Fixed parameters.

<p>Parameters fixed for both the pedigree and niche models. is a constant based on the area of contact and separation between cell i and the basement membrane (see Equation 5).</p

Stem cells (navy) are lost in the pedigree model if there is no attachment force to hold them in place.

<p>A: a snap-shot produced by the Repast modelling interface of a typical steady state cell distribution for the pedigree model crypt with stem cells attached to the base. B & C: when stem cell attachment is disabled stem cells are progressively transported out of the crypt and the crypt becomes a non-proliferating crypt full of mature cells. This state is likely to lead to crypt involution.</p

Cell shape representation.

<p>Representing cells as elastic 2D spheres via a linear spring model (Hooke's law). The implied cell shapes are shown on the right.</p

Visual snapshots of best and worst virtual crypts at steady state.

<p>A: Chosen best models. B: Worst performance on <i>Number of cells</i>. C: Worst performance on <i>Cell production rate</i>. D: Worst performance on <i>Mature cell order</i>. E: Worst performance on <i>Mature cell proportion</i>. Pedigree model results are shown in the top row and niche model results in the bottom row.</p

Simulation output of the adapted pedigree (left panel) and niche (right panel) model.

<p>A: Visual snapshot at steady state. B: LI simulations (mean trajectory: blue line and X's; standard deviation: light grey shade) overlaid with experimental data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0073204#pone.0073204-Sunter1" target="_blank">[7]</a> (mean trajectory: green dots; 95% confidence interval: green shade.)</p

Results summary.

<p>Results summary.</p

Biological significance of free parameters.

<p>Biological significance of free parameters.</p

The Pedigree and Niche concept.

<p>A: The Pedigree Concept. Key characteristics for this model of self-renewal are a preprogrammed differentiation hierarchy and asymmetric division of stem cells. The differentiation hierarchy and colour coding used by our model are also shown. TA denotes transit-amplifying cells, and the number denotes the cell generation for the TA cell lineage. B: The Niche concept. Maturity and proliferation are determined by the environment. Here we use the same colour for stem cells and other proliferating cells. Note that all cell divisions are symmetric.</p

Cell cycle parameters.

<p>Values used for the Smith-Martin cell cycle model (all values are given in units of hours). Values for stem cells are estimated using the ODE model.</p

Simulation output of our chosen best performing pedigree (left panel) and niche (right panel) model.

<p>A: Visual snapshot at steady state. The fact that the pedigree model has no lateral cell movement is evident, whilst the extremely high ordering in mature cells and separation between proliferative and mature cells of the niche model are also clearly visible. B: Cell number output of each of the individual thirty simulations. It is evident how the pedigree model takes longer to reach a steady state. C: LI simulations (mean trajectory: blue line and X's; standard deviation: light grey shade) overlaid with experimental data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0073204#pone.0073204-Sunter1" target="_blank">[7]</a> (mean trajectory: green dots; 95% confidence interval: green shade.</p