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. 2011 Apr;3(4):408-21.
doi: 10.1039/c0ib00092b. Epub 2011 Mar 4.

Phenotypic transition maps of 3D breast acini obtained by imaging-guided agent-based modeling

Jonathan Tang  1 , Heiko Enderling, Sabine Becker-Weimann, Christopher Pham, Aris Polyzos, Chen-Yi Chen, Sylvain V Costes
Affiliations

Phenotypic transition maps of 3D breast acini obtained by imaging-guided agent-based modeling

Jonathan Tang et al. Integr Biol (Camb). 2011 Apr.

Abstract

We introduce an agent-based model of epithelial cell morphogenesis to explore the complex interplay between apoptosis, proliferation, and polarization. By varying the activity levels of these mechanisms we derived phenotypic transition maps of normal and aberrant morphogenesis. These maps identify homeostatic ranges and morphologic stability conditions. The agent-based model was parameterized and validated using novel high-content image analysis of mammary acini morphogenesis in vitro with focus on time-dependent cell densities, proliferation and death rates, as well as acini morphologies. Model simulations reveal apoptosis being necessary and sufficient for initiating lumen formation, but cell polarization being the pivotal mechanism for maintaining physiological epithelium morphology and acini sphericity. Furthermore, simulations highlight that acinus growth arrest in normal acini can be achieved by controlling the fraction of proliferating cells. Interestingly, our simulations reveal a synergism between polarization and apoptosis in enhancing growth arrest. After validating the model with experimental data from a normal human breast line (MCF10A), the system was challenged to predict the growth of MCF10A where AKT-1 was overexpressed, leading to reduced apoptosis. As previously reported, this led to non growth-arrested acini, with very large sizes and partially filled lumen. However, surprisingly, image analysis revealed a much lower nuclear density than observed for normal acini. The growth kinetics indicates that these acini grew faster than the cells comprising it. The in silico model could not replicate this behavior, contradicting the classic paradigm that ductal carcinoma in situ is only the result of high proliferation and low apoptosis. Our simulations suggest that overexpression of AKT-1 must also perturb cell-cell and cell-ECM communication, reminding us that extracellular context can dictate cellular behavior.

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Figures

Fig. 1
Fig. 1. Quantification of acini properties
(A) Center slice of a 12 day MCF10A acinus grown on top of Matrigel™ is shown: DAPI for nuclear staining (blue), α6 for basement membrane staining (green) and Ki67 for proliferation marks (red). Merged image is also shown as a color image in the right panel. Values for various imaging properties are displayed for this acinus. (B) Illustration of image analysis. An overlay of the masks for the nuclei (blue mask), for the basement membrane (green contour), and for the proliferating nuclei (purple mask) are shown below each corresponding channel. An overlay of all three binary masks with their corresponding colors is shown in the right panel.
Fig. 2
Fig. 2. Depiction of the 3D lattice and the Cell Agent Rules of Interaction
(A) A 3D image and 2D cross-sectional views of an example in silico acinus consisting of 12 cell agents and 1 central lumen object surrounded by 42 basement membrane objects on the lattice. (B) When the Polarization variable is set TRUE, and the rules of cell polarization are enabled, each cell agent determines its polarity direction by taking the arithmetic sum of vectors pointing towards neighboring basement membrane objects (red dashed arrows). Rules are applied in 3D, but are shown above as 2D cross-sections. (C) The closest of the twelve neighboring positions to which the vector sum points towards determines the polarity (blue arrows). If multiple directions are equally distant, polarity is chosen from these at random (black dashed arrows). (D) An example execution through a simulation time step is depicted with Polarization enabled. Numbers and colors on a cell indicate the rule it will execute based on its local environment. During polarized division, the dividing cell agent places the daughter cell agent in the direction that maximizes contacts with other cell agents, except in the two directions along its axis of polarity. (E) For comparison, an example execution through a simulation time step is also shown with Polarization disabled. During nonpolarized cell division, dividing cell agents can place daughter cell agents in any neighboring position occupied by a basement membrane or lumen object with preference towards the lumen. (F) An event flow diagram for a cell agent summarizes the 6 rules of interaction.
Fig. 3
Fig. 3. In silico phenotypic transition maps depicting acinar characteristics as a function of apoptosis efficiency θ and proliferation potential after 12 days in culture - Polarization ON. (A) Cell Count, (C)% of growth arrested acini, (F) Acini volume, (H) Sphericity
All simulations were performed with Polarization set to TRUE. (B,D,E,G) Example images of simulations at day 12 for four parameter sets( [θ=0.3, Pp=0.9], [θ=0.3, Pp=0.4], [θ=0.9, Pp=0.9], [θ=0.9, Pp=0.4]).
Fig. 4
Fig. 4. In silico phenotypic transition maps depicting acinar characteristics as a function of apoptosis efficiency θ and proliferation potential after 12 days in culture - Polarization OFF. (A) Cell Count, (C)% of growth arrested acini, (F) Acini volume, (H) Sphericity
All simulations are done with polarization set to off. (B,D,E,G) Example images of simulations at day 12 for four parameter sets( [θ=0.3, Pp=0.9], [θ=0.3, Pp=0.4], [θ=0.9, Pp=0.9], [θ=0.9, Pp=0.4]).
Fig 5
Fig 5. Achieving a normal phenotype in silico and in vitro validation
(A-C) Experimental data as a function of days in culture. Average and standard deviations from ~100 to 200 acini per time point are shown as red diamonds. (A) Average number of cells contained in one acinus. (B) Average acinar volume (in cell unit). (C) Average acinar sphericity. (D-E) Transition maps are used to identify the parameter space that matches in vitro measurements at day 12. The average ± standard deviation of the measurements set the boundaries for each map. Overlap between the different areas delimits the parameter space matching all considered measurements. Cell number, Acini volume, Acini Sphericity and Growth arrest levels are used to delimit this space. (D) Resulting overlap with Polarization enabled maps from Fig. 3. It leads to a possible region of overlap. The red circle indicates the chosen parameter values (θ = 0.9, Pp = 0.4) within this area. The corresponding predicted in silico measurements for these parameters are displayed in panels A-C as solid blue curves with standard deviations shown as blue shadows. Note for all simulations: agent doubling time was set to 0.6 days with a 1.2 day delay for cells to reenter cycle. (E) Resulting overlap with Polarization disabled maps from Fig. 4. These maps lead to no overlap and therefore no possible fit of the experimental data. (F) Representative center slices of normal acini during the first 12 days in culture (nuclear stain with DAPI in blue, proliferation marks with Ki67 in red, basement membrane with α6 in green). (G) Example of 2D cross-sectional view of an in silico acinus with a normal phenotype obtained with parameters θ = 0.9, Pp = 0.4, and Polarization enabled. (H) 2D cross-sectional view of the same in silico acinus after transforming epithelial and basement membrane agents coordinates into pseudo microscope 3D image. Pseudo images are used to compute acini sphericity index (SI) for each simulation (displayed below each acinus). Red marks proliferating agents, green marks basement membrane agents and blue marks all epithelial agents.
Fig. 6
Fig. 6. Contrary to density, epithelium thickness β is an invariant property of an acinus and can be used as an indicator of lumen formation
(A) Density alone is a poor indicator of normal lumen formation, as it does not only depend on the number of epithelial layers alone (β) but also on the volume of the acinus. One can compute the theoretical density of a spherical acinus of radius R and agents of diameters d with β epithelial layers, as a function of the acinar volume (V) normalized to the cellular occupation (Vcell). (B) Four distinct simulations with different apoptotic efficiencies q and proliferation potential Pp, lead to very distinct lumen formation. Even though simulated acini are not perfectly spherical, simulated densities versus acinar volume can be fitted very accurately. (C) The dependency of density variation versus acinar volume for simulations with θ = 0.9 and Pp=0.4 match experimental data. Experimental densities are averaged over 7 different acini volume bins, mixing all densities from day 1 to day 12, as it was done for simulations. (D) β transition maps. The location of the four parameters conditions whose β values were fitted in panel (B) are marked with the same symbols and colors on the map. The normal phenotype simulated in Fig. 5 is shown as a red circle.
Fig 7
Fig 7. Locating ductal carcinoma in situ using the transition map
The MCF10A-pER Akt, which have a compromised apoptotic pathways where grown on top of Matrigel™ and quantified similarly to normal MCF10A. (A-C) Experimental data as a function of days in culture. Average and standard deviations from ~100 to 200 acini per time point are shown as red diamonds. (A) Average number of cells contained in one acinus. (B) Average acinar volume (in cell unit). (C) Average acinar sphericity. (D) Satisfying all three measurements at day 12 is impossible with Polarization enabled, as there are no overlapping regions for the different maps. (E) When disabling polarization, there are still no overlapping regions, indicating some additional mechanism is involved. (F) Akt-on acini density decreases much faster with acinar volume compared to normal MCF10A, leading to fit for β of 0.45. (G) Representative center slices of Akt-on acini during the first 12 days in culture (nuclear stain with DAPI in blue, proliferation marks with Ki67 in red, basement membrane with α6 in green).
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References

    1. Barcellos-Hoff MH, Aggeler J, Ram TG, Bissell MJ. Development. 1989;105:223–235. - PMC - PubMed
    1. Plachot C, Chaboub LS, Adissu HA, Wang L, Urazaev A, Sturgis J, Asem EK, Lelievre SA. BMC biology. 2009;7:77. - PMC - PubMed
    1. Weaver VM, Howlett AR, Langton-Webster B, Petersen OW, Bissell MJ. Semin Cancer Biol. 1995;6:175–184. - PubMed
    1. Petersen OW, Ronnov-Jessen L, Howlett AR, Bissell MJ. Proceedings of the National Academy of Sciences of the United States of America. 1992;89:9064–9068. - PMC - PubMed
    1. Park CC, Zhang H, Pallavicini M, Gray JW, Baehner F, Park CJ, Bissell MJ. Cancer research. 2006;66:1526–1535. - PMC - PubMed

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