arXiv subjects

Reidun Twarock

Publications and source records attributed to Reidun Twarock.

14 recordsLinked to original sources

arXiv2023

An interaction network approach predicts protein cage architectures in bionanotechnology

Protein nanoparticles play pivotal roles in many areas of bionanotechnology, including drug delivery, vaccination and diagnostics. These technologies require control over the distinct particle morphologies that protein nanocontainers can adopt during self-assembly from their constituent protein components. The geometric construction principle of virus-derived protein cages is by now fairly well understood by analogy to viral protein shells in terms of Caspar and Klug's quasi-equivalence principle. However, many artificial, or genetically modified, protein containers violate this principle, because identical protein subunits do not interact in quasi-equivalent ways, leading to gaps in the particle surface. We introduce a method that exploits information on the local interactions between the assembly units, called capsomers, to infer the geometric construction principle of these nanoparticle architectures. The predictive power of this approach is demonstrated here for a prominent system in nanotechnology, the AaLS pentamer. Our method not only rationalises hitherto discovered cage structures, but also predicts geometrically viable options that have not yet been observed. The classification of nanoparticle architecture based on the geometric properties of the interaction network closes a gap in our current understanding of protein container structure and can be widely applied in protein nanotechnology, paving the way to programmable control over particle polymorphism.

q-bio.QM↗

arXiv2021

Comparing antiviral strategies against COVID-19 via multiscale within-host modelling

Within-host models of COVID-19 infection dynamics enable the merits of different forms of antiviral therapy to be assessed in individual patients. A stochastic agent-based model of COVID-19 intracellular dynamics is introduced here, that incorporates essential steps of the viral life cycle targeted by treatment options. Integration of model predictions with an intercellular ODE model of within-host infection dynamics, fitted to patient data, generates a generic profile of disease progression in patients that have recovered in the absence of treatment. This is contrasted with the profiles obtained after variation of model parameters pertinent to the immune response, such as effector cell and antibody proliferation rates, mimicking disease progression in immunocompromised patients. These profiles are then compared with disease progression in the presence of antiviral and convalescent plasma therapy against COVID-19 infections. The model reveals that using both therapies in combination can be very effective in reducing the length of infection, but these synergistic effects decline with a delayed treatment start. Conversely, early treatment with either therapy alone can actually increase the duration of infection, with infectious virions still present after the decline of other markers of infection. This suggests that usage of these treatments should remain carefully controlled in a clinical environment.

q-bio.QM↗

arXiv2021

Therapeutic Interfering Particles Exploiting Viral Replication and Assembly Mechanisms Show Promising Performance: A Modelling Study

Defective interfering particles arise spontaneously during a viral infection as mutants lacking essential parts of the viral genome. Their ability to replicate in the presence of the wild-type (WT) virus (at the expense of viable viral particles) is mimicked and exploited by therapeutic interfering particles. We propose a strategy for the design of therapeutic interfering RNAs (tiRNAs) against positive-sense single-stranded RNA viruses that assemble via packaging signal-mediated assembly. These tiRNAs contain both an optimised version of the virus assembly manual that is encoded by multiple dispersed RNA packaging signals and a replication signal for viral polymerase, but lack any protein coding information. We use an intracellular model for hepatitis C viral (HCV) infection that captures key aspects of the competition dynamics between tiRNAs and viral genomes for virally produced capsid protein and polymerase. We show that only a small increase in the assembly and replication efficiency of the tiRNAs compared with WT virus is required in order to achieve a treatment efficacy greater than 99%. This demonstrates that the proposed tiRNA design could be a promising treatment option for RNA viral infections.

q-bio.QM↗

arXiv2021

An age-structured model of hepatitis B viral infection highlights the potential of different therapeutic strategies

Hepatitis B virus is a global health threat, and its elimination by 2030 has been prioritised by the World Health Organisation. Here we present an age-structured model for the immune response to an HBV infection, which takes into account contributions from both cell-mediated and humoral immunity. The model has been validated using published patient data recorded during acute infection. It has been adapted to the scenarios of chronic infection, clearance of infection, and flare-ups via variation of the immune response parameters. The impacts of immune response exhaustion and non-infectious subviral particles on the immune response dynamics are analysed. A comparison of different treatment options in the context of this model reveals that drugs targeting aspects of the viral life cycle are more effective than exhaustion therapy, a form of therapy mitigating immune response exhaustion. Our results suggest that antiviral treatment is best started when viral load is declining rather than in a flare-up. The model suggests that a fast antibody production rate always lead to viral clearance, highlighting the promise of antibody therapies currently in clinical trials.

q-bio.QM↗

arXiv2020

A multi-scale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called \textit{SARS--CoV--2 Severe Acute Respiratory Syndrome, corona virus n.2}. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focused also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

q-bio.PE↗

arXiv2016

A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays

In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally proposed by Kramer, to the case of aperiodic structures with icosahedral symmetry; these rotations induce a rotation of the physical and orthogonal spaces invariant under the icosahedral group, and hence, via the cut-and-project method, a continuous transformation of the corresponding model sets. We prove that this approach allows for a characterisation of such transitions in a purely group theoretical framework, and provide explicit computations and specific examples. Moreover, we prove that this approach can be used in the case of finite point sets with icosahedral symmetry, which have a wide range of applications in carbon chemistry (fullerenes) and biology (viral capsids).

math-ph↗

arXiv2015

Orbits of crystallographic embedding of non-crystallographic groups and applications to virology

The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is still lacking. We present here a group theoretical method for the construction of finite nested point set with non-crystallographic symmetry. Akin to the construction of quasicrystals, we embed a non-crystallographic group $G$ into the point group $\mathcal{P}$ of a higher dimensional lattice and construct the chains of all $G$-containing subgroups. We determine the orbits of lattice points under such subgroups, and show that their projection into a lower dimensional $G$-invariant subspace consists of nested point sets with $G$-symmetry at each radial level. The number of different radial levels is bounded by the index of $G$ in the subgroup of $\mathcal{P}$. In the case of icosahedral symmetry, we determine all subgroup chains explicitly and illustrate that these point sets in projection provide blueprints that approximate the organisation of simple viral capsids, encoding information on the structural organisation of capsid proteins and the genomic material collectively, based on two case studies. Contrary to the affine extensions previously introduced, these orbits endow virus architecture with an underlying finite group structure, which lends itself better for the modelling of its dynamic properties than its infinite dimensional counterpart.

math-ph↗

arXiv2015

On the subgroup structure of the hyperoctahedral group in six dimensions

We investigate the subgroup structure of the hyperoctahedral group in six dimensions. In particular, we study the subgroups isomorphic to the icosahedral group. We classify the orthogonal crystallographic representations of the icosahedral group and analyse their intersections and subgroups, using results from graph theory and their spectra.

math.GR↗

arXiv2014

Viruses and Fullerenes - Symmetry as a Common Thread?

We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational principle in virus structure and assembly. We adapt this group theoretic framework here to the physical requirements dictated by carbon chemistry, and show that we can derive mathematical models for carbon onions within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in Nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.

math-ph↗

arXiv2012

Affine extensions of non-crystallographic Coxeter groups induced by projection

In this paper, we show that affine extensions of non-crystallographic Coxeter groups can be derived via Coxeter-Dynkin diagram foldings and projections of affine extended versions of the root systems E_8, D_6 and A_4. We show that the induced affine extensions of the non-crystallographic groups H_4, H_3 and H_2 correspond to a distinguished subset of the Kac-Moody-type extensions considered in Dechant et al. This class of extensions was motivated by physical applications in icosahedral systems in biology (viruses), physics (quasicrystals) and chemistry (fullerenes). By connecting these here to extensions of E_8, D_6 and A_4, we place them into the broader context of crystallographic lattices such as E_8, suggesting their potential for applications in high energy physics, integrable systems and modular form theory. By inverting the projection, we make the case for admitting different number fields in the Cartan matrix, which could open up enticing possibilities in hyperbolic geometry and rational conformal field theory.

math-ph↗

arXiv2012

Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups

Motivated by recent results in mathematical virology, we present novel asymmetric Z[tau]-integer-valued affine extensions of the non-crystallographic Coxeter groups H_2, H_3 and H_4 derived in a Kac-Moody-type formalism. In particular, we show that the affine reflection planes which extend the Coxeter group H_3 generate (twist) translations along 2-, 3- and 5-fold axes of icosahedral symmetry, and we classify these translations in terms of the Fibonacci recursion relation applied to different start values. We thus provide an explanation of previous results concerning affine extensions of icosahedral symmetry in a Coxeter group context, and extend this analysis to the case of the non-crystallographic Coxeter groups H_2 and H_4. These results will enable new applications of group theory in physics (quasicrystals), biology (viruses) and chemistry (fullerenes).

math-ph↗

arXiv2008

DNA cages with icosahedral symmetry in bionanotechnology

Blueprints of polyhedral cages with icosahedral symmetry made of circular DNA molecules are provided. The basic rule is that every edge of the cage is met twice in opposite directions by the DNA strand, and vertex junctions are realised by a set of admissible junction types. As nanocontainers for cargo storage and delivery, the icosidodecahedral cages are of special interest as they have the largest volume per surface ratio of all cages discussed here.

q-bio.BM↗

arXiv2005

Lie algebras associated with one-dimensional aperiodic point sets

The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive graded composition law and permits the introduction of Lie algebras over such aperiodic point sets. These infinite dimensional Lie algebras are shown to be representatives of a new type of semi-direct product induced Lie algebras.

math-ph↗

arXiv2005

A toolkit for the construction of icosahedral particles with local symmetry axes

A formalism is developed which allows to determine the locations of all local symmetry axes of three-dimensional particles with overall icosahedral symmetry. It relies on the fact that the root system of the non-crystallographic Coxeter group H_3 encodes the locations of the planes of reflection that generate the discrete rotational symmetries of the particles. Via an appropriate extension of the root system, new planes of reflection are introduced which determine local axes of rotational symmetry. An easy-to-implement formalism is derived that allows to compute the surface structure of any three-dimensional icosahedral particle with local symmetries. It can be used also for particles with overall octahedral and tetrahedral symmetry in conjunction with the root systems of the corresponding reflection groups. Applications to viruses are discussed explicitly. It is shown that the concept of quasi-equivalence in Caspar-Klug Theory corresponds to the special case of local six-fold symmetry axes contained in the theory developed here, and the corresponding geometries can hence be obtained with this formalism based on the root system of H_3. Moreover, as a by-product, the theory answers the long-standing open question why only certain types of capsomeres, i.e. clusters of protein subunits, are observed in the surface structures of viruses. Since the types of the capsomeres are determined by the orders of the local symmetry axes on which they are located, the possible types of capsomeres are restricted by the spectrum of local symmetry axes allowed by the theory. Based on this we determine the spectrum of all capsomere types that may occur in viral capsids and give explicit examples for the lower-order cases.

q-bio.BM↗