61 research outputs found
Classification of self-assembling protein nanoparticle architectures for applications in vaccine design
We introduce here a mathematical procedure for the structural classification of a specific class of self-assembling protein nanoparticles (SAPNs) that are used as a platform for repetitive antigen display systems. These SAPNs have distinctive geometries as a consequence of the fact that their peptide building blocks are formed from two linked coiled coils that are designed to assemble into trimeric and pentameric clusters. This allows a mathematical description of particle architectures in terms of bipartite (3,5)-regular graphs. Exploiting the relation with fullerene graphs, we provide a complete atlas of SAPN morphologies. The classification enables a detailed understanding of the spectrum of possible particle geometries that can arise in the self-assembly process. Moreover, it provides a toolkit for a systematic exploitation of SAPNs in bioengineering in the context of vaccine design, predicting the density of B-cell epitopes on the SAPN surface, which is critical for a strong humoral immune response
Surface stresses in complex viral capsids and non-quasiequivalent viral architectures
Many larger and more complex viruses deviate from the capsid layouts predicted in the seminal Caspar-Klug theory of icosahedral viruses. Instead of being built from one type of capsid protein, they code for multiple distinct structural proteins that either break the local symmetry of the capsid protein building blocks (capsomers) in specific positions, or exhibit auxiliary proteins that stabilise the capsid shell. We investigate here the hypothesis that this occurs as a response to mechanical stress. For this, we construct a coarse-grained model of a viral capsid, derived from the experimentally determined atomistic positions of the capsid proteins, that represents the basic features of protein organisation in the viral capsid as described in Caspar-Klug theory. We focus here on viruses in the PRD1-adenovirus lineage. For T=28 viruses in this lineage, that have capsids formed from two distinct structural proteins, we show that the tangential shear stress in the viral capsid concentrates at the sites of local symmetry breaking. In the T=21,25 and 27 capsids, we show that stabilizing proteins decrease the tangential stress. These results suggest that mechanical properties can act as selective pressures on the evolution of capsid components, offsetting the coding cost imposed by the need for such additional protein components
Classification of self-assembling protein nanoparticle architectures for applications in vaccine design
We introduce here a mathematical procedure for the structural classification of a specific class of self-assembling protein nanoparticles (SAPNs) that are used as a platform for repetitive antigen display systems. These SAPNs have distinctive geometries as a consequence of the fact that their peptide building blocks are formed from two linked coiled coils that are designed to assemble into trimeric and pentameric clusters. This allows a mathematical description of particle architectures in terms of bipartite (3,5)-regular graphs. Exploiting the relation with fullerene graphs, we provide a complete atlas of SAPN morphologies. The classification enables a detailed understanding of the spectrum of possible particle geometries that can arise in the self-assembly process. Moreover, it provides a toolkit for a systematic exploitation of SAPNs in bioengineering in the context of vaccine design, predicting the density of B-cell epitopes on the SAPN surface, which is critical for a strong humoral immune response
Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups
Motivated by recent results in mathematical virology, we present novel asymmetric -integer-valued affine extensions of the non-crystallographic Coxeter groups H2, H3 and H4 derived in a Kac–Moody-type formalism. In particular, we show that the affine reflection planes which extend the Coxeter group H3 generate (twist) translations along two-, three- and five-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 H2 and H4. These results will enable new applications of group theory in physics (quasicrystals), biology (viruses) and chemistry (fullerenes)
Representations of derived from quantum flag manifolds
A relationship between quantum flag and Grassmann manifolds is revealed. This
enables a formal diagonalization of quantum positive matrices. The requirement
that this diagonalization defines a homomorphism leads to a left \Uh -- module
structure on the algebra generated by quantum antiholomorphic coordinate
functions living on the flag manifold. The module is defined by prescribing the
action on the unit and then extending it to all polynomials using a quantum
version of Leibniz rule. Leibniz rule is shown to be induced by the dressing
transformation. For discrete values of parameters occuring in the
diagonalization one can extract finite-dimensional irreducible representations
of \Uh as cyclic submodules.Comment: LaTeX file, JMP (to appear
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).Peer reviewe
A coarse-grained model of the expansionof the human rhinovirus 2 capsid revealsinsights in genome release
Human rhinoviruses are causative agents of the common cold. In order torelease their RNA genome into the host during a viral infection, these smallviruses must undergo conformational changes in their capsids, whosedetailed mechanism is strictly related to the process of RNA extrusion,which has been only partially elucidated. We study here a mathematicalmodel for the structural transition between the native particle of human rhi-novirus type 2 and its expanded form, viewing the process as an energycascade, i.e. a sequence of metastable states with decreasing energy connectedby minimum energy paths. We explore several transition pathways anddiscuss their implications for the RNA exit proces
Structural transformations in quasicrystals induced by higher-dimensional lattice transitions
An age-structured model of hepatitis B viral infection highlights the potential of different therapeutic strategies
Hepatitis B virus (HBV) 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 leads to viral clearance, highlighting the promise of antibody therapies currently in clinical trials
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