arXiv subjects

Stefan Paquay

Publications and source records attributed to Stefan Paquay.

7 recordsLinked to original sources

arXiv2023

Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T=3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose 3D geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case, and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.

cond-mat.soft↗

arXiv2019

Morphology Formation in Binary Mixtures upon Gradual Destabilisation

Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation takes place close to the critical point. Using kinetic Monte Carlo and molecular dynamics simulations of a binary surface fluid under these conditions, we show that the characteristic length scale of the emerging structure decreases, in 2D, with the 4/15 dynamic critical exponent of the quench rate rather than the mean-field 1/6th power. Hence, the dynamics of cluster formation governed by thermodynamically undriven Brownian motion is much more sensitive on the rate of destabilisation than expected from mean-field theory. We discuss the expected implications of this finding to 3D systems with ordering liquid crystals, as well as phase-separating passive or active particles.

cond-mat.soft↗

arXiv2017

Self-organisation of semi-flexible rod-like particles

We report on a comprehensive computer simulation study of the liquid-crystal phase behaviour of purely repulsive, semi-flexible rod-like particles. For the four aspect ratios we consider, the particles form five distinct phases depending on their packing fraction and bending flexibility: the isotropic, nematic, smectic A, smectic B and crystal phase. Upon increasing the particle bending flexibility, the various phase transitions shift to larger packing fractions. Increasing the aspect ratio achieves the opposite effect. We find two different ways how the layer spacing of the particles in the smectic A phase may respond to an increase in concentration. The layer spacing may either decrease or increase depending on the aspect ratio and flexibility. For the smectic B and the crystalline phases, increasing the concentration always decreases the layer spacing. We find that the layer spacing jumps to a larger value on transitioning from the smectic A to the smectic B phase.

cond-mat.soft↗

arXiv2017

Impact of Interaction Range and Curvature on Crystal Growth of Particles Confined to Spherical Surfaces

When colloidal particles form a crystal phase on a spherical template, their packing is governed by the effective interaction between them and the elastic strain of bending the growing crystal. For example, if growth commences under appropriate conditions, and the circular crystal that forms reaches a critical size, growth continues by incorporation of defects to alleviate elastic strain. Recently it was found experimentally that, if defect formation is somehow not possible, the crystal instead continues growing in ribbons that protrude from the original crystal. Here we report on computer simulations in which we observe both the formation of ribbons at short interaction ranges and packings that incorporate defects if the interaction is longer-ranged. The ribbons only form above some critical crystal size, below which the nucleus is roughly spherically shaped. We find that the scaling of the critical crystal size differs slightly from the one proposed by the Manoharan group, and reason this is because the actual process is a two-step heterogeneous nucleation of ribbons on top of roughly circular crystals.

cond-mat.soft↗

arXiv2017

Energetically favoured defects in dense packings of particles on spherical surfaces

The dense packing of interacting particles on spheres has proved to be a useful model for virus capsids and colloidosomes. Indeed, icosahedral symmetry observed in virus capsids corresponds to potential energy minima that occur for magic numbers of, e.g., 12, 32 and 72 identical Lennard-Jones particles, for which the packing has exactly the minimum number of twelve five-fold defects. It is unclear, however, how stable these structures are against thermal agitation. We investigate this property by means of basin-hopping global optimisation and Langevin dynamics for particle numbers between ten and one hundred. An important measure is the number and type of point defects, that is, particles that do not have six nearest neighbours. We find that small icosahedral structures are the most robust against thermal fluctuations, exhibiting fewer excess defects and rearrangements for a wide temperature range. Furthermore, we provide evidence that excess defects appearing at low non-zero temperatures lower the potential energy at the expense of entropy. At higher temperatures defects are, as expected, thermally excited and thus entropically stabilised. If we replace the Lennard-Jones potential by a very short-ranged (Morse) potential, which is arguably more appropriate for colloids and virus capsid proteins, we find that the same particle numbers give a minimum in the potential energy, although for larger particle numbers these minima correspond to different packings. Furthermore, defects are more difficult to excite thermally for the short-ranged potential, suggesting that the short-ranged interaction further stabilises equilibrium structures.

cond-mat.soft↗

arXiv2016

A method for molecular dynamics on curved surfaces

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focussed on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to combine standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface, in which such interactions can be taken into account. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates allowing for the reuse of many other standard tools without modifications, including parallelisation through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, confined Brownian motion is obtained, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: (i) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes and (ii) the self-assembly of a coarse-grained virus capsid protein model.

physics.comp-ph↗

arXiv2014

Confinement without boundaries: Anisotropic diffusion on the surface of a cylinder

Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly affected by physical confinement, e.g., by the walls. In this Letter, we explore the effects of confinement by shape, not rigid boundaries, on the diffusion of particles by confining them to the surface of a cylinder. We find that both the magnitude and the directionality of lateral diffusion is strongly influenced by the radius of the cylinder. An anisotropy between diffusion in the longitudinal and circumferential direction of the cylinder develops. We demonstrate that the origin of this effect lies in the fact that screw-like packings of mono- and oligodisperse discs on the surface of a cylinder induce preferential collective motions in the circumferential direction, but also show that even in polydisperse systems lacking such order an intrinsic finite size confinement effect increases diffusivity in the circumferential direction.

cond-mat.stat-mech↗