SoftBio Theory Seminar: Liquid Hopfield model - retrieval and localization in heterogeneous liquid mixtures

Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures compete with each other for the same components. This raises several questions, such as what types of interactions allow the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. Following Ref.[1], I will present in this seminar an analytically tractable model for liquids capable of retrieving states with target compositions. This model was named the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. By solving this model, we will show that non-linear repulsive interactions are necessary for retrieval of target structures. This is because liquid mixtures at low temperatures tend to transition to phases with few components, a phenomenon that we term localization. These results demonstrate a trade-off between retrieval and localization phenomena in liquid mixtures. 

[1] https://arxiv.org/abs/2310.18853