Ideal glass transition in a simple two-dimensional lattice model

Amphiphiles Formed from Synthetic DNA-Nanomotifs Mimic the Stepwise Dispersal of Transcriptional Clusters in the Cell Nucleus

Stem cells exhibit prominent clusters controlling the transcription of genes into RNA. These clusters form by a phase-separation mechanism, and their size and shape are controlled via an amphiphilic effect of transcribed genes. Here, we construct amphiphile-nanomotifs purely from DNA, and we achieve similar size and shape control for phase-separated droplets formed from fully synthetic, self-interacting DNA-nanomotifs. Increasing amphiphile concentrations induce rounding of droplets, prevent droplet fusion, and, at high concentrations, cause full dispersal of droplets. Super-resolution microscopy data obtained from zebrafish embryo stem cells reveal a comparable transition for transcriptional clusters with increasing transcription levels. Brownian dynamics and lattice simulations further confirm that the addition of amphiphilic particles is sufficient to explain the observed changes in shape and size. Our work reproduces key aspects of transcriptional cluster formation in biological cells using relatively simple DNA sequence-programmable nanostructures, opening novel ways to control the mesoscopic organization of synthetic nanomaterials.

A DNA Segregation Module for Synthetic Cells

The bottom-up construction of an artificial cell requires the realization of synthetic cell division. Significant progress has been made toward reliable compartment division, yet mechanisms to segregate the DNA-encoded informational content are still in their infancy. Herein, droplets of DNA Y-motifs are formed by liquid-liquid phase separation. DNA droplet segregation is obtained by cleaving the linking component between two populations of DNA Y-motifs. In addition to enzymatic cleavage, photolabile sites are introduced for spatio-temporally controlled DNA segregation in bulk as well as in cell-sized water-in-oil droplets and giant unilamellar lipid vesicles (GUVs). Notably, the segregation process is slower in confinement than in bulk. The ionic strength of the solution and the nucleobase sequences are employed to regulate the segregation dynamics. The experimental results are corroborated in a lattice-based theoretical model which mimics the interactions between the DNA Y-motif populations. Altogether, engineered DNA droplets, reconstituted in GUVs, can represent a strategy toward a DNA segregation module within bottom-up assembled synthetic cells.

Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases

We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hard-core lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first k next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for k=1,2,3 both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.

Jamming, relaxation, and crystallization of a supercooled fluid in a three-dimensional lattice

Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next-nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Nonequilibrium filling, through random sequential adsorption with diffusion, creates amorphous structures and terminates at a disordered state with random closest packing density that lies in the equilibrium solid regime. The approach toward random closest packing is characterized by two distinct power-law regimes, reflecting the formation of small densely packed grains in the long-time regime of the filling process. We then study the fixed-density relaxation of these amorphous structures toward the solid phase. The route to crystallization for the high-density, deeply supercooled regime is shown to deviate from the simple grain growth proposed by classical nucleation theory. Our measurements suggest that relaxation in this regime is driven mainly by coalescence of neighboring crystallized grains which exist in the initial amorphous state.

Direct measurements of the dynamical correlation length indicate its divergence at an athermal glass transition

The supercooled N3 model exhibits an increasingly slow dynamics as density approaches the random closest packing density. Here, we present a direct measurement of the dynamical correlation function G4(r,t), showing the emergence of a growing length scale ξ(4) across which the dynamics is correlated. The correlation length measured, up to 120 lattice sites, power law diverges as the density approaches ρ(t), the density at which the fluid phase of the model is predicted to terminate. The four-point susceptibility, often used as an agent to estimate ξ(4), does not depend simply on the latter. Rather, it depends strongly on the short-range behavior of G4(r,t). Consequently, χ(4) peaks before ξ(4) reaches its maximal value. The two quantities should therefore be studied independently.