it.     

Intestinal crypt properties fit a model that incorporates replicative ageing and deep and proximate stem cells

A model of intestinal crypt organization is suggested based on the assumption that stem cells have a finite replicative life span. The model assumes the existence in a crypt of a quiescent ('deep') stem cell and a few more actively cycling ('proximate') stem cells. Monte Carlo computer simulation of published intestinal crypt mutagenesis data is used to test the model. The results of the simulation indicate that stabilization of the crypt mutant phenotype following treatment with external mutagen is consistent with a stem cell replicative life span of about 40 divisions for mouse colon and 90-100 divisions for mouse small intestine, corresponding to a deep stem cell cycle time of about 3.9 and 8.5 weeks for colon and small intestine, respectively. Simulation of the data obtained for human colorectal crypts suggests that the proximate stem cell cycle time is about 80 h, assuming a replicative life span of 50-150 divisions, and that the deep stem cell divides approximately every 30 weeks.     

The effect of T-lymphocytes on epithelial proliferation of the jejunal mucosa in thymectomized mice

Following 1.5 month period after thymectomy of adult mice the crypt 3H-thymidine labelling index is decreased and the proliferative zone is reduced. Analysis of labeled cell distributions in the crypt revealed that thymectomy resulted in the initiation of enterocyte entering a maturation phase in the site shifted to the crypt base. Syngeneic T-lymphocytes injected intravenously to thymectomized mice increased the labeling index, but exerted no effect on the size of proliferative zone. The proliferative changes described were not due to changes in the number of divisions of rapidly proliferating enterocytes. The role of T-lymphocytes in modulation of intestinal epithelium proliferation and steady state maintenance is discussed.     

The crypt cycle. Crypt and villus production in the adult intestinal epithelium.

We propose a model for the growth of individual crypts that is able to account for the observed changes in the number of cells in crypts under normal conditions, after irradiation, and after 30% resection. Parameter values for this model are estimated both for mouse and man, and detailed predictions of crypt growth rates are made. This model does not predict a steady-state crypt size; rather it suggests that crypts grow until they bifurcate. We therefore propose a crypt cycle (analogous to the cell cycle) and present evidence that most if not all crypts in the adult mouse are cycling asynchronously and independently. This evidence consists of four experiments that indicate that branching crypts are randomly distributed over the intestinal epithelium, that the plane of bifurcation of branching crypts is randomly oriented with respect to the villus base, and that the size distribution of crypts is consistent with an expanding crypt population. We also report for the first time evidence of villus production in the adult mouse intestinal epithelium. We conclude that the crypt and villus populations in the adult mouse are not in a steady state.     

Intestinal crypt proliferation. II. Computer modelling of mitotic index data provides further evidence for lateral and vertical cell migration in the absence of mitotic activity

The position-dependent mitotic index before, and 1, 2 and 3 h after vincristine was scored. The accumulation of cells in mitosis leads to an increase in the mitotic index from 0.06 to 0.34 at crypt positions 8-12. Surprisingly, the leading edge of the position-related mitotic index distribution moves to higher crypt positions although cell division was stopped. In addition, the vertical clustering of mitotic figures in sections was recorded. The data were examined using a previously described computer crypt model. We conclude: the average mitotic phase duration is about 0.7 h (40 min) and varies little with cell position; the geometrical correction factor for overscoring mitoses in crypt sections is about 0.6-0.7 and adjacent cell columns can merge. Lateral cell displacement after mitosis, as predicted in a previous model analysis, would be a mechanism to counteract other forces that tend to reduce the crypt circumference. In the normal steady state merging and expansion processes would just balance each other. This would not follow if one mechanism was blocked. Thus we propose a new concept in which the crypt geometry would be dynamically determined by cell proliferative activity in connection with lateral positioning of new cells on one hand and contracting forces on the other hand.     

Intestinal Crypt Proliferation. Ii. Computer Modelling of Mitotic Index Data Provides Further Evidence For Lateral and Vertical Cell Migration In the Absence of Mitotic Activity

Abstract. The position-dependent mitotic index before, and 1, 2 and 3 h after vincristine was scored. the accumulation of cells in mitosis leads to an increase in the mitotic index from 0.06 to 0.34 at crypt positions 8-12. Surprisingly, the leading edge of the position-related mitotic index distribution moves to higher crypt positions although cell division was stopped. In addition, the vertical clustering of mitotic figures in sections was recorded. the data were examined using a previously described computer crypt model. We conclude: the average mitotic phase duration is about 0.7 h (40 min) and varies little with cell position; the geometrical correction factor for overscoring mitoses in crypt sections is about 0.6-0.7 and adjacent cell columns can merge. Lateral cell displacement after mitosis, as predicted in a previous model analysis, would be a mechanism to counteract other forces that tend to reduce the crypt circumference. In the normal steady state merging and expansion processes would just balance each other. This would not follow if one mechanism was blocked. Thus we propose a new concept in which the crypt geometry would be dynamically determined by cell proliferative activity in connection with lateral positioning of new cells on one hand and contracting forces on the other hand.     

A stochastic branching model with formation of subunits applied to the growth of intestinal crypts

The intestinal epithelium is one of the most rapidly regenerating tissues in mammals. Cell production takes place in the intestinal crypts which contain about 250 cells. Only a minority of 1-60 proliferating cells are able to maintain a crypt over a long period of time. However, so far attempts to identify these stem cells were unsuccessful. Therefore, little is known about their cellular growth and selfmaintenance properties. On the other hand, the crypts appear to exhibit a life cycle which starts by fission of existing crypts and ends by fission or extinction. Data on these processes have recently become available. Here, we demonstrate how these data on the life cycle of the macroscopic crypt structure can be used to derive a quantitative model of the microscopic process of stem cell growth. The model assumptions are: (1) stem cells undergo a time independent supracritical Markovian branching process (Galton-Watson process); (2) a crypt divides if the number of stem cells exceeds a given threshold and the stem cells are distributed to both daughter crypts according to binomial statistics; (3) the size of the crypt is proportional to the stem cell number. This model combining two different stochastic branching processes describes a new class of processes whose stationary stability and asymptotic behavior are examined. This model should be applicable to various growth processes with formation of subunits (e.g. population growth with formation of colonies in biology, ecology and sociology). Comparison with crypt data shows that intestinal stem cells have a probability of over 0.8 of dividing asymmetrically and that the threshold number should be 8 or larger.     

Modelling Spatially Regulated β-Catenin Dynamics and Invasion in Intestinal Crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt.     

SpatialDemography: a spatially explicit,stage‐structured,metacommunity model

The responses of species and populations to changes in the environment (e.g. changes in climate and land use) are often complex and difficult to predict. We have created the SpatialDemography model (R package: spatialdemography). The model is a spatially explicit, stage‐structured, matrix‐based metacommunity model, with the potential for modeling species’ and populations’ potential responses to environmental heterogeneity and change. The SpatialDemography model assumes a cellular landscape populated by organisms with four life stages: a mobile dispersing stage, two sessile non‐reproductive stages, and a reproductive adult stage. Individuals are assumed to originate at the center of a given cell and disperse according to a specified dispersal kernel (e.g. log‐normal). All adult individuals are capable of producing offspring. The model approach and framework are described in the context of a hypothetical example with multiple competing species in a four cell landscape. In this example simulation, both spatial location and species interactions were important for understanding population dynamics. SpatialDemography can be applied to questions where an understanding of transient and long‐term demographic responses to spatiotemporal changes is desired. It is primarily applicable to metapopulations and metacommunities of organisms with early dispersal and sessile adults (i.e. modular organisms such as plants and some marine organisms). SpatialDemography differs from other population models in that it is spatially explicit, can incorporate biotic interactions, and is implemented in R.     

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.     

Intestinal Cell Proliferation. I. A Comprehensive Model of Steady-State Proliferation In the Crypt

Abstract. 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 (T_c= 16 hr, T_s= 9 hr), and four subsequent transit cell divisions (T_c= 11 to 12 hr, T_s= 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 μCi [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.     

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.     

Circadian variation of the cell proliferation in the jejunal epithelium of rats at weaning phase

Circadian variation in cell proliferation of the jejunal epithelium of 18-day-old rats was studied using the 2-h arrested metaphase score and crypt isolation method. A continuous decrease in the arrested metaphases occurred from 07.00 h to 13.00 h. From 17.00 h arrested metaphase values increased and were maintained at the higher level during the dark period as showed by Cosinor analyses (P < 0.05). These results indicate that in the young rat there is already a circadian variation in jejunal epithelial cell proliferation as early as 18 days. We can even suggest that the presence of a circadian rhythm at weaning contributes to the steady state of cell proliferation in the intestinal epithelium observed in adult life.     

Renewal of the epithelium in the descending colon of the mouse. IV. Cell population kinetics of vacuolated-columnar and mucous cells.

Proliferation and migration of cells in the vacuolated-columnar and mucous cell lines were studied in the descending colon of adult female mice given a single injection or a continuous infusion of 3H-thymidine and killed at various intervals from one hour to 12 days. This investigation was carried out using one mum-thick Epon sections which were radioautographed after staining with the periodic acid-Schiff technique and iron-hematoxylin. In the normalized crypts with ten equal segments, labeled vacuolated cells at one hour after injection of 3H-thymidine were encountered in the lower four segments and in decreasing numbers in segments 5 through 7. From the percent labeled cells in segments of the crypt, the birth rate and fluxes of cells were computed. Moreover, it was found that a cell in the vacuolated-columnar cell line would undergo three mitotic cycles on the average from its birth at the cryptal base to its extrusion from the surface; of these three cycles, the last one which took place from segment 3 to segment 7 appeared to be a changeover from dividing cells to non-dividing cells, in accordance with the "slow cut-off" model of Cairnie et al. ('65b). Mucous cells located in segments 1 through 6 of the crypt were capable of incorporating 3H-thymidine and thus capable of undergoing mitosis. However, the rate of turnover of mucous cells based on proliferative rate was found to be much lower than the rate of turnover of mucous cells based on the transit time in the non-dividing segments of the crypt. Since there was a concomitant overproduction of cells in the vacuolated cells and newly formed mucous cells in the lower portion of the crypt, it was concluded that some vacuolated cells would give rise to mucous cells. This putative transformation occurred in the lower four segments of the crypt. Mucous cells which were formed by transformation would migrate upward along the cryptal wall and accumulate more mucus in the theca; in doing so, they would undergo two divisions, on the average, before they became non-dividing mucous cells. In ascending the cryptal walls, both vacuolated-columnar cells and mucous cells appeared to migrate at a similar speed; they moved much slower at the base of the crypt and accelerated toward the upper portion of the crypt, but they migrated at a constant speed in the non-dividing segments of the crypt.     

Clusterin gene transcription is activated by caudal-related homeobox genes in intestinal epithelium

Caudal-related homeobox (Cdx) proteins play an important role in development and differentiation of the intestinal epithelium. Using cDNA differential display, we identified clusterin as a prominently induced gene in a Cdx2-regulated cellular model of intestinal differentiation. Transfection experiments and DNA-protein interaction assays showed that clusterin is an immediate downstream target gene for Cdx proteins. The distribution of clusterin protein in the intestine was assessed during development and in the adult epithelium using immunohistochemistry. In the adult mouse epithelium, clusterin protein was localized in both crypt and villus compartments but not in interstitial cells of the intestinal mucosa. Together, these data suggest that clusterin is a direct target gene for Cdx homeobox proteins, and the pattern of clusterin protein expression suggests that it is associated with the differentiated state in the intestinal epithelium.     

Colon Cryptogenesis: Asymmetric Budding

The process of crypt formation and the roles of Wnt and cell-cell adhesion signaling in cryptogenesis are not well described; but are important to the understanding of both normal and cancer colon crypt biology. A quantitative 3D-microscopy and image analysis technique is used to study the frequency, morphology and molecular topography associated with crypt formation. Measurements along the colon reveal the details of crypt formation and some key underlying biochemical signals regulating normal colon biology. Our measurements revealed an asymmetrical crypt budding process, contrary to the previously reported symmetrical fission of crypts. 3D immunofluorescence analyses reveals heterogeneity in the subcellular distribution of E-cadherin and β-catenin in distinct crypt populations. This heterogeneity was also found in asymmetrical budding crypts. Singular crypt formation (i.e. no multiple new crypts forming from one parent crypt) were observed in crypts isolated from the normal colon mucosa, suggestive of a singular constraint mechanism to prevent aberrant crypt production. The technique presented improves our understanding of cryptogenesis and suggests that excess colon crypt formation occurs when Wnt signaling is perturbed (e.g. by truncation of adenomatous polyposis coli, APC protein) in most colon cancers.     

Linking biotic homogenization to habitat type, invasiveness and growth form of naturalized alien plants in North America

Aim Biotic homogenization is a growing phenomenon and has recently attracted much attention. Here, we analyse a large dataset of native and alien plants in North America to examine whether biotic homogenization is related to several ecological and biological attributes. Location North America (north of Mexico). Methods We assembled species lists of native and alien vascular plants for each of the 64 state‐ and province‐level geographical units in North America. Each alien species was characterized with respect to habitat (wetland versus upland), invasiveness (invasive versus non‐invasive), life cycle (annual/biennial versus perennial) and habit (herbaceous versus woody). We calculated a Jaccard similarity index separately for native, for alien, and for native and alien species. We used the average of Jaccard dissimilarity index (1 ? Jaccard index) of all paired localities as a measure of the mean beta diversity of alien species for each set of localities examined in an analysis. We used a homogenization index to quantify the effect of homogenization or differentiation. Results We found that (1) wetland, invasive, annual/biennial and herbaceous alien plants markedly homogenized the state‐level floras whereas non‐invasive and woody alien plants tended to differentiate the floras; (2) beta diversity was significantly lower for wetland, invasive, annual/biennial and herbaceous alien plants than their counterparts (i.e. upland, non‐invasive, perennial and woody alien plants, respectively); and (3) upland and perennial alien plants each played an equal role in homogenizing and differentiating the state‐level floras. Main conclusions Our study shows that biotic homogenization is clearly related to habitat type (e.g. wetland versus uplands), species invasiveness and life‐history traits such as life cycle (e.g. annual/biennial and herbaceous versus woody species) at the spatial scale examined. These observations help to understand the process of biotic homogenization resulting from alien vascular plants in North America.     

Competitive abilities in experimental microcosms are accurately predicted by a demographic index for R*

Resource competition theory predicts that R*, the equilibrium resource amount yielding zero growth of a consumer population, should predict species' competitive abilities for that resource. This concept has been supported for unicellular organisms, but has not been well-tested for metazoans, probably due to the difficulty of raising experimental populations to equilibrium and measuring population growth rates for species with long or complex life cycles. We developed an index (R(index)) of R* based on demography of one insect cohort, growing from egg to adult in a non-equilibrium setting, and tested whether R(index) yielded accurate predictions of competitive abilities using mosquitoes as a model system. We estimated finite rate of increase (λ') from demographic data for cohorts of three mosquito species raised with different detritus amounts, and estimated each species' R(index) using nonlinear regressions of λ' vs. initial detritus amount. All three species' R(index) differed significantly, and accurately predicted competitive hierarchy of the species determined in simultaneous pairwise competition experiments. Our R(index) could provide estimates and rigorous statistical comparisons of competitive ability for organisms for which typical chemostat methods and equilibrium population conditions are impractical.     

Development of the pattern of cell renewal in the crypt-villus unit of chimaeric mouse small intestine

We have previously shown that the epithelium of each adult intestinal crypt in chimaeric mice is derived from a single progenitor cell. Whether the crypts are monoclonal from the outset-that is, are formed by the proliferation of a single cell-or whether their formation is initiated by several cells was not known. Here we report that many crypts contain cells of both chimaeric genotypes in the neonatal period indicating a polyclonal origin at this stage of morphogenesis. The cellular organization of the early neonatal crypt is therefore different from that of the adult crypt, which includes a zone of 'anchored' stem cells above the crypt base. Within 2 weeks, however, the crypt progenitor cell and its descendants displace all other cells from the crypt and the crypt attains monoclonality. The distribution of enterocytes on chimaeric villi in the neonate shows a mottled pattern of mosaicism which is progressively replaced by coherent sheets of cells from the crypts, and within two weeks the orderly adult clonal pattern is established.