Despite the absence of a membrane-enclosed nucleus, the bacterial DNA is typically condensed into a compact body—the nucleoid. This compaction influences the localization and dynamics of many cellular processes including transcription, translation, and cell division. Here, we develop a model that takes into account steric interactions among the components of the Escherichia coli transcriptional–translational machinery (TTM) and out-of-equilibrium effects of messenger RNA (mRNA) transcription, translation, and degradation, to explain many observed features of the nucleoid. We show that steric effects, due to the different molecular shapes of the TTM components, are sufficient to drive equilibrium phase separation of the DNA, explaining the formation and size of the nucleoid. In addition, we show that the observed positioning of the nucleoid at midcell is due to the out-of-equilibrium process of mRNA synthesis and degradation: mRNAs apply a pressure on both sides of the nucleoid, localizing it to midcell. We demonstrate that, as the cell grows, the production of these mRNAs is responsible for the nucleoid splitting into two lobes and for their well-known positioning to 1/4 and 3/4 positions on the long cell axis. Finally, our model quantitatively accounts for the observed expansion of the nucleoid when the pool of cytoplasmic mRNAs is depleted. Overall, our study suggests that steric interactions and out-of-equilibrium effects of the TTM are key drivers of the internal spatial organization of bacterial cells.
Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and soft-matter physics which appear to deviate from the ideal-solution behaviour. Particularly striking is the case of liquid-liquid phase separation, which is typically caused by inter-particle interactions. Here, we revisit a number of known results in the domain of ideal CRNs, and we generalise and adapt them to arbitrary interactions between the solutes which stem from a given free energy. We start by reviewing the theory of chemical reaction networks, linking it to concepts in statistical physics. Then we obtain a number of new results for non-ideal complex-balanced networks, where the creation and annihilation rates are equal for all chemical complexes which appear as reactants or products in the CRN. Among these is the form of the steady-state probability distribution and Lyapunov functions for such networks. Finally, this allows us to draw a phase diagram for complex-balanced reaction-diffusion systems based on the minimisation of such Lyapunov function, with a rationale similar to that of equilibrium thermodynamics but for systems that may sustain non-equilibrium chemical currents at steady state. In addition, we show that for complex-balanced networks at steady-state, there are no diffusion currents.
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