Finite element modeling of α-helices and tropocollagen molecules referring to spike of SARS-CoV-2.

The newly developed finite element (FE) modeling at the atomic scale was used to predict the static and dynamic response of the α-helix (AH) and tropocollagen (TC) protein fragments, the main building blocks of the spike of the SARS-CoV-2. The geometry and morphology of the spike's stalk and its connection to the viral envelope were determined from the combination of most recent molecular dynamics (MD) simulation and images of cryoelectron microscopy. The stiffness parameters of the covalent bonds in the main chain of the helix were taken from the literature. The AH and TC were modeled using both beam elements (wire model) and shell elements (ribbon model) in FE analysis to predict their mechanical properties under tension. The asymptotic stiffening features of AH and TC under tensile loading were revealed and compared with a new analytical solution. The mechanical stiffnesses under other loading conditions, including compression, torsion, and bending, were also predicted numerically and correlated with the results of the existing MD simulations and tests. The mode shapes and natural frequencies of the spike were predicted using the built FE model. The frequencies were shown to be within the safe range of 1-20 MHz routinely used for medical imaging and diagnosis by means of ultrasound. These results provide a solid theoretical basis for using ultrasound to study damaging coronavirus through transient and resonant vibration at large deformations.