Instabilities in complex mixtures with a large number of components

TL;DR

This paper introduces a statistical method using random matrix theory to analyze the stability and phase separation of complex biological mixtures with many components, bypassing the need to characterize individual interactions.

Contribution

It develops a novel approach that models the second virial coefficient matrix as a random matrix to assess mixture stability.

Findings

The stability of complex mixtures can be predicted from the spectrum of a random matrix.

The approach provides insights into phase separation conditions in biological systems.

It offers a scalable method for analyzing large-component mixtures.

Abstract

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.