Recent advancements in viral hydrodynamics afford the calculation of the transport properties of particle suspensions from first principles, namely, from the detailed particle shapes. For coronavirus suspensions, for example, the shape can be approximated by beading (i) the spherical capsid and (ii) the radially protruding peplomers. The general rigid bead-rod theory allows us to assign Stokesian hydrodynamics to each bead. Thus, viral hydrodynamics yields the suspension rotational diffusivity, but not without first arriving at a configuration for the cationic peplomers. Prior work considered identical peplomers charged identically. However, a recent pioneering experiment uncovers remarkable peplomer size and charge heterogeneities. In this work, we use energy minimization to arrange the spikes, charged heterogeneously to obtain the coronavirus spike configuration required for its viral hydrodynamics. For this, we use the measured charge heterogeneity. We consider 20 000 randomly generated possibilities for cationic peplomers with formal charges ranging from 30 to 55. We find the configurations from energy minimization of all of these possibilities to be nearly spherically symmetric, all slightly oblate, and we report the corresponding breadth of the dimensionless rotational diffusivity, the transport property around which coronavirus cell attachment revolves.

1.
M. A.
Kanso
,
J. H.
Piette
,
J. A.
Hanna
, and
A. J.
Giacomin
, “
Coronavirus rotational diffusivity
,”
Phys. Fluids
32
(
11
),
113101
(
2020
); Feature article, cover article.
2.
M. A.
Kanso
,
V.
Chaurasia
,
E.
Fried
, and
A. J.
Giacomin
, “
Peplomer bulb shape and coronavirus rotational diffusivity
,”
Phys. Fluids
33
(
3
),
033115
(
2021
); Part2, Editor's Pick.
3.
M. A.
Kanso
,
M.
Naime
,
V.
Chaurasia
,
K.
Tontiwattanakul
,
E.
Fried
, and
A. J.
Giacomin
, “
Coronavirus pleomorphism
,”
Phys. Fluids
34
(
6
),
063101
(
2022
); Part 1, Feature article, Scilight. Errata: In Table III, rows 1–4 of columns 2–5 and 10 should be divided by k, and of columns 7 and 11, by k−1, where k = 522. In FIG. 11, the ordinate should be divided by k−1. In Fig. 7, the ordinate and abscissa should be divided by k.
4.
M. A.
Kanso
, “
Coronavirus hydrodynamics
,” Ph.D. thesis (
Polymers Research Group, Chemical Engineering Department, Queen's University
,
Kingston, ON, Canada
,
2022
).
5.
N.
Moreno
,
D.
Moreno-Chaparro
,
F. B.
Usabiaga
, and
M.
Ellero
, “
Hydrodynamics of spike proteins dictate a transport-affinity competition for SARS-CoV-2 and other enveloped viruses
,”
Sci. Rep.
12
,
11080
(
2022
).
6.
M. A.
Kanso
and
A. J.
Giacomin
, “
General rigid bead-rod macromolecular theory
,” in
Recent Advances in Rheology: Theory, Biorheology, Suspension and Interfacial Rheology
,
1st ed.
, edited by
D.
De Kee
and
A.
Ramachandran
(
AIP Publishing
,
Melville, NY
,
2022
), Chap. 2, pp.
2-1
2-32
; Errata: Below Eq. (2.78), “…increases with N” should be “…increases with N3.” Above Eq. (2.80), “(77)” should be “(2.77).”
7.
M. A.
Kanso
,
A. J.
Giacomin
,
C.
Saengow
, and
J. H.
Piette
, “
Macromolecular architecture and complex viscosity
,”
Phys. Fluids
31
(
8
),
087107
(
2019
); Editor's pick. Errata: In the caption of Fig. 1., “(rightmost)” should be “(leftmost),” and “(leftmost)” should be “(rightmost).”
8.
R. B.
Bird
,
C. F.
Curtiss
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids
,
2nd ed
. (
Wiley
,
New York
,
1987
), Vol.
2
; Errata: In Table 16.4–1, under entry “length of rod”should be “bead center to center length of a rigid dumbbell.”
9.
R. B. Bird, O. Hassager, R. C. Armstrong, and C. F. Curtiss, Dynamics of Polymeric Liquids, 1st ed. (John Wiley and Sons Inc., New York, 1977), Vol. 2; Errata: In Problem 11.C.1 d., “and φ2” should be “through φ4”; in Eq. 13.6–17, “Rν1” should be “Rν2.”
10.
P.
Moscato
,
M. N.
Haque
, and
A.
Moscato
, “
Continued fractions and the Thomson problem
” Research Square (published online 2022).
11.
Y.
Yang
,
D. G.
Ivanov
, and
I. A.
Kaltashov
, “
The challenge of structural heterogeneity in the native mass spectrometry studies of the SARS-CoV-2 spike protein interactions with its host cell-surface receptor
,”
Anal. Bioanal. Chem.
413
(
29
),
7205
7214
(
2021
).
12.
V.
Chaurasia
,
Y.-C.
Chen
, and
E.
Fried
, “
Interacting charged elastic loops on a sphere
,”
J. Mech. Phys. Solids
134
,
103771
(
2020
).
13.
V.
Chaurasia
, “
Variational formulation of charged curves constrained to a sphere
,” Ph.D. thesis (
Department of Mechanical Engineering, University of Houston
,
Houston, TX
,
2018
).
14.
L. M.
Miller
,
L. F.
Barnes
,
S. A.
Raab
,
B. E.
Draper
,
T. J.
El-Baba
,
C. A.
Lutomski
,
C. V.
Robinson
,
D. E.
Clemmer
, and
M. F.
Jarrold
, “
Heterogeneity of glycan processing on trimeric SARS-CoV-2 spike protein revealed by charge detection mass spectrometry
,”
J. Am. Chem. Soc.
143
(
10
),
3959
3966
(
2021
).
15.
M. C.
Pak
,
K.-I.
Kim
,
M. A.
Kanso
, and
A. J.
Giacomin
, “
General rigid bead-rod theory with hydrodynamic interaction for polymer viscoelasticity
,”
Phys. Fluids
34
(
2
),
023106
(
2022
); Part 1.
16.
M. A.
Kanso
,
M. C.
Pak
,
K.
Kwang-Il
,
S. J.
Coombs
, and
A. J.
Giacomin
, “
Hydrodynamic interaction and complex viscosity of multi-bead rods
,”
Phys. Fluids
34
(
4
),
043102
(
2022
); Part 1, Editor's Pick.
17.
M. C.
Pak
,
R.
Chakraborty
,
M. A.
Kanso
,
K.
Tontiwattanakul
,
K.
Kwang-Il
, and
A. J.
Giacomin
, “
Coronavirus peplomer interaction
,”
Phys. Fluids
34
,
113109
(
2022
); Part 1, Editor's Pick.
18.
Y.
Xie
,
W.
Guo
,
A.
Lopez-Hernadez
,
S.
Teng
, and
L.
Li
, “
The pH effects on SARS-CoV and SARS-CoV-2 spike proteins in the process of binding to hACE2
,”
Pathogens
11
(
2
),
238
(
2022
).
19.
O.
Hassager
, “
On the kinetic theory and rheology of multibead models for macromolecules
,” Ph.D. thesis (
Chemical Engineering Department, University of Wisconsin
,
Madison, WI
,
1973
).
20.
O.
Hassager
, “
Kinetic theory and rheology of bead–rod models for macromolecular solutions. II. Linear unsteady flow properties
,”
J. Chem. Phys.
60
(
10
),
4001
4008
(
1974
); Erratum: In Eq. (2), “1/2’ should be “−1/2” and “⪡” should be “⪢.”
21.
W. E.
Stewart
and
J. P.
Sørensen
, “
Hydrodynamic interaction effects in rigid dumbbell suspensions. II. Computations for steady shear flow
,”
Trans. Soc. Rheol.
16
(
1
),
1
13
(
1972
).
22.
J. H.
Piette
,
L. M.
Jbara
,
C.
Saengow
, and
A. J.
Giacomin
, “
Exact coefficients for rigid dumbbell suspensions for steady shear flow material function expansions
,”
Phys. Fluids
31
(2),
021212
(
2019
); Erratum: Above Eq. (83), “one other” should be “one other use.”
23.
R.
Chakraborty
,
D.
Singhal
,
M. A.
Kanso
, and
A. J.
Giacomin
, “
Macromolecular complex viscosity from space-filling equilibrium structure
,”
Phys. Fluids
34
(
9
),
093109
(
2022
); Part 1.
24.
M. A.
Kanso
, “
Polymeric liquid behavior in oscillatory shear flow
,” Master's thesis (
Polymers Research Group, Chemical Engineering Department, Queen's University
,
Kingston, ON, Canada
,
2019
).
25.
R. B.
Bird
and
A. J.
Giacomin
, “
Who conceived the complex viscosity?
,”
Rheol. Acta
51
(
6
),
481
486
(
2012
).
26.
A. J.
Giacomin
and
R. B.
Bird
, “
Erratum: Official nomenclature of the society of rheology:
η ,”
J. Rheol.
55
(
4
),
921
923
(
2011
).
27.
J. D.
Ferry
,
Viscoelastic Properties of Polymers
,
3rd ed
. (
Wiley
,
New York
,
1980
).
28.
R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 1st ed. (Wiley, New York, 1977), Vol. 1.
29.
J.
Guven
and
P.
Vázquez-Montejo
, “
Confinement of semiflexible polymers
,”
Phys. Rev. E
85
(
2
),
026603
(
2012
).
30.
J.
Guven
,
D. M.
Valencia
, and
P.
Vázquez-Montejo
, “
Environmental bias and elastic curves on surfaces
,”
J. Phys. A
47
(
35
),
355201
(
2014
).
31.
I. B.
Bischofs
,
S. S.
Schmidt
, and
U. S.
Schwarz
, “
Effect of adhesion geometry and rigidity on cellular force distributions
,”
Phys. Rev. Lett.
103
(
4
),
048101
(
2009
).
32.
J. J.
Thomson
, “
XXIV. On the structure of the atom: An investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; With application of the results to the theory of atomic structure
,”
London, Edinburgh, Dublin Philos. Mag. J. Sci.
7
(
39
),
237
265
(
1904
).
33.
D. J.
Wales
and
S.
Ulker
, “
Structure and dynamics of spherical crystals characterized for the Thomson problem
,”
Phys. Rev. B
74
(
21
),
212101
(
2006
).
34.
D. J.
Wales
,
H.
McKay
, and
E. L.
Altschuler
, “
Defect motifs for spherical topologies
,”
Phys. Rev. B
79
(
22
),
224115
(
2009
).
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