Tracking of fluorescently labeled chromosomal loci in live bacterial cells reveals a robust scaling of the mean square displacement (MSD) as τ0.39. Brownian dynamics simulations show that this anomalous behavior cannot be fully accounted for by the classic Rouse or reptation models for polymer dynamics. Instead, the observed motion arises from the characteristic relaxation of the Rouse modes of the DNA polymer within the viscoelastic environment of the cytoplasm. To demonstrate these physical effects, we exploit our general analytical solution of the subdiffusive scaling for a monomer in a polymer embedded in a viscoelastic medium. The time-averaged and ensemble-averaged MSD of chromosomal loci exhibit ergodicity, and the velocity autocorrelation function is negative at short time lags. These observations are most consistent with fractional Brownian motion and rule out a continuous time random walk model as an explanation for anomalous motion in vivo.

Nuclear bodies are RNA and protein-rich, membraneless organelles that play important roles in gene regulation. The largest and most well-known nuclear body is the nucleolus, an organelle whose primary function in ribosome biogenesis makes it key for cell growth and size homeostasis. The nucleolus and other nuclear bodies behave like liquid-phase droplets and appear to condense from the nucleoplasm by concentration-dependent phase separation. However, nucleoli actively consume chemical energy, and it is unclear how such nonequilibrium activity might impact classical liquid-liquid phase separation. Here, we combine in vivo and in vitro experiments with theory and simulation to characterize the assembly and disassembly dynamics of nucleoli in early Caenorhabditis elegans embryos. In addition to classical nucleoli that assemble at the transcriptionally active nucleolar organizing regions, we observe dozens of "extranucleolar droplets" (ENDs) that condense in the nucleoplasm in a transcription-independent manner. We show that growth of nucleoli and ENDs is consistent with a first-order phase transition in which late-stage coarsening dynamics are mediated by Brownian coalescence and, to a lesser degree, Ostwald ripening. By manipulating C. elegans cell size, we change nucleolar component concentration and confirm several key model predictions. Our results show that rRNA transcription and other nonequilibrium biological activity can modulate the effective thermodynamic parameters governing nucleolar and END assembly, but do not appear to fundamentally alter the passive phase separation mechanism.RNA/protein droplets | intracellular phase separation | Brownian coalescence | Ostwald ripening | Flory-Huggins regular solution theory L iving cells are composed of complex and spatially heterogeneous materials that partition into functional compartments called organelles. Many organelles are vesicle-like structures with an enclosing membrane. However, a large number of RNA and protein-rich bodies maintain a dynamic but coherent structure even in the absence of a membrane. These so-called RNA/ protein granules are found in the cytoplasm and in the nucleus, where they are referred to as nuclear bodies. The mechanisms by which such structures form and stably persist are not well understood. However, recent evidence suggests that these membraneless organelles, such as P granules (1, 2), nucleoli (3), and stress granules (4), are liquid-phase droplets that may assemble by intracellular phase separation (5, 6). This concept is supported by work on synthetic systems, including repetitive protein domains that form droplets in vitro and in the cytoplasm (7) and intrinsically disordered protein domains that show signatures of liquid-liquid phase separation when expressed in the cell nucleus (8).By examining the cell size-dependent assembly of nucleoli in early Caenorhabditis elegans embryos, we previously showed that nucleolar assembly is controlled by a concentration-dependent phase transition (9). Using a simple model based on the de...

Nonmembrane-bound organelles such as RNA granules behave like dynamic droplets, but the molecular details of their assembly are poorly understood. Several recent papers identify structural features that drive granule assembly, shedding light on how phase transitions functionally organize the cell and may lead to pathological protein aggregation.

Chromosomal loci jiggle in place between segregation events in prokaryotic cells and during interphase in eukaryotic nuclei. This motion seems random and is often attributed to Brownian motion. However, we show here that locus dynamics in live bacteria and yeast are sensitive to metabolic activity. When ATP synthesis is inhibited, the apparent diffusion coefficient decreases, whereas the subdiffusive scaling exponent remains constant. Furthermore, the magnitude of locus motion increases more steeply with temperature in untreated cells than in ATP-depleted cells. This "superthermal" response suggests that untreated cells have an additional source of molecular agitation, beyond thermal motion, that increases sharply with temperature. Such ATP-dependent fluctuations are likely mechanical, because the heat dissipated from metabolic processes is insufficient to account for the difference in locus motion between untreated and ATP-depleted cells. Our data indicate that ATP-dependent enzymatic activity, in addition to thermal fluctuations, contributes to the molecular agitation driving random (sub)diffusive motion in the living cell.T he cytoplasm is a crowded and dynamic medium, with molecules constantly jostling around and colliding with each other. This molecular motion is often attributed to Brownian motion, the random movement of suspended particles driven by thermal fluctuations of the solvent (1, 2). Classic Brownian motion theory assumes a system at thermal equilibrium. However, cells are far from equilibrium. They use the chemical energy of ATP (and GTP) to drive active biological processes, such as transport and metabolism.Recent work in eukaryotic cells demonstrates that biological activity generates nonthermal fluctuations of greater magnitude than thermal fluctuations (3-8). These active fluctuations can drive diffusive-like motion of molecules inside the cell, a phenomenon known as "active" diffusion (9, 10). In vitro experiments and analytical theory suggest that these active fluctuations are generated by the cytoskeletal molecular motor myosin (11-13). Thus, random molecular motion in vivo, at least in eukaryotic cytoplasm, may be due to active motor-driven forces in addition to passive thermal forces.Here we present evidence suggesting that ATP-dependent fluctuations contribute to the motion of chromosomal loci in bacterial and yeast cells. By modulating the temperature at which cells are observed, we were able to identify nonthermal forces that contribute to intracellular motion. Unlike active microrheology (7,8,11), temperature modulation presents a simple perturbation that can be applied to any experimental system to explore the physical processes underlying molecular motion in vivo. Our results suggest that "active" diffusion is not unique to systems containing eukaryotic cytoskeletal motors. This phenomenon may in fact be a general property of macromolecular motion in all living cells. Resultsis calculated to determine the subdiffusive scaling exponent α and the apparent diffusion coefficient D ap...

Summary Just as organ size typically increases with body size, the size of intracellular structures changes as cells grow and divide. Indeed, many organelles, such as the nucleus [1, 2], mitochondria [3], mitotic spindle [4, 5] and centrosome [6], exhibit size scaling, a phenomenon in which organelle size depends linearly on cell size. However, the mechanisms of organelle size scaling remain unclear. Here, we show that the size of the nucleolus, a membrane-less organelle important for cell size homeostasis [7], is coupled to cell size by an intracellular phase transition. We find that nucleolar size directly scales with cell size in early C. elegans embryos. Surprisingly, however, when embryo size is altered, we observe inverse scaling: nucleolar size increases in small cells and decreases in large cells. We demonstrate that this seemingly contradictory result arises from maternal loading of a fixed number, rather than a fixed concentration of nucleolar components, which condense into nucleoli only above a threshold concentration. Our results suggest that the physics of phase transitions can dictate both whether an organelle assembles, and if so, its size, providing a mechanistic link between organelle assembly and cell size. Since the nucleolus is known to play a key role in cell growth, this biophysical read-out of cell size could provide a novel feedback mechanism for growth control.