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Citation: Burkhartsmeyer, J.;
Wong, K.S. Molecular Dynamics
Simulations of Shockwave Affected
STMV Virus to Measure the
Frequencies of the Oscillatory
Response. Acoustics 2022,4, 268–275.
https://doi.org/10.3390/
acoustics4010016
Academic Editors: Fardin Khalili,
AmirtahàTaebi and Hansen
A. Mansy
Received: 10 December 2021
Accepted: 14 March 2022
Published: 18 March 2022
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4.0/).
acoustics
Article
Molecular Dynamics Simulations of Shockwave Affected
STMV Virus to Measure the Frequencies of the
Oscillatory Response
Jeffrey Burkhartsmeyer * and Kam Sing Wong
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon,
Hong Kong, China; phkswong@ust.hk
*Correspondence: jmb@connect.ust.hk
Abstract:
Acoustic shockwaves are of interest as a possible means of the selective inactivation of
viruses. It has been proposed that such inactivation may be enhanced by driving the virus particles
at frequencies matching the characteristic frequency corresponding to acoustic modes of the viral
structures, setting up a resonant response. Characteristic frequencies of viruses have been previously
studied through opto-mechanical techniques. In contrast to optical excitation, shockwaves may be
able to probe acoustic modes without the limitation of optical selection rules. This work explores
molecular dynamics simulations of shockwaves interacting with a single STMV virus structure,
in full atomistic detail, in order to measure the frequency of the response of the overall structure.
Shockwaves of varying energy were set up in a water box containing the STMV structure by assigning
water molecules at the edge of the box with an elevated velocity inward—in the direction of the
virus. It was found that the structure compressed and stretched in a periodic oscillation of frequency
65 ±6.5 GHz
. This measured frequency did not show strong dependency on the energy of the
shockwave perturbing the structure, suggesting the frequency is a characteristic of the structure. The
measured frequency is also consistent with values predicted from elastic theory. Additionally, it was
found that subjecting the virus to repeated shockwaves led to further deformation of the structure
and the magnitude of the overall deformation could be altered by varying the time delay between
repeated shockwave pulses.
Keywords: molecular dynamics; acoustic shockwave; virus biophysics; harmonic modes
1. Introduction
Laser-generated acoustic shockwaves or “transients” have been previously used to
break apart viruses in order to study their structural bonding forces [
1
,
2
]. Elsewhere,
selective inactivation of viruses by pulsed laser irradiation has been observed [
3
], with
impulsive stimulated Raman scattering as the suggested mechanism. Recent work proposes
acoustic shockwaves may play a role in pulsed laser inactivation of viruses with plasmonic
enhancement of the laser absorption, from the addition of metal nanoparticles [
4
]. Other
works have proposed the inactivation of viruses via resonant absorption of ultrasonic [
5
]
or microwave energy [
6
,
7
]. Resonant absorption would involve driving the virus at its
characteristic frequencies, such that the vibrational response matches the frequency of
driving energy, leading to increasing amplitude of oscillations and eventual failure of the
structure. For this purpose it is useful to have an estimate of the characteristic frequencies
of a target virus.
Early analytical models used elastic theory to predict vibrational frequencies of
viruses [
8
–
12
]. More recent computational models have been developed to study such fre-
quencies using elastic network normal mode analysis [
13
–
15
]. Another study [
16
] models
the subunits of the structure at the atomic level, applying constraints due to the inherent
symmetries of the icosahedral structure, to predict the vibrational frequencies of a virus
Acoustics 2022,4, 268–275. https://doi.org/10.3390/acoustics4010016 https://www.mdpi.com/journal/acoustics
Acoustics 2022,4269
in the absence of explicit water. In contrast to these, the present work treats the entire
structure of a fully solvated virus in full atomistic detail, by manipulating the surrounding
water molecules to perturb the system with an acoustic shock wave, and measures the
resulting oscillations in the structure.
Opto-mechanical studies involving Brillouin and Raman scattering techniques have
previously been conducted to measure the optically active modes of viruses [
17
–
23
]. Opti-
cally active modes in these cases are those which obey selection rules for light coupling
with the acoustic modes of the material [
24
]. In contrast to this, shock wave perturbation is
a direct mechanical displacement of molecules via Coulombic and other near-field forces
between the water molecules and those of the virus structure. Thus, the modes available
for probing by shockwave perturbation are not restricted by the optical selection rules.
The Satellite Tobacco Mosaic Virus (STMV) has been studied extensively, as a small-
sized virus~17 nm in diameter. Its structure is well-known from crystallography studies—
its geometry is icosahedral as are many other viruses, and thus it is a representative case
study for such viruses. The capsid is comprised of 60 identical copies of a single protein with
molecular weight of 14,500. The structure has been studied via molecular dynamics (MD)
simulations [
25
,
26
]. In fact, because it is a relatively large structure for such MD simulations,
comprised of millions of molecules, it is often used as a benchmark to test the performance
of computing systems [
27
,
28
]. Shockwaves and their effects on biological systems have
been simulated in previous work [
29
–
33
], using different methods to set up the shockwaves
in the simulation. For example Surdutovich [
29
–
31
] initiates the shock waves using a “hot
cylinder” of atoms in a specified radius with average velocities higher than those of the
surrounding media, which in turn expand and interact with neighboring atoms and thus
propagate outward. These simulated shockwaves then passed through DNA structures,
in order to study whether such waves would damage DNA. Since molecular dynamics
simulations treat covalent bonds as harmonic oscillators, and do not take into account
such bonds breaking, Surdutovich considered any bonds exhibiting vibrational energies
above a certain threshold as being broken during the simulation. Other methods for setting
up shockwaves such as that of [
32
,
33
] also involve selecting a region of water molecules
surrounding the biological system of interest, and giving these water molecules a velocity
in a particular direction. This is also the approach used in the present work, described in
more detail below.
2. Materials and Methods
The structure of the Satellite Tobacco Mosaic Virus (STMV), solvated in a cube of
water of cell dimensions 22 nm, was prepared based on files available from the website
of the Theoretical and Computational Biophysics group, NIH Center for Macromolecular
Modeling and Bioinformatics, at the Beckman Institute, University of Illinois at Urbana-
Champaign. The Protein Structure File (PSF) contains the structure of the virus capsid
and RNA, along with water molecules of the solution. The Protein Data Bank (PDB) file
contains information about the coordinates of the atoms from the PSF file, for the start of the
simulation. Using Nanoscale Molecular Dynamics (NAMD) simulation software [
34
], the
system was then allowed to equilibrate under a constant pressure of 1 atm, and a constant
temperature of 298 K for 15 ps. The output from this step was used as the input for the
subsequent step, in which a shockwave was introduced in the following way. Along the
edge of the water box, perpendicular to the Z-axis, atoms falling within a certain distance
of the edge of the box (arbitrarily chosen to be ~3 nm) had their velocities altered. The
X and Y velocities were left unchanged, but the Z velocity was changed to be a fixed value
for these specific atoms. This method for producing simulated shockwaves is similar to
the one employed in [
33
]. The forces on all atoms in the system are then computed via the
force field resulting from interaction with neighboring atoms within the cutoff distance—in
this case 12 Å. For a given time-step, the velocity and new position of each atom are then
numerically computed from the velocity and position of the prior time-step and the overall
force on the atom from the current time-step. This process is repeated for each time-step,
Acoustics 2022,4270
of duration 1 fs in this case, and a trajectory for all atoms is computed. Since the selected
water molecules were given an elevated velocity inward, towards the rest of the water
box containing the virus, they move closer to other water molecules, resulting in forces
acting on these neighboring atoms, so that they too gain an elevated velocity. In this
manner, in subsequent time-steps the shockwave propagates through water molecules until
it eventually encounters the molecules of the virus structure.
Perhaps a more realistic model of the initial velocities which would occur in an actual
physical shockwave would instead have a distribution of velocities centered around this
chosen value, but this method of using a uniform value was simply chosen for convenience,
since it made identifying the affected atoms simple for debugging purposes and to easily
vary the parameter of energy input. To justify the use of this simplistic approach to creating
shockwaves in the water box, it should be noted that the water molecules which have
been subjected to this artificial instantaneous Z-direction velocity, will quickly (by the next
processing step) encounter other water molecules outside the affected region. As they
interact with these unaltered water molecules, there will be an exchange of momentum
through the force field, and the random distribution of the velocities of those unaffected
water molecules will once again smooth out and randomize the velocities of those molecules
which underwent the artificial velocity change. Further processing steps will lead to more
interactions with randomly moving water molecules and the strong pulse of velocities
in the Z-direction will disperse into other directions, but the overall momentum will be
biased in the Z-direction and the pulse will propagate through the rest of the system. Thus,
provided the molecules of the biological system (the virus in this case) are far enough
away from the edge of the box, by the time this pulse reaches the molecules of interest, it
should resemble a planar acoustic wave transient, such as that which could be produced by
an ultrashort laser pulse. Indeed, measuring the distribution of Z-direction velocities at
various times shows that after a few time-steps, the velocities of the water molecules fall in a
skewed Gaussian distribution. In addition to the aforementioned convenience of being able
to quickly pick out the atoms which were subject to the artificial velocity change (since they
are all assigned the same Z-direction value for the initial step), there is the added benefit of
being able to inject a very high initial Z-directed energy pulse, while avoiding the velocity
limits of the NAMD simulation system. If more energy is still needed, this can be achieved
by simply choosing a larger slice of atoms along the boundary. Another approach would be
to instead simply reverse the Z-direction velocities of these same atoms, since they should
already have a realistic distribution of velocities after the equilibrium step; this approach is
known as a “momentum mirror.” [
35
] It has the advantage of not altering the overall kinetic
energy of the system—however, this would not be representative of a real laser-generated
shock wave as in this case kinetic energy is added to the system via absorption of the laser
energy. In another, similar approach, a slowly moving boundary could be applied, and
atoms reaching this boundary would have their velocities reversed—like a “hard edge.”
This is the “piston” approach of [
32
], and it has the advantage of avoiding clashes of atoms
which may arise when the sudden change in velocities causes atoms to come too close
together. Such clashes can cause the simulation to fail, since the calculated forces become so
large that they are beyond the ability for the computer to store and compute. However, if a
sufficiently small time-step is chosen, clashes can be avoided since the atoms have time to
react to the forces generated when they approach one another, thus altering their direction
and avoiding unmanageably large force values. For this reason, for some simulations
performed in this work—those involving the highest energies—a very short timestep of 1
fs was used for parts of the simulation.
3. Results
Using NAMD, the STMV virus structure in a water box was subjected to a single pulse
of a simulated acoustic shockwave using the method described above, at various pulse
energies, and the response of the system studied. Using Visual Molecular Dynamics (VMD)
software [
36
], conformational changes were studied. The Root Mean Squared Displacement
Acoustics 2022,4271
(RMSD) for the entire protein backbone of the virus capsid structure was calculated using
the built-in plug-in of this software. A higher value indicates a larger overall conformational
change to the entire structure throughout the trajectory. Shown in Figure 1a are the RMSD
curves for simulated shockwaves at various energies. Shown in Figure 1b are RMSD curves
for repeated shockwaves compared to a single pulse. For each pulse, the initial velocity
of water molecules is 39.999 Å/ps—a relatively gentle pulse. By varying the time delay
between pulses, the amplitude of the overall deformation of the structure is seen to vary.
Shown in Figure 2are screenshots from the VMD visualization of the virus subject to a
shockwave of initial water speed 99.999 Å/ps (the maximum allowable velocity of the
software—chosen to show the deformation most clearly), at time points corresponding to
extrema in the RMSD curve. Figure 2a shows an illustration of a planar cross-section of a
sphere with the L3 mode at maximum deformation for comparison. Figure 2b shows the
virus before encountering the shockwave—at time 0 and 0 RMSD, with the spherical cross-
section from Figure 2a overlaid for comparison. Figure 2c shows the virus at maximum
deformation, with the cross-section of L3 mode at max deformation overlaid.
Acoustics 2022, 4 FOR PEER REVIEW 4
3. Results
Using NAMD, the STMV virus structure in a water box was subjected to a single
pulse of a simulated acoustic shockwave using the method described above, at various
pulse energies, and the response of the system studied. Using Visual Molecular Dynam-
ics (VMD) software [36], conformational changes were studied. The Root Mean Squared
Displacement (RMSD) for the entire protein backbone of the virus capsid structure was
calculated using the built-in plug-in of this software. A higher value indicates a larger
overall conformational change to the entire structure throughout the trajectory. Shown in
Figure 1a are the RMSD curves for simulated shockwaves at various energies. Shown in
Figure 1b are RMSD curves for repeated shockwaves compared to a single pulse. For
each pulse, the initial velocity of water molecules is 39.999 Å /ps—a relatively gentle
pulse. By varying the time delay between pulses, the amplitude of the overall defor-
mation of the structure is seen to vary. Shown in Figure 2 are screenshots from the VMD
visualization of the virus subject to a shockwave of initial water speed 99.999 Å /ps (the
maximum allowable velocity of the software—chosen to show the deformation most
clearly), at time points corresponding to extrema in the RMSD curve. Figure 2a shows an
illustration of a planar cross-section of a sphere with the L3 mode at maximum defor-
mation for comparison. Figure 2b shows the virus before encountering the shock-
wave—at time 0 and 0 RMSD, with the spherical cross-section from Figure 2a overlaid for
comparison. Figure 2c shows the virus at maximum deformation, with the cross-section
of L3 mode at max deformation overlaid.
(a)
0
2
4
6
8
10
0246810 12 14
RMSD (Å)
Time (ps)
RMSD Virus Backbone
for Varying Initial Water Velocities
99.999 (Å/ps)
89.999 ( Å/ps)
79.999 ( Å/ps)
69.999 (Å/ps)
59.999 (Å/ps)
49.999 (Å/ps)
39.999 (Å/ps)
Acoustics 2022, 4 FOR PEER REVIEW 5
(b)
Figure 1. Response of virus structure to shockwave pulses (a) RMSD curves exhibiting the oscilla-
tory response of the virus to single shockwave pulses—each curve represents the time evolution of
the deformation of the virus structure for a given initial velocity value assigned to water molecules
in the water slice to initialize the shockwave. (b) RMSD curves showing response of the virus to
repeated shockwaves pulses compared to a single shockwave pulse—a varying delay between
pulses leads to variation in the overall amplitude of deformation of the structure.
(a)
(b)
(c)
Figure 2. Output from VMD visualization software for the shockwave with initial water velocities
of 99.999 Å /ps showing: (a) Illustration of cross-sectional shape of L3 spheroidal mode at maximum
deformation (solid line), compared to initial spherical shape (dashed line) (b) The virus in its
equilibrated state (time = 0.0 ps)—before encountering the shockwave, with spherical cross-section
overlaid (dashed line) (c) The virus in the maximum compression state (time = 1.4 ps), corre-
sponding to the first peak in the RMSD value, with cross-section of L3 mode of a sphere at maxi-
mum deformation overlaid (solid line). The color scheme shows the different types of mole-
cules—the purple molecules are the nucleic acid of the core while the green molecules are the pro-
tein capsid.
As seen in Figures 1 and 2, as well as video SV1, when the simulated shockwave
front begins to hit the virus at time 200 fs, the structure begins to deform and the mag-
nitude of this deformation increases as the wave propagates through the structure and
the surrounding water medium, peaking at time 1.4 ps, when the structure is at maxi-
mum compression. As the wave reaches the end of the structure, it is stretched out, re-
0
2
4
6
8
10
0 5 10 15 20 25 30
RMSD (Å)
Time (ps)
RMSD Virus Backbone
for Varying Repetition Rate
Single Pulse
Repeated Pulses (6 ps delay)
Repeated Pulses (8 ps delay)
Repeated Pulses (9 ps delay)
Figure 1.
Response of virus structure to shockwave pulses (
a
) RMSD curves exhibiting the oscillatory
response of the virus to single shockwave pulses—each curve represents the time evolution of the
deformation of the virus structure for a given initial velocity value assigned to water molecules in the
water slice to initialize the shockwave. (
b
) RMSD curves showing response of the virus to repeated
shockwaves pulses compared to a single shockwave pulse—a varying delay between pulses leads to
variation in the overall amplitude of deformation of the structure.
Acoustics 2022,4272
Acoustics 2022, 4 FOR PEER REVIEW 5
(b)
Figure 1. Response of virus structure to shockwave pulses (a) RMSD curves exhibiting the oscilla-
tory response of the virus to single shockwave pulses—each curve represents the time evolution of
the deformation of the virus structure for a given initial velocity value assigned to water molecules
in the water slice to initialize the shockwave. (b) RMSD curves showing response of the virus to
repeated shockwaves pulses compared to a single shockwave pulse—a varying delay between
pulses leads to variation in the overall amplitude of deformation of the structure.
(a)
(b)
(c)
Figure 2. Output from VMD visualization software for the shockwave with initial water velocities
of 99.999 Å /ps showing: (a) Illustration of cross-sectional shape of L3 spheroidal mode at maximum
deformation (solid line), compared to initial spherical shape (dashed line) (b) The virus in its
equilibrated state (time = 0.0 ps)—before encountering the shockwave, with spherical cross-section
overlaid (dashed line) (c) The virus in the maximum compression state (time = 1.4 ps), corre-
sponding to the first peak in the RMSD value, with cross-section of L3 mode of a sphere at maxi-
mum deformation overlaid (solid line). The color scheme shows the different types of mole-
cules—the purple molecules are the nucleic acid of the core while the green molecules are the pro-
tein capsid.
As seen in Figures 1 and 2, as well as video SV1, when the simulated shockwave
front begins to hit the virus at time 200 fs, the structure begins to deform and the mag-
nitude of this deformation increases as the wave propagates through the structure and
the surrounding water medium, peaking at time 1.4 ps, when the structure is at maxi-
mum compression. As the wave reaches the end of the structure, it is stretched out, re-
0
2
4
6
8
10
0 5 10 15 20 25 30
RMSD (Å)
Time (ps)
RMSD Virus Backbone
for Varying Repetition Rate
Single Pulse
Repeated Pulses (6 ps delay)
Repeated Pulses (8 ps delay)
Repeated Pulses (9 ps delay)
Figure 2.
Output from VMD visualization software for the shockwave with initial water velocities of
99.999 Å/ps showing: (
a
) Illustration of cross-sectional shape of L3 spheroidal mode at maximum
deformation (solid line), compared to initial spherical shape (dashed line) (
b
) The virus in its equili-
brated state (time = 0.0 ps)—before encountering the shockwave, with spherical cross-section overlaid
(dashed line) (
c
) The virus in the maximum compression state (time = 1.4 ps), corresponding to the
first peak in the RMSD value, with cross-section of L3 mode of a sphere at maximum deformation
overlaid (solid line). The color scheme shows the different types of molecules—the purple molecules
are the nucleic acid of the core while the green molecules are the protein capsid.
As seen in Figures 1and 2, as well as video SV1, when the simulated shockwave front
begins to hit the virus at time 200 fs, the structure begins to deform and the magnitude of this
deformation increases as the wave propagates through the structure and the surrounding
water medium, peaking at time 1.4 ps, when the structure is at maximum compression.
As the wave reaches the end of the structure, it is stretched out, resulting in a secondary
peak in the RMSD at time (9 ps). Finally, there is a recoiling of the overall structure as
the structure is compressed from the recoil. This is reminiscent of a damped harmonic
oscillator type motion, better described in the model of [
8
], with spherical Bessel functions.
The time in between the first and second peaks ranges from 7.0 ps to 8.4 ps, for pulses with
average initial velocity ranging from 99.999 Å/ps and 29.999 Å/ps. Since the primary and
secondary peaks represent the times of maximal compression and stretching, respectively,
the overall time for the complete oscillatory motion is double the time between first and
second peak. These times correspond to 59.5 to 71.4 GHz. As seen in Table 1, there is little
correlation between this measured frequency and the initial velocities of the water slice
molecules used to set up the simulated shockwave.
Table 1.
Initial velocity of water molecules in shockwave initialization water slice vs. measured
frequency of the virus structure oscillation.
Initial Velocity Period of Oscillation (ps) Frequency (GHz)
Water Slice (Å/ps)
99.999 15.2 65.79
89.999 16 62.5
79.999 16.4 60.98
69.999 16.4 60.98
59.999 16.8 59.52
49.999 14 71.43
39.999 14 71.43
29.999 14.8 67.57
4. Discussion
The simulated structural response of STMV exposed to a shockwave exhibited oscilla-
tory behavior, the periodicity of which did not show high dependency on the initial energy
Acoustics 2022,4273
of the shockwave. This suggests that the frequency may be an intrinsic property of the
structure. This frequency was determined to be 65 ±6.5 GHz.
For a comparison with values predicted from elastic theory, the icosahedral virus can
be approximated as a sphere, in order to employ Lamb’s theory [
9
,
37
,
38
] for estimating
vibrational frequencies. Taking values of longitudinal wave speed and Poisson’s ratio to be
1800 m/s and 0.30, respectively (corresponding to a transverse wave speed of 900 m/s),
consistent with values used in prior works [
6
,
11
,
18
,
22
], and with a radius of 17 nm, the
L1 and L3 modes are predicted to be ~60.6 GHz and 66.6 GHz, respectively, which are
in good agreement with the measured value. It should not be surprising that these odd-
numbered modes would be activated by a pulse energy which asymmetrically compresses
the structure from one side, leaving the other side initially unperturbed. Indeed from
visual inspection of the oscillatory motion using the VMD software, the shape of the
compressed state appears to most resemble that of the L3 mode, as seen in Figure 2c. Thus,
it seems reasonable that the predicted L3 mode frequency (66.6 GHz) should be a good
approximation of the measured values (65
±
6.5 GHz.) Note, however that the error in this
measurement is quite significant (10%), so the L1 mode could be considered an equally
good numeric fit. Table A1 shows the first few spheroidal modes, for comparison. Further,
the real motion of the virus oscillations is more complex than that of a simple sphere, as
the composition of the structure is very complex and the shockwave perturbation can
activate more than one mode. Moreover, the parameters (Poisson’s ratio, wave speeds of
the material) used in the Lamb’s theory approximation are not entirely well-established
in the literature, so these should be considered estimations as well. Given all the sources
of error, it is reassuring that the predicted values match the measured values so well, but
this should be taken with some care. For example if a Poisson’s ratio of 0.40 were instead
used, this would result in a predicted value of 53.6 GHz for the frequency of the L3 mode.
It is also worth noting that, although it is reassuring that elastic theory gives similar values
for vibrational frequencies, the full atomistic molecular dynamics model gives additional
information by taking into account atomic interactions of the biological components with
one another and with the water molecules. These could be approximated by introducing a
damping term to the elastic theory model, but molecular dynamics simulation gives a more
comprehensive understanding of the dynamics of the system. For example, it appears that
the vibrations quickly dissipate and begin to level off after the first couple of peaks in the
RMSD curve, as seen in Figure 1a.
It was further observed that an enhancement of the amplitude of deformation could
be achieved by subjecting the virus to repeated shock-wave pulses. By choosing a time
delay between pulses, such that the deformation of the structure is at a maximum as a
subsequent shockwave pulse arrives at the structure, the overall deformation increased,
as seen in Figure 1b. This supports the plausibility of achieving a resonant response by
driving the virus structure at the proper frequency, via acoustic waves such as shockwaves.
Future research may explore lower energy perturbations—for example, using water
speeds which do not exceed the wave speed of water, in order to see if the oscillatory mo-
tions are still observable and whether the frequencies of such motions would be consistent
with those measured using these super-sonic shockwave pulses. If oscillatory frequencies
are ubiquitous, irrespective of excitation energy, it may suggest the possibility of driving
the virus structure at such frequencies, in order to set up a resonant response.
Another interesting direction for future study would be to examine the possibility
of virus inactivation, by investigating bond-breaking events which may occur during
shockwave excitation. The results described here treated bonds as a simple harmonic
potential, which is unrealistic as bond energies simply increase unbounded with bond-
length. More interesting would be to simulate shockwave interaction with viruses using
more advanced MD simulation techniques such as ab initio or reactive force field methods
in order to study bond-breaking and re-formation. This would give a more realistic view as
to the plausibility of viral inactivation via resonant excitation of the structure.
Acoustics 2022,4274
In spite of the relative simplicity of this model, some useful observations can be made.
To wit: frequencies of oscillation due to shockwave perturbation seem to correspond to
the odd-numbered spheroidal modes (L1 and L3), and the frequencies are around 65 GHz,
irrespective of shockwave energy. With these observations, it may be possible to tailor a
scheme whereby selective inactivation of viruses could be enhanced by driving the system
at such a characteristic frequency—either via shockwaves or otherwise.
Supplementary Materials:
The following supporting information can be downloaded at: https:
//www.mdpi.com/article/10.3390/acoustics4010016/s1, Video S1: VMD Visualization of Virus
Response to Shockwave. File S1: NAMD instruction file.
Author Contributions:
Conceptualization, J.B. and K.S.W.; software and simulation, J.B.; supervision,
K.S.W.; writing—original draft preparation, J.B.; writing—review and editing, K.S.W. All authors
have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the Research Grants Council of Hong Kong through grant
numbers AoE/P-02/12 and C7035-20G.
Data Availability Statement:
Datasets and NAMD instruction files can be found at the following:
https://figshare.com/articles/software/stmv_shockwave_zip/19380299 (accessed on
8 December 2021
).
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Shockwave simulations were performed with Charm22 force field [
39
], rigid water
bonds and periodic boundary conditions. For further simulation details, the NAMD
simulation instruction file is provided in the supplementary materials section.
Table A1.
Frequencies of the first few modes of a sphere, with longitudinal wave speed 1800 m/s
and Poisson’s ratio 0.30.
Spheroidal Mode Number Frequency (GHz)
L0 92.47
L1 60.60
L2 44.67
L3 66.57
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