Modelling Spatially Regulated β-Catenin Dynamics and Invasion in Intestinal Crypts

Murray, Philip J.; Kang, Jun Won; Mirams, Gary R.; Shin, Sung-Young; Byrne, Helen M.; Maini, Philip K.; Cho, Kwang Hyun

doi:10.1016/j.bpj.2010.05.016

Cited by 56 publications

(40 citation statements)

References 36 publications

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“…One resolution of the problem is to develop coarsegrained models, which replicate the essential features of the original model, but to which established mathematical techniques such as asymptotic and bifurcation analysis may be applied. This remains an area of current research (Fozard et al, 2010;Murray et al, 2010), the key difficulty being how to retain in such coarse-grained models the necessary level of detail and spatial resolution to represent mutations in single cells.…”

Section: Discussionmentioning

confidence: 99%

A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt

Mirams

Fletcher

Maini

et al. 2012

Journal of Theoretical Biology

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The surface epithelium lining the intestinal tract renews itself rapidly by a coordinated programme of cell proliferation, migration and differentiation events that is initiated in the crypts of Lieberkühn. It is generally believed that colorectal cancer arises due to mutations that disrupt the normal cellular dynamics of the crypts. Using a spatially structured cell-based model of a colonic crypt, we investigate the likelihood that the progeny of a mutated cell will dominate, or be sloughed out of, a crypt. Our approach is to perform multiple simulations, varying the spatial location of the initial mutation, and the proliferative and adhesive properties of the mutant cells, to obtain statistical distributions for the probability of their domination. Our simulations lead us to make a number of predictions. The process of monoclonal conversion always occurs, and does not require that the cell which initially gave rise to the population remains in the crypt. Mutations occurring more than one to two cells from the base of the crypt are unlikely to become the dominant clone. The probability of a mutant clone persisting in the crypt is sensitive to dysregulation of adhesion. By comparing simulation results with those from a simple one-dimensional stochastic model of population dynamics at the base of the crypt, we infer that this sensitivity is due to direct competition between wild-type and mutant cells at the base of the crypt. We also predict that increases in the extent of the spatial domain in which the mutant cells proliferate can give rise to counter-intuitive, non-linear changes to the probability of their fixation, due to effects that cannot be captured in simpler models.

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Section: Discussionmentioning

confidence: 99%

A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt

Mirams

Fletcher

Maini

et al. 2012

Journal of Theoretical Biology

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“…So far, most studies have focused either on the impact of a gradient in the context of the signal transduction (Melen et al, 2005; Murray et al, 2010) or in the context of gene regulatory networks (Balaskas et al, 2012) but did not interlace both aspects. Our analysis showed that the differential integration of the Wnt and the APC concentration into the signaling processes has two consequences.…”

Section: Discussionmentioning

confidence: 99%

Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions

Benary¹,

Kofahl²,

Hecht³

et al. 2013

Front. Physiol.

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The Wnt/β-catenin pathway is involved in the regulation of a multitude of physiological processes by controlling the differential expression of target genes. In certain tissues such as the adult liver, the Wnt/β-catenin pathway can attain different levels of activity due to gradients of Wnt ligands and/or intracellular pathway components like APC. How graded pathway activity is converted into regionally distinct patterns of Wnt/β-catenin target gene expression is largely unknown. Here, we apply a mathematical modeling approach to investigate the impact of different regulatory mechanisms on target gene expression within Wnt or APC concentration gradients. We develop a minimal model of Wnt/β-catenin signal transduction and combine it with various mechanisms of target gene regulation. In particular, the effects of activation, inhibition, and an incoherent feedforward loop (iFFL) are compared. To specify activation kinetics, we analyze experimental data that quantify the response of β-catenin/TCF reporter constructs to different Wnt concentrations, and demonstrate that the induction of these constructs occurs in a cooperative manner with Hill coefficients between 2 and 5. In summary, our study shows that the combination of specific gene regulatory mechanisms with a time-independent gradient of Wnt or APC is sufficient to generate distinct target gene expression patterns as have been experimentally observed in liver. We find that cooperative gene activation in combination with a TCF feedback can establish sharp borders of target gene expression in Wnt or APC gradients. In contrast, the iFFL renders gene expression independent of gradients of the upstream signaling components. Our subsequent analysis of carcinogenic pathway mutations reveals that their impact on gene expression is determined by the gene regulatory mechanism and the APC concentration of the cell in which the mutation occurs.

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“…β-Catenin is one of the key proteins in Wnt signaling pathway [23, 27], the change of the concentration of β-Catenin have been modeled by equation (3) [30, 31].

\frac{d [β C a t e n i n]}{d t} = a - true(true(\frac{[W n t] + b}{c \cdot [W n t] + d} true) \cdot true(\frac{e}{e + [β C a t e n i n]} true) + f true) \cdot [β C a t e n i n] .

…”

Section: Methodsmentioning

confidence: 99%

Cytokine combination therapy prediction for bone remodeling in tissue engineering based on the intracellular signaling pathway

Sun

Bao

et al. 2012

Biomaterials

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The long-term performance of tissue-engineered bone grafts is determined by a dynamic balance between bone regeneration and resorption. We proposed using embedded cytokine slow-releasing hydrogels to tune this balance toward a desirable final bone density. In this study we established a systems biology model, and quantitatively explored the combinatorial effects of delivered cytokines from hydrogels on final bone density. We hypothesized that: 1) bone regeneration was driven by transcription factors Runx2 and Osterix, which responded to released cytokines, such as Wnt, BMP2, and TGFβ, drove the development of osteoblast lineage, and contributed to bone mass generation; and 2) the osteoclast lineage, on the other hand, governed the bone resorption, and communications between these two lineages determined the dynamics of bone remodeling. In our model, Intracellular signaling pathways were represented by ordinary differential equations, while the intercellular communications and cellular population dynamics were modeled by stochastic differential equations. Effects of synergistic cytokine combinations were evaluated by Loewe index and Bliss index. Simulation results revealed that the Wnt/BMP2 combinations released from hydrogels showed best control of bone regeneration and synergistic effects, and suggested optimal dose ratios of given cytokine combinations released from hydrogels to most efficiently control the long-term bone remodeling. We revealed the characteristics of cytokine combinations of Wnt/BMP2 which could be used to guide the design of in vivo bone scaffolds and the clinical treatment of some diseases such as osteoporosis.

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Modelling Spatially Regulated β-Catenin Dynamics and Invasion in Intestinal Crypts

Cited by 56 publications

References 36 publications

A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt

A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt

Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions

Cytokine combination therapy prediction for bone remodeling in tissue engineering based on the intracellular signaling pathway

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