Phase-separation dynamics of a ternary mixture coupled with reversible chemical reaction

Phase separation reduces cell-to-cell variability of transcriptional bursting

Gene expression is a stochastic and noisy process often occurring in "bursts". Experiments have shown that the compartmentalization of proteins by liquid-liquid phase separation is conducive to reducing the noise of gene expression. Therefore, an important goal is to explore the role of bursts in phase separation noise reduction processes. We propose a coupled model that includes phase separation and a two-state gene expression process. Using the timescale separation method, we obtain approximate solutions for the expectation, variance, and noise strength of the dilute phase. We find that a higher burst frequency weakens the ability of noise reduction by phase separation, but as the burst size increases, this ability first increases and then decreases. This study provides a deeper understanding of phase separation to reduce noise in the stochastic gene expression with burst kinetics.

Time-reversal and parity-time symmetry breaking in non-Hermitian field theories

We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry-breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-Hermitian dynamics, namely, oscillatory instabilities and critical exceptional points, a low-noise expansion exposes a pretransitional surge of the mesoscale (informatic) entropy production rate, inside the static phases. Its scaling in the susceptibility contrasts conventional critical points (such as second-order phase transitions), where the susceptibility also diverges, but the entropy production generally remains finite. The difference can be attributed to active fluctuations in the wavelengths that become unstable. For critical exceptional points, we identify the coupling of eigenmodes as the entropy-generating mechanism, causing a drastic noise amplification in the Goldstone mode.

A systematic study on immiscible binary systems undergoing thermal/photo reversible chemical reactions

In this work, we systematically study an immiscible binary system undergoing thermal/photo reversible reactions in theory. For the thermal reaction case, no dissipative structures can be formed and only uniform equilibrium states are observed but the dynamical evolution to these trivial states witnesses a new type of sophisticated phase amplification phenomenon-temporary phase separation (TPS). Linear analysis and light-scattering calculations confirm that TPS is predominated either by spinodal decomposition or nucleation and growth mechanism, or by both successively. For the photo reaction case, steady dissipative patterns exist and are maintained by the external energy input of lights. Linear analysis together with simulations reveals that the characteristic wavelength (ξ) of these structures shortens as the input energy density increases and they obey the relation of ln ξ∝ 1/T_b with T_b the effective temperature of lights. The TPS phenomenon and length-scale dependency of dissipative patterns observed in this simple binary system might have rich implications for the non-equilibrium thermodynamics of biological systems.

Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling

We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well-known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis, we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.

Liquid-liquid phase separation driven compartmentalization of reactive nucleoplasm

The nucleus of eukaryotic cells harbors active and out of equilibrium environments conducive to diverse gene regulatory processes. On a molecular scale, gene regulatory processes take place within hierarchically compartmentalized sub-nuclear bodies. While the impact of nuclear structure on gene regulation is widely appreciated, it has remained much less clear whether and how gene regulation is impacting nuclear order itself. Recently, the liquid-liquid phase separation emerged as a fundamental mechanism driving the formation of biomolecular condensates, including membrane-less organelles, chromatin territories, and transcriptional domains. The transience and environmental sensitivity of biomolecular condensation are strongly suggestive of kinetic gene-regulatory control of phase separation. To better understand kinetic aspects controlling biomolecular phase-separation, we have constructed a minimalist model of the reactive nucleoplasm. The model is based on the Cahn-Hilliard formulation of ternary protein-RNA-nucleoplasm components coupled to non-equilibrium and spatially dependent gene expression. We find a broad range of kinetic regimes through an extensive set of simulations where the interplay of phase separation and reactive timescales can generate heterogeneous multi-modal gene expression patterns. Furthermore, the significance of this finding is that heterogeneity of gene expression is linked directly with the heterogeneity of length-scales in phase-separated condensates.

Triphase Separation of a Ternary Symmetric Highly Viscous Mixture

We discuss numerical results of diffusion-driven separation into three phases of a symmetric, three-component highly viscous liquid mixture after an instantaneous quench from the one-phase region into an unstable location within the tie triangle of its phase diagram. Our theoretical approach follows a diffuse-interface model of partially miscible ternary liquid mixtures that incorporates the one-parameter Margules correlation as a submodel for the enthalpic (so-called excess) component of the Gibbs energy of mixing, while its nonlocal part is represented based on a square-gradient (Cahn–Hilliard-type) modeling assumption. The governing equations for this phase-field ternary mixture model are simulated in 3D, showing the segregation kinetics in terms of basic segregation statistics, such as the integral scale of the pair-correlation function and the separation depth for each component. Based on the temporal evolution of the integral scales, phase separation takes place via the simultaneous growth of three phases up until a symmetry-breaking event after which one component continues to separate quickly, while phase separation for the other two seems to be delayed. However, inspection of the separation depths reveals that there can be no symmetry among the three components at any instant in time during a triphase segregation process.

Modeling self-assembly and phase behavior in complex mixtures

Using a variety of computational techniques, I investigate how the self-assembly of complex mixtures can be guided by surfaces or external stimuli to form spatially regular or temporally periodic patterns. Focusing on mixtures in confined geometries, I examine how thermodynamic and hydrodynamic effects can be exploited to create regular arrays of nanowires or monodisperse, particle-filled droplets. I also show that an applied light source and chemical reaction can be harnessed to create hierarchically ordered patterns in ternary, phase-separating mixtures. Finally, I consider the combined effects of confining walls and a chemical reaction to demonstrate that a swollen polymer gel can be driven to form dynamically periodic structures. In addition to illustrating the effectiveness of external factors in directing the self-organization of multicomponent mixtures, the selected examples illustrate how coarse-grained models can be used to capture both the equilibrium phase behavior and the dynamics of these complex systems.

Dynamics of ternary mixtures with photosensitive chemical reactions: creating three-dimensionally ordered blends

Using computer simulations, we establish an approach for creating defect-free, periodically ordered polymeric materials. The system involves ABC ternary mixtures where the A and B components undergo a reversible photochemical reaction. In addition, all three components are mutually immiscible and undergo phase separation. Through the simulations, we model the effects of illuminating a three-dimensional (3D) sample with spatially and temporally dependent light irradiation. Experimentally, this situation can be achieved by utilizing both a uniform background light and a spatially localized, higher intensity light, and then rastering a higher-intensity light over the 3D sample. We first focus on the case where the higher-intensity light is held stationary and focused in a distinct region within the system. The C component is seen to displace the A and B within this region and replicate the pattern formed by the higher-intensity light. In effect, one can write a pattern of C onto the AB binary system by focusing the higher-intensity light in the desired arrangement. We isolate the conditions that are necessary for producing clearly written patterns of C (i.e., for obtaining sharp interfaces between the C and A/B domains). We next consider the effect of rastering a higher-intensity light over this sample and find that this light "combs out" defects in the AB blend as it moves through the system. The resulting material displays a defect-free structure that encompasses both a periodic ordering of the A and B domains and a well-defined motif of C. In this manner, one can create hierarchically patterned materials that exhibit periodicity over two distinct length scales. The approach is fully reversible, noninvasive, and points to a novel means of patterning with homopolymers, which normally do not self-assemble into periodic structures.

Exploiting photoinduced reactions in polymer blends to create hierarchically ordered, defect-free materials

Computer simulations reveal how photoinduced chemical reactions can be exploited to create long-range order in binary and ternary polymeric materials. The process is initiated by shining a spatially uniform light over a photosensitive AB binary blend, which thereby undergoes both a reversible chemical reaction and phase separation. We then introduce a well-collimated, higher intensity light source. Rastering this secondary light over the sample locally increases the reaction rate and causes formation of defect-free, spatially periodic structures. These binary structures resemble either the lamellar or hexagonal phases of microphase-separated diblock copolymers. We measure the regularity of the ordered structures as a function of the relative reaction rates for different values of the rastering speed and determine the optimal conditions for creating defect-free structures in the binary systems. We then add a nonreactive homopolymer C, which is immiscible with both A and B. We show that this component migrates to regions that are illuminated by the secondary, higher intensity light, allowing us to effectively write a pattern of C onto the AB film. Rastering over the ternary blend with this collimated light now leads to hierarchically ordered patterns of A, B, and C. The findings point to a facile, nonintrusive process for manufacturing high quality polymeric devices in a low-cost, efficient manner.

Harnessing light to create defect-free, hierarchically structured polymeric materials

Computer simulations reveal how photoinduced chemical reactions in polymeric mixtures can be exploited to create long-range order in materials with features that range from the submicron to the nanoscale. The process is initiated by shining a spatially uniform light on a photosensitive AB binary blend, which thereby undergoes both a reversible chemical reaction and a phase separation. When a well-collimated, higher intensity light is rastered over the sample, the system forms defect-free, spatially periodic structures. If a nonreactive homopolymer C is added to the system, this component localizes in regions that are irradiated with a higher intensity light, and one can effectively "write" a pattern of C onto the AB film. Rastering over the ternary blend with the collimated light now leads to hierarchically ordered patterns of A, B, and C. Because our approach involves homopolymers, it significantly expands the range of materials that can be fashioned into a periodic pattern. The findings point to a facile process for manufacturing high-quality polymeric components in an efficient manner.