• Computer Simulation
• Cell Proliferation
• Cell Culture Techniques/methods
• Models, Biological
• Cell Movement

• Animals
• Intestinal Mucosa/metabolism
• Intestinal Mucosa/cytology
• Intestinal Mucosa/physiology
• Methylation
• Cell Plasticity/genetics
• Regeneration/genetics
• Histones/metabolism
• Histones/genetics
• Mice
• Mice, Inbred C57BL
• Cell Lineage
• Cell Differentiation
• Epithelial Cells/metabolism
• Intestine, Small/metabolism

• R35GM142884 Foundation for the National Institutes of Health (Foundation for the National Institutes of Health, Inc.)
• R35GM126900 Foundation for the National Institutes of Health (Foundation for the National Institutes of Health, Inc.)
• R35 GM126900 NIGMS NIH HHS
• T32GM142607 Foundation for the National Institutes of Health (Foundation for the National Institutes of Health, Inc.)
• F32DK135241-01 Foundation for the National Institutes of Health (Foundation for the National Institutes of Health, Inc.)
• R35GM142884-02S Foundation for the National Institutes of Health (Foundation for the National Institutes of Health, Inc.)
• F32 DK135241 NIDDK NIH HHS

• branching process
• cell population dynamics
• colonic crypts
• colorectal tumorigenesis
• homeostasis

• Humans
• Models, Biological
• Colon/pathology
• Carcinogenesis/genetics
• Carcinogenesis/pathology
• Homeostasis
• Mutation

• National Science Foundation

• Mice
• Humans
• Animals
• Citrulline
• Fluorouracil/toxicity
• Fluorouracil/metabolism
• Intestinal Mucosa/metabolism
• Diarrhea/chemically induced
• Drug-Related Side Effects and Adverse Reactions
• Doxorubicin/toxicity

• 15 lipoxygenase
• Apoptosis
• Fatty acids
• Monoamine oxidase
• Oleic acid
• Polyunsaturated Fatty acid
• Stearic acid

• Aging
• Mathematical modeling
• Negative feedback
• Neural stem cell
• Neurogenesis
• Optimal control
• Quiescence
• Self-renewal
• Stem cell lineage

• agent-based modeling
• bifurcation analysis
• quantitative systems pharmacology
• quantitative systems toxicology
• systems modeling

• Mathematical modeling
• cell population dynamics
• evolution
• multiscale simulation algorithms

• Algorithms
• Cell Differentiation
• Cell Division
• Cell Physiological Phenomena
• Cell Proliferation
• Markov Chains
• Models, Biological
• Monte Carlo Method

• R35 GM122561 NIGMS NIH HHS

• Mathematical modeling
• cell population dynamics
• evolution
• multiscale simulation algorithms

• Antipsychotics
• Breast cancer
• Cancer
• JAK
• Mammary gland
• Neuroleptics
• Prolactin
• Ruxolitinib
• STAT5

• GRI
• PK/PD
• QSP
• cancer growth modeling
• drug combination
• myelosuppression
• pharmacokinetics
• toxicity
• translational
• xenograft

Oligodendrocyte precursor cells (OPCs) have remarkable properties: they represent the most abundant cycling cell population in the adult normal brain and they manage to achieve a uniform and constant density throughout the adult brain. This equilibrium is obtained by the interplay of four processes: division, differentiation or death, migration and active self-repulsion. They are also strongly suspected to be at the origin of gliomas, when their equilibrium is disrupted. In this article, we present a model of the dynamics of OPCs, first in a normal tissue. This model is based on a cellular automaton and its rules are mimicking the ones that regulate the dynamics of real OPCs. The model is able to reproduce the homeostasis of the cell population, with the maintenance of a constant and uniform cell density and the healing of a lesion. We show that there exists a fair quantitative agreement between the simulated and experimental parameters, such as the cell velocity, the time taken to close a lesion, and the duration of the cell cycle. We present three possible scenarios of disruption of the equilibrium: the appearance of an over-proliferating cell, of a deadless/non-differentiating cell, or of a cell that lost any contact-inhibition. We show that the appearance of an over-proliferating cell is sufficient to trigger the growth of a tumor that has low-grade glioma features: an invasive behaviour, a linear radial growth of the tumor with a corresponding growth velocity of less than 2 mm per year, as well a cell density at the center which exceeds the one in normal tissue by a factor of less than two. The loss of contact inhibition leads to a more high-grade-like glioma. The results of our model contribute to the body of evidence that identify OPCs as possible cells of origin of gliomas.

Gliomas are the most common brain tumors and result in more years of life lost than any other tumor. Standard treatments only confer a limited improvement in overall survival, underscoring the need for new therapies. Finding the type of cells at the origin of these tumors could lead to the development of new drugs, specifically targeted towards these cells. The oligodendrocyte precursor cells are suspected to be these cells of origin, because they continue to proliferate through all the adult life. In this article, we present a model of the dynamics of these cells, first in the normal brain, and then we extrapolate our model to the pathological situation. We study several scenarios where, from the normal situation, a cell appears with one property different from those of the normal cells. We show that the alteration of only one of the properties of these cells in the model can lead to the formation of gliomas with different aggressiveness and very similar to real gliomas, reinforcing the suspicion that the precursor cells are at the origin of gliomas.

• Animals
• Cell Count
• Cell Differentiation
• Cell Proliferation
• Computational Biology
• Glioma/physiopathology
• Humans
• Mice
• Models, Biological
• Oligodendrocyte Precursor Cells/cytology
• Oligodendrocyte Precursor Cells/physiology

• IN2P3, CNRS
• Université Paris-Saclay

• Cancer
• Homeostasis
• Mathematical models
• Negative feedback
• Robustness
• Self-renewal
• Stem cell lineage
• Tissue regeneration

• Bifurcation analysis
• Colorectal cancer
• Complex behavior
• Phenotypes
• Time delay model

• Immunohistochemistry
• Ki-67
• Local advanced nasopharyngeal carcinoma
• Radiation resistance

• Adolescent
• Adult
• Aged
• Aged, 80 and over
• Antibodies, Monoclonal, Humanized/therapeutic use
• Antineoplastic Agents/therapeutic use
• Biomarkers, Tumor/genetics
• Biomarkers, Tumor/metabolism
• Carcinoma/diagnosis
• Carcinoma/genetics
• Carcinoma/mortality
• Carcinoma/therapy
• Cetuximab/therapeutic use
• Female
• Gamma Rays/therapeutic use
• Humans
• Ki-67 Antigen/genetics
• Ki-67 Antigen/metabolism
• Male
• Middle Aged
• Nasopharyngeal Carcinoma
• Nasopharyngeal Neoplasms/diagnosis
• Nasopharyngeal Neoplasms/genetics
• Nasopharyngeal Neoplasms/mortality
• Nasopharyngeal Neoplasms/therapy
• Neoplasm Staging
• Prognosis
• Retrospective Studies
• Survival Analysis

Gastrointestinal (GI) adverse events (AEs) are frequently dose limiting for oncology agents, requiring extensive clinical testing of alternative schedules to identify optimal dosing regimens. Here, we develop a translational mathematical model to predict these clinical AEs starting from preclinical GI toxicity data. The model structure incorporates known biology and includes stem cells, daughter cells, and enterocytes. Published data, including cellular numbers and division times, informed the system parameters for humans and rats. The drug‐specific parameters were informed with preclinical histopathology data from rats treated with irinotecan. The model fit the rodent irinotecan‐induced pathology changes well. The predicted time course of enterocyte loss in patients treated with weekly doses matched observed AE profiles. The model also correctly predicts a lower level of AEs for every 3 weeks (Q3W), as compared to the weekly schedule.

• Animals
• Antineoplastic Agents/administration & dosage
• Antineoplastic Agents/toxicity
• Dose-Response Relationship, Drug
• Drug Administration Schedule
• Drug-Related Side Effects and Adverse Reactions/etiology
• Gastrointestinal Tract/drug effects
• Gastrointestinal Tract/physiology
• Humans
• Irinotecan/administration & dosage
• Irinotecan/toxicity
• Models, Biological
• Predictive Value of Tests
• Species Specificity
• Systems Biology/methods
• Translational Research, Biomedical

• Algorithms
• Alleles
• Genotype
• Models, Genetic
• Mutation

• R01 GM115562 NIGMS NIH HHS
• R01 OD010974 NIH HHS
• U01 CA187956 NCI NIH HHS

• Homeostasis regulation
• Mathematical modeling
• Stem cells

• agent-based model
• anoikis
• colonic crypt
• homeostasis

• The University of Sheffield

Based on a deterministic continuous model of cell populations dynamics in the colonic crypt and in colorectal cancer, we propose four combinations of feedback mechanisms in the differentiations from stem cells (SCs) to transit cells (TCs) and then to differentiated cells (DCs), the four combinations include the double linear (LL), the linear and saturating (LS), the saturating and linear (SL), and the double saturating (SS) feedbacks, respectively. The relative fluctuations of the population of SCs, TCs, and DCs around equilibrium states with four feedback mechanisms are studied by using the Langevin method. With the increasing of net growth rate of TCs, it is found that the Fano factors of TCs and DCs go to a peak in a transient phase, and then increase again to infinity in the cases of LS and SS feedbacks. The “up-down-up” characteristic on the Fano factor (like the van der Waals loop) demonstrates that there exists a transient phase between the normal and cancerous phases, our novel findings suggest that the mathematical model with LS or SS feedback might be better to elucidate the dynamics of a normal and abnormal (cancerous) phases.

• Cancer stem cells
• Cell culture
• Head and neck squamous cell carcinoma
• Mathematical modeling
• Mouse models of human cancer
• Orospheres
• Statistical models

• Carcinoma, Squamous Cell/metabolism
• Carcinoma, Squamous Cell/pathology
• Cell Transformation, Neoplastic
• Drug Resistance, Neoplasm
• Head and Neck Neoplasms/metabolism
• Head and Neck Neoplasms/pathology
• Humans
• Mitosis
• Models, Biological
• Neoplastic Stem Cells/cytology
• Neoplastic Stem Cells/metabolism

• R01 DE023220 NIDCR NIH HHS
• P50 CA097248 NCI NIH HHS
• R21 DE019279 NIDCR NIH HHS
• R01 DE021139 NIDCR NIH HHS
• T32 CA009357 NCI NIH HHS
• National Cancer Institute
• National Institute of Dental and Craniofacial Research
• National Institutes of Health

Homeostatic maintenance of tissues is orchestrated by well tuned networks of cellular signaling. Such networks regulate, in a stochastic manner, fates of all cells within the respective lineages. Processes such as symmetric and asymmetric divisions, differentiation, de-differentiation, and death have to be controlled in a dynamic fashion, such that the cell population is maintained at a stable equilibrium, has a sufficiently low level of stochastic variation, and is capable of responding efficiently to external damage. Cellular lineages in real tissues may consist of a number of different cell types, connected by hierarchical relationships, albeit not necessarily linear, and engaged in a number of different processes. Here we develop a general mathematical methodology for near equilibrium studies of arbitrarily complex hierarchical cell populations, under regulation by a control network. This methodology allows us to (1) determine stability properties of the network, (2) calculate the stochastic variance, and (3) predict how different control mechanisms affect stability and robustness of the system. We demonstrate the versatility of this tool by using the example of the airway epithelium lineage. Recent research shows that airway epithelium stem cells divide mostly asymmetrically, while the so-called secretory cells divide predominantly symmetrically. It further provides quantitative data on the recovery dynamics of the airway epithelium, which can include secretory cell de-differentiation. Using our new methodology, we demonstrate that while a number of regulatory networks can be compatible with the observed recovery behavior, the observed division patterns of cells are the most optimal from the viewpoint of homeostatic lineage stability and minimizing the variation of the cell population size. This not only explains the observed yet poorly understood features of airway tissue architecture, but also helps to deduce the information on the still largely hypothetical regulatory mechanisms governing tissue turnover, and lends insight into how different control loops influence the stability and variance properties of cell populations.

Tissue stability is the basic property of healthy organs, and yet the mechanisms governing the stable, long-term maintenance of cell numbers in tissues are poorly understood. While more and more signaling pathways are being discovered, for the most part it remains unknown how they are being put together by different cell types into complex, nonlinear, hierarchical control networks that, on the one hand, reliably maintain constant cell numbers, and on the other hand, quickly adjust to oversee the robust response to tissue damage. Theoretical approaches can fill the gap by being able to reconstruct the underlying control network, based on the observations about the aspects of cellular dynamics. We argue that while many hypothetical networks may be capable of basic cell lineage maintenance, some are much more efficient from the viewpoint of variance minimization. Thus, we developed a new methodology that can test various control networks for stability, variance, and robustness. In the example of the airway epithelium that we highlight, it turns out that the evolutionary selected, actual architecture coincides with the mathematically optimal solution that minimizes the fluctuations of cell numbers at homeostasis.

• Animals
• Cell Lineage
• Computational Biology
• Epithelial Cells/cytology
• Homeostasis/physiology
• Mice
• Models, Biological
• Signal Transduction
• Stem Cells/cytology
• Stochastic Processes

• R01 AR067273 NIAMS NIH HHS
• U01 CA187956 NCI NIH HHS
• Foundation for the National Institutes of Health
• NIH National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS)
• Edward Mallinckrodt Jr. Foundation grant
• University of California Cancer Research Coordinating Committee grant

• Animals
• Cell Differentiation/physiology
• Cell Division/physiology
• Cells, Cultured
• Computer Simulation
• Epidermal Cells
• Epidermis/physiology
• Feedback, Physiological/physiology
• Homeostasis/physiology
• Humans
• Models, Biological
• Stem Cells/cytology
• Stem Cells/physiology

• R01 AR067273 NIAMS NIH HHS
• U01 CA187956 NCI NIH HHS
• 1 U01 CA187956-01 NCI NIH HHS
• R01-AR067273 NIAMS NIH HHS

Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt.

• Potts model
• cancer
• colorectal cancer
• mathematical modeling
• multicellular
• multiscale model

• Chronic cancers
• Feedback control
• Stem cells
• Tumor growth dynamics

The epithelium of the small intestinal crypt, which has a vital role in protecting the underlying tissue from the harsh intestinal environment, is completely renewed every 4–5 days by a small pool of stem cells at the base of each crypt. How is this renewal controlled and homeostasis maintained, particularly given the rapid nature of this process? Here, based on the recent observations from in vitro “mini gut” studies, we use a hybrid stochastic model of the crypt to investigate how exogenous niche signaling (from Wnt and BMP) combines with auto-regulation to promote homeostasis. This model builds on the sub-cellular element method to account for the three-dimensional structure of the crypt, external regulation by Wnt and BMP, internal regulation by Notch signaling, as well as regulation by internally generated diffusible signals. Results show that Paneth cell derived Wnt signals, which have been observed experimentally to sustain crypts in cultured organs, have a dramatically different influence on niche dynamics than does mesenchyme derived Wnt. While this signaling can indeed act as a redundant backup to the exogenous gradient, it introduces a positive feedback that destabilizes the niche and causes its uncontrolled expansion. We find that in this setting, BMP has a critical role in constraining this expansion, consistent with observations that its removal leads to crypt fission. Further results also point to a new hypothesis for the role of Ephrin mediated motility of Paneth cells, specifically that it is required to constrain niche expansion and maintain the crypt’s spatial structure. Combined, these provide an alternative view of crypt homeostasis where the niche is in a constant state of expansion and the spatial structure of the crypt arises as a balance between this expansion and the action of various sources of negative regulation that hold it in check.

The small intestinal epithelium, like our skin, is constantly being renewed. In the intestine however, this epithelium is exposed to the harsh digestive environment, necessitating much more rapid renewal. Remarkably, the entire epithelium is renewed every 4–5 days. This raises the question, how can the size and structure of this tissue be maintained given this pace. Motivated by recent experimental observations, we construct a three-dimensional, hybrid stochastic model to investigate the mechanisms responsible for homeostasis of this tissue. We find that there are redundant signals created by both the epithelium itself and surrounding tissues that act in parallel to maintain epithelial structure. This redundancy comes at a price however: it introduces the possibility of explosive stem cell population growth. Additional results suggest that other signals along with choreographed motion of cells are responsible for repressing this expansion. Taken together, our results provide a novel hypothesis for how robust but fast renewal of the crypt is achieved: as a balance between expansion, which drives fast renewal and repression, which holds that expansion in check to maintain the crypt’s structure.

• Stem cells
• differentiated cells
• differentiation
• proliferation
• stochastic modeling

• Cell Physiological Phenomena
• Models, Biological
• Stem Cells/physiology
• Stochastic Processes

• R01 CA129286 NCI NIH HHS
• U01 CA187956 NCI NIH HHS

This review discusses quantitative modeling studies of stem and non-stem cancer cell interactions and the fraction of cancer stem cells.

The involvement of Cancer Stem Cells (CSCs) in tumor progression and tumor recurrence is one of the most studied subjects in current cancer research. The CSC hypothesis states that cancer cell populations are characterized by a hierarchical structure that affects cancer progression. Due to the complex dynamics involving CSCs and the other cancer cell subpopulations, a robust theory explaining their action has not been established yet. Some indications can be obtained by combining mathematical modeling and experimental data to understand tumor dynamics and to generate new experimental hypotheses. Here, we present a model describing the initial phase of ErbB2⁺ mammary cancer progression, which arises from a joint effort combing mathematical modeling and cancer biology. The proposed model represents a new approach to investigate the CSC-driven tumorigenesis and to analyze the relations among crucial events involving cancer cell subpopulations. Using in vivo and in vitro data we tuned the model to reproduce the initial dynamics of cancer growth, and we used its solution to characterize observed cancer progression with respect to mutual CSC and progenitor cell variation. The model was also used to investigate which association occurs among cell phenotypes when specific cell markers are considered. Finally, we found various correlations among model parameters which cannot be directly inferred from the available biological data and these dependencies were used to characterize the dynamics of cancer subpopulations during the initial phase of ErbB2⁺ mammary cancer progression.

• Adult Stem Cells/classification
• Adult Stem Cells/cytology
• Adult Stem Cells/physiology
• Animals
• Biomarkers/metabolism
• Carcinogenesis
• Cell Differentiation
• Homeostasis
• Humans
• Intestines/cytology
• Intestines/physiology
• Intestines/radiation effects
• Models, Biological
• Paneth Cells/cytology
• Paneth Cells/physiology
• Stem Cell Niche

• R01 DK089933 NIDDK NIH HHS
• R01-DK089933 NIDDK NIH HHS
• T32 HD007505 NICHD NIH HHS
• F30-DK095517 NIDDK NIH HHS
• R01 DK078927 NIDDK NIH HHS
• T32-GM07863 NIGMS NIH HHS
• T32-HD007515 NICHD NIH HHS
• T32 GM007863 NIGMS NIH HHS
• R01 DK096972 NIDDK NIH HHS
• F30 DK095517 NIDDK NIH HHS
• R01-DK078927 NIDDK NIH HHS

• Cell Differentiation/physiology
• Cells, Cultured
• Colon/cytology
• Colon/physiology
• Computer Simulation
• Enterocytes/cytology
• Enterocytes/physiology
• Humans
• Models, Biological
• Models, Statistical
• Stem Cells/cytology
• Stem Cells/physiology

• apoptosis
• cancer
• cell cycle
• cell-cell signalling
• colon crypt
• differentiation
• mathematical model

• Apoptosis/physiology
• Cell Communication/physiology
• Cell Differentiation/physiology
• Cell Transformation, Neoplastic/pathology
• Colon/pathology
• Colon/physiopathology
• Colorectal Neoplasms/pathology
• Colorectal Neoplasms/physiopathology
• Disease Progression
• Enteroendocrine Cells/pathology
• Enteroendocrine Cells/physiology
• Humans
• Models, Theoretical
• Stem Cells/pathology
• Stem Cells/physiology

• crypt morphogenesis
• growth dynamics
• stem cells
• tissue mechanics

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a consequence of two “hits”, and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more specialized cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.

• Cell Differentiation
• Cell Lineage
• Homeostasis
• Models, Biological

• R01 CA129286 NCI NIH HHS
• 1R01CA129286-01A1 NCI NIH HHS

• Carcinogenesis
• Cell Division
• Cell Line, Tumor
• Cell Lineage
• Cell Proliferation
• Cell Transformation, Neoplastic
• DNA Mutational Analysis
• Homeostasis
• Humans
• Models, Theoretical
• Mutation
• Neoplasms/metabolism
• Neoplastic Stem Cells/cytology
• Point Mutation
• Probability
• Signal Transduction
• Stem Cell Niche

Normal human tissue is organized into cell lineages, in which the highly differentiated mature cells that perform tissue functions are the end product of an orderly tissue-specific sequence of divisions that start with stem cells or progenitor cells. Tissue homeostasis and effective regeneration after injuries requires tight regulation of these cell lineages and feedback loops play a fundamental role in this regard. In particular, signals secreted from differentiated cells that inhibit stem cell division and stem cell self-renewal are important in establishing control. In this article we study in detail the cell dynamics that arise from this control mechanism. These dynamics are fundamental to our understanding of cancer, given that tumor initiation requires an escape from tissue regulation. Knowledge on the processes of cellular control can provide insights into the pathways that lead to deregulation and consequently cancer development.

• cancer
• cell linage control
• mathematical models
• tissue regeneration
• tissue stability

• Cell Differentiation/physiology
• Models, Biological
• Numerical Analysis, Computer-Assisted
• Stem Cells/cytology
• Stem Cells/physiology
• Stochastic Processes

• P50 GM076516 NIGMS NIH HHS
• R01 CA129286 NCI NIH HHS

Colon crypts, a single sheet of epithelia cells, consist of a periodic pattern of stem cells, transit-amplifying cells, and terminally differentiated cells that constantly renew and turnover. Experimental evidence suggests that Wnt signaling promotes and regulates stem cell division, differentiation, and possible cell migrations while intestinal BMP signaling inhibits stem cell self-renewal and repression in crypt formation. As more molecular details on Wnt and BMP in crypts are being discovered, little is still known about how complex interactions among Wnt, BMP, and different types of cells, and surrounding environments may lead to de novo formation of multiple crypts or how such interactions affect regeneration and stability of crypts.

We present a mathematical model that contains Wnt and BMP, a cell lineage, and their feedback regulations to study formation, regeneration, and stability of multiple crypts. The computational explorations and linear stability analysis of the model suggest a reaction–diffusion mechanism, which exhibits a short-range activation of Wnt plus a long-range inhibition with modulation of BMP signals in a growing tissue of cell lineage, can account for spontaneous formation of multiple crypts with the spatial and temporal pattern observed in experiments. Through this mechanism, the model can recapitulate some distinctive and important experimental findings such as crypt regeneration and crypt multiplication. BMP is important in maintaining stability of crypts and loss of BMP usually leads to crypt multiplication with a fingering pattern.

The study provides a mechanism for de novo formation of multiple intestinal crypts and demonstrates a synergetic role of Wnt and BMP in regeneration and stability of intestinal crypts. The proposed model presents a robust framework for studying spatial and temporal dynamics of cell lineages in growing tissues driven by multiple signaling molecules.