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Good luck. Related Current Papers. September 10, Ultimately, descendants of a the tips of villi, they went through cell apoptosis, as shown by the particular stem cell with the optimal renewal efficiency won out apoptosis assay Figure 1A, middle panel , and were then while others disappeared. These results led us to employ an exfoliated. Based on these results, four compartments might be optimization method to be shown below to find out the optimal identified along the villus axis, as illustrated in Figure 1B right dynamics of crypts as selected by the natural process.

In other animals including mouse and human, the intestinal epithelium was organized and renewed in essentially Workflow of the model the same manner [23]. Thus, our model was built on the general The overall workflow of the model is illustrated in Figure 2. Based paradigm of stem cell — transit amplification — differentiation — apoptosis on the assumptions mentioned earlier and using measured populations for intestinal epithelium, which was applicable to both teleost and of transit amplifying TA cells and differentiated cells, the optimization mammalian intestinal tracts.

Species-dependent outcome of the model would require dynamics comes from literature. Mutational analysis of mice species-specific input information about the two populations of cells. Figure 1. The paradigm of epithelium renewal in the intestine. A Cell proliferation and apoptosis in the intestine of zebrafish. Left panel: Cell proliferation assay with proliferating cells stained dark brown. Middle panel: Cell apoptosis assay with apoptotic cells stained green. Right panel: Compartmentalization of epithelium into stem cells, transit amplifying cells, differentiated cells and apoptotic cells.

B The intestinal epithelium is divided into four components while constructing the model, based on the analogous paradigm of epithelium renewal across teleost, murine and human species. Stem cells maintain their own population through self-renewal, and in the mean time, they produce progenies that will differentiate later on.

Transit amplifying cells are directly derived from stem cells and go through rapid expansion. Then they go for cell differentiation and finally apoptosis.

Denotation: x1 - population of stem cells; x2 - population of transit amplifying cells; x3 - population of differentiated cells. Note that all populations are normalized against their homeostatic populations in the model. The model takes experimental measurement of transit amplifying and differentiated cell populations as input information.

By optimizing the turnover dynamics, it yields the number of stem cells required on each section of pocket or crypt of the intestine. It also provides information on epithelium turnover changes, for example, extended turnover cycles due to a reduction in the transit amplifying cells. This model is composed of three components: the stem cells, respectively. It is worth noting that here we define the transit cells, the transit amplifying cells and the differentiated epithelial amplifying cells as fast dividing cells that are derived from the stem cells.

The population of stem cells is maintained through self- cells and they are not committed to any lineage yet. Those lineage- renewal and production of progenies.

The population of transit committed cells will become part of the differentiated cells. If c1. The population of differentiated model exhibits exponential growth unbounded growth of stem epithelial cells is maintained through supply from transit cells ; whereas if c1,c0, the model exhibits exponential decay amplifying progenitors and expense to apoptosis. All the extinction of stem cells and finally, of everything. Here, the stem cells are defined to be actively holds and the system is structurally unstable.

Biological distur- involved in TA cell production instead of remaining quiescent for bances may easily lead to unbounded growth of cells.

In order for long periods of time ; the TA population is defined to be fast the system to maintain tissue homeostasis in a robust manner, as is dividing cells that are derived from the stem cells and that are not observed in the real world, it is necessary to incorporate a feedback committed to any lineage yet.

Once committed to a particular mechanism into the model. Based on Fig. In view of the tight regulation on stem cells by various signals Transit amplifying cells do not reversely dedifferentiate to stem from both epithelial and mesenchymal cells [27], the marginally cells which was suggested a possibility under some special stable equation 1 hardly captures the homeostatic feature of the circumstances [23]. Using denotations shown in Fig.

Equation 1 may be modified to become model reads as follows: structurally stable based on the assumption that stem cell differentiation is related to the second order of stem cell population. Equations 5 and 6 are of special interest as division [29,30,31,32,33,34,35,36,37,38]. The denoting the ratio of differentiated population over transit Jacobian matrix of for equation 5 and 6 is given as follows: amplifying population, were incorporated into the model, respectively.

For euqation 5 , the nonlinear term represents a link between Its eigenvalues are given in two parts. The first part is given by: the TA population and the differentiated population. The modelled by the nonlinear term in equation 5.

Upon perturbations, they may re-establish homeostasis with mechanism of the differentiated population. Biologically, it has different dynamics, depending on the parametric values ie. This is a two-dimensional, multi-variate optimization problem Dynamics of the intestinal epithelium turnover process with nonlinear objective function and nonlinear constraints.

The steady state of the system is 1. It represents the homeostatic of the stem cells. Given the species-specific value of a, c and b, we posteriori-corrected value of b. Then the model needs to be solved are able to find out the stem cell number by solving the above again.

This posteriori-correction process is repeated several times formulation. This ratio is kept below 0. The For bigger value of b, the system needs to support a larger villus The actual number of stem cells is dependent on their in vivo size and the epithelium will be renewed at a lower rate.

Figure 3B division frequency. If stem cells only divide once per day, there shows the quantitative relationship. The results are summarized in Table 1. For ated epithelium. The system responds by initiating tissue the transit amplifying cells, the amplifying factor c assumes the restitution process.

In the beginning stage, the value of b starts value of 2. As new epithelium are being generated, the amplifying cells and stem cells to be Based on respective homeostatic states upon completion of epithelium these data, b assumes the value of 8.

Figure 3. General relationships between s, t and b. A In general, s is positively correlated with b. For teleosts where b is smaller, s is lower; For humans where b is bigger, s is higher.

B The epithelium renewal cycle is also correlated to the value of b. Bigger value of b means longer renewal cycle. Cycles are normalized to be dimensionless.

Zebrafish 8. So b epithelium turnover cycle in zebrafish is shown in Figure 4A. So b assumes the value of Based on the population of transit amplifying cells, the number of Similar perturbation was applied as before. If stem cells only divide once per day, there should be 4. To compare the epithelium renewal paradigm among three Results are summarized in Table 1.

There is a changes in the number of stem cells in mice. Results of tissue higher transit amplifying-to-stem cell ratio in teleost. It is the Figure 4.

Adaptive changes in the intestinal stem cell number. A Intestine of zebrafish. B Small intestine of mouse. C Duodenum of human. Upper and lower limits of the division frequency of stem cells in vivo once to twice per day define a range of the number of stem cells required to be present on each section of inter-villi pocket in zebrafish intestine.

Reduction in cell proliferation would result in a bigger value of b and thus a prolonged epithelium renewal cycle. That would be accompanied by less number of stem cells around. On the other hand, enhanced cell proliferation would result in a smaller value of b and thus an accelerated epithelium renewal process, accompanied by an increase in stem cell population. That would be the case where hyperplasia or adenoma starts to develop.

Comparison of epithelium renewal dynamics in different species. A The transit amplifying-to-stem cell ratio is the highest in teleost but the lowest in human during normal homeostasis. B The differentiated-to-transit amplifying cell ratio is the lowest in teleost but the highest in human during normal homeostasis. D Recovery time varies in these species.

In teleost, epithelium can be restituted in a shorter period of time, but this is achieved by allowing a bigger transient expansion in the transit amplifying population.

In human, it takes longer time to complete epithelium restitution, but this is achieved with a tighter mediation over the expansion of the transit amplifying population. These data suggest that these species employ different strategies in maintenance of homeostasis. Compared with intestines of other species, human intestine harbors minimum number of stem cells to support a larger villus size and restitutes epithelium through tightly mediated proliferation to maintain genome integrity and minimize the possibility of carcinogenic transformations.

Utilizing these data, amplifying cell ratio. The chi-test for duodenal ulcer shows that it is in human, with achievement of high fidelity in genomic significantly different from the healthy duodenum p,0.

As duplication and reduction in susceptibility of carcinogenic the output suggests, there is an increase in the stem cell transformations. This is important as unrestrained significantly different from the healthy duodenum p,0.

As expansion of transit amplifying population will lead to develop- the output suggests, there is an increase in the stem cell ment of cancer. As the model reveals, that may happen during population and an accelerated epithelium renewal rate about epithelium restitution in teleost and murine models, but it is less 1. The actual likely in human intestine Figure 6.

They intended to find out the presence of epithelium A novel model for stem cell number in the intestine hyperplasia. That may be achieved by quantitative analysis using In this work, we have devised a novel model that directly this model. Based on the histological results, the villi were addresses stem cell number in the intestine. Changes in cell populations during epithelium restitution. The transit amplifying population will transiently expand during epithelium restitution.

As the intestinal stem cells constantly Achieving optimal epithelium renewal rate is essential to compete against each other for optimal renewal dynamics sustainable organ function [25,26], the optimization formulation was devised following this The renewal rate of the intestinal epithelium tissue becomes philosophy.

Solution to the optimal model then allowed us to critical in terms of maintenance of tissue integrity, organ function infer the stem cell number. Design of the model based on the and potential risk of carcinogenic transformation during the life general stem cells — TA cells — differentiated cells — apoptosis paradigm span of the host organism.

A high turnover rate would allow quick has made it possible for the model to be applied to intestines of restitution of the lost tissue due to damage; but on the other hand, different species. To our best knowledge, this is the first model of high turnover rate would require the presence of more active stem its kind ever reported so far. These dimensional crypt-villus structures into a two- two opposing requirements ultimately lead to optimization of the dimensional model epithelium turnover rate for a defined organism, allowing Though the villi and crypts constitute a three-dimensional inner maintenance of tissue integrity and organ function with minimal surface of the intestine, the linear nature of epithelial cell migration stem cells and cell divisions required.

This may be the driving force [16,17,18] nicely simplifies the tissue renewal process into a two- behind the neutral competition dynamics, and this optimizing dimensional model. Cell proliferation is restricted near the bottom procedure persists throughout the adulthood [25,26].

The of crypts in mammals or in the inter-villus pocket region in optimization model based on this principle has successfully yielded cryptless zebrafish , whereas apoptosis is restricted at the tips of estimates of the stem cell number contained on a section of crypt villi.

Epithelium is renewed through cell migration along the villus or inter-villi pocket , and they largely agrees with previous axis. All cells except the Paneth cells are migrating upward, speculations [45,54].

STORM model has produced data in general agreement Differences have been noticed between the two-dimensional with previous literature systems. In mouse, only a few number of cells are going through In previous reports, Bjerknes et al [16] and Potten [23,54] apoptosis along each villus about 7 apoptotic cells over villi estimated that there were 4—6 stem cells in each crypt of mouse [48].

While in contrast, the number of apoptotic cells is notably intestine in three dimension. The recent work by Barker et al larger in zebrafish, typically around 15—20 cells per section of [55,56], through discovery of stem cell marker Lgr5, showed 6 villus Figure 1A.

The difference in cell apoptosis agrees with identifiable stem cells in a section of crypt. Based on their what the model suggests that tissue renewal process goes faster in histological results [55,56], there were approximately 3. Thus in terms of two- recovery, the system recovered more quickly in zebrafish dimensional section, our model is able to produce data that Figure 5D.