Peplomer bulb shape and coronavirus rotational diffusivity

Abstract

Recently, the rotational diffusivity of the coronavirus particle in suspension was calculated, from first principles, using general rigid bead-rod theory [M. A. Kanso, Phys. Fluids 32, 113101 (2020)]. We did so by beading the capsid and then also by replacing each of its bulbous spikes with a single bead. However, each coronavirus spike is a glycoprotein trimer, and each spike bulb is triangular. In this work, we replace each bulbous coronavirus spike with a bead triplet, where each bead of the triplet is charged identically. This paper, thus, explores the role of bulb triangularity on the rotational diffusivity, an effect not previously considered. We thus use energy minimization for the spreading of triangular bulbs over the spherical capsid. The latter both translates and twists the coronavirus spikes relative to one another, and we then next arrive at the rotational diffusivity of the coronavirus particle in suspension, from first principles. We learn that the triangularity of the coronavirus spike bulb decreases its rotational diffusivity. For a typical peplomer population of 74, bulb triangularity decreases the rotational diffusivity by $39\%$ .

FIG 1.

General rigid bead-rod model of single beaded coronavirus, $N_c=256$, $N_p=74$ (row 1 of Table III).

FIG. 2.

This paper explores the role of bulb triangularity (three blue circles) on the rotational diffusivity. This improves upon the previously considered singly beaded bulb (black circle). Bulb-end view of trimeric SARS-CoV peplomer (generated using 6CRZ.PDB data available from Ref. 15).

FIG. 3.

General rigid bead-rod model of three beads peplomer head.

FIG. 4.

General rigid bead-rod model of triple beaded coronavirus, $N_c=256$, $N_p=74$ (row 2 of Table III).

FIG. 5.

Dimensionless rotational diffusivity ${\lambda }_0{D}_r$ from Eq. (3) vs peplomer population $N_p$ ( $N_c=256$): single (red) and triple beading (blue) corresponds to, respectively, rows 1 and 2 of Table III.

FIG. 6.

Effect of single (red) and triple beading (blue) on minus the imaginary part of the complex viscosity ( $N_c=256$, $N_p=74$ corresponds to, respectively, rows 1 and 2 of Table III). The polymer contribution $\left(\eta \prime -{\eta }_s\right)/\mathit{nkT}\lambda$ is nearly constant: $\left({\eta }_0-{\eta }_s\right)/\mathit{nkT}\lambda =3/2$.