Approximation of virus structure by icosahedral tilings

Area of Science:

• Structural Biology
• Nanotechnology
• Computational Biology

Background:

• Viruses exhibit nanoscale order, primarily through icosahedral symmetry in their protein shells (capsids).
• Previous work utilized lattice theory for viral organization blueprints.
• Icosahedral symmetry is non-crystallographic in 3D, necessitating alternative modeling approaches.

Purpose of the Study:

• To develop an alternative approach to modeling viral capsids using icosahedral tilings.
• To approximate viral capsid geometry using 3D quasicrystal construction methods.
• To assess the applicability of icosahedral tilings for describing capsid surface features.

Main Methods:

• A numerical procedure was developed to approximate icosahedral virus capsids with icosahedral tiles.
• The method projects high-dimensional tiles using a cut-and-project scheme.
• Goodness of fit was assessed using polygonal approximation of curves theory.

Main Results:

• The icosahedral tiling approach successfully approximates viral capsid geometry.
• Detailed capsid surface features are satisfactorily described by these tilings.
• The method complements existing models based on icosahedral group extensions.

Conclusions:

• Icosahedral tilings provide a viable coarse-grained model for viral capsids.
• These models can aid in studying virus assembly and structural transitions.
• The approach offers new insights for designing protein containers in nanotechnology.