Multicell-Fold: geometric learning in folding multicellular life

TL;DR

This model achieves interpretable 4-D morphological sequence alignment, and predicting cell rearrangements before they occur at single-cell resolution, and offers a pathway toward a unified dynamic atlas for a variety of developmental processes.

Abstract

During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how every single cell decides to position itself relative to its neighboring cells. Despite its importance, it remains a major challenge to understand and predict the behavior of every cell within the living tissue over time during such intricate processes. To tackle this question, we propose a geometric deep learning model that can predict multicellular folding and embryogenesis, accurately capturing the highly convoluted spatial interactions among cells. We demonstrate that multicellular data can be represented with both granular and foam-like physical pictures through a unified graph data structure, considering both cellular interactions and cell junction networks. We successfully use our model to achieve two important tasks, interpretable 4-D morphological sequence alignment, and predicting local cell rearrangements before they occur at single-cell resolution. Furthermore, using an activation map and ablation studies, we demonstrate that cell geometries and cell junction networks together regulate local cell rearrangement which is critical for embryo morphogenesis. This approach provides a novel paradigm to study morphogenesis, highlighting a unified data structure and harnessing the power of geometric deep learning to accurately model the mechanisms and behaviors of cells during development. It offers a pathway toward creating a unified dynamic morphological atlas for a variety of developmental processes such as embryogenesis.

Figures (4)

• Figure 1: Overview of our multicellular folding algorithm (Multicell-Fold). (From left to right) A representative snapshot of a developing embryo (Drosophila, imaging and tracking data from stern2022deconstructing). To build a data-driven model to study these mesoscale living systems, we propose that these data can be represented as a dual graph structure, consisting of a primary graph of cells $\{\mathcal{C}\}$ and cell-cell adjacency $\{\mathcal{E}_{c-c}\}$, and an auxiliary graph of vertices $\{\mathcal{V}\}$ and cell edges $\{\mathcal{E}_{v-v}\}$. The two graphs are combined as inputs for the graph encoder, whose outputs can be used as node predictions. Alternatively, subsequently using a decoder or pooling operation generates edge or tissue-level prediction. An example prediction is shown, where orange indicates our model prediction of future cell rearrangements, and true cell rearrangement is indicated with black circles. (From right to left) Using a trained model, an activation map can be used to visualize the regional information the model has used to make predictions.
• Figure 2: Interpretable geometric video sequence alignment using activation map. (a) Align the two embryo sequences. Three independent models are trained; the markers indicate the mean values and the dashed color indicates the standard deviation. (b) The activation map visualizes the features the model used to make the alignment prediction.
• Figure 3: Predicting local cell rearrangement. (a) Example prediction at different angles of a 3-D Drosophila embryo. The embryo at $t=30$ min is shown here, and consecutive predictions over time are shown in Supplementary Video 1. Cells predicted to lose cell-cell junction with any of their neighbors in the next 1 minute are colored in orange. (b) Model accuracy over time. (c) Average accuracy.
• Figure 4: Ablation study. (a) AUC and (b) BCE loss. For each class, we train 3 independent models using 3 random seed numbers for 500 epochs and report the model performance of the last 5 epochs (n=15). One-way ANOVA tests are performed. (***: p-value $<0.001$).