Homeostasis, injury, and recovery dynamics at multiple scales in a self-organizing mouse intestinal crypt
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eLife assessment
The authors developed a valuable mathematical model that describes the spatiotemporal dynamics of cells in the intestinal crypt. The proposed model makes an important contribution to the field, allowing a better understanding of the formation and response dynamics of the intestinal crypt through the effective evaluation of health, disease, and treatment conditions. The authors provided solid evidence of the validity of their model and their conclusions, but some minor claims are not properly justified in the current manuscript. This paper is meant for computational biologists and cancer researchers working on oncotherapies for the intestinal epithelium.
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Abstract
The maintenance of the functional integrity of the intestinal epithelium requires a tight coordination between cell production, migration, and shedding along the crypt–villus axis. Dysregulation of these processes may result in loss of the intestinal barrier and disease. With the aim of generating a more complete and integrated understanding of how the epithelium maintains homeostasis and recovers after injury, we have built a multi-scale agent-based model (ABM) of the mouse intestinal epithelium. We demonstrate that stable, self-organizing behaviour in the crypt emerges from the dynamic interaction of multiple signalling pathways, such as Wnt, Notch, BMP, ZNRF3/RNF43, and YAP-Hippo pathways, which regulate proliferation and differentiation, respond to environmental mechanical cues, form feedback mechanisms, and modulate the dynamics of the cell cycle protein network. The model recapitulates the crypt phenotype reported after persistent stem cell ablation and after the inhibition of the CDK1 cycle protein. Moreover, we simulated 5-fluorouracil (5-FU)-induced toxicity at multiple scales starting from DNA and RNA damage, which disrupts the cell cycle, cell signalling, proliferation, differentiation, and migration and leads to loss of barrier integrity. During recovery, our in silico crypt regenerates its structure in a self-organizing, dynamic fashion driven by dedifferentiation and enhanced by negative feedback loops. Thus, the model enables the simulation of xenobiotic-, in particular chemotherapy-, induced mechanisms of intestinal toxicity and epithelial recovery. Overall, we present a systems model able to simulate the disruption of molecular events and its impact across multiple levels of epithelial organization and demonstrate its application to epithelial research and drug development.
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Author Response
Joint Public Review
(1) The developed model considers the interaction of multiple signaling networks that are essential for morphogenesis and homeostasis in the intestinal tissue, as well as other elements that had been proposed as relevant in the literature. Nevertheless, the details of how these interactions are modeled couldn't be evaluated in the current revision as the model was not shared with the reviewers and it is not available yet online, nor specified in any detail in the current manuscript. Additionally, how quantitative information from Wnt and BMP signaling pathways is incorporated in a quantitative way in the model is not clear.
Model files are provided with this reply. These are ‘.jl’ files for use with Julia. The model (the files provided with this reply) will be freely publicly available through …
Author Response
Joint Public Review
(1) The developed model considers the interaction of multiple signaling networks that are essential for morphogenesis and homeostasis in the intestinal tissue, as well as other elements that had been proposed as relevant in the literature. Nevertheless, the details of how these interactions are modeled couldn't be evaluated in the current revision as the model was not shared with the reviewers and it is not available yet online, nor specified in any detail in the current manuscript. Additionally, how quantitative information from Wnt and BMP signaling pathways is incorporated in a quantitative way in the model is not clear.
Model files are provided with this reply. These are ‘.jl’ files for use with Julia. The model (the files provided with this reply) will be freely publicly available through BioModels upon acceptance of this manuscript for publication.
The model includes abstracted values to reproduce Wnt and BMP signalling gradients and their effect on cell proliferation and differentiation to generate the three-dimensional crypt spatial cell distribution. To further clarify the implementation of the quantitative information from Wnt and BMP signalling pathways in the model, we have added the following paragraph in the Appendix Section 8) Cell fate: proliferation, differentiation, arrest, apoptosis
"…During this migration the Wnt content in absorptive progenitors is halved in each division and, away from Wnt sources, progressively decreases, while BMP signals increase, towards the villus. In our model, differentiation into enterocytes occurs when progenitors encounter a BMP signal level, higher that their Wnt signal content. For instance, in the ileal crypt in homeostasis this occurs approximately at cell position 16 from the crypt base, where progenitors migrating from the stem cell niche reach a reduced content of Wnt signals of about 8 a.u. On the other hand, the BMP signalling level has a maximum value of 64 at approximately cell position 23 from the crypt base, where BMP signals are generated by mature enterocytes. These BMP signals diffuse towards the crypt base and, hence, decrease exponentially to reach values of 8 a.u. at approximately position 16, which, hence, enable differentiation into enterocytes. Epithelial injuries resulting in a decreased number of enterocytes reduce BMP signal production and its diffusion range which results in the enlargement of the proliferation compartment as cells encounter the required level of BMP signals for differentiation only at higher positions in the crypt."
(2) Some conclusions by the authors are not properly justified in the text, as "Paneth cells are the main driver behind the differential mechanical environment in the niche", "Wnt-mediated feedback loop prevents the uncontrolled expansion of the niche", the specific effect of p27 in contrast with Wee1 phosphorylation over the cell cycle length, and "their recovery [absorptive progenitors] started before the end of the treatment, driven by a negative feedback loop from mature enterocytes to their progenitors".
We have reworded these statements as described below.
The paragraph “Paneth cells are the main driver behind the differential mechanical environment in the niche, where cells with longer cycles accumulate more Wnt and Notch signals. In agreement with experimental reports {Pin, 2015 #719}, in our model Paneth cells are assumed to be stiffer and larger than other epithelial cells, requiring higher forces to be displaced and generating high intercellular pressure in the region” has been modified and now reads as follows “In agreement with experimental reports {Pin, 2015 #719}, Paneth cells are assumed to be stiffer and larger than other epithelial cells, requiring higher forces to be displaced and generating high intercellular pressure in the niche. Due to this increased mechanical pressure, cells in the niche have longer division cycles and can accumulate more Wnt and Notch signals.”
The sentence “Wnt-mediated feedback loop prevents the uncontrolled expansion of the niche” has been deleted from paragraph, that now reads “To generate a niche of stable size, we implemented a negative Wnt-mediated feedback loop that resembles the reported stem cell production of RNF43/ZNRF3 ligands to increase the turnover of Wnt receptors in nearby cells {Hao, 2012 #2086;Koo, 2012 #2089;Clevers, 2013 #538;Clevers, 2013 #2098}. Similarly, in our model, a number of stem cells in excess of the homeostatic value reduces cell tethering of Wnt ligands and hence inhibits Paneth and stem cell generation (Figures 1A-B).”
Regarding the specific effect of p27 in contrast with Wee1 phosphorylation over the cell cycle length. We have simplified the text in the main manuscript that now reads “Using the model of Csikasz-Nagy et al. {Csikasz-Nagy, 2006 #1870}, we modulated the duration of G1 through the production rate of the p27 protein. The p27 protein has been reported to regulate the duration of G1 by preventing the activation of Cyclin E-Cdk2 which induces DNA replication and the beginning of S-phase {Morgan, 2007 #2073}. We, hence, hypothesized that rapid cycling absorptive progenitors located in regions of low mechanical pressure outside the stem cell niche have low levels of p27, which bring forward the start of S-phase to shorten G1 (Figures 2D). In support of this hypothesis, it has been demonstrated that p27 inhibition has no effect on the proliferation of absorptive progenitors {Zheng, 2008 #2074} (see the Appendix for a full description).
In the Appendix Section 2 we provide an extended explanation of the use of the p27 and Wee1 kinetic governing parameters to decrease the length of the cell cycle by decreasing mainly G1 but maintaining the length of S phase constant, which is as follows
"Regarding G1 phase, the p27 protein has been reported to regulate the duration of G1 by preventing the activation of Cyclin E-Cdk2 which induces DNA replication and defines the beginning of S-phase {Morgan, 2007 #2073}. We hypothesized that fast cycling cells have low levels of p27 which result in earlier DNA replication, bringing forward the start of S-phase and shortening the length of G1. In support of this hypothesis, it has been experimentally demonstrated that inhibiting p27 has no effect on the proliferation of absorptive progenitors {Zheng, 2008 #2074}. In the Csikasz-Nagy model {Csikasz-Nagy, 2006 #1870}, the duration of G1 can be modulated through the parameter V_si, which is the basal production rate of p21/p27 (in the Csikasz-Nagy model, the p21 and p27 proteins are represented by a single variable, here we refer to that model quantity as p21/p27).
Additionally, the end of S-phase is associated with the decrease of Wee1 to basal levels due to Cdc14 mediated phosphorylation of Wee1. In the Csikasz-Nagy model {Csikasz-Nagy, 2006 #1870}, this reaction is described by a Goldbeter-Koshland function, which includes the parameter KA_Wee1p to regulate the level of Cdc14 required for the phosphorylation of Wee1.
Therefore, we modified these two parameters, V_si and KA_Wee1p, to ensure that variations of the cycle duration mostly impact on G1 while the length of S phase remains constant. We assumed that the value of the two parameters scales linearly with the duration of the division cycle, t_cycle, between a lower and upper bound, which prevent aberrant behaviour of the cell cycle model in the dynamically changing conditions of the crypt."
The paragraph related to “their recovery started before the end of the treatment…” sentence has been amended in the text and now reads “Simulated proliferative absorptive progenitors were indirectly affected by stem cell ablation and their decrease was followed by a reduction in mature enterocytes. The progenitors recovered soon after treatment interruption to later reach values above baseline when responding to the negative feedback signalling from mature enterocytes (Figure 3A).”
(3) Only the results of the "main" model are shown, with no information about its sensitivity to parameter values, and how their conclusions depend on specific decisions on the model. For example, the authors said that "an optimal crypt cell composition is achieved when BMP and Wnt differentiation thresholds result in progenitors dividing approximately four times before differentiating into enterocytes", but the results of alternative scenarios are not shown.
To address this comment, we have included a new section in the Appendix, called “What-if Analysis”, and new figures (Figure S4-S8) with simulations of alternative scenarios affecting the main signalling pathways that govern crypt composition, in particular, we simulated stronger and weaker Wnt, BMP, Notch and ZNRF3/RNF43 signalling.
We attach the new section here:
"10) What-if Analysis
We investigated the effect on the simulated crypt of increasing and decreasing the strength of the main signalling pathways, Wnt, BMP and ZNRF3/RNF43 signalling, and modifying the Notch thresholds. For each alternative parameterisation, except when decreasing ZNRF3/RNF43 signalling, the simulation was run for 30 days to ensure stability was reached with the new parameter set and the final 10 days were included in the analysis. When decreasing ZNRF3/RNF43 signalling, we simulated 60 days to demonstrate the expansion of the niche and analysed the final 10 days. The reference parameter set used as baseline was the ileal mouse crypt parameter set reported in Appendix Table 1. In all cases, we only consider modifications of one signalling mechanism at a time.
To study alternative Wnt signalling scenarios, we used the WntRange parameter (Appendix Table 1), to double and halve the spreading area of Wnt signals emitted by Paneth cells while we maintained the original WntRange value for Wnt-emitting mesenchymal cells at the bottom of the crypt (Appendix Section 7.1) (Figures S4A-S4F). When WntRange was doubled, we observed increased number of stem and Paneth cells in a noticeably enlarged niche (Figures S4C-S4D), with cells choosing the stem cell fate instead of differentiating into absorptive progenitors. On the other hand, decreasing Wnt signalling, by halving WntRange in Paneth cells but maintaining its homeostatic value in mesenchymal cells, resulted in no apparent changes in the niche cell composition (Figures S4E-S4F) which resembled published experimental results of persisting functional stem cells after Paneth cell ablation {Durand, 2012 #434}.
The ZNRF3/RNF43-mediated negative feedback mechanism regulates the size of the niche by modulating Wnt signalling. We simulated increasing and decreasing the strength of the ZNRF3/RNF43, by doubling and halving, respectively, the parameter Z described in the Appendix Section 7.2 (Figures S5A-S5F). Following the increase of the intensity of ZNRF3/RNF43 signalling, we observed a decrease in the number of stem and Paneth cells together with relatively minor changes in the transit-amplifying region (Figures S5C-S5D). On the other hand, when decreasing ZNRF3/RNF43 signalling levels, the niche expanded , resulting in a crypt dominated by Paneth and stem cells (Figures S5E-S5F ) which replicates reported experimental phenotypes {Koo, 2012 #2089}.
To modify Notch signalling, we increased and decreased by 1 A.U. the Notch threshold required for lateral inhibition (Figures S6A-S6F). This Notch signalling threshold determines the number of contacting Notch-secreting cells (secretory lineage) to inhibit the differentiation of stem cells into the secretory lineage. Thus, increasing this Notch threshold enhances the production of secretory cells leading to the increase of Paneth, goblet and enteroendocrine cells (Figure S6C-S6D). Alternatively, decreasing the Notch threshold enhances differentiation into the absorptive lineage, reducing the number of Paneth and secretory cells (Figure S6E-S6F).
We modified the range of diffusion of BMP signals by doubling and halving the parameter A , (Figures S7A-S7F) which denotes the amount of diffusing BMP signals towards the base of the crypt (Appendix Section 7.4). When we increased the BMP signalling range, enterocytes differentiated at lower crypt positions effectively reducing the transit-amplifying zone (Figure S7A, Figure S7B). Decreasing BMP signalling strength by halving A resulted in the increase of proliferative absorptive progenitors, which reach higher positions in the crypt (Figure S7C-S7D). The niche was largely unaffected in both cases (Figure S7E-S7F)."
(4) Regarding the construction of the model, the authors used "counts of Ki-67 positive cells recorded by position" while the original data reported "overall cell counts per crypt and villus". Some explanation about how this conversion was made, why it is valid, as well as any potential problems, is needed. Additionally, the model is based on experiments done by others in mouse models; the similarity to the response in human intestinal crypts is not discussed.
Ki-67 immunostaining data during 5-FU treatment was derived from the same experiments. The overall cell counts per crypt and villus are published in {Jardi, 2022 #2416}. For this manuscript, we reanalysed the intestinal samples to estimate counts of cell types by position in the crypt.
We have clarified the text, which now reads …“The samples from this later study {Jardi, 2022 #2416} were analysed again to count Ki-67 positive cells at each position along the longitudinal crypt axis, for 30-50 individual hemi crypt units per tissue section per mouse as previously described {Williams, 2016 #2165}.”
We agree that the understanding of the translation of results derived from animal models into a human or clinical context is of high relevance. The mouse crypt is a model of choice to study epithelial biology and exhibits remarkable similarities with the human crypt. In our team, we are focussed on developing translational modelling strategies and have a version of the model that describes a human crypt. That model assumes mostly conserved crypt biology and structure across species and includes changes in parameter values needed to compensate reported differences in morphometrics and cell cycle duration. Due to the relevance and extent of this translational work, we chose to focus on the mouse crypt entirely in this manuscript. We think the translational modelling strategy to explore the quantitative translation between human and mouse and/or other species/settings merits a full report.
(5) The authors imply that their mathematical model of the intestinal crypt is an improvement over those already published but there is no direct comparison or review of the literature to substantiate this claim.
An extended literature review including more details of previous ABMs to enable a direct comparison with our model is now included in the manuscript and reads as follows:
“Several agent-based models (ABMs) have been proposed to describe the complexity and dynamic nature of the intestinal crypt. Early models were used as in silico platforms to study the dynamics and cellular organisation of the crypt. For instance, one of the pioneering ABMs was used to study the distribution and organisation of labelling and mitotic indices {Meineke, 2001 #326}. This model comprises a fixed ring of Paneth cells beneath a row of stem cells, which divide asymmetrically to produce a stem cell and a transit-amplifying cell that terminally differentiates after a fixed number of divisions. Some subsequent models are lattice-free, recapitulate neutral drift of equipotent stem cells and describe proliferation and cell fate regulated by a fixed Wnt signalling spatial gradient, which is defined by the distance from the crypt base, with proliferating cells progressing through discrete phases of the cell cycle and showing variable duration of the G1 phase {Pitt-Francis, 2009 #129}. Further model refinements can be seen in the model of Buske et al (2011), with stochastic cell growth and division time {Buske, 2011 #1}, Wnt levels defined by the fixed local curvature of the crypt and lateral inhibition driven by Notch signalling. Here, we present a lattice-free agent-based model that describes the spatiotemporal dynamics of single cells in the small intestinal crypt driven by the interaction of surface tethered Wnt signals, cell-cell Notch signalling, BMP diffusive signals, RNF43/ZNRF3-mediated feedback mechanisms and the cycle protein network responding to the crypt mechanical environment. We show that our computational model enables the simulation of the ablation and recovery of the stem cell niche as well as of how drug-induced molecular perturbations trigger a cascade of disruptive events spanning from the cell cycle to single cell arrest and/or apoptosis, altered cell migration and turnover and ultimately loss of epithelial integrity.”
(6) The authors claim that the simulated data and the available mouse data match up. Nevertheless, the data vs the model still appear both quantitatively and qualitatively different (as presented in Figures 2E, F, and 5C, D). This puts in doubt how much the model can actually reproduce the experimental data. In conclusion, the model would benefit from further refinement, particularly if the goal is to use the model for predicting the dynamics of oncogenic drug candidates.
To address this comment, we have made several adjustments: we refined the counting algorithm that determines cell position and improved the Ki67 and BrdU staining simulations by modifying the simulated staining criteria and adding an estimation of the experimental error to the simulated responses. A description of these changes is described in a new section in the appendix called “ABM simulation of Ki-67 and BrdU Staining”
With these changes we think we have achieved a more satisfactory agreement between observed and predicted results and updated all figures with Ki67 and BrdU staining simulated results.
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eLife assessment
The authors developed a valuable mathematical model that describes the spatiotemporal dynamics of cells in the intestinal crypt. The proposed model makes an important contribution to the field, allowing a better understanding of the formation and response dynamics of the intestinal crypt through the effective evaluation of health, disease, and treatment conditions. The authors provided solid evidence of the validity of their model and their conclusions, but some minor claims are not properly justified in the current manuscript. This paper is meant for computational biologists and cancer researchers working on oncotherapies for the intestinal epithelium.
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Joint Public Review
In this manuscript, the authors develop a multi-scale agent-based model (ABM) capable of reproducing the self-organizing behavior observed in the intestinal crypt. By considering just the signaling pathways -previously reported as regulatory in the intestinal crypt- and local physical cell-to-cell interactions, the proposed model not only explains the emergence of the spatial organization, but also recapitulates cell composition dynamics in the crypt (proliferation, migration, and differentiation of cells), as previously characterized in the complex tissue of the small intestine epithelium in mice. The authors show that the self-organized system resulting from the model displays a stable composition over time. Additionally, the authors show how this model can be effectively used to test different conditions, such as …
Joint Public Review
In this manuscript, the authors develop a multi-scale agent-based model (ABM) capable of reproducing the self-organizing behavior observed in the intestinal crypt. By considering just the signaling pathways -previously reported as regulatory in the intestinal crypt- and local physical cell-to-cell interactions, the proposed model not only explains the emergence of the spatial organization, but also recapitulates cell composition dynamics in the crypt (proliferation, migration, and differentiation of cells), as previously characterized in the complex tissue of the small intestine epithelium in mice. The authors show that the self-organized system resulting from the model displays a stable composition over time. Additionally, the authors show how this model can be effectively used to test different conditions, such as biomedically relevant perturbations (e.g. stem cell ablation, cell cycle inhibition, and toxicity of particular drug treatments) and the posterior recovery, allowing to predict the safety of potential oncotherapies.
In summary, the authors provide a powerful and versatile model, which can be applied to better understand the formation and response of the intestinal crypt, as well as the functional heterogeneity of the intestinal epithelium at multiple scales. The proposed mathematical model simulates features across scales in the intestinal crypt such as multiple signaling pathways, the mechanical environment and its forces, and cell cycle regulation. The model demonstrates the stability of the homeostatic crypt and recovery following stem cell ablation. The model also simulates the cell cycle protein network and demonstrates that CDK1 inhibition creates oversized cells. In sum, the model generated by the authors increases the understanding of how these biological processes take place in vivo, exploring not only healthy cell behavior but also cell response to injury by oncotherapies or other external factors. Additionally, the authors provide a series of fascinating movies that show the spatial organization of the crypt during these processes, and the manuscript has clear applications for the clinics.
Nevertheless, in its current form, the manuscript has some weaknesses that are worth mentioning:
(1) The developed model considers the interaction of multiple signaling networks that are essential for morphogenesis and homeostasis in the intestinal tissue, as well as other elements that had been proposed as relevant in the literature. Nevertheless, the details of how these interactions are modeled couldn't be evaluated in the current revision as the model was not shared with the reviewers and it is not available yet online, nor specified in any detail in the current manuscript. Additionally, how quantitative information from Wnt and BMP signaling pathways is incorporated in a quantitative way in the model is not clear.
(2) Some conclusions by the authors are not properly justified in the text, as "Paneth cells are the main driver behind the differential mechanical environment in the niche", "Wnt-mediated feedback loop prevents the uncontrolled expansion of the niche", the specific effect of p27 in contrast with Wee1 phosphorylation over the cell cycle length, and "their recovery [absorptive progenitors] started before the end of the treatment, driven by a negative feedback loop from mature enterocytes to their progenitors".
(3) Only the results of the "main" model are shown, with no information about its sensitivity to parameter values, and how their conclusions depend on specific decisions on the model. For example, the authors said that "an optimal crypt cell composition is achieved when BMP and Wnt differentiation thresholds result in progenitors dividing approximately four times before differentiating into enterocytes", but the results of alternative scenarios are not shown.
(4) Regarding the construction of the model, the authors used "counts of Ki-67 positive cells recorded by position" while the original data reported "overall cell counts per crypt and villus". Some explanation about how this conversion was made, why it is valid, as well as any potential problems, is needed. Additionally, the model is based on experiments done by others in mouse models; the similarity to the response in human intestinal crypts is not discussed.
(5) The authors imply that their mathematical model of the intestinal crypt is an improvement over those already published but there is no direct comparison or review of the literature to substantiate this claim.
(6) The authors claim that the simulated data and the available mouse data match up. Nevertheless, the data vs the model still appear both quantitatively and qualitatively different (as presented in Figures 2E, F, and 5C, D). This puts in doubt how much the model can actually reproduce the experimental data. In conclusion, the model would benefit from further refinement, particularly if the goal is to use the model for predicting the dynamics of oncogenic drug candidates.
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