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This study aims to analyze the solution of a system of differential equations that describes the mathematical modeling of cell population dynamics in colonic crypt and colorectal cancer. The Caputo–Fabrizio fractional order derivatives are used to fractionalize the model. The corresponding mathematical model is solved by the Laplace transform, which helps transform differential equations into terms of algebraic equations. The Partial fraction technique is used to find the inverse Laplace of the governing equations. To assess the credibility of the results, graphical simulation has been investigated by manipulating certain parameters. There is a special scenario, namely when α→1, where the solutions obtained align with those already documented in the literature. This alignment ensures that the initial conditions are met and confirms the accuracy of our solutions. [ABSTRACT FROM AUTHOR]

Colorectal cancer (CRC) represents the second leading cause of cancer incidence and the third leading cause of cancer deaths worldwide. There is currently a lack of understanding of the onset of CRC, hindering the development of effective prevention strategies, early detection methods and the selection of appropriate therapies. This article outlines the key aspects of host genetics currently known about the origin and development of CRC. The organisation of the colonic crypts is described. It discusses how the transformation of a normal cell to a cancer cell occurs and how that malignant cell can populate an entire colonic crypt, promoting colorectal carcinogenesis. Current knowledge about the cell of origin of CRC is discussed, and the two morphological pathways that can give rise to CRC, the classical and alternative pathways, are presented. Due to the molecular heterogeneity of CRC, each of these pathways has been associated with different molecular mechanisms, including chromosomal and microsatellite genetic instability, as well as the CpG island methylator phenotype. Finally, different CRC classification systems are described based on genetic, epigenetic and transcriptomic alterations, allowing diagnosis and treatment personalisation., (Copyright © 2024. Published by Elsevier Inc.)

Stem cell renewal and differentiation in the human colonic crypt are linked to the Wnt/β-catenin pathway. The spatial balance of Wnt factors in proliferative cells within the crypt maintain an appropriate level of cellular reproduction needed for normal crypt homeostasis. Mutational events at the gene level are responsible for deregulating the balance of Wnt factors along the crypt, causing an overpopulation of proliferative cells, a loss of structure of the crypt domain, and the initiation of colorectal carcinomas. We formulate a PDE model describing cell movement and reproduction in a static crypt domain. We consider a single cell population whose proliferative capabilities are determined by stemness, a quantity defined by intracellular levels of adenomatous polyposis coli (APC) scaffold protein and β-catenin. We fit APC regulation parameters to biological data that describe normal protein gradients in the crypt. We also fit cell movement and protein flux parameters to normal crypt characteristics such as renewal time, total cell count, and proportion of proliferating cells. The model is used to investigate abnormal crypt dynamics when subjected to a diminished APC gradient, a scenario synonymous to mutations in the APC gene. We find that a 25% decrease in APC synthesis leads to a fraction of 0.88 proliferative, which is reflective of normal-appearing FAP crypts. A 50% drop in APC activity yields a fully proliferative crypt showing a doubling of the level of stemness, which characterizes the initial stages of colorectal cancer development. A sensitivity analysis of APC regulation parameters shows the perturbation of factors that is required to restore crypt dynamics to normal in the case of APC mutations. [ABSTRACT FROM AUTHOR]

Colorectal cancer (CRC) is a major cause of cancer mortality. Colon crypts are multi-cellular flask-shaped invaginations of the colonic epithelium, with stem cells at their base which support the continual turnover of the epithelium with loss of cells by anoikis from the flat mucosa. Mutations in these stem cells can become embedded in the crypts, a process that is strongly implicated in CRC initiation. We describe a computational model which includes novel features, including an accurate representation of the geometry of the crypt mouth. Model simulations yield previously unseen emergent phenomena, such as localization of cell death to a small region of the crypt mouth which corresponds with that observed in vivo. A mechanism emerges in the model for regulation of crypt cellularity in response to changes in either cell proliferation rates or membrane adhesion strengths. We show that cell shape assumptions influence this behaviour, with cylinders recapitulating biology better than spheres. Potential applications of the model include determination of roles of mutations in neoplasia and exploring factors for altered crypt morphodynamics.

The Wnt/ $$\beta $$ -catenin pathway plays a crucial role in stem cell renewal and differentiation in the normal human colonic crypt. The balance between $$\beta $$ -catenin and APC along the crypt axis determines its normal functionality. The mechanism that deregulates this balance may give insight into the initiation of colorectal cancer. This is significant because the spatial dysregulation of $$\beta $$ -catenin by the mutated tumor suppressor gene/protein APC in human colonic crypts is responsible for the initiation and growth of colorectal cancer. We consider a regulatory function that promotes APC synthesis within the cell and its effect on the accumulation of the Wnt target protein, $$\beta $$ -catenin. It is evident that an APC gradient exists along the crypt axis; however, the mechanism by which APC expression is regulated within the cell is not well known. We investigate the dynamics of an APC regulatory mechanism with an increased level of Axin at the subcellular level. Model output shows an increase of APC for a diminished Wnt signal, which explains the APC gradient along the crypt. We find that the dynamic interplay between $$\beta $$ -catenin, APC, and Axin produces oscillatory behavior, which is controlled by the Wnt stimulus. In the presence of reduced functional APC, the oscillations are amplified, which suggests that the cell remains in a more proliferative state for longer periods of time. Increased Axin levels (typical of mammalian cells) reduce oscillatory behavior and minimize the levels of $$\beta $$ -catenin within the cell while raising the levels of APC. [ABSTRACT FROM AUTHOR]

• Numerical method for convection-diffusion-reaction equations with mixed derivatives. • Semi-discrete finite difference method considered in nonuniform rectangular grid. • Proof of Stability and Second convergence order with respect to a discrete H 1 -norm. • Application of the method for simulating the cell dynamics in a colonic crypt. This paper proposes a finite difference method for a differential-algebraic system that couples an elliptic equation with a convection-diffusion-reaction equation with mixed derivatives. Herein the parabolic equation depends on the gradient of the solution of the elliptic equation. If the numerical approximation for this gradient presents lower accuracy then the numerical approximations for the solution of the parabolic equation can be deteriorated. In order to get a second order approximation for the solution of the parabolic equation, the challenges that we have to face are the construction of the right discretizations of the elliptic and parabolic equations that lead to a second order approximation for the gradient as well as the development of the numerical analysis of the proposed method. The differential system analysed can be used to describe the cell density and pressure dynamics in colonic crypts. Numerical simulations of cell dynamics in a crypt of the human colon during the formation of a micro-adenoma are presented. [ABSTRACT FROM AUTHOR]

The emergence of hypervirulent clade 2 Clostridioides difficile is associated with severe symptoms and accounts for >20% of global infections. TcdB is a dominant virulence factor of C. difficile , and clade 2 strains exclusively express two TcdB variants (TcdB2 and TcdB4) that use unknown receptors distinct from the classic TcdB. Here, we performed CRISPR/Cas9 screens for TcdB4 and identified tissue factor pathway inhibitor (TFPI) as its receptor. Using cryo-EM, we determined a complex structure of the full-length TcdB4 with TFPI, defining a common receptor-binding region for TcdB. Residue variations within this region divide major TcdB variants into 2 classes: one recognizes Frizzled (FZD), and the other recognizes TFPI. TFPI is highly expressed in the intestinal glands, and recombinant TFPI protects the colonic epithelium from TcdB2/4. These findings establish TFPI as a colonic crypt receptor for TcdB from clade 2 C. difficile and reveal new mechanisms for CDI pathogenesis. [Display omitted] • CRISPR screen identifies TFPI as a receptor for TcdB from the clade 2 C. difficile • Cryo-EM structure of TcdB4-TFPI reveals detailed receptor-binding interface • TFPI is a pathophysiologically relevant receptor for clade 2 C. difficile TcdB • Dual inhibition of TFPI and CSPG4 reduces colonic pathology caused by TcdB2 Clade 2 hypervirulent strains of Clostridioides difficile express disease-causing toxins TcdB2 and TcdB4, but the intestinal epithelial receptors that allow them to initiate damage have not been known. Here, tissue factor pathway inhibitor (TFPI) was found to be a receptor for both TcdB2 and −4, the TFPI-TcdB4 interaction was structurally characterized, and the ability of TFPI blockers to protect mice from hypervirulent C. difficile TcdB-induced intestinal damage was examined. [ABSTRACT FROM AUTHOR]

Abstract: Background: Probe-based confocal laser endomicroscopy enables microscopic examination of the digestive mucosa. Aims: (1) To identify and validate quantitative endomicroscopic criteria for evaluation of the colonic mucosa and (2) to compare these criteria between healthy and Crohn's disease patients in clinical remission. Methods: Six healthy controls and ten Crohn's disease patients in clinical remission were included in this prospective study. Methylene blue-stained biopsies of the right colon and corresponding endomicroscopic images were analyzed. Major axis, minor axis, and major axis/minor axis ratio of crypt lumens were quantified. Results: Quantitative assessment was performed on 21±4 crypt lumens per patient. Major axis/minor axis ratio values measured with endomicroscopy or methylene blue-stained biopsies were linearly correlated (r =0.63, p =0.01). All macroscopically inflamed mucosa had values of major axis/minor axis ratio higher than the median of controls. Interestingly, 50% (3/6) of Crohn's disease patients with macroscopically normal mucosa had also a higher ratio than pooled controls. Histological analysis showed that 6/7 patients with major axis/minor axis ratio superior to 1.7 had microscopic inflammation. Conclusion: Probe-based confocal laser endomicroscopy allows quantitative analysis of colonic pit structure. Endomicroscopic analysis of major axis/minor axis ratio allows the detection of microscopic residual inflammation with greater accuracy than standard endoscopy in Crohn's disease patients in clinical remission. [Copyright &y& Elsevier]

Abstract: Colorectal cancer is initiated in colonic crypts as a consequence of alterations leading to the disruption of the normal colonic cellular process. We propose a model, which couples a convection-diffusion type equation with a level set equation, for tracking the time evolution of an epithelial cell set, inside a colonic crypt, until it reaches the top of the crypt. The convection-diffusion equation describes the evolution of the density of the cells in the epithelial cell set. The parameters of this equation regulate the geometric and temporal cellular mechanism, and different parameter choices lead to distinct cell behavior. The level set equation tracks the location and shape of the epithelial cell set, inside the crypt, as well as its interface, separating the cell set from the others cells, which reside within the crypt. The interfacial velocity of the epithelial cell set is obtained from the convection-diffusion type equation. Some in silico experiments are described. They are performed in a relative small time, with respect to the real biological evolution. [ABSTRACT FROM AUTHOR]

Abstract: Previous studies from our laboratory demonstrated that 17β-estradiol (E2) rapidly inhibits Cl− secretion in rat and human distal colonic epithelium. The inhibition has been shown to occur via targeting of a basolateral K+ channel identified as the KCNQ1 (KvLQT1) channel. E2 indirectly modulates the channel activity via a cascade of second messengers which are rapidly phosphorylated in response to E2. The anti-secretory mechanism may be the manner by which E2 induces fluid retention in the intestine during periods of high circulating plasma E2. Here we review the sex-dependent and estrous cycle regulation of this novel rapid response to E2. The inhibition of KCNQ1 channel activity and Cl− secretion will be of interest in the future in the investigation of the retentive effects of estrogen in female tissue and also in the study of secretory disorders and drugable targets of the intestine. [Copyright &y& Elsevier]

Although aging is shown to be associated with decreased apoptosis and increased survival of cells in the colonic mucosa of Fischer 344 rats, the regulatory mechanisms are poorly understood. The current investigation examines the involvement of phosphotidylinositol 3-kinase (PI3K)/Akt signaling pathway in mediating the events of colonic mucosal cell survival during aging. We have observed that aging is associated with activation of PI3K/Akt signaling, as evidenced by the higher levels of phosphorylated forms of p85, the regulatory subunit of PI3K and of Akt in the proximal and distal colonic mucosa, of aged (21-23 mo) than in young (4-7 mo) rats. These increases are accompanied by a concomitant rise in phosphorylation of proapoptotic protein Bad, which is sequestered by the 14-3-3 family of proteins following phosphorylation by Akt, resulting in a reduction in non-phosphorylated Bad. The amount of antiapoptotic Bcl-xL bound to nonphosporylated Bad in the colonic mucosa is found to be substantially lower in aged than in young rats, resulting in a marked rise in the unbound/free form of Bcl-xL in the aging colon. The age-related activation of PI3K and the reduction in caspase-3 activity could be reversed by wortmannin, a specific inhibitor of PI3K. Increased levels of Bcl-xL and phosphorylated forms of Akt and Bad and reduction in caspase-3 activity were observed throughout the entire length of the colonic crypt of aged rats. We conclude that the constitutive activation of the PI3K/Akt-signaling pathway is partly responsible for the age-related increase in colonic mucosal cell survival. This is evident throughout the entire length of the colonic crypt. [ABSTRACT FROM AUTHOR]

The aim of this study was to establish a long-term culture system for rat colon epithelial cells. Colonic crypts were isolated by incubating a 4-cm-long rat colon segment cut longitudinally with an ethylenediaminetetraacetic acid [disodium salts]-containing buffer, taken up in conditioned medium from the normal rat kidney fibroblast cell line NRK (i.e., the supernatant of pure NRK cultures), directly plated on mitomycin C-treated NRK cells and subcultured with conditioned medium from NRK cells. Cells started to migrate out of the crypts shortly after plating them on NRK feeder layers. Some of the crypts fell apart during the isolation procedure, whereas the vast majority of them did it within 1 to 2 h after plating. The cells proliferated extremely slowly but continuously over a period of 4 mo and were epithelial because they expressed cytokeratin 19 and were stained by crystal violet at pH 2.8. In conclusion, the experimental system described in this study allows to maintain rat colon epithelial cells for up to 4 mo in culture and can be used to study the effects of a variety of tumor-modulating factors on growth and gene expression of normal colon epithelial cells in vitro. [ABSTRACT FROM AUTHOR]

Abstract Background Methylation of CpG sites in genomic DNA plays an important role in gene regulation and especially in gene silencing. We have reported mechanisms of epigenetic regulation for expression of mucins, which are markers of malignancy potential and early detection of human neoplasms. Epigenetic changes in promoter regions appear to be the first step in expression of mucins. Thus, detection of promoter methylation status is important for early diagnosis of cancer, monitoring of tumor behavior, and evaluating the response of tumors to targeted therapy. However, conventional analytical methods for DNA methylation require a large amount of DNA and have low sensitivity. Methods Here, we report a modified version of the bisulfite-DGGE (denaturing gradient gel electrophoresis) using a nested PCR approach. We designated this method as methylation specific electrophoresis (MSE). The MSE method is comprised of the following steps: (a) bisulfite treatment of genomic DNA, (b) amplification of the target DNA by a nested PCR approach and (c) applying to DGGE. To examine whether the MSE method is able to analyze DNA methylation of mucin genes in various samples, we apply it to DNA obtained from state cell lines, ethanol-fixed colonic crypts and human pancreatic juices. Result The MSE method greatly decreases the amount of input DNA. The lower detection limit for distinguishing different methylation status is < 0.1% and the detectable minimum amount of DNA is 20 pg, which can be obtained from only a few cells. We also show that MSE can be used for analysis of challenging samples such as human isolated colonic crypts or human pancreatic juices, from which only a small amount of DNA can be extracted. Conclusions The MSE method can provide a qualitative information of methylated sequence profile. The MSE method allows sensitive and specific analysis of the DNA methylation pattern of almost any block of multiple CpG sites. The MSE method can be applied to analysis of DNA methylation status in many different clinical samples, and this may facilitate identification of new risk markers.

Patients from a hereditary nonpolyposis colorectal cancer (HNPCC) kindred (Lynch Type 1 and Type 2) have an increased risk of developing large-bowel cancer. Tumors occur at a young age and are characteristically right-sided. Colonic mucosal proliferation is known to be increased in several groups of patients at risk of colorectal cancer.This study was performed to assess the pattern of mucosal proliferation at different sites in the colon of patients at risk of HNPCC and to determine whether this pattern differs from normal patients.Mucosal biopsies were obtained at colonoscopy from 21 patients at risk for HNPCC (16 females; mean age, 42 years) and from 7 normal patients (4 females; mean age, 38 years), and mucosal proliferation was quantified using the whole crypt mitotic count (WCMC) technique.In patients from HNPCC families, WCMC and crypt area were significantly greater in the cecum than in the transverse colon and left colon (P < 0.001). Compared with normal patients, WCMC in HNPCC patients was significantly greater in the cecum only (P < 0.05). A significant right-to-left shift was also observed in normal patients, but the percentage increase from right to left was two-fold greater in HNPCC patients.These results confirm a proximalto-distal proliferative gradient in the human colon and suggest that this may be exaggerated in HNPCC. This increased proximal proliferative rate may be a factor in the development of right-sided cancer in these patients. [ABSTRACT FROM AUTHOR]

Mitochondria produce cellular energy via oxidative phosphorylation (OXPHOS), mediated by respiratory chain complexes I to IV and ATP synthase (complex V). Mitochondrial respiratory complexes have been shown to decline with age in several tissues. As the intestinal epithelium is a tissue with a high energy demand, the aim of the present study was to establish whether the expression profile of OXPHOS subunits in the intestinal mucosa changes during the aging process. Biopsies of intestinal mucosa with no evidence of endoscopic or histomorphologic abnormalities, taken from 55 patients (mean age 42 years, age range 4–82 years; 62% female), were divided into four age groups (4–19, 20–39, 40–59, ≥60 years). Sections from different intestinal segments (terminal ileum, ascending colon, and sigmoid colon/rectum) were stained immunohistochemically (IHC) for subunits of OXPHOS complexes I–V and the voltage-dependent anion-selective channel 1 protein (VDAC1, porin), a marker of mitochondrial mass. Scores for IHC staining were determined by multiplication of the staining intensity and the percentage of positive cells. In addition, the numbers of intestinal crypts staining positive, partly positive, and negative were assessed. The average protein expression levels of OXPHOS subunits increased continuously from childhood onward, peaked in persons aged 20 to 59 years, and declined thereafter. This was seen for complexes II to V in the terminal ileum, complexes I to V in the ascending colon, and complexes I to IV in the sigmoid colon/rectum. Across all age groups, no effect of age on expression of the porin subunit VDAC1 was detected. The number of complex I- and IV-negative crypts in different intestinal segments increased with age. The protein expression levels of OXPHOS complexes increases from childhood onward and declines in elderly individuals, while the numbers of crypts with partial or complete loss of expression of complexes I and IV increase continuously with age. These data suggest that the continued reductions in the levels of mitochondrial OXPHOS complexes in crypts might be compensated in adulthood, but that, ultimately, reduced expression levels occur in persons aged 60 years and older. These findings raise two important questions: first, can the process of aging could be delayed through (pharmacological) intervention of mitochondrial pathways, and second, pathophysiologically, are these findings associated with disorders of the intestinal mucosa, e.g. inflammation? • Mitochondria play a role in the aging process in human intestine. • The levels of oxidative phosphorylation complexes are reduced in elderly persons. • Colonic crypts showing loss of expression of certain complexes increase with age. [ABSTRACT FROM AUTHOR]

Colonic polyps, which are abnormal growths in the colon, are a major concern in colon cancer diagnosis and prevention. Medical studies evidence that there is a correlation between histopathology and the shapes of the orifices in colonic crypts. We propose a biomathematical model for simulating the appearance of anomalous shapes for the orifices of colonic crypts, associated to an abnormal cell proliferation. It couples a mechanical model that is a mixed elastic/viscoelastic quasi-static model describing the deformation of the crypt orifice, with a convection-diffusion model that simulates the crypt cell dynamics in space and time. The coupling resides in the variation of pressure generated by abnormal proliferative cells that induce a mechanical force and originate the change in shape of the crypt orifice. Furthermore the model is formulated in a two-dimensional setting, for emulating the top view of the colonic mucosa, observed in vivo in colonoscopy images. The primary focus of this study is on the modeling of this complex biological phenomenon, by defining an appropriate reduced biomathematical model. Additionally, a numerical procedure to determine its solution is also addressed. The overall numerical simulations indicate that an excess of cell proliferation, in different crypt locations, creates some of the anomalous patterns of the colonic crypt orifices, observed in vivo in medical images., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Human intestinal organoids have enabled performance of functional epithelial studies and modeling of human diseases of the intestine. This unit describes 1) a method to isolate and culture crypts from human intestinal tissue, 2) use of combinatorial methods to expand stem cell-enriched spheroids and differentiate them into organoids composed of various intestinal epithelial cell types, and 3) methods to stimulate these organoids with and measure their responsiveness to external stimuli. To validate the differentiation, organoids can be stained to qualitatively evaluate the presence of colonic crypt morphology and specialized epithelial cell markers. These organoids are responsive to challenge with tumor necrosis factor α (TNFα), resulting in cytokine-induced apoptosis. TNFα-driven apoptosis can be blocked by a small-molecule inhibitor of Ire1α (4μ8C), an endoplasmic-reticulum stress sensor. This is one example of how the human intestinal organoid model can be a powerful tool to elucidate important biological pathways involved in human disease in intestinal epithelial cells. © 2019 by John Wiley & Sons, Inc., (© 2019 John Wiley & Sons, Inc.)