Physical theory of biological noise buffering by multi-component phase separation

Abstract

Maintaining homeostasis is a fundamental characteristic of living systems. In cells, this is contributed to by assembly of biochemically-distinct organelles, many of whom are not membrane-bound, but form by the physical process of liquid-liquid phase separation (LLPS). By analogy with LLPS in binary solutions, cellular LLPS was hypothesized to contribute to homeostasis by facilitating "concentration buffering", which renders the local protein concentration within the organelle robust to global variations in the average, cellular concentration (e.g. due to expression noise). Interestingly, concentration buffering was experimentally measured in vivo, in a simple organelle with a single solute, while it was observed not to be obeyed in one with several solutes. Here, we formulate theoretically and solve analytically a physical model of LLPS in a ternary solution of two solutes (A and B) that interact both homotypically (A-A attractions) and heterotypically (A-B attractions). Our physical theory predicts how the equilibrium concentrations in LLPS are related to expression noise and thus generalizes the concept of concentration buffering to multi-component systems. This allows us to reconcile the seemingly contradictory experimental observations. Furthermore, we predict that incremental changes of the homotypic and heterotypic interactions among the molecules that undergo LLPS, such as those that are caused by mutations in the genes encoding the proteins, may increase the efficiency of concentration buffering of a given system. Thus, we hypothesize that evolution may optimize concentration buffering as an efficient mechanism to maintain LLPS homeostasis, and suggest experimental approaches to test this in different systems. SignificanceThe stochastic nature of transcription/translation implies that the concentrations of cellular proteins are "noisy" and not constant in time or across cell populations. Liquid-liquid phase separation (LLPS), can reduce or "buffer" this noise by maintaining well-defined concentrations, even in the presence of concentration distributions. However, this idea was recently challenged experimentally in multicomponent systems. Our physical theory of LLPS in ternary systems (solutes A and B in a solvent), predicts their LLPS properties as a function of the A-A (homotypic) and A-B (heterotypic) interaction strengths. We show how buffering can be effective if the noise distribution aligns with the tie-lines of the phase diagram and suggest that evolution may optimize concentration buffering by selecting mutations that lead to this.