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• Viruses
• Symmetry
• Triangulation number
• Viral folds
• Size matters
• Breaking the symmetry
Icosahedral structures
Workshop	
Single-Particle	Cryo-EM	and	Tomography
University	of	Otagomihnea.bostina@otago.ac.nz
Viruses played essential roles in EM history
- First EM images
bacteriophage and E. coli
- First 3D reconstruction
bacteriophage T4 tail, 1968
- First secondary structure elements
hepatitis B virus, 1997
- First atomic models
aquareovirus, adenovirus, 2010
Ruska et al, 1940
DeRosier and Klug, 1968
Symmetry is cheap
Use a small amount of genetic information
to construct large structures
http://www.rcsb.org/p
Symmetry is useful
More signal to align – better CC
Less parameters to search for – faster computation
Good Euler coverage (for complex symmetry)
http://www.rcsb.org/p
Quarterly Reviews of Biophysics 41, 2 (2008),
Symmetry:
cyclic (Cn), dihedral (Dn), tetrahedral (T),
octahedral (O), icosahedral (I)
Viral morphologies
http://www.nlv.ch/Virologytutorials/Classification.htm
RNA & DNA
Capsid & Membrane
Icosahedral & Helical
Spikes, Fibers, Tail, etc
Building a capsid from identical proteins
A ratio of 3 nucleotides for one amino acid à the size of the viral genome is
insufficient to code for a large number of non-identical subunits.
The viral shell must consist of few protein subunits, repeated several times.
à many identical copies surround the genome.
à regular polyhedra
à Caspar – icosahedral symmetry TSBV (1956)
à 1962, Caspar and Klug : identical subunits able to adapt to slightly different
environments
Quasi-equivalence
• subunits in the icosahedral shell have similar bonding interactions
with minor distortions in order to adapt to the nonsymmetry-related
environments
Physical Principles in the Construction of Regular Viruses” (Casper & Klug, 1962)
Building a structure from identical proteins
Wikipedia.com
Buckminster Fuller dome
Montreal, 1967
Quasi-equivalence
• Conformational Switching – flexible arms as molecular switches
à subunits adapt to quasi-equivalent (the capsid protein remains
structurally invariant)
Triangulation number
T = h2 + k2 + hk
M
Triangulation number
• The are only certain possible values for T
• The T-number suggests the size of the capsid.
T = h2 + k2 + hk
Adv Exp Med Biol. 2012;726:17-47. doi:10.1007/978-1-4614-0980-9_3.
Principles of virus structural organization.
Icosahedral capsids
Microbiol Mol Biol Rev. 1999; 63(4):862-922
assembly
protection
host recognition
genome uncoating
Tomato bushy stunt virus (TBSV)
First virus capsid solved (Steve Harrison, 1978)
Jelly-roll domain responsible for capsid interactions
Poliovirus and Rhinovirus
First animal virus capsids (Hogle 1985; Rossmann 1985)
Four capsid proteins with similar fold : VP1, VP2, VP3 and (VP4)
The same jelly-roll fold responsible for capsid interactions
Capsid protein folds: HK97
• Prototype for bacteriophage MCP
• Common for all tailed bacteriophages
• Conformational changes occurs during the maturation of the capsid
Wikoff et al, Science 2000
Capsid protein folds: HK97
• Common for all tailed of bacteriophages and HSV
Yuan et al, Science 2018
Wikoff et al, Science 2000
Quasi-equivalence
• The same protein can adopt many different conformations
Yuan et al, Science 2018
• Variants of HK97 folds are found in phage capsid
• They can form capsids with different triangulation numbers numbers
Bacteriophage – capsid
Microbiol Mol Biol Rev. 2011 75(3):423-33
Capsid protein folds
• Structure-based phylogenetic tree – four different lineages detected by
structural comparison of viral capsid protein
• The defining feature of a virus is its protein capsid (viral self).
• The structure is more persistent than its genome or protein sequences.
Annu Rev	Biochem.	2012;	81:795-822.	doi:	10.1146/annurev-biochem-060910-095130.	
Structure	unifies	the	viral	universe.
VIRUSES
are faced with
a challenge:
their genomes
need to encode all
of their proteins, but
at the same time, these
genomes need to fit into the
tiny space of a viral capsid.
When the first 3D structures of
spherical viruses were determined
experimentally, researchers discovered
this challenge is solved using a modular
approach: many identical copies of a small
protein subunit are assembled to form a
large spherical capsid. The smallest viruses
build perfectly symmetrical capsids consisting of
60 copies of a single, small protein, providing enough
internal space to hold a tiny genome that encodes only
a handful of proteins. Other viruses use one or more types
of proteins in quasisymmetrical arrangements to build even
larger capsids that enclose larger and more complex genomes.
The coloring scheme highlights the
NUMBER OF PROTEIN CHAINS in each capsid:
960-828090084078048042036030024018012060
Learn more about how these proteins form symmetrical and
quasisymmetrical capsids at PDB-101 (pdb101.rcsb.org)
Explore these viruses in 3D
at RCSB PDB (rcsb.org)
SCALE:
100 nm
100 Å
0
200ICOSAHEDRAL
VIRUSES
FROM THE
PDB
Icosahedral structures
• Large structures – good contrast (+)
• More thon rings from a particle than from a full micrograph
• Thickness (-)
• Local flexibility (-)
3000	Å
Large dsDNA viruses
• Relationship between genome and capsid size
(Yan et	al.,	2009)
(Zhang	et	al.,	2011)
(Yan et	al.,	2005)
Okamoto et	al,	2018)
(Klose	et	al.,	2016)
(Xiao	et	al.,	2017)
(Xiao	et	al.,	2009)
WIV,	CIV
PBCV-1
PpV01
FaustoV
CroV
Mimivirus
T7
phiKZ
MelV
0
200
400
600
800
1000
1200
0 1000 2000 3000 4000 5000
Sample thickness
Zhu	et	al,	Nat	Comm 2019
• Differences in particle defocus between the upper and lower regions
• Resolution limited at worst than 4Å
Sample thickness
Zhu	et	al,	Nat	Comm 2019
• Differences in particle defocus between the upper and lower regions
• Resolution limited at worst than 4Å
• Solution: reconstruct (refine) by using regions of particle for which
coordinates and defocus are known
Viral architectures: PBCV1
Fang	et	al,	Nat	Com	2019
Viral architectures: NCLDV
Architectural modules may not be symmetrical modules
Okamoto	et	al,	2018
Viral architectures: Mimivirus
PLoS	Biol.	2009	;7(4):e92
Structural	studies	of	the	giant	mimivirus.
• Fiber coated capsid ~750 nm
• Icosahedral T>1000
• dsDNA genome1.2 Mbp and >900 genes
• starfish-shaped feature vertex
• ‘Giruses’ (giant viruses) >250nm and >350 geness
Breaking the symmetry
• Symmetry mismatches are essential for molecular function
• Portal proteins,
• Decoration proteins, fibers, etc
• Many structures are not entirely symmetrical
• Genome structure
• Asymmetric conformational changes
• Most processes are not symmetrical
• Genome uncoating
• Incomplete binding (receptors, antibodies, etc)
Breaking the symmetry
Calicivirus VP2	forms	a	portal-like	
assembly	following	receptor	engagement		
(Conley	et	al.	Nature,	2019)		
In	situ	structures	of	the	genome	and	genome-delivery	
apparatus	in	a	single-stranded	RNA	virus	
(Dau et	al.	Nature,	2017)		
Novacek et	al,	PNAS,	2016	
Breaking the symmetry
Breaking the symmetry: tomography
Bostina et al, 2011
Peralta et al, 2013
Huet al, 2013
Okamoto et al, 2018
Dent et al, 2013
Dai et al, 2013
• standard asymmetric reconstruction (SAR)
• sub-particle based localized reconstruction methods (localRec)
• symmetry relaxation methods (SymRelax)
• symmetry expansion combined with focused classification
(SymExpand/FocusedClass)
Bioscience Reports (2018) 38 BSR20170203 https://doi.org/10.1042/BSR20170203
Breaking the symmetry: single particle reconstruction
Zhang et al. Nature 2015
Standard asymmetric reconstruction (SAR)
• Conventional single particle refinement
• Use an icosahedral structure as initial model
Koning et al. Nat Comm 2015
Liu et al. Science 2015
Symmetry relaxation methods (SymRelax)
• Calculate an icosahedral reconstruction
• Check all symmetry equivalent positions
• Calculate asymmetric reconstruction
Sub-particle based localized reconstruction
methods (localRec)
• Calculate an icosahedral reconstruction
• Localize regions of interest (receptor, fibres, etc)
• Subtract icosahedral signal (optional)
• Re-box the region of interest
• Reconstruct
• Classify
• Refine (with constraints)
Sub-particle based localized reconstruction
methods (localRec)
• Calculate an icosahedral reconstruction
• Localize regions of interest (receptor, fibres, etc)
• Subtract icosahedral signal (optional)
• Re-box the region of interest
• Reconstruct
• Classify
• Refine (with constraints)
Ilca et al, Nat Comm 2015
Sub-particle based localized reconstruction
methods (localRec)
• Calculate an icosahedral reconstruction
• Localize regions of interest (receptor, fibres, etc)
• Subtract icosahedral signal (optional)
• Re-box the region of interest
• Reconstruct
• Classify
• Refine (with constraints)
Kotecha et al, Nat Comm 2017
Summary :
Icosahedral structures
• High molecular weight
• Good contrast
• High complexity
• Various degree of flexibility
• Computational cost
• Defocus variation
• Local asymmetry

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Mb viruses

  • 1. • Viruses • Symmetry • Triangulation number • Viral folds • Size matters • Breaking the symmetry Icosahedral structures Workshop Single-Particle Cryo-EM and Tomography University of Otagomihnea.bostina@otago.ac.nz
  • 2. Viruses played essential roles in EM history - First EM images bacteriophage and E. coli - First 3D reconstruction bacteriophage T4 tail, 1968 - First secondary structure elements hepatitis B virus, 1997 - First atomic models aquareovirus, adenovirus, 2010 Ruska et al, 1940 DeRosier and Klug, 1968
  • 3. Symmetry is cheap Use a small amount of genetic information to construct large structures http://www.rcsb.org/p
  • 4. Symmetry is useful More signal to align – better CC Less parameters to search for – faster computation Good Euler coverage (for complex symmetry) http://www.rcsb.org/p
  • 5. Quarterly Reviews of Biophysics 41, 2 (2008), Symmetry: cyclic (Cn), dihedral (Dn), tetrahedral (T), octahedral (O), icosahedral (I)
  • 6. Viral morphologies http://www.nlv.ch/Virologytutorials/Classification.htm RNA & DNA Capsid & Membrane Icosahedral & Helical Spikes, Fibers, Tail, etc
  • 7.
  • 8. Building a capsid from identical proteins A ratio of 3 nucleotides for one amino acid à the size of the viral genome is insufficient to code for a large number of non-identical subunits. The viral shell must consist of few protein subunits, repeated several times. à many identical copies surround the genome. à regular polyhedra à Caspar – icosahedral symmetry TSBV (1956) à 1962, Caspar and Klug : identical subunits able to adapt to slightly different environments
  • 9.
  • 10. Quasi-equivalence • subunits in the icosahedral shell have similar bonding interactions with minor distortions in order to adapt to the nonsymmetry-related environments Physical Principles in the Construction of Regular Viruses” (Casper & Klug, 1962)
  • 11. Building a structure from identical proteins Wikipedia.com Buckminster Fuller dome Montreal, 1967
  • 12. Quasi-equivalence • Conformational Switching – flexible arms as molecular switches à subunits adapt to quasi-equivalent (the capsid protein remains structurally invariant)
  • 13. Triangulation number T = h2 + k2 + hk M
  • 14. Triangulation number • The are only certain possible values for T • The T-number suggests the size of the capsid. T = h2 + k2 + hk Adv Exp Med Biol. 2012;726:17-47. doi:10.1007/978-1-4614-0980-9_3. Principles of virus structural organization.
  • 15. Icosahedral capsids Microbiol Mol Biol Rev. 1999; 63(4):862-922 assembly protection host recognition genome uncoating
  • 16. Tomato bushy stunt virus (TBSV) First virus capsid solved (Steve Harrison, 1978) Jelly-roll domain responsible for capsid interactions
  • 17. Poliovirus and Rhinovirus First animal virus capsids (Hogle 1985; Rossmann 1985) Four capsid proteins with similar fold : VP1, VP2, VP3 and (VP4) The same jelly-roll fold responsible for capsid interactions
  • 18. Capsid protein folds: HK97 • Prototype for bacteriophage MCP • Common for all tailed bacteriophages • Conformational changes occurs during the maturation of the capsid Wikoff et al, Science 2000
  • 19. Capsid protein folds: HK97 • Common for all tailed of bacteriophages and HSV Yuan et al, Science 2018 Wikoff et al, Science 2000
  • 20. Quasi-equivalence • The same protein can adopt many different conformations Yuan et al, Science 2018
  • 21. • Variants of HK97 folds are found in phage capsid • They can form capsids with different triangulation numbers numbers Bacteriophage – capsid Microbiol Mol Biol Rev. 2011 75(3):423-33
  • 22. Capsid protein folds • Structure-based phylogenetic tree – four different lineages detected by structural comparison of viral capsid protein • The defining feature of a virus is its protein capsid (viral self). • The structure is more persistent than its genome or protein sequences. Annu Rev Biochem. 2012; 81:795-822. doi: 10.1146/annurev-biochem-060910-095130. Structure unifies the viral universe.
  • 23. VIRUSES are faced with a challenge: their genomes need to encode all of their proteins, but at the same time, these genomes need to fit into the tiny space of a viral capsid. When the first 3D structures of spherical viruses were determined experimentally, researchers discovered this challenge is solved using a modular approach: many identical copies of a small protein subunit are assembled to form a large spherical capsid. The smallest viruses build perfectly symmetrical capsids consisting of 60 copies of a single, small protein, providing enough internal space to hold a tiny genome that encodes only a handful of proteins. Other viruses use one or more types of proteins in quasisymmetrical arrangements to build even larger capsids that enclose larger and more complex genomes. The coloring scheme highlights the NUMBER OF PROTEIN CHAINS in each capsid: 960-828090084078048042036030024018012060 Learn more about how these proteins form symmetrical and quasisymmetrical capsids at PDB-101 (pdb101.rcsb.org) Explore these viruses in 3D at RCSB PDB (rcsb.org) SCALE: 100 nm 100 Å 0 200ICOSAHEDRAL VIRUSES FROM THE PDB
  • 24. Icosahedral structures • Large structures – good contrast (+) • More thon rings from a particle than from a full micrograph • Thickness (-) • Local flexibility (-) 3000 Å
  • 25. Large dsDNA viruses • Relationship between genome and capsid size (Yan et al., 2009) (Zhang et al., 2011) (Yan et al., 2005) Okamoto et al, 2018) (Klose et al., 2016) (Xiao et al., 2017) (Xiao et al., 2009) WIV, CIV PBCV-1 PpV01 FaustoV CroV Mimivirus T7 phiKZ MelV 0 200 400 600 800 1000 1200 0 1000 2000 3000 4000 5000
  • 26. Sample thickness Zhu et al, Nat Comm 2019 • Differences in particle defocus between the upper and lower regions • Resolution limited at worst than 4Å
  • 27. Sample thickness Zhu et al, Nat Comm 2019 • Differences in particle defocus between the upper and lower regions • Resolution limited at worst than 4Å • Solution: reconstruct (refine) by using regions of particle for which coordinates and defocus are known
  • 29. Viral architectures: NCLDV Architectural modules may not be symmetrical modules Okamoto et al, 2018
  • 30. Viral architectures: Mimivirus PLoS Biol. 2009 ;7(4):e92 Structural studies of the giant mimivirus. • Fiber coated capsid ~750 nm • Icosahedral T>1000 • dsDNA genome1.2 Mbp and >900 genes • starfish-shaped feature vertex • ‘Giruses’ (giant viruses) >250nm and >350 geness
  • 32. • Symmetry mismatches are essential for molecular function • Portal proteins, • Decoration proteins, fibers, etc • Many structures are not entirely symmetrical • Genome structure • Asymmetric conformational changes • Most processes are not symmetrical • Genome uncoating • Incomplete binding (receptors, antibodies, etc) Breaking the symmetry
  • 34. Breaking the symmetry: tomography Bostina et al, 2011 Peralta et al, 2013 Huet al, 2013 Okamoto et al, 2018 Dent et al, 2013 Dai et al, 2013
  • 35. • standard asymmetric reconstruction (SAR) • sub-particle based localized reconstruction methods (localRec) • symmetry relaxation methods (SymRelax) • symmetry expansion combined with focused classification (SymExpand/FocusedClass) Bioscience Reports (2018) 38 BSR20170203 https://doi.org/10.1042/BSR20170203 Breaking the symmetry: single particle reconstruction
  • 36. Zhang et al. Nature 2015 Standard asymmetric reconstruction (SAR) • Conventional single particle refinement • Use an icosahedral structure as initial model Koning et al. Nat Comm 2015
  • 37. Liu et al. Science 2015 Symmetry relaxation methods (SymRelax) • Calculate an icosahedral reconstruction • Check all symmetry equivalent positions • Calculate asymmetric reconstruction
  • 38. Sub-particle based localized reconstruction methods (localRec) • Calculate an icosahedral reconstruction • Localize regions of interest (receptor, fibres, etc) • Subtract icosahedral signal (optional) • Re-box the region of interest • Reconstruct • Classify • Refine (with constraints)
  • 39. Sub-particle based localized reconstruction methods (localRec) • Calculate an icosahedral reconstruction • Localize regions of interest (receptor, fibres, etc) • Subtract icosahedral signal (optional) • Re-box the region of interest • Reconstruct • Classify • Refine (with constraints) Ilca et al, Nat Comm 2015
  • 40. Sub-particle based localized reconstruction methods (localRec) • Calculate an icosahedral reconstruction • Localize regions of interest (receptor, fibres, etc) • Subtract icosahedral signal (optional) • Re-box the region of interest • Reconstruct • Classify • Refine (with constraints) Kotecha et al, Nat Comm 2017
  • 41. Summary : Icosahedral structures • High molecular weight • Good contrast • High complexity • Various degree of flexibility • Computational cost • Defocus variation • Local asymmetry