Agent based modelling helps in understanding the rules by which fibroblasts support keratinocyte colony formation

Background: Autologous keratincoytes are routinely expanded using irradiated mouse fibroblasts and bovine serum for clinical use. With growing concerns about the safety of these xenobiotic materials, it is desirable to culture keratinocytes in media without animal derived products. An improved understanding of epithelial/mesenchymal interactions could assist in this. Methodology/Principal Findings: A keratincyte/fibroblast o-culture model was developed by extending an agent-based keratinocyte colony formation model to include the response of keratinocytes to both fibroblasts and serum. The model was validated by comparison of the in virtuo and in vitro multicellular behaviour of keratinocytes and fibroblasts in single and co-culture in Greens medium. To test the robustness of the model, several properties of the fibroblasts were changed to investigate their influence on the multicellular morphogenesis of keratinocyes and fibroblasts. The model was then used to generate hypotheses to explore the interactions of both proliferative and growth arrested fibroblasts with keratinocytes. The key predictions arising from the model which were confirmed by in vitro experiments were that 1) the ratio of fibroblasts to keratinocytes would critically influence keratinocyte colony expansion, 2) this ratio needed to be optimum at the beginning of the co-culture, 3) proliferative fibroblasts would be more effective than irradiated cells in expanding keratinocytes and 4) in the presence of an adequate number of fibroblasts, keratinocyte expansion would be independent of serum. Conclusions: A closely associated computational and biological approach is a powerful tool for understanding complex biological systems such as the interactions between keratinocytes and fibroblasts. The key outcome of this study is the finding that the early addition of a critical ratio of proliferative fibroblasts can give rapid keratinocyte expansion without the use of irradiated mouse fibroblasts and bovine serum

A hierarchical Bayesian model for understanding the spatiotemporal dynamics of the intestinal epithelium

Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions-uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales

A Multicellular Model of Intestinal Crypt Buckling and Fission

Crypt fission is an in vivo tissue deformation process that is involved in both intestinal homeostasis and colorectal tumourigenesis. Despite its importance, the mechanics underlying crypt fission are currently poorly understood. Recent experimental development of organoids, organ-like buds cultured from crypt stem cells in vitro, has shown promise in shedding light on crypt fission. Drawing inspiration from observations of organoid growth and fission in vivo, we develop a computational model of a deformable epithelial tissue layer. Results from in silico experiments show the stiffness of cells and the proportions of cell subpopulations affect the nature of deformation in the epithelial layer. In particular, we find that increasing the proportion of stiffer cells in the layer increases the likelihood of crypt fission occurring. This is in agreement with and helps explain recent experimental work

Combined changes in Wnt signalling response and contact inhibition induce altered proliferation in radiation treated intestinal crypts

Curative intervention is possible if colorectal cancer is identified early, underscoring the need to detect the earliest stages of malignant transformation. A candidate biomarker is the expanded proliferative zone observed in crypts before adenoma formation, also found in irradiated crypts. However, the underlying driving mechanism for this is not known. Wnt signaling is a key regulator of proliferation, and elevated Wnt signaling is implicated in cancer. Nonetheless, how cells differentiate Wnt signals of varying strengths is not understood. We use computational modeling to compare alternative hypotheses about how Wnt signaling and contact inhibition affect proliferation. Direct comparison of simulations with published experimental data revealed that the model that best reproduces proliferation patterns in normal crypts stipulates that proliferative fate and cell cycle duration are set by the Wnt stimulus experienced at birth. The model also showed that the broadened proliferation zone induced by tumorigenic radiation can be attributed to cells responding to lower Wnt concentrations and dividing at smaller volumes. Application of the model to data from irradiated crypts after an extended recovery period permitted deductions about the extent of the initial insult. Application of computational modeling to experimental data revealed how mechanisms that control cell dynamics are altered at the earliest stages of carcinogenesis

Tipping the Balance: Robustness of Tip Cell Selection, Migration and Fusion in Angiogenesis

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, ‘stabilised’ tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer

Development of a Three Dimensional Multiscale Computational Model of the Human Epidermis

Transforming Growth Factor (TGF-β1) is a member of the TGF-beta superfamily ligand-receptor network. and plays a crucial role in tissue regeneration. The extensive in vitro and in vivo experimental literature describing its actions nevertheless describe an apparent paradox in that during re-epithelialisation it acts as proliferation inhibitor for keratinocytes. The majority of biological models focus on certain aspects of TGF-β1 behaviour and no one model provides a comprehensive story of this regulatory factor's action. Accordingly our aim was to develop a computational model to act as a complementary approach to improve our understanding of TGF-β1. In our previous study, an agent-based model of keratinocyte colony formation in 2D culture was developed. In this study this model was extensively developed into a three dimensional multiscale model of the human epidermis which is comprised of three interacting and integrated layers: (1) an agent-based model which captures the biological rules governing the cells in the human epidermis at the cellular level and includes the rules for injury induced emergent behaviours, (2) a COmplex PAthway SImulator (COPASI) model which simulates the expression and signalling of TGF-β1 at the sub-cellular level and (3) a mechanical layer embodied by a numerical physical solver responsible for resolving the forces exerted between cells at the multi-cellular level. The integrated model was initially validated by using it to grow a piece of virtual epidermis in 3D and comparing the in virtuo simulations of keratinocyte behaviour and of TGF-β1 signalling with the extensive research literature describing this key regulatory protein. This research reinforces the idea that computational modelling can be an effective additional tool to aid our understanding of complex systems. In the accompanying paper the model is used to explore hypotheses of the functions of TGF-β1 at the cellular and subcellular level on different keratinocyte populations during epidermal wound healing

Modelling the Spatio-Temporal Cell Dynamics Reveals Novel Insights on Cell Differentiation and Proliferation in the Small Intestinal Crypt

We developed a slow structural relaxation model to describe cellular dynamics in the crypt of the mouse small intestine. Cells are arranged in a three dimensional spiral the size of which dynamically changes according to cell production demands of adjacent villi. Cell differentiation and proliferation is regulated through Wnt and Notch signals, the strength of which depends on the local cell composition. The highest level of Wnt activity is associated with maintaining equipotent stem cells (SC), Paneth cells and common goblet-Paneth cell progenitors (CGPCPs) intermingling at the crypt bottom. Low levels of Wnt signalling area are associated with stem cells giving rise to secretory cells (CGPCPs, enteroendocrine or Tuft cells) and proliferative absorptive progenitors. Deciding between these two fates, secretory and stem/absorptive cells, depends on Notch signalling. Our model predicts that Notch signalling inhibits secretory fate if more than 50% of cells they are in contact with belong to the secretory lineage. CGPCPs under high Wnt signalling will differentiate into Paneth cells while those migrating out from the crypt bottom differentiate into goblet cells. We have assumed that mature Paneth cells migrating upwards undergo anoikis. Structural relaxation explains the localisation of Paneth cells to the crypt bottom in the absence of active forces. The predicted crypt generation time from one SC is 4–5 days with 10–12 days needed to reach a structural steady state. Our predictions are consistent with experimental observations made under altered Wnt and Notch signalling. Mutations affecting stem cells located at the crypt floor have a 50% chance of being propagated throughout the crypt while mutations in cells above are rarely propagated. The predicted recovery time of an injured crypt losing half of its cells is approximately 2 days

Comparing individual-based approaches to modelling the self-organization of multicellular tissues.

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage

Growth-induced buckling of an epithelial layer

We use a proof-of-concept experiment and two mathematical models to explore growth-induced tissue buckling, as may occur in colorectal crypt formation. Our experiment reveals how growth of a cultured epithelial monolayer on a thin flexible substrate can cause out-of-plane substrate deflections. We describe this system theoretically using a 'bilayer' model in which a growing cell layer adheres to a thin compressible elastic beam. We compare this with the 'supported-monolayer' model due to Edwards and Chapman (Bull Math Biol 69:1927-1942, 2007) for an incompressible expanding beam (representing crypt epithelium), which incorporates viscoelastic tethering to underlying stroma. We show that the bilayer model can exhibit buckling via parametric growth (in which the system passes through a sequence of equilibrium states, parameterised by the total beam length); in this case, non-uniformities in cell growth and variations in cell-substrate adhesion are predicted to have minimal effect on the shape of resulting buckled states. The supported-monolayer model reveals how competition between lateral supports and stromal adhesion influences the wavelength of buckled states (in parametric growth), and how non-equilibrium relaxation of tethering forces influences post-buckled shapes. This model also predicts that non-uniformities in growth patterns have a much weaker influence on buckled shapes than non-uniformities in material properties. Together, the experiment and models support the concept of patterning by growth-induced buckling and suggest that targeted softening of a growing cell layer provides greater control in shaping tissues than non-uniform growth