Related papers: Density waves, dodecahedral geometry and structure…
The structural organisation of the viral genome within its protein container, called the viral capsid, is an important aspect of virus architecture. Many single-stranded (ss) RNA viruses organise a significant part of their genome in a…
Minimal energy shapes of closed, elastic shells with twelve pentagonal disclinations introduced in otherwise hexagonally coordinated crystalline lattice are studied. The geometry and the total energy of shells are studied as a function of…
In this work we study how a viral capsid can change conformation using techniques of Large Deviations Theory for stochastic differential equations. The viral capsid is a model of a complex system in which many units - the proteins forming…
We propose a Ginzburg-Landau model for the expansion of a dodecahedral viral capsid during infection or maturation. The capsid is described as a dodecahedron whose faces, meant to model rigid capsomers, are free to move independent of each…
Studying physical mechanisms and common geometric principles underlying known spherical packings is crucial for rational design of synthetic nanocontainers. Here we model the growth of small spherical shells containing n<72 identical…
In a seminal paper Caspar and Klug established a theory that provides a family of polyhedra as blueprints for the structural organisation of viral capsids. In particular, they encode the locations of the proteins in the shells that…
The protein shells, or capsids, of all sphere-like viruses adopt icosahedral symmetry. In the present paper we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral…
By using a mixture model for the density distribution of the three pseudobond angles formed by $C_\alpha$ atoms of four consecutive residues, the local structural states are discretized as 17 conformational letters of a protein structural…
Understanding protein self-assembly is important for many biological and industrial processes. Proteins can self-assemble into crystals, filaments, gels, and other amorphous aggregates. The final forms include virus capsids and condensed…
The majority of viruses are organised according to the structural blueprints of the seminal Caspar-Klug theory. However, there are a number of notable exceptions to this geometric design principle. Prominent examples are the cancer-causing…
Ordered states on spheres require a minimum number of topological defects. For the case of crystalline order, triangular lattices must be interrupted by an array of at least 12 five-fold disclination defects, typically sitting at the…
A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Assembly models are developed for viral capsids built from protein building blocks that can…
Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific…
Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer…
A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose for formulation of analogue of Bell theorem "without probabilities." The model was later reformulated using so-called Witting…
The best-understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold. But crystals that assemble on closed…
Spherical nanoclusters and nanoparticles are rising materials whose functional design provides many useful applications ranging from catalysis, molecular sensing, gas storage to drug targeting and delivery. Here, we develop phenomenological…
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…
Many cell functions require a concerted effort from multiple membrane proteins, for example, for signaling, cell division, and endocytosis. One contribution to their successful self-organization stems from the membrane deformations that…
The interplay between order and geometry in soft condensed matter systems is an active field with many striking results and even more open problems. Ordered structures on curved surfaces appear in multi-electron helium bubbles, viral and…