Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

Kerner, Richard

doi:10.1051/mmnp/20116608

Cited by 7 publications

(6 citation statements)

References 19 publications

(17 reference statements)

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“…Applicable models proposed for regulating capsid geometry during assembly fall under two general headings: 1) local rule models 51; 52 , where each subunit obeys abstract rules about how it can or cannot interact with its immediate neighbors in order to assemble correctly or 2) hexamer-type or hexamer-shape models 53; 54 , where a limited set of hexamer shapes can only bind to each other in specific ways to produce a capsid of a specific size. Hexamer-shape models are attractive because the smaller T numbers only require 1, 2, or 3 hexamer shapes for T numbers up to 19, but hexamer-shape models require an unspecified mechanism by which hexamer shape can be regulated.…”

Section: Discussionmentioning

confidence: 99%

Transient Contacts on the Exterior of the HK97 Procapsid That Are Essential for Capsid Assembly

Tso¹,

Hendrix²,

Duda³

2014

Journal of Molecular Biology

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The G-loop is a 10-residue glycine-rich loop that protrudes from the surface of the mature bacteriophage HK97 capsid at the C-terminal end of the long backbone helix of major capsid protein subunits. The G-loop is essential for assembly, is conserved in related capsid and encapsulin proteins, and plays its role during HK97 capsid assembly by making crucial contacts between the hill-like hexamers and pentamers in precursor proheads. These contacts are not preserved in the flattened capsomers of the mature capsid. Aspartate 231 in each of the ~400 G-loops interacts with Lysine 178 of the E-loop (Extended Loop) of a subunit on an adjacent capsomer. Mutations disrupting this interaction prevented correct assembly, and in some cases induced abnormal assembly into tubes, or small, incomplete capsids. Assembly remained defective when D231 and K178 were replaced with larger charged residues or when their positions were exchanged. Second-site suppressors of lethal mutants containing substitution D231L replaced the ionic interaction with new interactions between neutral or hydrophobic residues of about the same size: D231L/K178V, D231L/K178I, and D231L/K178N. We conclude that it is not the charge, but the size and shape of the side chains of residues 178 and 231 that are important. These two residues control the geometry of contacts between the E-loop and the G-loop, which apparently must be precisely spaced and oriented for correct assembly to occur. We present a model for how the G-loop could control HK97 assembly and identify G-loop-like protrusions in other capsid proteins that may play analogous roles.

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Section: Discussionmentioning

confidence: 99%

Transient Contacts on the Exterior of the HK97 Procapsid That Are Essential for Capsid Assembly

Tso¹,

Hendrix²,

Duda³

2014

Journal of Molecular Biology

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“…For example, the structure of the protein units 0, 2, 5, 6, and 7 can be generated by the command "capgen -c 0, 2, 5−7 -tp file1 > file2", as shown in Figure 3. The atomic coordinates in file1 are rotated with R[0], R [2], R [5], R [6], and R [7] and stored in file2. When the option -tp is omitted, the labels of rotation matrices adopted in the BIOMT lines of "file1" are used.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…Although their theory is widely used to classify virus species, the experimental structures of papovavirus capsids have been reported to be deviating from the theory and the more general viral tiling theory has been proposed . Many mathematical and theoretical studies including the tiling theory have thus been performed for the interests in the structure and energetics of icosahedrally symmetric viral capsids. − In the field of crystallography, symmetry has been used to reduce the degree of freedom and many X-ray structures have been determined. Recently, some large viral capsids, including that of HIV-I, have been shown to be not perfectly symmetric but the structures of other small icosahedrally symmetric capsids are a mine of information for viral research, including the development of effective antiviral compounds .…”

Section: Introductionmentioning

confidence: 99%

CAPLIB: A New Program Library for the Modeling and Analysis of Icosahedrally Symmetric Viral Capsids

et al. 2018

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A new program library named “CAPLIB” was developed for the modeling and analysis of icosahedrally symmetric virus capsids. CAPLIB is equipped with the mathematical data of 60 rotation matrices of icosahedral symmetry, 15 planes bisecting the entire capsid structure, and a table summarizing how the 60 asymmetric units (cells) are partitioned by the planes. CAPLIB contains the function to determine the cell numbers of atoms from the atomic positions and the function to determine the rotation axes and angles from the rotation matrices. Using CAPLIB, it is possible to generate the structure of any selected protein unit within the entire capsid by rotating a single protein unit structure. CAPLIB can classify Protein Data Bank files of capsids with the directions of rotation axes, rotate the protein structure onto the standard position, and perform various deformations of the entire capsid. The interface to the molecular graphics software, PyMOL, was also developed for efficient modeling of capsids.

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“…In education, several works have been carried out in the teaching of mathematical biology. In structural biology, Kerner (2011) addressed the combinatorics and symmetry of protein dimers to construct possible icosahedral viral capsids and developed an affinity table to establish a good taxonomy of the icosahedral viral capsid diversity system. His method helps students answer questions about the susceptibility of configuration changes to mutation and understand which viral capsids may be evolutionarily closer.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Biology in High School Mathematics Education

Beqqali,

Hattaf,

Achtaich

2023

JESR

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Mathematical biology has made great progress in recent years, particularly in epidemiology during or even before the COVID-19 pandemic. Mathematical modeling has played a key role in this progress. In this paper, we examine whether the teaching and learning of mathematics in Moroccan high school takes into consideration specialty disciplines such as biology. To do this, we are looking for the applications of biology in the Moroccan mathematical programs in the second year of the baccalaureate option life and earth sciences. First, we analyze the pedagogical guidelines concerning mathematical applications in specialty disciplines. In addition, we analyze the textbooks concerning the second year of baccalaureate option life and earth sciences. The results show that mathematical applications in experimental sciences, especially in biology, for the mathematics program of the second year of the baccalaureate are still very limited in the Moroccan curriculum, whether in learning activities or exercises. Received: 21 September 2023 / Accepted: 20 October 2023 / Published: 5 November 2023

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Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

Cited by 7 publications

References 19 publications

Transient Contacts on the Exterior of the HK97 Procapsid That Are Essential for Capsid Assembly

Transient Contacts on the Exterior of the HK97 Procapsid That Are Essential for Capsid Assembly

CAPLIB: A New Program Library for the Modeling and Analysis of Icosahedrally Symmetric Viral Capsids

Mathematical Biology in High School Mathematics Education

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