Crystallisation in a two-dimensional granular system at constant temperature

We study the crystallisation processes occurring in a nonvibrating two-dimensional magnetic granular system at various fixed values of the effective temperature. In this system, the energy loss due to dissipative effects is compensated by the continuous energy input coming into the system from a sinusoidal magnetic field. When this balance leads to high values of the effective temperature, no aggregates are formed, because particles’ kinetic energy prevents them from aggregating. For lower effective temperatures, formation of small aggregates is observed. The smaller the values of the applied field’s amplitude, the larger the number of these disordered aggregates. One also observes that when clusters form at a given effective temperature, the average effective diffusion coefficient decreases as time increases. For medium values of the effective temperature, formation of small crystals is observed. We find that the sixth bond-orientational order parameter and the number of bonds, when considering more than two, are very sensitive for exhibiting the order in the system, even when crystals are still very small.

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard–Jones Systems

In the condensed liquid phase, both single- and multicomponent Lennard–Jones (LJ) systems obey the “hidden-scale-invariance” symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank–Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob–Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.

Could network structures generated with simple rules imposed on a cubic lattice reproduce the structural descriptors of globular proteins?

A direct way to spot structural features that are universally shared among proteins is to find proper analogues from simpler condensed matter systems. In most cases, sphere-packing arguments provide a straightforward route for structural comparison, as they successfully characterize a wide array of materials such as close packed crystals, dense liquids, and structural glasses. In the current study, the feasibility of creating ensembles of artificial structures that can automatically reproduce a large number of geometrical and topological descriptors of globular proteins is investigated. Towards this aim, a simple cubic (SC) arrangement is shown to provide the best background lattice after a careful analysis of the residue packing trends from 210 proteins. It is shown that a minimalistic set of ground rules imposed on this lattice is sufficient to generate structures that can mimic real proteins. In the proposed method, 210 such structures are generated by randomly removing residues (beads) from clusters that have a SC lattice arrangement until a predetermined residue concentration is achieved. All generated structures are checked for residue connectivity such that a path exists between any two residues. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing (RMC-SA) algorithm, which targets the average radial distribution function (RDF) of 210 globular proteins. The initial and relaxed structures are compared to real proteins via RDF, bond orientational order parameters, and several descriptors of network topology. Based on these features, results indicate that the structures generated with 40% occupancy via the proposed method closely resemble real residue networks. The broad correspondence established this way indicates a non-superficial link between the residue networks and the defect laden cubic crystalline order. The presented approach of identifying a minimalistic set of operations performed on a target lattice such that each resulting cluster possess structural characteristics largely indistinguishable from that of a coarse-grained globular protein opens up new venues in structural characterization, native state recognition, and rational design of proteins.

Enhanced sampling of cylindrical microphase separation via a shell-averaged bond-orientational order parameter

The underlying free energy surfaces for the order–disorder transition of hexagonal mesophase were identified along with the metstable state.