Anže Lošdorfer Božič

Energies and pressures in viruses: contribution of nonspecific electrostatic interactions.

We summarize some aspects of electrostatic interactions in the context of viruses. A simplified but, within well defined limitations, reliable approach is used to derive expressions for electrostatic energies and the corresponding osmotic pressures in single-stranded RNA viruses and double-stranded DNA bacteriophages. The two types of viruses differ crucially in the spatial distribution of their genome charge which leads to essential differences in their free energies, depending on the capsid size and total charge in a quite different fashion. Differences in the free energies are trailed by the corresponding characteristics and variations in the osmotic pressure between the inside of the virus and the external bathing solution.

Serum microRNAs in patients with genetic amyotrophic lateral sclerosis and pre-manifest mutation carriers

Knowledge about the nature of pathomolecular alterations preceding onset of symptoms in amyotrophic lateral sclerosis is largely lacking. It could not only pave the way for the discovery of valuable therapeutic targets but might also govern future concepts of pre-manifest disease modifying treatments. MicroRNAs are central regulators of transcriptome plasticity and participate in pathogenic cascades and/or mirror cellular adaptation to insults. We obtained comprehensive expression profiles of microRNAs in the serum of patients with familial amyotrophic lateral sclerosis, asymptomatic mutation carriers and healthy control subjects. We observed a strikingly homogenous microRNA profile in patients with familial amyotrophic lateral sclerosis that was largely independent from the underlying disease gene. Moreover, we identified 24 significantly downregulated microRNAs in pre-manifest amyotrophic lateral sclerosis mutation carriers up to two decades or more before the estimated time window of disease onset; 91.7% of the downregulated microRNAs in mutation carriers overlapped with the patients with familial amyotrophic lateral sclerosis. Bioinformatic analysis revealed a consensus sequence motif present in the vast majority of downregulated microRNAs identified in this study. Our data thus suggest specific common denominators regarding molecular pathogenesis of different amyotrophic lateral sclerosis genes. We describe the earliest pathomolecular alterations in amyotrophic lateral sclerosis mutation carriers known to date, which provide a basis for the discovery of novel therapeutic targets and strongly argue for studies evaluating presymptomatic disease-modifying treatment in amyotrophic lateral sclerosis.

The Role of Solution Conditions in the Bacteriophage PP7 Capsid Charge Regulation

We investigate and quantify the effects of pH and salt concentration on the charge regulation of the bacteriophage PP7 capsid. These effects are found to be extremely important and substantial, introducing qualitative changes in the charge state of the capsid such as a transition from net-positive to net-negative charge depending on the solution pH. The overall charge of the virus capsid arises as a consequence of a complicated balance with the chemical dissociation equilibrium of the amino acids and the electrostatic interaction between them, and the translational entropy of the mobile solution ions, i.e., counterion release. We show that to properly describe and predict the charging equilibrium of viral capsids in general, one needs to include molecular details as exemplified by the acid-base equilibrium of the detailed distribution of amino acids in the proteinaceous capsid shell.

Symmetry effects in electrostatic interactions between two arbitrarily charged spherical shells in the Debye-Hückel approximation

Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by patchy charge distributions exhibiting certain point group symmetries. We derive a general form of the electrostatic interaction energy of two permeable, arbitrarily charged spherical shells in the Debye-Hückel approximation and apply it to the case of particles with icosahedral, octahedral, and tetrahedral inhomogeneous charge distributions. We analyze in detail how charge distribution symmetry modifies the interaction energy and find that local charge inhomogeneities reduce the repulsion of two overall equally charged particles, while sufficient orientational variation in the charge distribution can turn the minimum interaction energy into an attraction. Additionally, we show that larger patches and thus lower symmetries and wave numbers result in bigger attraction given the same variation.

How simple can a model of an empty viral capsid be? Charge distributions in viral capsids

We investigate and quantify salient features of the charge distributions on viral capsids. Our analysis combines the experimentally determined capsid geometry with simple models for ionization of amino acids, thus yielding a detailed description of spatial distribution for positive and negative charges across the capsid wall. The obtained data is processed in order to extract the mean radii of distributions, surface charge densities, as well as dipole moment densities. The results are evaluated and examined in light of previously proposed models of capsid charge distributions, which are shown to have to some extent limited value when applied to real viruses.

Electrostatic self-energy of a partially formed spherical shell in salt solution: application to stability of tethered and fluid shells as models for viruses and vesicles.

We investigate the electrostatics of a partially formed, charged spherical shell in a salt solution. We solve the problem numerically at the Poisson-Boltzmann level and analytically in the Debye-Hückel regime. From the results on energetics of partially formed shells we examine the stability of tethered (crystalline) and fluid shells toward rupture. We delineate different regimes of stability, where, for fluid shells, we also include the effects of bending elasticity of the shells. Our analysis shows how charging of the shell induces its instability toward rupture but also provides insight regarding growth of charged shells.

pH Dependence of Charge Multipole Moments in Proteins

Electrostatic interactions play a fundamental role in the structure and function of proteins. Due to ionizable amino acid residues present on the solvent-exposed surfaces of proteins, the protein charge is not constant but varies with the changes in the environment-most notably, the pH of the surrounding solution. We study the effects of pH on the charge of four globular proteins by expanding their surface charge distributions in terms of multipoles. The detailed representation of the charges on the proteins is in this way replaced by the magnitudes and orientations of the multipole moments of varying order. Focusing on the three lowest-order multipoles-the total charge, dipole, and quadrupole moment-we show that the value of pH influences not only their magnitudes, but more notably and importantly also the spatial orientation of their principal axes. Our findings imply important consequences for the study of protein-protein interactions and the assembly of both proteinaceous shells and patchy colloids with dissociable charge groups.

Effects of long-range interactions on curvature energies of viral shells.

We formulate a theory of the effects of long-range interactions on the surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek mesoscale approach to colloid stability. We derive the full renormalization formulas for the elastic properties of the shell and consider in detail the renormalization of the spontaneous curvature as a function of the corresponding Hamaker coefficient, inner and outer capsid charges, and bathing solution properties. The renormalized spontaneous curvature is found to be a nonmonotonic function of several parameters describing the system.

Electrostatic stability and encapsidation of charged nano-droplets

We investigate the electrostatic stability of charged droplets, modeled as permeable, charged spheres, and their encapsidation in thin, arbitrarily charged nano-shells, immersed in a neutralizing asymmetric electrolyte background. The latter consists of a small concentration of mobile multivalent counterions in a bathing solution of monovalent (positive and negative) ions. We use extensive Monte Carlo simulations to investigate the spatial distribution of multivalent counterions and the electrostatic component of their osmotic pressure on the bounding surface of the spherical nano-shells. The osmotic pressure can be negative (inward pressure), positive (outward pressure) or zero, depending on system parameters such as the charge density of the droplet, the charge density of the shell, and electrolyte screening, which thus determine the stability of the nano-container. The counter-intuitive effects of multivalent counterions comprise the increased stability of the charged droplet with larger charge density, increased stability in the case of an encapsidating shell of charge density of the same sign as the charged droplet, as well as the possibility to dispense altogether with the encapsidating shell, its confining effect being taken over by the multivalent counterions. These dramatic effects are in stark contrast to the conventional mean-field picture, which in particular implies that a more highly charged spherical droplet should be electrostatically less stable because of its larger (repulsive) self-energy.

From discrete to continuous description of spherical surface charge distributions

The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface -- characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids -- we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.