Interacting associative memory networks as a model for tissue self-organization

The rapid development of single-cell RNA sequencing has led to widespread interest in dynamical modelling of cell state. Cell types are defined by stable patterns of gene expression in the transcriptomic data, which has led theorists to search for dynamical models capable of encoding identified cell types as stable fixed points. Hopfield networks offer an elegant solution and have been used to describe reprogramming in individual cells. To capture cell-cell interactions we propose to model interacting cells using a lattice of interacting Hopfield networks. We consider cell-cell interactions mediated by paracrine (ligand-receptor) signalling and exosomes, and use a single parameter to tune the relative strength of intra-cell and inter-cell gene regulation. We investigate under what conditions the single-cell attractors remain stable, and whether cell-cell interactions can facilitate the emergence of new stable single-cell states. This approach captures multiple levels of biological organization and displays self-organizing properties which resemble multicellular development and homeostasis.