Figure 1.
Cartoon representing the hierarchical model of stem-cell driven tissues.
In this formulation, each stem can undergo two types of division, either symmetric (with probability ) or asymmetric (with probability
). Each subsequently generated transient amplifying cell (TAC) can then undergo a certain number (
) of round of amplification before differentiating into a terminally differentiated cell (TD) which will live for a certain amount of time before dying (
timesteps). It is these three parameters, which we assume are intrinsic to a given stem cell, which we explore in this paper.
Figure 2.
Differential phenotypes in cultures enriched for brain tumour initiating cells.
Bright field images of CD133+ patient derived glioblastoma cell lines cultured in Neurobasal supplemented with EGF, FGF and B27, exhibiting striking phenotypic variability. These differences highlight the heterogeneity present even in a highly controlled static environment between cells that are putatively the same.
Figure 3.
Size of tissues vs. progenitor proliferative potential achieved by simulations using different levels of vascularisation and rates of symmetric vs. asymmetric divisions.
Lines represent averages for each of the three realisations in each scenario. (Left). Low vascularisation density of 0.01 (Centre) Normal vascularisation density of 0.05 (Right) High vascularisation density of 0.1. In each of these cases, the maximum tissue size will depend on the right combination of and
.
Figure 4.
Three different examples of simulations resulting from the computational model. Each simulation represents one of the typical outcomes.
Each begins with a single TIC seeded in the middle of the computational domain. In each situation the phenotype parameters are slightly different, resulting in (A) An unsustainable tissue (parameters: ,
,
and
day), (B) A homeostatic tissue where the balance of stem cell renewal and progenitor proliferation leads to a tissue whose overall size remains relatively constant over time, possibly representing a dormant tumor (parameters:
,
,
and
day) and, (C) Neoplastic-like tissue where the tissue overgrows the computational domain (parameters:
,
,
and
day). On the right of the final time point, we have shown an example of the oxygen tension in the computational domain. n.b. these images are zoomed in to illustrate detail and do not represent the entire computational domain.
Figure 5.
The three qualitatively different tissue scale phenotypes plotted as cell numbers over time for the example simulations in figure 4.
The black trace, representing the unsustainable simulation, grows quickly though never expands its stem population and then outstrips the available oxygen and collapses. The blue trace, representing the homeostatic simulation, reaches a critical size and then maintains a steady birth-death balance. The red trace, representing the tumorigenic simulation, settles into an effectively linear trace on this log-log plot, suggesting power law growth.
Figure 6.
Computational model description.
(A) The model includes three different cell types: stem, progenitor and differentiated. All cell types interact with the microenvironment in the form of oxygen tension. (B) The behaviour of each cell type is captured by a flowchart. The last segment with discontinuous arrows represents behaviour that is specific to the stem cells. (C) The cells are represented as agents inhabiting points in a grid in a 2D space with 500×500 grid points. Stem cells are represented as red points, progenitor as green and fully differentiated as blue. The vasculature is represented as oxygen source points in black.
Figure 7.
Model parameters.