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.

A proposed simulation method for directed self-assembly of nanographene.

A methodology for predictive kinetic self-assembly modeling of bottom-up chemical synthesis of nanographene is proposed. The method maintains physical transparency in using a novel array format to efficiently store molecule information and by using array operations to determine reaction possibilities. Within a minimal model approach, the parameter space for the bond activation energies (i.e. molecule functionalization) at fixed reaction temperature and initial molecule concentrations is explored. Directed self-assembly of nanographene from functionalized tetrabenzanthracene and benzene is studied with regions in the activation energy phase-space showing length-to-width ratio tunability. The degree of defects and reaction reproducibility in the simulations is also determined, with the rate of functionalized benzene addition providing additional control of the dimension and quality of the nanographene. Comparison of the reaction energetics to available density functional theory data suggests the synthesis may be experimentally tenable using aryl-halide cross-coupling and noble metal surface-assisted catalysis. With full access to the intermediate reaction network and with dynamic coupling to density functional theory-informed tight-binding simulation, the method is proposed as a computationally efficient means towards detailed simulation-driven design of new nanographene systems.

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.

Identification of novel RNA secondary structures within the hepatitis C virus genome reveals a cooperative involvement in genome packaging.

The specific packaging of the hepatitis C virus (HCV) genome is hypothesised to be driven by Core-RNA interactions. To identify the regions of the viral genome involved in this process, we used SELEX (systematic evolution of ligands by exponential enrichment) to identify RNA aptamers which bind specifically to Core in vitro. Comparison of these aptamers to multiple HCV genomes revealed the presence of a conserved terminal loop motif within short RNA stem-loop structures. We postulated that interactions of these motifs, as well as sub-motifs which were present in HCV genomes at statistically significant levels, with the Core protein may drive virion assembly. We mutated 8 of these predicted motifs within the HCV infectious molecular clone JFH-1, thereby producing a range of mutant viruses predicted to possess altered RNA secondary structures. RNA replication and viral titre were unaltered in viruses possessing only one mutated structure. However, infectivity titres were decreased in viruses possessing a higher number of mutated regions. This work thus identified multiple novel RNA motifs which appear to contribute to genome packaging. We suggest that these structures act as cooperative packaging signals to drive specific RNA encapsidation during HCV assembly.

Approximation of virus structure by icosahedral tilings.

Viruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tiles via projection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications.

Simple rules for efficient assembly predict the layout of a packaged viral RNA.

Single-stranded RNA (ssRNA) viruses, which include major human pathogens, package their genomes as they assemble their capsids. We show here that the organization of the viral genomes within the capsids provides intriguing insights into the highly cooperative nature of the assembly process. A recent cryo-electron microscopy structure of bacteriophage MS2, determined with only 5-fold symmetry averaging, has revealed the asymmetric distribution of its encapsidated genome. Here we show that this RNA distribution is consistent with an assembly mechanism that follows two simple rules derived from experiment: (1) the binding of the MS2 maturation protein to the RNA constrains its conformation into a loop, and (2) the capsid must be built in an energetically favorable way. These results provide a new level of insight into the factors that drive efficient assembly of ssRNA viruses in vivo.

Dynamic allostery controls coat protein conformer switching during MS2 phage assembly.

Previously, an RNA stem-loop (TR) encompassing 19 nt of the genome of bacteriophage MS2 was shown to act as an allosteric effector of conformational switching in the coat protein during in vitro capsid assembly. TR RNA binding to symmetric coat protein dimers results in conformational changes, principally at the FG-loop connecting the F and G beta-strands in each subunit, yielding an asymmetric structure. The FG-loops define the quasi-equivalent conformers of the coat protein subunit (A, B, and C) in the T=3 capsid. Efficient assembly of this capsid in vitro requires that both symmetrical and asymmetrical forms of the coat protein dimer be present in solution, implying that they closely resemble the quasi-equivalent dimers (A/B and C/C) seen in the final capsid. Experiments show that assembly can be triggered by a number of RNA stem-loops unrelated to TR in sequence and detailed secondary structure, suggesting that there is little sequence specificity to the allosteric effect. Since the stem-loop binding site on the coat protein dimer is distal to the FG-loops the mechanism of this switching effect needs to be investigated. We have analyzed the vibrational modes of both TR-bound and RNA-free coat protein dimers using an all-atom normal-mode analysis. The results suggest that asymmetric contacts between the A-duplex RNA phosphodiester backbone and the EF-loop in one coat protein subunit result in the FG-loop of that subunit becoming more dynamic, whilst the equivalent loop on the other monomer decreases its mobility. The increased dynamic behaviour occurs in the FG-loop of the subunit required to undergo the largest conformational change when adopting the quasi-equivalent B conformation. The free energy barrier on the pathway to form this new structure would consequently be reduced compared to the unbound subunit. Our results also imply that the allosteric effect should be independent of the base sequence of the bound stem-loop, as observed experimentally. As a test of this model, we also examined the vibrational modes of a known assembly mutant, W82R, which cannot assemble beyond dimer. This mutation leads to an increased mobility of the DE-loop rather than the FG-loop after TR binding, consistent with the non-assembling phenotype of this mutant protein.

Affine extensions of the icosahedral group with applications to the three-dimensional organisation of simple viruses.

Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognised that icosahedral symmetry is crucial for the structural organisation of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, information on their tertiary structures and the organisation of the viral genome within the capsid are inaccessible. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to describe those aspects of the three-dimensional structure of simple viruses. This approach complements Caspar-Klug theory and provides details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.

Blueprints for viral capsids in the family of polyomaviridae.

In a seminal paper, Caspar and Klug [1962. Physical principles in the construction of regular viruses. Cold Spring Harbor Symp. Quant. Biol. 27, 1-24] derived a family of surface lattices as blueprints for the structural organisation of the protein shells, called viral capsids, which encapsulate and hence protect the viral genome. These lattices schematically encode, and hence predict, the locations of the proteins in the viral capsids. Despite the huge success and numerous applications of this theory in virology, experimental results have provided evidence for the fact that it is too restrictive to describe all known viruses [Casjens, S., 1985. Virus Structure and Assembly. Jones and Bartlett, Boston, MA]. Especially, the family of Polyomaviridae, which contains cancer-causing viruses, falls out of the scope of this theory. In [Twarock, R., 2004. A tiling approach to virus capsid assembly explaining a structural puzzle in virology. J. Theor. Biol. 226, 477], we have shown that a member of the family of Polyomaviridae can be described via an icosahedrally symmetric tiling. We show here that all viruses in this family can be described by tilings with vertices corresponding to subsets of a quasi-lattice that is constructed based on an affine extended Coxeter group, and we use this methodology to derive their coordinates explicitly. Since the particles appear as different subsets of the same quasi-lattice, their relative sizes are predicted by this approach, and there hence exists only one scaling factor that relates the sizes of all particles collectively to their biological counterparts. It is the first mathematical result that provides a common organisational principle for different types of viral particles in the family of Polyomaviridae, and paves the way for modelling Polyomaviridae polymorphism.

Dynamical implications of Viral Tiling Theory.

The Caspar-Klug classification of viruses whose protein shell, called viral capsid, exhibits icosahedral symmetry, has recently been extended to incorporate viruses whose capsid proteins are exclusively organised in pentamers. The approach, named 'Viral Tiling Theory', is inspired by the theory of quasicrystals, where aperiodic Penrose tilings enjoy 5-fold and 10-fold local symmetries. This paper analyses the extent to which this classification approach informs dynamical properties of the viral capsids, in particular the pattern of Raman active modes of vibrations, which can be observed experimentally.

Master equation approach to the assembly of viral capsids.

The distribution of inequivalent geometries occurring during self-assembly of the major capsid protein in thermodynamic equilibrium is determined based on a master equation approach. These results are implemented to characterize the assembly of SV40 virus and to obtain information on the putative pathways controlling the progressive build-up of the SV40 capsid. The experimental testability of the predictions is assessed and an analysis of the geometries of the assembly intermediates on the dominant pathways is used to identify targets for anti-viral drug design.

Crosslinking in viral capsids via tiling theory.

A vital part of a virus is its protein shell, called the viral capsid, that encapsulates and hence protects the viral genome. It has been shown in Twarock [2004. A tiling approach to vius capsids assembly explaining a structural puzzle in virology. J. Theor. Biol. 226, 477-482] that the surface structures of viruses with icosahedrally symmetric capsids can be modelled in terms of tilings that encode the locations of the protein subunits. This theory is extended here to multi-level tilings in order to model crosslinking structures. The new framework is demonstrated for the case of bacteriophage HK97, and it is shown, how the theory can be used in general to decide if crosslinking, and what type of crosslinking, is compatible from a mathematical point of view with the geometrical surface structure of a virus.

Assembly models for Papovaviridae based on tiling theory.

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 assume different local bonding structures in the capsid. This situation occurs, for example, for viruses in the family of Papovaviridae, which are linked to cancer and are hence of particular interest for the health sector. More specifically, the viral capsids of the (pseudo-) T = 7 particles in this family consist of pentamers that exhibit two different types of bonding structures. While this scenario cannot be described mathematically in terms of Caspar-Klug theory (Caspar D L D and Klug A 1962 Cold Spring Harbor Symp. Quant. Biol. 27 1), it can be modelled via tiling theory (Twarock R 2004 J. Theor. Biol. 226 477). The latter is used to encode the local bonding environment of the building blocks in a combinatorial structure, called the assembly tree, which is a basic ingredient in the derivation of assembly models for Papovaviridae along the lines of the equilibrium approach of Zlotnick (Zlotnick A 1994 J. Mol. Biol. 241 59). A phase space formalism is introduced to characterize the changes in the assembly pathways and intermediates triggered by the variations in the association energies characterizing the bonds between the building blocks in the capsid. Furthermore, the assembly pathways and concentrations of the statistically dominant assembly intermediates are determined. The example of Simian virus 40 is discussed in detail.

Mathematical models for tubular structures in the family of Papovaviridae.

An important part of a virus is its protein shell, called the viral capsid, that protects the viral genome. While the viral capsids of viruses in the family of Papovaviridae are usually spherical, their protein building blocks are known to assemble also as tubular structures [Kiselev, N.A., Klug, A., 1969. J. Mol. Biol. 40, 155]. In Twarock [2004. J. Theor. Biol. 226, 477] Viral Tiling Theory has been introduced for the structural description of the protein stoichiometry of the spherical capsids in this family. This approach is extended here to the tubular case and is used to classify the surface lattices of tubular structures in the family of Papovaviridae. The predictions of the theory are compared with the experimental results in Kiselev and Klug [1969. J. Mol. Biol. 40, 155].

A tiling approach to virus capsid assembly explaining a structural puzzle in virology.

A novel approach for the description of the protein stoichiometry of viral capsids, that is the protein shells protecting the viral genome, is introduced based on tiling theory. This approach generalizes Caspar-Klug theory of quasi-equivalence to account also for non-quasi-equivalent subunit arrangements in icosahedral virus capsids that have been observed experimentally but are not covered by the Caspar-Klug approach. In particular, the new approach is used to explain the structure of polyoma virus, Simian Virus 40 and L-A virus capsids, which are considered structural puzzles in view of Caspar-Klug theory.