This interdisciplinary workshop on “Mathematical Virology” has brought together high-profile researchers as well as young scientists and research students from the disciplines Mathematics, Biophysics and Biology, to discuss experimental and theoretical challenges at the forefront of virology. A collaboration of these disciplines is key for our understanding of the mechanisms underlying viral diseases. This workshop focused on important aspects of virus research such as the structure and physical properties of viruses, their formation, the structure and injection of the viral genomic material, and viral evolution. The workshop has shown how theoretical approaches, such as mathematical and biophysical techniques, can make a real impact on research in virology, and that also approaches from pure mathematics are very relevant in this context. As a result of this workshop, a number of new collaborations were formed within and across discipline boundaries, and new experimental and theoretical approaches were inspired. The meeting has intensified the interdisciplinary dialogue between the leading groups in that area, and has sparked crucial new insights that ultimately lead to new developments with impact on the greater public, for example, via anti-viral drug design or applications in gene therapy and bio-nanotechnology.
Participants list and links to available presentations are further down this page.
Download the pdf file of the full report
Mathematical models in virology are of strong current interest because they constitute important milestones for the understanding of viral replication mechanisms and hence ultimately for the design of anti-viral therapeutics.
The primary objective of this workshop is to bring together mathematicians, biologists and biophysicists working on various aspects of structure and assembly of viruses, and to open new avenues of collaborative research in this key area of Mathematical Biology.
The main focus of the workshop will be on structure and assembly of viral capsids and the packaging of the viral genome.
This workshop is for invited participants only. The workshop will be held in the St Trinnean Room of St Leonard's Hall, Pollock Halls of Residence, University of Edinburgh. It will begin with Registration from 11.30 until 14.00 of Monday 6 August 2007, a sandwich lunch being provided between 12.00 and 13.30. The workshop will close at 13.30 on Friday 10 August 2007.
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| Agbandje-McKenna, Mavis |
| Elucidating the structural mechanisms of spherical viral capsid assembly for ssDNA viruses |
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Virus assembly, utilizing a limited number of coat protein (CP) building blocks, is an excellent example of directed macromolecular interactions occurring in nature. Two basic principles govern the assembly of spherical (icosahedral) viruses: (I) Genetic Economy – the encapsidated genome encodes many copies of a single or few CPs that assemble a protective shell (the viral capsid) around it; (II) Specificity – the CPs must recognize each other and form exact interfacial interactions. Employing structural biology tools, such as X-ray crystallography and cryo-electron microscopy combined with homology model building, and biochemical, biophysical, and molecular biology analyses, our studies are aimed at elucidating the nature of the interactions between protein-protein subunits and protein-nucleic acids that facilitate spherical viral capsid assembly. Our viral models are members of the ssDNA Geminiviridae with a unique twinned quasi-isometric (geminate) T=1 icosahedral virion and the Parvoviridae with a T=1 icosahedral capsid formed from the common overlapping region of 2 or 3 viral CPs that have unique N-terminal extensions. These studies suggest that successful capsid assembly utilizes structural polymorphisms, dictated by CP:CP and/or CP:genome contacts, to facilitate required interactions and the assembly of mature infectious virions.
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| Arsuaga, Javier |
| DNA knots from bacteriophage P4 suggest a chromosomal organisation with high writhe values |
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Extraction of DNA from P4 phage capsids results in a large proportion of highly knotted DNA circles. These knots are formed inside the viral capsid and are believed to be driven by the effects of the confinement. The sole effect of the confinement on the knot formation predicts an increase of the knotting probability with increasing chromosome length. However observations by Wolfson et al. on P4 deletion mutants show that shorter viral chromosomes have higher knotting probability than longer ones. We here show that elevated writhe values can account for these differences on knotting probabilities. First, by combining experimental and computational methods, we provide evidence for a chiral arrangement of the DNA inside the viral capsids. Next we perform computational investigations on how the knotting probability is affected by the writhe. We conclude that both the writhe and the confinement are important contributors to the formation of P4 knots.
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| Bamford, Dennis |
| What are the ways to assemble a virion - lessons from nature |
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The number of viruses in the biosphere is astronomical. Is it possible to make order to this megalomanic entity? Obviously genome comparisons help to cluster viruses but only with closely related ones and only a miniscule fraction of viruses can be sequenced. The usage of viral protein folds would reduce the search space as the number of protein topologies is limited and those making a viral capsid is only a small subset of all folds. Grouping of viruses by their architectural principles leads to a limited number of viral lineages with possibly an ancient origin.
In these lineqages the host organismis is irrelevant as well as how they replicate their genomes and interact with their host cells. This concept leads to the definition of a virus self,
always inhereted to the progeny. The other viral components can be chaged in respect to the self.
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| Brooks, Charles |
| Exploring viral capsid assembly, mechanics and dynamics |
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In this talk I will discuss recent work on the physical processes associated with viral capsid assembly using coarse-grained models to describe the assembly processes for T=1 and T=3 viral capsid. Additionally, I will describe work aimed at quantitatively characterizing the material properties of viral capsids using all atom models and force fields. Finally, I will present recent work aimed at examining the role of different collective motions in achieving large-scale conformational transitions associated with viral capsid maturation.
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| Bruinsma, Robijn |
| Physics and the HIV virus |
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The talk will discuss the application of physical and mathematical principles to the assembly of the polymorphic retroviruses, such as the HIV virus, with that of small viruses that have an icosahedral architecture.
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| Carloni, Paolo |
| Hybrid coarse-grain/molecular mechanics approach for the investigation of viral and bacterial proteins |
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Conformational fluctuations are believed to play a role for the function of protease enzymatic superfamily. Here we used hybrid molecular mechanics/coarse-grained approach (1) to investigate the dynamics (in the microsecond timescale) of viral and bacterial proteases. We find that large scale motions and fluctuations of the electric field impact on the biological function. Such conclusion can not be drawn within the time scale typical of molecular dynamic simulations. The MM/CG approach is further shown to be a fast and useful tool to provide structure/ function relationships of mutants affecting the enzymatic activity.
(1)M. Neri, C. Anselmi, M. Cascella, A. Maritan, and P. Carloni. Coarse grained model of proteins incorporating atomistic detail of the active site. Phys. Rev. Lett., 95, 2005, p. 218102
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| ElSawy, Karim |
| Towards an understanding of assembly polymorphism in Papovaviridae viruses from an energy landscape perspective |
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A two dimensional approximation of the potential energy landscape of different trimers of pentamers wthin the SV40 virus capsid has been constructed using the packing angles as two collective degrees of freedom. The topology of the energy landscape is primarily dictated by van der Waals interactions whilst its detailed energetics is very much dependent on electrostatic interactions. The dependence of the topology of the potential energy landscape on the pH value can be quantified and is related to the change in the ratio of protonated Histidine residues. The relative propensities of the configurational states at different pH values match reasonably well known experimental trends
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| Evilevitch, Alex |
| Internal DNA pressure effect on phage capsid stability and infectivity. Evolutionary optimization of phage |
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By balancing DNA ejecting force from viral capsids with an osmotic force resisting ejection, we estimated the internal DNA pressure in phage lambda to be tens of atmospheres. We also show how the internal capsid pressure changes in response to packaged genome length and ambient salt conditions, which correlates to viral infectivity. However, our experiments show that viral ejection is incomplete with only about half of DNA being ejected at few atmospheres of external osmotic pressure, corresponding to the osmotic pressure in a bacterial cell. We demonstrate that the rest of ejected DNA is pulled out from phage by either non-specific DNA-binding proteins or spermine, suggesting a mechanism for complete DNA ejection in vivo. Furthermore, we investigate the correlation between packaged DNA length in phage lambda and capsid strength in response to nano-indentation with an AFM tip. We found, that the force exerted on the capsid walls by “pressurized” wt DNA inside the capsid is equal to the maximum force that an empty capsid can withstand before it breaks. This internal DNA-force provides extra support for the capsid making it two times stronger compared to an empty one, which can be the evolutionary reason for the stability and survival of wt phages in nature.
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| Garcea, Robert |
| Confounding biologic variables in modeling virus assembly |
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Cell chaperone proteins facilitating virus assembly will be discussed. These accessory factors greatly complicate the in silico modeling of subunit interactions.
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| Gelbart, William |
| Sizes of viral genomes and viral capsids |
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In this talk I discuss two experimental programs we have been pursuing on dsDNA and ssRNA viruses, designed to clarify fundamental differences in the packaging of their genomes.
The dsDNA virus we study is lambda, which we believe is representative of the large majority of dsDNA bacteriophages. In particular, we measure the pressure in the viral capsid as a function of genome length and ambient salt conditions, and show that the high pressure – typically tens of atmospheres – is dominated by DNA-DNA repulsions, with a significant role played as well by DNA bending elasticity. By applying an external osmotic pressure – mimicking that of the host cell cytoplasm –j we demonstrate that the extent of genome ejection can be quantitatively controlled. An immediate biological consequence of these findings is that the work done in packaging the viral genome is insufficient to deliver it to its host cell. Our pressure measurements are in agreement with a variety of recent single-molecule experiments measuring packaging and ejection forces.
The ssRNA virus we study is cowpea chlorotic mottle virus (CCMV), representative of many plant and animal viruses whose nucleocapsids self-assemble spontaneously in vitro from purified components – RNA genome and capsid protein. Here we focus on the measurement of the 3D size (e.g., radius of gyration) as a function of sequence, for a given molecular weight (nucleotide length). I present preliminary data, obtained from small-angle X-ray scattering (SAXS) and fluorescence correlation spectroscopy (FCS) experiments, comparing a series of 2117-nucleotide-long ssRNA molecules whose sequences have been chosen to give very different 3D sizes, including a wild-type viral sequence (CCMV RNA3) and specific sequences pulled out of a yeast chromosome. We compare these molecules to test the hypothesis that viral ssRNA genomes have evolved to give rise to especially compact 3D structures.
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| Hendrix, Roger |
| Viral capsid assembly: the evolutionary dimension |
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When the crystal structure of the phage HK97 capsid was solved, its polypeptide fold was unique. Psi-Blast searches identify ~300 related capsid protein sequences, representing perhaps 50% of sequenced capsid protein genes. Of the phages outside this sequence-related group, structural studies imply for a half dozen of them the HK97-like polypeptide fold. The same is true for the herpesvirus. The provisional conclusion is that the capsid proteins of all tailed phages plus those of herpesviruses share common ancestry. Examination of the structures suggests that what has been conserved is the core domain of the protein, with considerable variation in the parts of the protein that stabilize the mature capsid, including non-homologous exchange into the protein structure.
The proteins of this putatively homologous family assemble capsids ranging in size from T=1 to T=52, and their homology implies that they are descendants of an ancestral capsid structure. We are therefore thinking about how a capsid protein ‘learns’ to assemble a new capsid size over the course of phage evolution and how such a change affects genome evolution. Examples will be given for phages with T=1, 4, 7, 13, 13 prolate, 16 and 52, among others.
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| Janner, Aloysio |
| Exploring the interplay between molecular crystallography and geometrical virology |
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Some basic aspects of molecular crystallography are introduced and put
in relation with structural properties of viruses.
The global approach, where crystals and biomacromolecules are considered together despite their intrinsic difference, leads to concepts like form lattice, indexed molecular form, crystallographic scaling (linear, planar and isotropic) and crystallographic decoration (edge, face and vertex) of indexed molecular forms. Properties are then observed like integral lattices and strongly correlated (one-parameter) systems. Illustrative examples of crystals, nucleic acids,
axial-symmetric proteins, cubic holoenzymes and icosahedral viruses (the rhinovirus in particular), are presented in their conceptual interplay.
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| Johnson, Jack |
| Biophysical analysis of virus particles and their maturation: insights into elegantly programmed nanomachines |
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Bacteriophages, herpesviruses and other large dsDNA viruses contain powerful molecular machines that pump DNA into preassembled procapsids triggering maturation. This event commences when DNA pressures within the capsid exceed 10-fold that of bottled champagne and are detected by a protein switch that transduces a signal outside of the particle. We investigated two bacteriophage systems to understand the structural basis for these events. The asymmetric structure of the mature P22 bacteriophage was determined to 17Å resolution by cryoEM and image processing, revealing the portal protein implicated in DNA packaging and pressure sensing as well as ordered dsDNA in the vicinity of the portal. Virus particle maturation was studied with the lambda-like bacteriophage HK97. Intermediates in the maturation trajectory were characterized by cryoEM, solution x-ray scattering, crystallography and single particle fluorescence, allowing the creation of a movie* that depicts the particle dynamics. *Wikoff, W., Conway, J., Tang, J., Lee, K., Gan, L., Cheng, N., Duda, R., Hendrix, R., Steven, A., and Johnson, J. 2006. Time-resolved molecular dynamics of HK97 virus maturation interpreted by electron cryo-microscopy and x-ray crystallography. J Struct Biol 153:300-306.
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| Keef, Thomas |
| A Hamiltonian paths approach to viral capsid assembly of RNA viruses |
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For many families of viruses, such as Papovaviridae, viral capsid assembly can be modelled as tile assembly, where tiles are schematic representations of suitable protein building blocks of the capsid. However, for certain classes of RNA viruses where interactions between the capsid proteins and the RNA are crucial for assembly, this approach is not sufficient. We therefore developed a method that incorporates these interactions as boundary conditions into tile assembly. We demonstrate this for the case of bacteriophage MS2: the capsid of MS2 assembles from two types of protein dimers, which are distinguished by the fact that one of them is bound to the packaged RNA via stem loops. This connection between the capsid area and the first layer of RNA implies a boundary condition on tile assembly, and we show that different tile assembly scenarios of the capsid are encoded by the Hamiltonian paths on a polyhedron that represents the organisation of the first layer of RNA. These results then provide the information necessary to determine quantities of interest such as the concentration profile of the assembly intermediates.
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| Kegel, Willem |
| Charge regulation as a stabilization mechanism for shell-like assemblies |
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Large inorganic molecules known as polyoxometallates (POMs) can organize themselves into hollow spherical superstructures in a globally comparable manner as virus capsids.
Here we focus on the thermodynamic stability of the hollow superstructures and the parameters that dictate their equilibrium size. We propose a model that explains the stability of these superstructures formed by POMs based on the low ionic strength conditions where such structures are observed. The main ingredients of the model are charge regulation and defect energetics of POMs on a sphere. We find excellent agreement with the experimentally observed size.
We also address the possible tiling of the POMs. Comparison with POM crystal structure points to four-fold symmetry and not the usual six-fold symmetry.
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| Kerner, Richard |
| Evolutionary trends in icosahedral virus capsids: a combinatorial approach |
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A combinatorial and statistical analysis of all possible icosahedral capsids is presented. The triangular number T is related to the total number of differentiated proteins necessary to encode capsid's size and type. The isomers are pointed out and classified, and the combinatorial rules strongly suggesting possible mutation pathways and evolutionary trends are discussed.
We also analyze chemical and energetic bariers responsible for proteins' agglomeration and optimizing the yield during capsid construction phase.
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| Mannige, Ranjan |
| Constraints and freedoms in virus capsids: a theoretical perspective |
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There are numerous constraints that may bear on the working of a virus capsid. Many of these play important roles in the virus life cycle (such as the availability of buckling transitions, size specific assembly, etc.). We show how a number of these constraints can be explained from a topological and graph theoretical perspective. First, we will present the empirical evidence that indicates that a large number of spherical capsids may be represented as bound tiled surfaces formed from a single prototile.
We will then show that topological constraints play a dominant role in determining the shapes available to the tile (or subunit). Finally, we will focus on dihedral angle constraints, and show how the graph of the mathematical spherical capsid (called the canonical capsid) reveals constraints that are crucial in explaining (1) spherical capsid size (or 'T') specificity, (2) the availability of buckling transitions to capsids of different sizes and (3) the need for auxiliary proteins in larger capsids.
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| Marenduzzo, Davide |
| The dynamics of polymer packaging and ejection in viral capsids |
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We use a mesoscale simulation approach to explore the impact of different capsid geometries on the packaging and ejection dynamics of polymers of different flexibility. We find that both packing and ejection times are faster for flexible polymers. For such polymers a sphere packs more quickly and ejects more slowly than an ellipsoid. For semiflexible polymers, however, the case relevant to DNA, a sphere both packs and ejects more easily. We interpret our results by considering both the thermodynamics and the relaxational dynamics of the polymers. The predictions could be tested with biomimetic experiments with synthetic polymers inside artificial vesicles. Our results suggest that phages may have evolved to be roughly spherical in shape to optimize the speed of genome ejection, which is the first stage in infection.
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| McPherson, Alexander |
| Conformation of RNA in small icosahedral viruses |
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Satellite Tobacco Mosaic Virus (STMV) and Turnip Yellow Mosaic Virus (TYMV) are T=1 and T = 3 icosahedral viruses containing 1058 and 6318 nucleotide ssRNA genomes. The two viruses may prove the best model systems for understanding the packing of single stranded nucleic acid in simple, spherical viruses, as X-ray crystallography has revealed a substantial amount of the RNA to be icosahedrally ordered and, therefore, visible. X-ray diffraction, along with atomic force microscopy imaging, showed the encapsidated RNA to exist as a linear sequence of secondary structural domains, helical stem – loops, or clusters of stem – loops. Upon synthesis in the host cell, these present themselves for binding by the coat protein, which, presumably, marshals the RNA into its requisite tertiary conformation as it assembles into an icosahedral shell about it. This aggregation process is envisioned as simultaneous with nucleic acid replication, such that a linear mode of assembly is concomitant with the formation and appearance of secondary structural elements.
In an attempt to map the base sequence of the viral RNAs onto three dimensional models, a computational analysis was performed based on nucleotide pairing, with numerous alternatives permitted for non canonical pairs, and allowances for mismatches and bulges. There were two principal conclusions. First, there appears to be no unique or clearly dominant solution to the problem, but many, almost equally probable arrangements. Second, virtually any nucleotide sequence, randomly selected, but of the correct length, yields a broad set of solutions that are as good as those provided by the true viral RNA. The results suggest why, for many small icosahedral viruses, virtually any heterologous RNA of roughly the proper length may be encapsidated with approximately the correct native conformation.
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| Micheletti, Cristian |
| Common large-scale movements in HIV-1 protease and other proteolytic enzymes: a coarse-grained approach |
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Proteases regulate various aspects of the life cycle in all organisms
by cleaving specific peptide bonds. Their action is so central for
biochemical processes that at least 2% of any known genome encodes for
proteolytic enzymes. By adopting a coarse-grained model and using
statistical mechanics concept and tools we show that selected
proteases pairs, despite differences in oligomeric state, catalytic
residues and fold, share a common structural organization of
functionally relevant regions which are further shown to undergo
similar concerted movements. The structural and dynamical similarities
found pervasively across evolutionarily distant clans point to
unexpectedly common mechanisms underlying the catalytic action of
these enzymes.
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| Nelson, David |
| Deformations of viral shells by point forces and osmotic pressure |
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Recent theoretical work and numerical simulations that bear on the response of viral shells to atomic force microscope tips and osmotic pressure is reviewed. We focus in part on the response of very large viruses, at high Foppl von-Karman number.
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| Nguyen, Hung D |
| Towards understanding of structural polymorphism and precise control of viral capsid self-assembly |
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Elucidating self-assembly of viral proteins into icosahedral capsids has significant potential for beneficial applications in materials science and medicine. Using coarse-grained but geometrically accurate models with molecular dynamics, we delineate conditions of temperature and capsid protein concentration that lead to the spontaneous self-assembly of T=1 and T=3 capsids (1-2). We decipher kinetic mechanisms responsible for the self-assembly of desired icosahedral capsids as well as self-assembly of aberrant structures arising from kinetically trapped dislocations of
pentamer-templated proteins with hexameric organization; confirming the important role of capsid protein conformational switching as a control mechanism for structural polymorphism and pointing to design strategies for the precise assembly of icosahedral and other closed isometric capsids.
(1) H.D. Nguyen, V.S. Reddy, and C.L. Brooks III, "Deciphering the kinetic mechanism of spontaneous self-assembly of icosahedral capsids," Nano Lett., 7(2), 338-344 (2007)
(2) H.D. Nguyen, V.S. Reddy, and C.L. Brooks III, "When viral capsid self-assembly goes wrong..." in preparation.
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| Oppenheim, Ariella |
| SV40 assembly in vivo and in vitro |
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The SV40 capsid is a T=7d icosahedral lattice ~45 nm in diameter surrounding the ~5 kb circular minichromosome. The outer shell is composed of 360 monomers of the major capsid protein VP1, tightly bound in 72 pentamers. VP1 is a jellyroll beta-barrel, with extending N- and C-terminal arms. The N-terminal arms bind DNA and face the interior of the capsid. The flexible C-arms tie together the 72 pentamers in three distinct kinds of interactions, thus facilitating the formation of a T=7 icosahedron from identical pentameric building blocks. Assembly in vivo was shown to occur by addition of capsomers around the DNA. We apply a combination of biochemical and genetic approaches to study SV40 assembly. Our in vivo and in vitro studies suggest the following model: One or two capsomers bind at a high affinity to ses, the viral DNA encapsidation signal, forming the nucleation center for assembly. Next, multiple capsomers attach concomitantly, at lower affinity, around the minichromosome. This increases their local concentration facilitating rapid, cooperative assembly reaction. Formation of the icosahedron proceeds either by gradual addition of single pentamers to the growing shell or by concerted assembly of pentamer clusters.
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| Prevelige, Peter |
| Incorporation of the portal protein complex into bacteriophage Phi-29 |
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The portal protein has been incorporated into the procapsid of bacteriophage Phi-29 in vitro. Using this system we have explored the nature of the interaction between the portal and scaffolding proteins and mapped the regions involved.
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| Rapaport, Dennis |
| Interactively exploring supramolecular assembly: a molecular dynamics approach to virus construction |
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The self-assembly of polyhedral virus shells (capsids) provides a fascinating example of the complex processes that occur in the simplest of organisms. Little is known about assembly mechanisms, but the fact that different viruses adopt similar structures hints at common design principles and suggests that simplified models ought to be helpful in understanding the process. In order to establish the viability of this approach we have carried out molecular dynamics simulations in which relatively large polyhedral shells assemble spontaneously. Interactive computer visualization plays an important role in this work, and the talk includes a series of molecular dynamics demonstrations of various kinds that illustrate the power of the technique, and which eventually lead to the software used in the self-assembly work.
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| Reguera, David |
| Hysteresis and kinetics of viral self-assembly |
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One of the fundamental stages in the replication of a virus is the self-assembly of its rigid envelope (or capsid) from the proteins that constitute it. A proper description of this process is essential to understand, interfere and control the structure and properties of these nanosized entities. Although large progress has been achieved in recent years in understanding the equilibrium structure of viral capsids, the kinetics aspects remain largely unexplored. Many evidences exist suggesting that the mechanism responsible for this process is nucleation, that underlies most phase transitions. In this talk, we will present a simple but realistic model to describe the kinetics of both viral self-assembly and disassembly. This model is able to account for the hysteretic behavior of capsid assembly and offers predictions for the critical size and the rate of formation of capsids, as well as for the dependency of these magnitudes on the protein concentration and their binding energy. We will compare the predictions of our model with experiments, and discuss their potential biological and practical implications.
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| Rolfsson, Ottar |
| Probing MS2 capsid assembly with ESI-MS |
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Mass spectrometry has proved to be a valuable research method and has recently become an important tool in the study of macromolecular interactions. We have used electrospray ionization mass spectrometry (ESI-MS) to study the self assembly of the bacteriophage MS2 capsid. Assembly is initiated by a sequence recognition event between coat protein dimers and a 19 nucleotide RNA stem loop. Using mass spectrometry we are able to monitor the complete MS2 capsid assembly reaction from formation of the coat protein dimer and its complex with the RNA stem-loop, through the formation of higher order assembly intermediates and the final T=3 capsid product. Isotope pulse-chase experiments confirm that intermediates observed are competent for further coat protein dimer addition and that the unit of capsid growth is a coat protein dimer. The dominant capsid intermediate corresponds to the three-fold axes of symmetry suggesting a preferred pathway towards T = 3 capsid formation.
Surprisingly the initial RNA-protein complex is meta-stable and assembly is only efficient when RNA-free coat protein is in excess, suggesting that RNA-bound and RNA-free forms of the coat protein dimer are distinct species, the obvious inference being that they represent both types of quasi equivalent dimer found in the final capsid. NMR has been used to confirm that stem-loop binding causes a conformational change in the FG-loop of the coat protein, the site of the conformational differences between quasi-conformers.
These results demonstrate the power of mass spectrometry for dissecting details of complex macromolecular reactions and provide the first experimental evidence of a detailed virus capsid assembly mechanism.
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| Schwartz, Russell |
| Exploring capsid assembly pathways through continuous-time discrete event simulation |
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Simulation methods have proven to be a powerful tool for exploring aspects of detailed capsid assembly dynamics that remain inaccessible to direct experimental observation. We describe work on the use of discrete event simulations to examine the nature of assembly pathways in capsid models. Our simulations combine local rule abstractions with methods for continuous-time discrete event simulation to allow unbiased sampling from all possible assembly trajectories for finite populations of model coat proteins. Early use of the models suggested the importance of oligomer/oligomer pathways under some assembly conditions, in contrast to a common assumption of prior modeling work. We therefore sought to examine more generally how assembly conditions and parameters control pathway choice. Our results show that even relatively simple models can exhibit several discrete productive assembly pathways. Large regions of parameter space, however, occupy hybrid assembly regions that are poorly described by the simple theoretical models assuming a single favored pathway. Furthermore, relatively modest changes in binding parameters, consistent with shifts from in vitro to in vivo assembly conditions, can substantially alter pathway selection for a single system. Further simulation experiments have shown that sensitivity to such parameter changes is dramatically different for even modestly complex capsid models compared to simpler model systems. Collectively, our results suggest that our understanding of capsid assembly, whether by theoretical models, experience with simpler model systems, or even direct observation of capsid assembly in vitro, may be less reliable than has generally been assumed.
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| Sitharam, Meera |
| Static modeling of virus assembly pathway probabilities |
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The talk will develop a 2-scale model of virus assembly pathways,
with the goal of isolating crucial factors that determine when
one type of pathway will prevail over another. Another goal is to
ensure that the 2-scales of the model can be independently tuned and tested. The emphasis will be on viral shells that can potentially assemble effectively without the interference of the encapsulated genomic material, or scaffolding or chaperones.
The finer scale of the model is obtained by inspecting the static geometric constraints satisfied by an assembled virus, treating the assembly as the reverse of a decomposition of
this viral geometric constraint system, and isolating
subassemblies that serve as building or gluing blocks. This part of
the theory borrows heavily from combinatorial rigidity theory.
The coarser scale of the model takes the gluing blocks predicted
by the finer scale model and combinatorially enumerates isomorphic pathways and pathway types based on the symmetry of the shell. This part of the theory borrows from algebraic combinatorics.
Joint work with M. Agbandje-Mckenna and M. B'ona.
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| Steven, Alasdair |
| Stochastically variable virus structure |
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The structures of protein molecules are deterministic, i.e. polypeptide chains fold (or are folded) into uniquely defined conformations which represent their “ground states” and which endow them with specific activities. Cells, on the other hand, are stochastically variable, although each cell type has distinctive traits that make it morphologically recognizable. Despite this intrinsic structural variability, a given cell type follows a fairly well defined cycle or exploits a particular set of options for differentiation. Viruses occupy an intermediate position, not only in size and complexity, but also in morphogenic determinism. In some viral systems, each virion is, to a close approximation, a carbon copy of the parent virus. In other systems, virions are pleiomorphic – i.e. they exhibit substantial variations in size and shape while still utilizing the same set of molecular building-blocks. In this context, a key question is: to what extent are crucial functional properties of a virus –such as, infectivity, tropism, replication-competence, and pathogenicity – affected by variations in structure? To begin to address this question requires an appropriately detailed account of the structures in question.
The advent of cryo-electron tomography (cryo-ET) has provided an imaging tool that is capable of rendering the three-dimensional structures of individual pleiomorphic virus particles at a resolution approaching the molecular scale [1]. This talk will outline the principles and prospects of cryo-ET and illustrate them with respect to studies on three pleiomorphic enveloped viruses: influenza A virus [2]; herpes simplex virus [3]; and retrovirus.
1. W. Baumeister & A.C. Steven. Trends in Biochem. Sci. 25, 624-631 (2000). Cryo-electron Microscopy in the Era of Structural Genomics.
2. A. Harris, G. Cardone, D.C. Winkler, J.B. Heymann, M. Brecher, J.M. White & A.C. Steven. Proc. Nat’l. Acad. Sci. USA 103, 19123-19127(2006). Influenza Virus Pleiomorphy Characterized by Cryo-electron Tomography.
3. K. Grünewald, P. Desai, D.C. Winkler, J.B. Heymann, D.M. Belnap, W. Baumeister & A.C. Steven. Science 302, 1396-1398 (2003). Three-dimensional Structure of Herpes Simplex Virus from Cryo-electron Tomography.
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| Stockley, Peter |
| Assembly of ssRNA viruses: the role(s) of the package during packing |
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It has become clear from work with a number of different viruses that ssRNA genomes must be able to fold into compact structures in order to fit the enclosed volumes of their protein capsids. This folding seems independent of the underlying RNA sequence in at least some cases. Using SELEX we have investigated the nature of the packaging signals for three different ssRNA viruses: the RNA bacteriophage MS2, a T=3 virus; a recombinant T=1 plant virus, Satellite Tobacco Necrosis Virus (STNV); and poliovirus, a pseudo-P=3 virus. Analysis of the SELEX products and comparison to the known genomic sequences suggests that these viruses use distinct strategies to ensure that they package their cognate genomes. For MS2, the packaging specificity is dominated by a single stem-loop packaging signal [1]. For STNV and poliovirus, however, there appear to be redundant coat protein recognition signals scattered throughout their genomes. X-ray electron density maps for STNV and intermediate resolution cryo-EM maps of STNV and MS2 (STNV, effective resolution ~6 Å; MS2, effective resolution ~11 Å) show that at the end of the packaging process in each case the genomic RNAs are packed with extended icosahedral symmetry. These results raise important questions about the role(s) of the RNAs during packaging. Does the RNA or the protein lead the folding/assembly process? Can RNA folding be independent of its primary sequence in such situations?
Work with the RNA phage adds further complications to this question. We have shown that T=3 capsid assembly is only efficient when two distinct conformers of the capsomer – a coat protein dimer (CP2) in this case – are present. Binding the RNA stem-loop packaging signal, which can exist in several distinct conformers at various stages of the phage life-cycle, leads to an allosteric conformational change forming a conformer of the CP2 distinct from the one in the absence of RNA. The data lead naturally to a model of assembly in which specific RNA binding causes a switch in quasi-equivalent conformer in the CP2, thus providing both types of species needed for the final T=3 capsid [2]. However this begs the question of how quasi-equivalent switching is achieved beyond the initiation complex? Does the RNA folding present appropriately positioned stem-loop mimics that can function in this way or is the initial conformational switch caused by the initiator stem loop binding sufficient to ‘template’ further coat protein dimers as they bind? The latest results with all three viral systems aimed at investigating these questions about the role(s) of the RNA package during the packaging process will be presented.
[1] Horn et al (2006). Structural basis of RNA binding discrimination between bacteriophages Q beta and MS2. Structure 14, 487-495.
[2] Stockley et al (2007). A Simple, RNA-Mediated Allosteric Switch Controls the Pathway to Formation of a T=3 Viral Capsid. J. Mol. Biol. 369, 541-552.
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| Stonehouse, Nicola |
| Phi29 – investigating a DNA packaging motor |
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Phi29 is a bacteriophage responsible for the infection of Bacillus species. The viral 19 Kb ds DNA genome is packaged into a preformed capsid through a channel composed of connector protein gp10 molecules arranged into a toroidal ring. This process involves an essential virus-derived RNA (pRNA) and is believed to occur via the action of a molecular motor which utilises protein: RNA interactions and ATP hydrolysis. Biological molecular motors can utilise rotary motion (e.g. bacterial flagella) or a linear movement (e.g. muscle contraction). One model to explain phi29 motor function includes rotation about the protein: RNA junction, permitting the linear translocation of DNA. The aim of our work is directed towards developing a detailed understanding of this system. In addition, exploring the mode of phi29 DNA packaging may provide insights into packaging events in other more complex DNA viruses. Data will be presented from a range of complimentary biophysical techniques, describing the affinities of RNA: RNA and protein: RNA interactions. Based on these findings, an alternative model of motor function will be presented involving conformational changes in both the connector protein and pRNA.
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| Sumners, De Witt |
| DNA knots reveal chiral packing of DNA in phage capsids |
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Bacteriophages are viruses that infect bacteria. They pack their double-stranded DNA genomes to near-crystalline density in viral capsids and achieve one of the highest levels of DNA condensation found in nature. Despite numerous studies some essential properties of the packaging geometry of the DNA inside the phage capsid are still unknown. Although viral DNA is linear double-stranded with sticky ends, the linear viral DNA quickly becomes cyclic when removed from the capsid, and for some viral DNA the observed knot probability is an astounding 95%. This talk will discuss comparison of the observed viral knot spectrum with the simulated knot spectrum, concluding that the packing geometry of the DNA inside the capsid is non-random and writhe-directed.
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| Taormina, Anne |
| Vibrational modes of viral capsids and Viral Tiling Theory |
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We use group theoretical methods to analyse the normal modes of vibration of T=3 icosahedral viral capsids whose building blocks are trimers (Caspar-Klug type) and dimers (Viral Tiling Theory type) and provide information related to their Raman spectroscopy.
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| Toropova, Katerina |
| The 3D structure of genomic RNA in bacteriophage MS2; implications for assembly |
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MS2 is an E.coli specific, positive sense, single-stranded RNA bacteriophage. Its small genome codes just four gene products: coat, replicase, lysis and maturation proteins. On binding of coat protein to an assembly initiation stem loop in the genome, 180 copies of coat protein assemble around the RNA to form a T=3 icosahedral protein shell. However, the mechanisms by which capsid assembly and genome folding operate and interact remain poorly understood. We have undertaken a structural study of the bacteriophage MS2 using the technique of cryo-electron microscopy in order to visualise the 3D structure of genomic RNA in the virus. The results show a novel arrangement for the genome with two concentric shells of RNA density, connected at each five-fold axis, that accounts for the vast majority of the RNA in the phage particle. The structure suggests that the genomic RNA follows a defined path with respect to the coat protein shell and can actively participate in the assembly pathway.
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| Tuma, Roman |
| Stochastic aspects of RNA packaging motor:from single molecule experiments to high resolution structure |
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The bacteriophages of Cystoviridae family package their single stranded RNA genomic precursors into empty capsid precursors (procapsids) using a hexameric packaging ATPase (P4) [1]. This molecular motor has sequence and structural similarity to the RecA-like hexameric helicases [1,2]. Biochemical and structural studies revealed that P4 hexamer exhibits a novel type of stochastic-sequential cooperativity during ATP hydrolysis [2,3]. The cooperativity stems from coordinated hydrolysis rather than cooperative binding of ATP. In order to delineate how the cooperative hydrolysis of ATP fuels RNA packaging we have developed a stochastic model of mechano-chemical coupling. The model was solved using Brownian dynamics. The theoretical results are compared with experimental data from both ensemble and single molecule assays. P4 hexamer seems to operate as a Brownian ratchet in which stochastic motions along the bound RNA trigger ATP hydrolysis and bias the net movement in forward direction.
[1] Kainov, D. E., Tuma, R., & Mancini, E (2006) Cell. Mol. Life Sci. 63, 1095-1105.
[2]Mancini, E. J., Kainov, D. E., Grimes, J. M., Tuma, R., Bamford, D. H. & Stuart, D. I. (2004) Cell 118, 743-755.
[3] Lísal, J. & Tuma. R. (2005) J. Biol. Chem.280, 23157-64.
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| Twarock, Reidun |
| A symmetry approach to the three-dimensional structure of simple viruses |
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It has long been recognised that viral capsids are highly symmetrical, and that their protein stoichiometries can be predicted in terms of surface lattices or tilings that obey icosahedral symmetry. In this talk we address the question of whether the full three-dimensional structure of simple viruses, from the capsid area down to the genomic material, is also constrained collectively by symmetry. Using algorithms derived from a new symmetry principle we have identified unique sets of nested polyhedra that determine the material boundaries in simple viruses. We have compared the predictions derived via this approach to the three-dimensional structures, determined by a combination of X-ray crystallography and cryo-EM, of three simple RNA viruses, Pariacoto virus, bacteriophage MS2 and a recombinant Satellite Tobacco Necrosis Virus. Remarkably the vertices of the symmetry-derived polyhedra in each case appear to map the boundaries of all of the molecular components in these viruses, and constrain the allowable spatial distributions of the encapsidated matter at all radii from the capsid area down to the innermost shell of RNA. These results show that the symmetry of the outer capsid surfaces in these viruses propagates all the way down into the centre of the particles, and that they must have evolved to maximize symmetry on all levels. This implies that there are additional evolutionary constraints on the components of virus particles that have not been appreciated previously, and that have to be taken into account when modelling viral assembly.
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| van der Schoot, Paul |
| Modified zipper model for the self assembly of tobacco mosaic virus |
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Tobacco mosaic virus is a rod-like, helical virus built up from 2134 identical coat proteins wrapped around a single ss RNA molecule. The in vitro assembly of the virus involves a double-disk aggregate of coat proteins, which upon interaction with the origin-of-assembly domain of the RNA transforms into a helical (lockwasher-type) structure. This lockwasher configuration act as the nucleation site for the fast incorporation of coat proteins into the growing structure eventually to produce the complete virus. A simple model based on the so-called Zipper model for the melting of DNA explains how the nucleation event prevents the formation of substantial amounts of partially complete virus particles, in spite of the quasi one-dimensional character of the assembly process. The model also explains why degraded or otherwise incomplete RNAs do not get incorporated into non-infectuous virus particles.
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| Wales, David |
| Energy landscapes and self-assembly of icosahedral shells |
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The observed structure, dynamics and thermodynamics of any system in molecular science are determined by the underlying potential energy surface. An efficient "structure-seeker" is a molecule or collection of molecules that relaxes to a reproducible structure on a relevant experimental time scale. To achieve this behaviour the underlying potential energy surface must support a well-defined free energy minimum for the structure in question. Moreover, this minimum must be kinetically accessible. A sufficient condition for self-assembly therefore corresponds to a potential energy landscape with a single "funnel" structure. Unconstrained systems composed of rigid pentagonal and hexagonal pyramids do indeed exhibit such landscapes for a wide range of intermolecular interaction parameters.
D.J. Wales, "Energy Landscapes", Cambridge University Press (2003) D.J. Wales and T.V. Bogdan, J. Phys. Chem. B, 110, 20765-20776 (2006) D.J. Wales, Phil. Trans. Roy. Soc. A, 363, 357-377 (2005)
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| Zlotnick, Adam |
| How much do you need to know to describe virus assembly? |
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Virus capsids are assembled from 10’s to 100’s of subunits. These reactions can encompass an astronomical number of assembly intermediates and an exponentially larger number of paths. However, very simple models with a limited number of paths seem to be sufficient to describe “successful” assembly reactions that yield normal capsids. Unsuccessful reactions that are misdirected or kinetically trapped occupy a larger and potentially open-ended phase space. Computational descriptions of assembly are successful in describing many features of assembly in vitro; both successful and unsuccessful reactions. We posit that the “decision” for an unsuccessful path is made early in the reaction trajectory.
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Mathematical Virology