Mathematical Virology: Assembly Models for Viral Capsids based on Tiling Theory

Project: Research project (funded)Research

Project Details

Description

Objectives:
The primary objective of this proposal is the development of mathematical models for viral capsid assembly. The approach is based on the tiling model for viral capsids, that has recently been established by the PI and opens a novel approach to this topic. In particular, the tiling approach specifies a set of basic mathematical building blocks called tiles, which represent interactions between proteins in the viral capsids and are hence suitable choices for building blocks in assembly models.
In the framework of this project, which is an extension of previous joint work with the named research student and his supervisor in the framework of his
Master thesis, we expect to achieve the following results:
1. A generalisation of our prototype of capsid assembly models to more realistic scenarios and families of viruses with more complicated geometries.
2. A generalisation of our models to tubular variants.
3. A derivation of an integrated model for assembly of spherical and tubular species, and an implementation of this model to study viral malformations
under assembly. Based on this, possible strategies for an interference with the viral assembly mechanism will be discussed.
4. An investigation of an alternative model for capsid assembly (the local rules approach of Berger) from the point of view of tiling theory, and a merger
of both approaches.
This research programme may sound ambitious for a PhD programme. However, given that the named research student has already achieved publishable results on this topic during his Master thesis and is in particular very well acquainted with the background of the topic, we consider this programme suitable for the proposed time-frame.
Objectives at report time:
We completed objectives 1-3 of the proposal and published a number of papers in highly recognised international journals. In particular, we were able
to generalise our prototype capsid assembly models to more realistic scenarios (item 1, 3 papers), and we provided models for the tubular
malformations (item 2, 1 paper). Moreover, we investigated the simultaneous assembly of different types of particles (item 3, 1 paper).
Instead of item 4, which was concerned with an investigation of the relation of the tiling model and the local rules model of Berger, we chose to follow
two more exciting lines of research inspired by interactions with our experimental collaborators at the Astbury Centre for Structural Molecular Biology in
Leeds:
(1) the assembly of viruses for which the viral RNA plays a pivotal role during assembly (1 paper to be submitted shortly),
(2) a symmetry approach generalising the tiling approach and its implication on virus assembly (1 paper submitted to J Math Biol, 1 paper to be
submitted shortly to Nature in collaboration with our experimental collaborators).
These results form the basis of Thomas Keef's PHD thesis that he defended successfully in autumn 2007. He is now a postdoc in my group (for 5
years, funded by the Leverhulme Trust). We note that some of this work was featured by an article in Science News (Vol. 168, No. 10, 2005).
Thomas Keef completed his PhD four months prior to the expiry of the grant. In agreement with the EPSRC, we used the remaining four-month salary
to fund Eric Stansifer, who brought new programming expertise into the project. Eric was able to write a computer programme for the study of the
assembly kinetics of viruses for which the viral RNA plays a crucial role during assembly (e.g. bacteriophage MS2). Based on this, we could explain a
number of experimental observations on the assembly of these viruses by our collaborators at the Astbury Centre for Structural Molecular Biology in Leeds. For example, we were able to provide an explanation for the phenomenon that viruses like bacteriophage MS2 start assembly predominantly around three-fold axes of symmetry (1 paper in final stages of write up, 1 paper in progress).

Output summary:
This research programme in the area of Mathematical Virology considers mathematical models for the assembly of viral capsids, that is shell structures
formed from protein subunits that encapsulate the viral genome. Such models 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.

In this project we exploit a novel mathematical approach in which viral capsids are modeled based on tiling theory. This approach has been shown to cover all experimentally discovered viruses, especially the family of Papovaviridae. This family of viruses is of prime importance for the public health sector because it contains cancer causing viruses, but could not be treated with previous mathematical approaches before. Based on our tiling models, we develop assembly models for viral capsids and study the role of malformation during assembly. As a result of this, we expect to be able to suggest strategies for interference with viral capsid assembly.

As expected from an interdisciplinary project, all mathematical results and models will constantly be discussed with biologist experts in the field, and visits to the group of Dr Zlotnick at the Department of Biochemistry and Molecular Biology at the Health Services Center of the University of Oklahoma are planned during the course of the project.

Report time summary:
In this research programme in the area of Mathematical Virology we considered mathematical models for the assembly of viruses. Particular focus was
placed on the assembly of the protein containers that encapsulate and hence provide protection for the viral genome. Such models are of strong
interest because they constitute important milestones for the understanding of viral replication mechanisms and hence ultimately for the design of antiviral
therapeutics.
We exploited a novel mathematical approach in which viral capsids are modeled based on tiling theory. This approach predicts the locations of the
proteins in the capsids and the bonds between them, and is in particular applicable to viruses such as Polyomaviridae and Papillomaviridae (note in
comparison with the original summary: the family of Papovaviridae has recently been split into Polyomaviridae and Papillomaviridae) that fall out of the
scope of previous theories. These families of viruses are of prime importance for the public health sector because they contain cancer-causing viruses.
We were able to derive assembly models for these viruses that explain how the protein containers are formed from the individual protein building
blocks, and we provided an analysis of how a change in the association energies of the proteins (e.g. via protein engineering) may influence the
assembly behaviour. In follow-up work we were able to determine the dominant pathways of assembly, which provides important insights into how best
to inhibit assembly.

In a next step, we classified the tubular malformations with end caps in the above families, and we addressed the issue of assembly polymorphism, i.e.
the simultaneous assembly of different viral particles from the same protein building blocks. We introduced a new symmetry principle that generalises
the tiling approach, and implemented it to derive models that take the role of the viral RNA during the assembly of certain classes of RNA viruses into
account. These models led to previously inaccessible insights into the assembly pathways of these viruses. Our study of their assembly kinetics
moreover provided explanations for a number of phenomena that had been observed in experiments by our collaborators at the Astbury Centre for
Structural Molecular Biology in Leeds.

The results of this research form the basis for a larger research programme that started recently with funding from the Leverhulme Trust (a Research
Leadership Award that provides funding for a number of PostDocs and PhD students over 5 years). Among others, it exploits the new symmetry
approach that was introduced as part of the research funded by this grant, and considers its implications for virus assembly and virus evolution.
StatusFinished
Effective start/end date1/02/0531/01/08

Funding

  • EPSRC: £67,938.00