Cell differentiation can underpin the reproducibility of morphogenesis

TL;DR

This work demonstrates that reproducible morphogenesis can emerge as an unselected-byproduct of evolving complex morphologies. Using a Cellular Potts Model with GRNs, morphogens, and cell-state dynamics, the authors show that highly reproducible shapes arise when moving progenitor cells shape structures and irreversibly differentiate into stationary, anchored differentiated cells—a morphogenetic division of labour. The presence of multiple SCCs in cell-state space, boundary-localised differentiation driven by morphogens, and differential adhesion collectively stabilize morphogenesis against noise. These findings suggest a fundamental role for differentiation in not only generating but also maintaining morphologies, with implications for organoid engineering and understanding evolutionary development. The work highlights three general principles for robust morphogenesis and points to progenitor-cell systems as a common, robust route to complex, repeatable tissue architectures.

Abstract

Morphogenesis of complex body shapes is reproducible despite the noise inherent in the underlying morphogenetic processes. However, how these morphogenetic processes work together to achieve this reproducibility remains unclear. Here, we ask how morphogenetic reproducibility is realised by developing a computational model that evolves complex morphologies. We find that evolved, complex morphologies are reproducible in a sizeable fraction of simulations, despite no direct selection for reproducibility. We show that high reproducibility is caused by segregating moving cells that "shape" morphologies from stationary cells that "maintain" morphologies during morphogenesis. Strikingly, most highly reproducible morphologies also evolved cell differentiation, where proliferative, moving stem cells (i.e., progenitor cells) irreversibly differentiate into non-dividing, stationary differentiated cells. These results suggest that cell differentiation observed in natural development plays a fundamental role in morphogenesis in addition to the production of specialised cell types. This previously-unrecognised role of cell differentiation has major implications for our understanding of how morphologies are generated and regenerated.

Figures (6)

• Figure 1: Multi-scale model of morphogenesis evolution. A Three neighbouring cells on a CPM grid. A cell consists of one or more pixels. Each cell is coloured by its "cell state" defined by the concentrations of all its proteins converted to boolean values (the medium is represented by white pixels). Pixels with alternating stripes indicate pixel copies at cell boundaries. Each cell contains a genome that encodes transcription factors (TFs; circles, squares, triangles), adhesion proteins (sticks with a lock or key) and membrane tension proteins (not shown). Arrows indicate regulation of gene expression by TFs (arrow head for activation, blunt head for inhibition). Double harpoon arrows indicate diffusion of morphogens (membrane-permeable TFs). B Adhesion proteins facilitate the binding of cells to each other via a lock and key mechanism, or to the surrounding medium (not shown). C. A population consists of 60 morphologies (only three depicted). Morphologies undergo a developmental phase on separate CPM grids for 12,000 DTS, and then a reproduction phase, where morphologies with complex shapes are selected. Reproduction can occur without mutation (black arrows) or with mutation (orange arrow), with mutation determined probabilistically. Mutations change the topology of the GRN (dashed orange arrow), with the example showing a change from inhibition of gene $y$ by gene $x$ to activation of gene $y$ by gene $x$. DE Illustration of the two measurements used to determine the complexity score on two morphologies (described in Methods \ref{['evolution']}). (D) depicts the measurement of how much the morphology deviates from a perfect circle (black), with the centre of the circle being the morphology's centre of mass. Black arrows at equidistant intervals around the circle mark directions where the morphology's shape deviates from the circle, with longer arrows contributing to a higher score. (E) depicts the measurement of inward folding using double sided arrows, with more arrows contributing to a higher score. The cells are all coloured grey to emphasise that only the shape, not cell states, determine the complexity score.
• Figure 2: Computational simulations showing the evolution of complex morphologies. AB The plots show a five-generation moving average of population fitness (shape complexity) over evolution. The morphologies above the plots each depict a separate morphology at the end of its development (12,000 DTS) from six different generations over the course of evolution. The generation number of each morphology is shown to its left. "Evolved morphologies", defined as the most complex morphology from the final generation of the simulation, are shown on the far right. The evolved morphology in (A) and (B) are referred to as morphology-1 and morphology-2, respectively.
• Figure 3: Both highly and poorly reproducible morphologies evolve in response to selection for shape complexity. A Reproducibility scores against shape complexity scores for the 90 morphologies that reached a threshold of shape complexity. Circles indicate morphologies with a single strongly connected component (SCC, defined in Section \ref{['stem-section']}) (mean reproducibility$=52.0\%$, $n=65$); filled triangles indicate morphologies with multiple SCCs with unidirectional transitions between them (mean reproducibility$=72.1\%$, $n=24$). The blue diamond is a morphology with multiple SCCs without unidirectional transitions (Fig. S8A). Numbered arrows refer to the morphologies in panels B, C, D, and E. BC Simplified cell state spaces for (B) morphology-1 and (C) morphology-2. Node colours correspond to cell state colours depicted in the morphologies to the left each of cell state space. Arrows are cell-state transitions. Cell states are partitioned into strongly connected components (SCCs, coloured boxes). Node sizes depict cell state frequency over all of development; node colours correspond to cell states from morphology-1 and morphology-2, respectively (shown to the left of each state space). See Fig. S5IJ for the state spaces without pruning of nodes and edges. D Four morphologies that are highly reproducible. E Four morphologies that are poorly reproducible. F Four highly reproducible morphologies from simulations where morphologies evolved with morphogens mutating (for more information see Fig. S9).
• Figure 4: Highly reproducible morphologies have moving and dividing cells that undergo unidirectional transitions to non-moving and non-dividing cells. AB Two developmental replicates of morphology-1 (A) and morphology-2 (B) are depicted after 2,600, 4,000, 8,000 and 12,000 DTS, showing a difference in their reproducibility. Dashed arrows in (B) indicate the presence (replicate-1) or absence (replicate-2) of a bifurcation in collective cell motion; asterisks indicate protrusions. Vector plots show the displacement of the centre of mass of each cell during 2,000 DTS at each respective time point, with colours indicating magnitude (the lighter, the larger). C Average cell momentum magnitude for each SCC from the 25 morphologies with multiple SCCs. Momentum is the distance travelled by a cell per DTS multiplied by its size in pixels (see Methods \ref{['Momentum']}). Black arrows indicate unidirectional transitions between SCCs. Grey lines connect SCCs from the same morphology that do not have unidirectional SCC transitions between each other. Filled orange triangles are SCCs from morphologies that have unidirectional SCC transitions. All transitory SCCs are excluded (see Methods \ref{['statespace']} for information about transitory SCCs). Blue diamonds are SCCs from the highly reproducible morphology that does not have unidirectional SCC transitions. The numbered morphologies correspond to those from Fig. \ref{['results']}D. D Stacked bar charts showing the proportion of developmental time spent in each cell state and the proportion of cell divisions undergone by each state across all cells during developmental replicate-1 of morphology-1 and development replicate-1 of morphology-2. Diagonal lattices are pruned states. E The rate at which cells divide per developmental time when their state belongs to an upstream SCC (left) or a downstream SCC (right). Each data point represents an SCC from (C). Black lines connect upstream SCCs to their counterpart downstream SCCs. Boxes show medians and interquartile ranges (IQR); the downstream SCC box is tiny because most division rates are either very low or 0. Numbers on top of the box plots are median cell division rates.
• Figure 5: Mechanisms underlying progenitor-cell differentiation and motion. A Development and cell state space of organism-6, showing two progenitor-cell types, one differentiated-cell type, and a transitory SCC (see Methods \ref{['statespace']} for information about transitory SCCs). The morphology is shown after 2,000, 6,000 and 12,000 DTS. B Contours showing the concentrations of the three morphogens ($x$, $y$ and $z$) overlaid on morphology-6 after 9,000 DTS. Each contour joins points of equal concentration of the same morphogen. C Schematic depicting type-1, type-2 and differentiated cell domains from (B), with progenitor-cell motion (grey arrows) and differentiation (black arrows) indicated. Vertical dashed lines indicate cell-type boundaries. Below, morphogen concentrations along the cross-section line are plotted, along with the sums of cell protein concentrations for cells along the cross-section (each cross is one cell). D Polar plots of momentum magnitude by angle of motion for each cell type summed over all cells over the 12,000 DTS of morphology-6 development (Methods \ref{['Momentum']}). E Development of type-1, type-2 and differentiated cells in isolation. Polar plots show distributions of cell momentum as in (D). F Development and cell state space of morphology-11, showing a progenitor-cell type, a differentiated cell-type and a transitory SCC. The morphology is shown after 2,000, 6,000 and 12,000 DTS and its state space. G Contours showing the concentrations of morphogens $y$ (green) and $z$ (orange, morphogen $x$ is hidden for visibility) overlaid on morphology-11 after 8,000 DTS. H A schematic depicting progenitor and differentiated cell domains for morphology-11, with progenitor-cell motion (grey arrows) and differentiation (black arrows) indicated. The combined presence of morphogens $y$ and $z$ induces differentiation of progenitor cells. I Polar plots of momentum magnitude by angle of motion for progenitor and differentiated cell types summed over all cells over the 12,000 DTS of morphology-11 development shown in (F). J Development of progenitor and differentiated cells from morphology-11 in isolation. Polar plots show distributions of cell momentum as in (I).