Physical observables to determine the nature of membrane-less cellular sub-compartments.

Mathias L Heltberg,Judith Miné-Hattab,Thierry Mora,Angela Taddei,Aleksandra M Walczak

doi:10.7554/elife.69181

Abstract

The spatial organization of complex biochemical reactions is essential for the regulation of cellular processes. Membrane-less structures called foci containing high concentrations of specific proteins have been reported in a variety of contexts, but the mechanism of their formation is not fully understood. Several competing mechanisms exist that are difficult to distinguish empirically, including liquid-liquid phase separation, and the trapping of molecules by multiple binding sites. Here, we propose a theoretical framework and outline observables to differentiate between these scenarios from single molecule tracking experiments. In the binding site model, we derive relations between the distribution of proteins, their diffusion properties, and their radial displacement. We predict that protein search times can be reduced for targets inside a liquid droplet, but not in an aggregate of slowly moving binding sites. We use our results to reject the multiple binding site model for Rad52 foci, and find a picture consistent with a liquid-liquid phase separation. These results are applicable to future experiments and suggest different biological roles for liquid droplet and binding site foci.

Highlights

The cell nucleus of eukaryotic cells is not an isotropic and homogeneous environment
Models have often been presented in the literature as opposing views, here we show under what conditions the Polymer bridging model (PBM) may be reduced to an effective description that is mathematically equivalent to the Liquid phase model (LPM), but with specific constraints linking its properties
To describe the situation measured in single particle tracking experiments, we consider the diffusive motion of a single molecule within the nucleus of a cell in the overdamped limit, described by the Langevin equation in 3 dimensions:

Summary

Introduction

The cell nucleus of eukaryotic cells is not an isotropic and homogeneous environment. It contains membrane-less sub-compartments, called foci or condensates, where the protein concentration is enhanced for certain proteins. An important aspect of these sub-compartments is their ability to both form at the correct time and place, and to dissolve after a certain time. Condensates have been 35 reported to be involved in gene regulation (Hnisz et al, 2017; Bing et al, 2020) and in the grouping of telomeres in yeast cells (Meister and Taddei, 2013; Ruault et al, 2021). A vast number of membrane-less cellular sub-compartments that have been reported in the literature with different names. We consider a focus to be a spherical condensate of size smaller than a few hundreds nanometers

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Conclusion