Joel Berry

RNA transcription modulates phase transition-driven nuclear body assembly

Significance Living cells contain various membraneless organelles whose size and assembly appear to be governed by equilibrium thermodynamic phase separation. However, the dynamics of this process are poorly understood. Here, we quantify the assembly dynamics of liquid-phase nuclear bodies and find that they can be explained by classical models of phase separation and coarsening. In addition, active nonequilibrium processes, particularly rRNA transcription, can locally modulate thermodynamic parameters to stabilize nucleoli. Our findings demonstrate that the classical phase separation mechanisms long associated with nonliving condensed matter can mediate organelle assembly in living cells, whereas chemical activity may serve to regulate these processes in response to developmental or environmental conditions. 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.

Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions

The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the phase field crystal model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two-dimensional hexagonal lattice. It is shown that the natural features of these processes are reproduced without any explicit consideration of elasticity theory or ad hoc construction of microscopic Peierls potentials. Particular attention is paid to the Peierls barrier for dislocation glide or climb and the ensuing dynamic behavior as functions of strain rate, temperature, and dislocation density. It is shown that the dynamics are accurately described by simple viscous motion equations for an overdamped point mass, where the dislocation mobility is the only adjustable parameter. The critical distance for the annihilation of two edge dislocations as a function of separation angle is also presented.

Melting at dislocations and grain boundaries: A Phase Field Crystal study

Dislocation and grain boundary melting are studied in three dimensions using the Phase Field Crystal method. Isolated dislocations are found to melt radially outward from their core, as the localized excess elastic energy drives a power law divergence in the melt radius. Dislocations within low-to-mid angle grain boundaries melt similarly until an angle-dependent first order wetting transition occurs when neighboring melted regions coalesce. High angle boundaries are treated within a screening approximation, and issues related to ensembles, metastability, and grain size are discussed.

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable defect structures that maintain high numerical efficiency. The general framework combines both long-range elastic fields and basic features of atomic-level core structures, with defect dynamics operable over diffusive time scales. Fundamental elements of the resulting defect physics are characterized for the case of fcc crystals. Stacking faults and split Shockley partial dislocations are stabilized for the first time within the PFC formalism, and various properties of associated defect structures are characterized. These include the dissociation width of perfect edge and screw dislocations, the effect of applied stresses on dissociation, Peierls strains for glide, and dynamic contraction of gliding pairs of partials. Our results in general are shown to compare favorably with continuum elastic theories and experimental findings.

Phase field crystal modeling as a unified atomistic approach to defect dynamics

Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and non- conservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-type glide mechanisms involving closed dislocation loops or grain boundaries as well as Bardeen-Herring-type climb mechanisms involving precipitates, inclusions, and/or voids. Both source classes are naturally and simultaneously captured at the atomistic level by PFC de- scriptions, with arbitrarily complex defect configurations, types, and environments. An unexpected dipole-to-quadrupole source transformation is identified, as well as various new and complex geomet- rical features of loop nucleation via climb from spherical particles. Results for the strain required to nucleate a dislocation loop from such a particle are in agreement with analytic continuum theories. Other basic features of FCC and BCC dislocation structure and dynamics are also outlined, and initial results for dislocation-stacking fault tetrahedron interactions are presented. These findings together highlight various capabilities of the PFC approach as a coarse-grained atomistic tool for the study of three-dimensional crystal plasticity.

Modeling Multiple Time Scales during Glass Formation with Phase-Field Crystals

The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase-field crystal free energies and dynamic density functional theory is shown to successfully describe several aspects of glass formation over multiple time scales. Agreement with mode coupling theory is demonstrated for underdamped liquids at moderate supercoolings, and a rapidly growing dynamic correlation length is found to be associated with fragile behavior.

Atomistic study of diffusion-mediated plasticity and creep using phase field crystal methods

The nonequilibrium dynamics of diffusion-mediated plasticity and creep in materials subjected to constant load at high homologous temperatures is studied atomistically using phase field crystal (PFC) methods. Creep stress and grain size exponents obtained for nanopolycrystalline systems, m similar or equal to 1.02 and p similar or equal to 1.98, respectively, closely match those expected for idealized diffusional Nabarro-Herring creep. These exponents are observed in the presence of significant stress-assisted diffusive grain boundary migration, indicating that Nabarro-Herring creep and stress-assisted boundary migration contribute in the same manner to the macroscopic constitutive relation. When plastic response is dislocation-mediated, power-law stress exponents inferred from dislocation climb rates are found to increase monotonically from m similar or equal to 3, as expected for generic climb-mediated natural creep, to m similar or equal to 5.8 as the dislocation density.d is increased beyond typical experimental values. Stress exponents m greater than or similar to 3 directly measured from simulations that include dislocation nucleation, climb, glide, and annihilation are attributed primarily to these large rho(d) effects. Extrapolation to lower rho(d) suggests that m similar or equal to 4-4.5 should be obtained from our PFC description at typical experimental rho(d) values, which is consistent with expectations for power-law creep via mixed climb and glide. The anomalously large stress exponents observed in our atomistic simulations at large rho(d) may nonetheless be relevant to systems in which comparable densities are obtained locally within heterogeneous defect domains such as dislocation cell walls or tangles.

Physical Principles of Intracellular Organization via Active and Passive Phase Transitions

Exciting recent developments suggest that phase transitions represent an important and ubiquitous mechanism underlying intracellular organization. We describe key experimental findings in this area of study, as well as the application of classical theoretical approaches for quantitatively understanding these data. We also discuss the way in which equilibrium thermodynamic driving forces may interface with the fundamentally out-of-equilibrium nature of living cells. In particular, time and/or space-dependent concentration profiles may modulate the phase behavior of biomolecules in living cells. We suggest future directions for both theoretical and experimental work that will shed light on the way in which biological activity modulates the assembly, properties, and function of viscoelastic states of living matter.