arXiv subjects

Anže Božič

Publications and source records attributed to Anže Božič.

10 recordsLinked to original sources

arXiv2026

Asphericity lifts the degeneracy among ordering mechanisms on curved surfaces

Spherical surfaces conceal the one-body signature of particle organization: area-uniform, conductor, and curvature-weighted measures coincide there, so the ordering mechanism leaves no trace in the density. Hard spheres and Coulomb charges confined to the sphere thus produce identical mean densities, and distinctions between their particle arrangements appear only in many-body correlations. Aspherical deformation lifts this degeneracy, and we show that on an ellipsoid, different ordering mechanisms separate by virtue of a single exponent $p$ of the distance from the shell center to its tangent plane. To leading order in deformation, the characteristic exponent $p$ can be obtained both from the quadrupole of the spherical structure factor and from the radius of gyration. Two interaction families demonstrate how this can be realized in practice: the Riesz $s$-energy, whose limiting measure is determined by the power $s$ and exhibits a transition at $s=d=2$, and the screened Coulomb potential, whose measure and thus the characteristic exponent are tuned continuously by the salt concentration. The value of the characteristic exponent $p$ positions the arrangement of particles between the conductor and packing limits, and its response to a control parameter such as salt concentration can be used experimentally to identify the interaction family.

cond-mat.soft↗

arXiv2026

Packaged DNA genome sets the long-range electrostatic anisotropy of a virus

Viruses are among the most highly charged objects in biology, and electrostatic interactions permeate nearly every stage of their life cycle. At the same time, an empty icosahedral capsid is almost isotropic as far as the surrounding electrolyte is concerned---its charge distribution is anisotropic only at high multipole order, and electrostatic screening removes such anisotropy long before it can be probed at a distance. Here, we show that the packaged genome of a filled virus imparts a long-range electrostatic anisotropy that extends throughout the surrounding medium, which is not present for empty capsids. We support these findings with a novel Poisson--Boltzmann continuum theory where the orientational order of dsDNA enters through an anisotropic dielectric tensor and an inhomogeneous volume-charge distribution, which is coupled to a charge-regulating shell containing ionizable amino acid residues of the capsid proteins. The resulting electrostatic potential profiles show that DNA packed in an inverse-spool geometry imprints a highly inhomogeneous potential distribution on the outer capsid surface, whose angular structure is a direct result of the DNA-free axial void. At high salinity, the multipole spectrum of this distribution persists at large distances, whereas at low salt concentration, higher-order multipoles decay more rapidly away from the surface. The surviving quadrupole renders virus--wall and virus--virus interactions orientation dependent at the $k_\mathrm{B}T$ level, with a preferred orientation controlled by the sign of the external charge and the pH. Using phage $λ$ as a model system and checking robustness of our results on two other phages, we find the same behavior across a range of pH and ionic strengths. This identifies the packaged genome, rather than the symmetry of the capsid, as the origin of the long-range electrostatic anisotropy of a filled virus.

physics.bio-ph↗

arXiv2026

A closed-form theory of charge-regulated electrostatic interactions between anisotropically charged spheres

Proteins and many other colloids carry ionizable surface groups that are both spatially inhomogeneous (patchy) and pH-responsive (charge-regulating). In the description of the electrostatic interactions between such particles, these two aspects are often treated separately, especially from a theoretical perspective. We present a unified, closed-form theory that unites charge regulation and patchiness within the linearized Poisson--Boltzmann approximation. For spherical particles with anisotropic distributions of titratable sites, we derive both the leading-order mean-field interaction energy as well as the Kirkwood--Shumaker fluctuation interaction. The theory exposes a qualitatively new effect between two electroneutral anisotropic particles: proximity-induced charge regulation generates a net monopole, and splits orientational branches that are degenerate in any linear fixed-charge model. The accompanying correction to the interaction energy has no fixed sign---it softens like-charge repulsion but can deepen or create attraction away from the isoelectric point. We benchmark three ingredients of the theory against published results; no existing simulation probes their combination, which would capture the central prediction of the theory. Lastly, we apply the theory to two proteins---lysozyme and $α$-chymotrypsinogen A---and show that it not only reproduces the measured second virial coefficients reasonably well but also predicts how charge regulation expands the range of pH and screening strength where the protein--protein interaction is attractive.

cond-mat.soft↗

arXiv2025

Normalized topological indices discriminate between architectures of branched macromolecules

Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many favourable properties that arise because of it. For instance, branched macromolecules are spatially compact and have a high surface functionality, which impacts their phase characteristics and self-assembly behaviour, among others. The relationship between branching and physical properties has been studied by mapping macromolecules to mathematical trees whose architecture can be characterized using topological indices. These indices, however, do not allow for a comparison of macromolecules that map to trees of different size, be it due to different mapping procedures or differences in their molecular weight. To alleviate this, we introduce a novel normalization of topological indices using estimates of their probability density functions. We determine two optimal normalized topological indices and construct a phase space that enables a robust discrimination between different architectures of branched macromolecules. We demonstrate the necessity of such a phase space on two practical applications, one being ribonucleic acid (RNA) molecules with various branching topologies and the other different methods of coarse-graining branched macromolecules. Our approach can be applied to any type of branched molecules and extended as needed to other topological indices, making it useful across a wide range of fields where branched molecules play an important role, including polymer physics, green chemistry, bioengineering, biotechnology, and medicine.

cond-mat.soft↗

arXiv2024

Anisotropic DLVO-like interaction for charge patchiness in colloids and proteins

The behaviour and stability of soft and biological matter depend significantly on electrostatic interactions, as particles such as proteins and colloids acquire a charge when dispersed in an electrolytic solution. A typical simplification used to understand bulk phenomena involving electrostatic interactions is the isotropy of the charge on the particles. However, whether arising naturally or by synthesis, charge distributions are often inhomogeneous, leading to an intricate particle-particle interaction landscape and complex assembly phenomena. The fundamental complexity of these interactions gives rise to models based on distinct assumptions and varying degrees of simplifications which can blur the line between genuine physical behaviour and artefacts arising from the choice of a particular electrostatic model. Building upon the widely-used linearized Poisson-Boltzmann theory, we propose a theoretical framework that -- by bridging different models -- provides a robust DLVO-like description of electrostatic interactions between inhomogeneously charged particles. By matching solely the {\em single-particle} properties of two different mean-field models, we find a quantitative agreement between the {\em pair interaction energies} over a wide range of system parameters. Our work identifies a strategy to merge different models of inhomogeneously charged particles and paves the way to a reliable, accurate, and computationally affordable description of their interactions.

cond-mat.soft↗

arXiv2023

Scaling properties of RNA as a randomly branching polymer

Formation of base pairs between the nucleotides of an RNA sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching -- for instance, for its spatial compactness or interaction with other biological macromolecules -- RNA branching topology remains largely unexplored. Here, we use the theory of randomly branching polymers to explore the scaling properties of RNAs by mapping their secondary structures onto planar tree graphs. Focusing on random RNA sequences of varying lengths, we determine the two scaling exponents related to their topology of branching. Our results indicate that ensembles of RNA secondary structures are characterized by annealed random branching and scale similarly to self-avoiding trees in three dimensions. We further show that the obtained scaling exponents are robust upon changes in nucleotide composition, tree topology, and folding energy parameters. Finally, in order to apply the theory of branching polymers to biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be obtained from the distributions of the related topological quantities of individual RNA molecules with fixed length. In this way, we establish a framework to study the branching properties of RNA and compare them to other known classes of branched polymers. By understanding the scaling properties of RNA related to its branching structure we aim to improve our understanding of the underlying principles and open up the possibility to design RNA sequences with desired topological properties.

physics.bio-ph↗

arXiv2023

Viral RNA as a branched polymer

Myriad viruses use positive-strand RNA molecules as their genomes. Far from being only a repository of genetic material, viral RNA performs numerous other functions mediated by its physical structure and chemical properties. In this chapter, we focus on its structure and discuss how long RNA molecules can be treated as branched polymers through planar graphs. We describe the major results that can be obtained by this approach, in particular the observation that viral RNA genomes have a characteristic compactness that sets them aside from similar random RNAs. We also discuss how different parameters used in the current RNA folding software influence the resulting structures and how they can be related to experimentally observable quantities. Finally, we show how the connection to branched polymers can be extended to take advantage of known results from polymer physics and can be further moulded to include additional interactions, such as excluded volume or electrostatics.

physics.bio-ph↗

arXiv2021

Measure of distance and overlap between two arbitrary ellipses on a sphere

Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a spherical surface, curvature and compactness lead to nontrivial behavior that finds uses in physics, computer science and geometry. A well-known idealized isotropic example is the Tammes problem of finding optimal non-intersecting packings of equal hard disks. The anisotropic case of elliptic particles remains, on the other hand, comparatively unexplored. We develop an algorithm to detect collisions between ellipses constrained to the two-dimensional surface of a sphere based on a solution of an eigenvalue problem. We investigate and discuss topologically distinct ways two ellipses may touch or intersect on a sphere, and define a contact function that can be used for construction of short- and long-range pair potentials.

cond-mat.soft↗

arXiv2020

Relative humidity in droplet and airborne transmission of disease

A large number of infectious diseases is transmitted by respiratory droplets. How long these droplets persist in the air, how far they can travel, and how long the pathogens they might carry survive are all decisive factors for the spread of droplet-borne diseases. The subject is extremely multifaceted and its aspects range across different disciplines, yet most of them have only seldom been considered in the physics community. In this review, we discuss the physical principles that govern the fate of respiratory droplets and any viruses trapped inside them, with a focus on the role of relative humidity. Importantly, low relative humidity -- as encountered, for instance, indoors during winter and inside aircraft -- facilitates evaporation and keeps even initially large droplets suspended in air as aerosol for extended periods of time. What is more, relative humidity affects the stability of viruses in aerosol through several physical mechanisms such as efflorescence and inactivation at the air-water interface, whose role in virus inactivation nonetheless remains poorly understood. Elucidating the role of relative humidity in the droplet spread of disease would permit us to design preventive measures that could aid in reducing the chance of transmission, particularly in indoor environment.

cond-mat.soft↗

arXiv2020

Symmetry breaking of dipole orientations on Caspar-Klug lattices

Anisotropic dipole-dipole interaction often plays a key role in biological, soft, and complex matter. For it to induce non-trivial order in the system, there must be additional repulsive interactions or external potentials involved that partially or completely fix the positions of the dipoles. These positions can often be represented as an underlying lattice on which dipole interaction induces orientational ordering of the particles. On lattices in the Euclidean plane, dipoles have been found to assume different ground state configurations depending on the lattice type, with a global ordering in the form of a macrovortex being observed in many cases. A similar macrovortex configuration of dipoles has recently been shown to be the sole ground state for dipoles positioned on spherical lattices based on solutions of the Thomson problem. At the same time, no symmetric configurations have been observed, even though the positional order of Thomson lattices exhibits a high degree of symmetry. Here, we show that a different choice of spherical lattices based on Caspar-Klug construction leads to ground states of dipoles with various degrees of symmetry, including the icosahedral symmetry of the underlying lattice. We analyze the stability of the highly symmetric metastable states, their symmetry breaking into subsymmetries of the icosahedral symmetry group, and present a phase diagram of symmetries with respect to lattice parameters. The observed relationship between positional order and dipole-induced symmetry breaking hints at ways of fine-tuning the structure of spherical assemblies and their design.

cond-mat.soft↗