Mathematical Virology Viruses under the mathematical microscope: An - - PowerPoint PPT Presentation
Mathematical Virology Viruses under the mathematical microscope: An opportunity to demonstrate the impact of in the classroom mathematics in biology in the classroom environment Reidun Twarock Departments of Mathematics and Biology York
Departments of Mathematics and Biology York Cross-disciplinary Centre for Systems Analysis
Viruses under the mathematical microscope: An opportunity to demonstrate the impact of mathematics in biology in the classroom environment
in virology and find novel anti-viral solutions?
classroom?
Viruses are responsible for a wide spectrum of devastating diseases in humans animals and plants. Examples:
type 1 diabetes
Challenges:
Viral capsids are like Trojan horses, hiding the genome from the defense mechanisms of their host.
An understanding of Viral Geometry enables discovery in virology and creates new opportunities in bionanotechnology and anti-viral therapy
The icosahedron has
Caspar and Klug’s Theory of Quasiequivalence (1962): ``The local environments of all capsid proteins look similar.’’ ’’ Dots mark the positions of capsid proteins
http://agrega.educacion.es/repositorio/24052014/07/es_2014052412_9134736/poliedros_regulares.html
planar representation superposition icosahedron
Question: In how many different ways can this be done?
T=S2=(H+K/2)2+3/4K2= H2+HK+K2
Caspar and Klug (1962) predict virus architecture based only on geometrical considerations
T=4: 80 small triangles; 60T=240 proteins T counts the number of small triangles per triangular face of the icosahedron The T-number can be used to enumerate different virus structures
Chikungunya virus (T=4; H=2, K=0) Herpes Simplex virus (T=16; H=4, K=0) Rotavirus (T=13; H=3, K=1)
Large viruses look like Buckminster Fuller’s Domes
is too restrictive to capture all virus architectures
information at different radial levels The cancer-causing papilloma virus falls
Pariacoto virus
You cannot tile your bathroom with pentagons without gaps and overlaps There are no lattices with 5-fold symmetry! Sir Roger Penrose
The solution: Viral Tiling Theory
5D Lattice 2D Quasilattice 3D “Control Space” 6D Lattice 3D Quasilattice 3D “Control Space” depends on lattice type 6D - minimal embedding dimension for icosahedral symmetry
Emilio Zappa
Construct point arrays from orbits in the hyperoctahedral group B6 via projection
Classification of subgroups of B6 containing the icosahedral group as a subgroup.
Pariacoto virus
2D 3D
Develop new (affine extended) group structures and 3D tilings
Vaccine Design: Predict the structures of self-assembling protein nanoparticles Fullerenes: Model the structures of carbon onions
Adapted from Chemistryworld (June 2014)
C60 C240 C540
Sir Harald Kroto Nobel Prize in Chemistry 1996
With Peter Burkhard CEO AOPeptides (vaccine design)
Crick and Watson, 1956: The principle of genetic economy
Viruses code for a small number of building blocks that are repeatedly used to form containers with symmetry. Containers with icosahedral symmetry are largest given fixed protein size, thus viruses minimise the length of the genome required to code for a protein container of sufficient volume to fit the genome. If the position of one red disk is known, then the positions of all others are implied by symmetry.
Assemble an icosahedron from 20 triangles: 20 x
Characterise each assembly pathway by a Hamiltonian paths (a connected path visiting every vertex precisely once) on the inscribed polyhedron: 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 1 3 4 5
A board game designed by Hamilton in 1857 based on the concept of Hamiltonian circuit (cycle)
the dodecahedron that visit every vertex precisely
Viral genome Viral capsid
Viral Enigma Machine
There is an “assembly code” hidden in the viral genome (i.e. in the code for the protein components)
Hamiltonian Paths Analysis enabled a discovery Note: This is challenging via bioinformatics alone due to the sequence/structure variation of the capsid protein recognition motif.
Prevelige (2015) Follow the Yellow Brick Road: A Paradigm Shift in Virus
A paradigm shift in our understanding of virus assembly
Article by Prof Peter Stockley, Leeds – Huffington Post
Can we break the mechanism?
PS-binding drugs are distinguished by:
RNAs
Richard Bingham Eric Dykeman
reveals a drug target with high barrier to resistance. Viruses 9, 347.
Small molecular weight compounds inhibiting assembly:
Ligands binding HBV PS1 inhibit virus formation
Example: Hepatitis B virus
Can we customise the mechanism to fulfill a specific purpose?
Cooperativity can be optimised: Example: STNV RNAs with optimised initiation cassette outcompete viral particles in a ratio 2:1
Develop stable particles as vaccines and for drug/gene delivery:
Combine geometry with biophysical modelling:
Cooperative action of packaging signals enables selective and efficient genome packaging
Viruses covered by our patents (with experimental collaborators at the Universities of Leeds and Helsinki) include: Opportunities:
design & drug delivery With Prof Peter Stockley Astbury Centre for Structural Molecular Biology University of Leeds
More material is available for download from our Teacher’s Resource Pack website: www-users.york.ac.uk/~rt507/teaching_resources.html
We would be very grateful for any comments and suggestions, as this will enable us to improve our content and apply for more funding to keep this initiative going!
Our interdisciplinary approach (iterative theory-experiment cycles) has uncovered a new virus assembly paradigm.
⇒New applications:
Collaborators: Wellcome Investigator Team at the Astbury Centre in Leeds: The York team: Eric Dykeman Richard Bingham German Leonov Pierre Dechant Giuliana Indelicato Eva Weiss Conor Haydon Funding is gratefully acknowledged from:
Peter Stockley Rebecca Chandler- Bostock Leeds: Neil Ranson, Dave Rowlands, Roman Tuma, Amy Barker, Dan Maskell, Simon White (now U Conn.) Helsinki University: Sarah Butcher, Shabih Shakeel (now Cambridge) NIH: Fardokht Abulwerdi, Stuart LeGrice Imperial College: Marcus Dorner UCL: Greg Towers, Lucy Thorne Rockefeller: Paul Bieniasz London School of Hygiene and Tropical Medicine: Polly Roy Nikesh Patel