Curating viscoelastic properties of icosahedral viruses, virus-based nanomaterials, and protein cages

Abstract

The beauty, symmetry, and functionality of icosahedral virus capsids has attracted the attention of biologists, physicists, and mathematicians ever since they were first observed. Viruses and protein cages assemble into functional architectures in a range of sizes, shapes, and symmetries. To fulfill their biological roles, these structures must self-assemble, resist stress, and are often dynamic. The increasing use of icosahedral capsids and cages in materials science has driven the need to quantify them in terms of structural properties such as rigidity, stiffness, and viscoelasticity. In this study, we employed Quartz Crystal Microbalance with Dissipation technology (QCM-D) to characterize and compare the mechanical rigidity of different protein cages and viruses. We attempted to unveil the relationships between rigidity, radius, shell thickness, and triangulation number. We show that the rigidity and triangulation numbers are inversely related to each other and the comparison of rigidity and radius also follows the same trend. Our results suggest that subunit orientation, protein-protein interactions, and protein-nucleic acid interactions are important for the resistance to deformation of these complexes, however, the relationships are complex and need to be explored further. The QCM-D based viscoelastic measurements presented here help us elucidate these relationships and show the future prospect of this technique in the field of physical virology and nano-biotechnology.

Keywords: Icosahedral; Protein cage; QCMD; Virus; Viscoelastic.

Fig. 1

T-number determination and virus and protein cage library. a Flat hexameric sheet showing the positions of h and k and their progression. h and k meet at an angle of 60° and are positive integers. b Replacing one of the hexameric units with a pentameric unit results in the introduction of curvature and formation of a convex pentamer (colored subunits in viruses). An example of such replacement (quasi-equivalence) is shown for a T = 3 capsid. c Fully assembled protein cages and viruses of radii ranging from ~5 to ~90 nm used in this study (shown to scale)

Fig. 2

Rigidity vs. T-number. Rigidity and T-number plotted for each virus tested. Rigidities decrease with increase in T-number with CCMV samples being the exceptions. Protein cages were not included due to the lack of an assigned T-number

Fig. 3

Rigidity vs. radius. Rigidity and radius of each sample were plotted for each sample type. With an increase in the radius, the rigidity decreased. Two extensively modified CCMV capsids were also included. Rigidity, T-number, and radius values of all samples are included in Table 1

Fig. 4

a Rigidity vs. radius. A plot of rigidity vs. radius revealed a strong exponential trend. The points were fit to a single exponential. b Rigidity vs. shell thickness. A plot of rigidity vs. shell thickness revealed a weak exponential trend. The dotted line shows a single exponential fit to the data

Fig. 5

Rigidity vs. (R/d)²