Motifs in self-organising cells

TL;DR

The study addresses how interacting units in a simulated system of Dynamically Self-Organising (DSO) cells form persistent motifs and how these motifs can be quantified to reveal underlying interaction dynamics. It introduces Voronoi-based nearest-neighbour motifs and a set of interpretable structural and dynamic features to describe local packing and motion, then demonstrates that these motif features capture strain, defects, and semi-periodic behavior across large cell aggregates. The authors use unsupervised learning (UMAP, HDBSCAN) to map motif-derived features to a phase-space of DSO dynamics and show that emergent dipolar vortices within motifs can predict aggregate motion, while a neural network can infer microscopic interaction parameters from motif data. Collectively, the results propose a general, hierarchical motif framework for analyzing complex many-body systems and suggest broad applicability to other self-organising collectives.

Abstract

In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another. Simultaneously, the motifs can also interact, causing new coarse-grained properties to emerge in the system. In this paper, we found motifs in a simulated system of Dynamically Self-Organising cells. We also found that quantifying these motifs with a set of physically interpretable structural and dynamic features efficiently captures the interaction dynamics of the motifs' underlying cells. Using these motif features, we revealed packing strain and defects in large compact aggregates, semi-periodicity in motif ensembles, and phase space classes with unsupervised machine learning. Additionally, we trained neural networks to infer the critical hidden microscopic interaction parameters within each motif from coarse-grained motif features extracted from snapshots of the system. Furthermore, we uncovered emergent features that can predict the movement of cell collectives by hierarchically coarse-graining smaller motifs into larger ones (e.g. motif clusters). We speculate that this concept of motif hierarchies may be applied broadly to many-body interacting systems that are otherwise too complex to understand.

Figures (24)

• Figure 1: Hierarchy of motifs formed by Dynamically Self-Organising (DSO) cells hiraiwaDynamicSelfOrganizationIdealized2020 at increasing length scales. Higher-level motifs can be formed by iteratively grouping low-level motifs together (e.g., grouping particles into nearest neighbour motifs, and nearest neighbour motifs into clusters), with each layer possibly revealing new emergent properties of the system.
• Figure 2: Quantifying local structural and dynamic properties with motif features.
• Figure 3: Prevalence and persistence of different nearest neighbour cell groups at various contact following ($\alpha_{\text{CF}}$) and contact inhibition of locomotion ($\alpha_{\text{CIL}}$) strengths. A red line is drawn to highlight the region with disordered dynamic self-organising (DSO) cell pattern.
• Figure 4: (LEFT) Voronoi cells coloured by their number of neighbours, showing the prevalence of 6 nearest neighbours (6NN) groups in static aggregates, motile aggregates and rings. (CENTRE) Neighbour distance contour lines (gray) showing strained and increasingly dense packing towards the centre of aggregates. Packing defects are evident from the isolated, adjacent pairs of 5/7NN cell groups (red segments), as well as the extended chains of alternating 5/7NN groups (blue lines). Adjacent defect pairs in rings are also generally radially aligned. (RIGHT) Distribution in speed of cell groups shows a second peak near 1.0 when cells circulate particularly quickly, like in rings.
• Figure 5: Cell groups in aggregates can have significantly longer lifetime when located outside of the aggregate's central fast moving stream.