Villoutreix P et al. (2016), An integrated modelling framework from cells to...

ECB-ART-45050

Sci Rep 2016 Dec 02;6:37438. doi: 10.1038/srep37438.

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An integrated modelling framework from cells to organism based on a cohort of digital embryos.

Villoutreix P , Delile J , Rizzi B , Duloquin L , Savy T , Bourgine P , Doursat R , Peyriéras N .

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We conducted a quantitative comparison of developing sea urchin embryos based on the analysis of five digital specimens obtained by automatic processing of in toto 3D+ time image data. These measurements served the reconstruction of a prototypical cell lineage tree able to predict the spatiotemporal cellular organisation of a normal sea urchin blastula. The reconstruction was achieved by designing and tuning a multi-level probabilistic model that reproduced embryo-level dynamics from a small number of statistical parameters characterising cell proliferation, cell surface area and cell volume evolution along the cell lineage. Our resulting artificial prototype was embedded in 3D space by biomechanical agent-based modelling and simulation, which allowed a systematic exploration and optimisation of free parameters to fit the experimental data and test biological hypotheses. The spherical monolayered blastula and the spatial arrangement of its different cell types appeared tightly constrained by cell stiffness, cell-adhesion parameters and blastocoel turgor pressure.

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Genes referenced: LOC100887844 LOC100893907 LOC115919910 LOC115925415

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	Figure 1. Methodological workflow.The technical content of each box is described in detail in the supplementary material. Bottom to top: increasing levels of abstraction, from raw data to theory and modelling. The concept of “augmented phenomenology” (second tier) represents the superposition of raw data and its reconstruction. Features extracted from the augmented phenomenology are combined into an organised dataset conveying maximum biological meaning and leading to the formulation of theoretical hypotheses. (a to d) Upward arrowheads indicate derivation from data, including reconstruction of digital specimens and statistical analysis leading to probabilistic models. (e and f, h and j) Downward arrowheads indicate prediction testing, whether analytically (e) or by simulation (f), (h) and (j). Horizontal arrow: (g) Aggregation step leading to the design of a “normal” prototype from measurable individual cell features across the five specimens. (i) The prototype is used as an input into the biomechanical model. (k) Bidirectional arrow indicating the quantitative comparison between model simulations and digital reconstruction. (l) Feedback loop tuning the parameter values of the biomechanical model as a function of realism.
	Figure 2. Reconstruction of digital sea urchins from 3D+ time in vivo and in toto imaging.(a to c) Raw and reconstructed data from one specimen (embryo 3) at different stages of development. Scale bar 20 μm. (a) Volume rendering of raw images (Amira software) from two-photon laser scanning microscopy. Total cell number indicated bottom left. (b,c) Reconstructed digital embryo, displayed with Mov-IT software. (b) Detected nuclear centres with colour code for cell types propagated along the lineage: mesomeres (Mes) in blue, macromeres (Mac) in red, large micromeres (LMic) in pink, and small micromeres (SMic) in purple. (c) Surface rendering of segmented cell membranes, colour code as in (b). (d) Temporal observation window for each specimen of the cohort, time scale in hours post-fertilisation (hpf) after temporal rescaling (details in Supplementary Fig. 2). Arrowheads for embryo 3 indicate the temporal window displayed in (e). (e) Flat representation of the reconstructed cell lineage of embryo 3 with the same cell type colour code as in (b), time scale in hpf.
	Figure 3. Multi-level statistics and probabilistic model for the cohort and its prototype.(a to c) Temporally rescaled macroscopic quantities (whole-embryo level) in each specimen, top groups of curves in each chart and each cell population (lower four groups of curves, top to bottom: Mes, Mac, LMic, SMic). Same embryo colour code as in Fig. 2d (details in Supplementary Fig. 2). (d to f) Statistics of individual cell features in each cell group clustered by common type and generation. Mean and standard deviation bars represent normal and log-normal approximations of the cell feature distributions. In black: statistics aggregated into a prototype (see Supplementary Figs 3 and 4). (g to i) Embryo-level features in one measured specimen (embryo 3) and in simulation based on the probabilistic model (see Supplementary Fig. 11 for details). In black: mean of 300 simulated cell lineages; in grey: their standard deviation; in colour: measured values (top curve: whole embryo, lower four curves: separate populations using the same cell type colours as Fig. 2b). Shaded areas: incomplete cycles, for which an accurate estimation was not possible. (j to l) Same as (a to c) with the prototype curves added in black and grey.
	Figure 4. Spatial embedding in a biomechanical model of the prototypical multi-level probabilistic model.(a) Principle of cell axis computation. (b) Intensity of the attraction-repulsion force as a function of the interparticle distance r, with and . (c) Phenotypic phase diagram: the similarity of the simulation with digital embryos is computed for various pairs of homotypic and heterotypic adhesion coefficients (ωadh,o, ωadh,e). The green parametric region corresponds to the domain of best fit (Supplementary Video 2 shows simulations of representative embryos for each region). (d) Upper panel: example of multilayered aspherical “deviant” embryo. Lower panel: most realistic embryo. For both, section along the sagittal plane. (e to g) Landscapes of the three objective functions: cell type population border similarity Ds, epithelial layer planarity Ps, and embryo shape sphericity Ss (details concerning the calculation of these three metrics are described in the supplementary material). The fitness colour map goes from blue (best values) to red (worst values). The white dotted lines delimit the domains where the differences between observed and simulated embryonic developments are minimal. These lines are reproduced in the general phase diagram of (c).

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Amat, Fast, accurate reconstruction of cell lineages from large-scale fluorescence microscopy data. 2014, Pubmed