Liquid Hopfield model: Retrieval and localization in multicomponent liquid mixtures

Area of Science:

• Physics
• Biophysics
• Computational Neuroscience

Background:

• Biological systems exhibit complex heterogeneity, leading to emergent mesoscopic structures like liquid phases with controlled compositions.
• Understanding the interactions governing the retrieval of multiple ordered mesoscopic structures from such mixtures is crucial.
• The competition for components among these structures presents challenges in predicting their formation and stability.

Purpose of the Study:

• To develop an analytically tractable model for multicomponent liquids that can retrieve states with target compositions.
• To identify the types of interactions necessary for the retrieval of multiple ordered mesoscopic structures.
• To explore the physical limitations and trade-offs involved in achieving target compositions in liquid mixtures.

Main Methods:

• Development of a novel model for multicomponent liquids, termed the liquid Hopfield model.
• Analytical investigation of interaction types required for structure retrieval.
• Analysis of phenomena such as localization in liquid mixtures at low temperatures.

Main Results:

• Nonlinear repulsive interactions are identified as a general requirement for the retrieval of target structures in multicomponent liquids.
• The phenomenon of 'localization,' where liquid mixtures transition to phases with fewer components at low temperatures, is demonstrated.
• A fundamental trade-off between the retrieval of target structures and the localization phenomenon is revealed.

Conclusions:

• The liquid Hopfield model provides insights into the formation of ordered structures in complex biological mixtures.
• Nonlinear repulsive interactions are essential for maintaining desired compositions against the tendency towards localization.
• This work establishes connections between neural computation principles and the behavior of liquid mixtures, opening new avenues for research.