Lethal DNA damage caused by ion-induced shock waves in cells

The elucidation of fundamental mechanisms underlying ion-induced radiation damage of biological systems is crucial for advancing radiotherapy with ion beams and for radiation protection in space. The study of ion-induced biodamage using the phenomenon-based multiscale approach (MSA) to the physics of radiation damage with ions has led to the prediction of nanoscale shock waves created by ions in a biological medium at the high linear energy transfer (LET). The high-LET regime corresponds to the keV and higher-energy losses by ions per nanometer, which is typical for ions heavier than carbon at the Bragg peak region in biological media. This paper reveals that the thermomechanical stress of the DNA molecule caused by the ion-induced shock wave becomes the dominant mechanism of complex DNA damage at the high-LET ion irradiation. Damage of the DNA molecule in water caused by a projectile-ion-induced shock wave is studied by means of reactive molecular dynamics simulations. Five projectile ions (carbon, oxygen, silicon, argon, and iron) at the Bragg peak energies are considered. For the chosen segment of the DNA molecule and the collision geometry, the number of DNA strand breaks is evaluated for each projectile ion as a function of the bond dissociation energy and the distance from the ion's path to the DNA strands. Simulations reveal that argon and especially iron ions induce the breakage of multiple bonds in a DNA double convolution containing 20 DNA base pairs. The DNA damage produced in segments of such size leads to complex irreparable lesions in a cell. This makes the shock-wave-induced thermomechanical stress the dominant mechanism of complex DNA damage at the high-LET ion irradiation. A detailed theory for evaluating the DNA damage caused by ions at high-LET is formulated and integrated into the MSA formalism. The theoretical analysis reveals that a single ion hitting a cell nucleus at high-LET is sufficient to produce highly complex, lethal damages to a cell by the shock-wave-induced thermomechanical stress. Accounting for the shock-wave-induced thermomechanical mechanism of DNA damage provides an explanation for the “overkill” effect observed experimentally in the dependence of cell survival probabilities on the radiation dose delivered with iron ions. This important observation provides strong experimental evidence of the ion-induced shock-wave effect and the related mechanism of radiation damage in cells.

Figure 1

Geometry of the DNA molecule and the studied parameters. Panel (a) shows an ion (C, O, Si, Ar, and Fe) propagating in close proximity to the DNA molecule consisting of 30 complementary base pairs. The ion track is oriented along the $z$ axis; the $x$ axis is oriented along one of the principal axis of inertia of the chosen DNA molecule, and the $y$ axis is along the line defining the shortest distance between the ion track and the selected principal axis of inertia. The collision parameter $d_{\text{geo}}$ is defined as the displacement of the ion's path along the $y$ axis with respect to the principal axis of inertia. The specific collision parameters $d_{\text{A}}$ and $d_{\text{B}}$ are defined as the shortest distances from the ion's path to DNA strands A and B, respectively. Panel (b) illustrates ${\mathrm{C}}_3^{\prime }$–O, ${\mathrm{C}}_4^{\prime }$–${\mathrm{C}}_5^{\prime }, {\mathrm{C}}_5^{\prime }$–O, and P–O bonds in the DNA sugar-phosphate backbone and the corresponding potential energy curves obtained by means of DFT [29]. Bond dissociation energy, $D_e$, defined as the depth of the associated potential energy well of the covalent bond is considered in the simulations as a variable parameter. The values of $D_e$ determined from the DFT calculations have been scaled by a factor of 2/3, 1/2, 1/3 and 1/6 (see main text for details).

Figure 2

(a) The LET for ${\mathrm{C}}^{6+}, {\mathrm{O}}^{8+}, {\mathrm{Si}}^{14+}, {\mathrm{Ar}}^{18+}$, and ${\mathrm{Fe}}^{26+}$ ions as a function of ion's kinetic energy, calculated using the analytical MSA model [3] (solid lines). The results are compared with the values compiled in the ICRU73 report [59] (open symbols) and the results of Monte Carlo simulations [60] performed using the Geant4-DNA software package [61] (closed symbols). (b) Comparison of the calculated LET for carbon ions (thick solid line) with experimental measurements [62] (open triangles) and other theoretical calculations performed using the widely-used SRIM [63] (thin solid line) and CasP [64] (dashed line) codes.

Figure 3

The dependence of the probability for a lethal DNA lesion, ${\mathcal{P}}_l$, on the average number of simple lesions within the DNA double twist, $\mathcal{N}(r,S_e)$. (a) The dependence calculated according to Eq. (21). In panels (b), (c) this dependence is compared with the limiting case of $\mathcal{N}(r,S_e)\lesssim \lambda \ll 1$ calculated according to Eq. (22) and with the limiting case of $1\ll \mathcal{N}(r,S_e)\ll {\nu }_{\max }$ calculated according to Eq. (26), respectively.

Figure 4

Average number of bond breaks in the DNA double twist calculated as a function of the collision parameter $d_{\text{geo}}$ for the five studied ions. $d_{\text{geo}}$ is the distance from the ion track to the principal axis of inertia of the DNA segment as shown in Fig. 1. Panels a, b, and c show the results of simulations employing the bond dissociation energies $D_e$ derived from the DFT calculations [see Fig. 1] and the values of $D_e$ scaled by the factors of 1/2 and 1/6. Two independent MD simulations have been performed for each projectile ion and each collision geometry; error bars indicate the corresponding standard deviation.

Figure 5

Spatial distribution of the total number of bond breaks occurring in a DNA double twist (color gradient) as a function of two collision parameters $d_A$ and $d_B$ (see Fig. 1), computed for Fe, Ar, Si, O and C ions in the Bragg peak region. The spatial region inaccessible for the given combination of collision parameters is marked with dashed grey lines. Note that the scale of the color bars for Fe, Ar and Si ions is twofold larger than for the O ion and tenfold larger than for the C ion.

Figure 6

Radial distance traveled by the front of the shock wave induced by the five studied ions in the Bragg peak region. The results are obtained using Eq. (40).

Figure 7

The average density of water as a function of radial distance from the ion track. The dynamics of the water medium is caused by propagation of the shock wave induced by iron, argon, silicon, oxygen and carbon ions inside a $49.5\text{nm}\times 49.5\text{nm}\times 8.0\text{nm}$ water box. The simulation time (measured in ps) is depicted as a color scale. The shock wave induced by iron, argon, and silicon ions (top row) has reached the simulation box boundary much faster than the shock wave induced by oxygen and carbon ions (bottom row). Therefore, the simulation time for iron, argon and silicon ions is about 3 times shorter than for the lighter ions.

Figure 8

(a) Variation of the density of water caused the carbon ion-induced shock wave as a function of radial distance from the ion track. The simulation time is indicated in the sidebar. The position of the shock-wave front $R$ calculated using Eq. (40) is indicated with dots. The position of the wave front separates the mass transported by the shock wave, that is considered as displaced (behind the wave front, i.e., at $r<R$) and excess (beyond the wave front, i.e., at $r>R$). (b) Time evolution of the linear mass density, defined as the water mass transported by the carbon ion-induced shock wave and normalized by the unit length of ion's trajectory. The displaced mass calculated behind the wave front is shown by the dashed black line whereas the excess mass beyond the wave front is shown by the solid green line.

Figure 9

(a) The radial position of the maximal density of water as a function of simulation time for the shock wave induced by a carbon ion in the Bragg peak region. The maximal distance of the shock-wave propagation is defined by a quadratic fit function (see the dashed line). The nonphysical region due to the shock-wave reflection from the simulation box boundaries is marked with grey color. (b) The pressure exerted by the shock-wave front generated by different ions in the Bragg peak region as a function of the wave front radius $R$. The red dot depicts the maximal propagation distance for the shock-wave front generated by a carbon ion (the “turning point”), calculated using Eq. (40). The corresponding time instance, $t=16.7$ ps, has been determined from the MD simulations as shown in panel (a). The dashed line shows the surface tension pressure on the surface of a cylindrical wake region with radius $R$.

Figure 10

Variation of the potential energy curve for a molecular bond upon the action of the external force $F$ caused by the pressure gradient due to the ion-induced shock wave. Solid black line shows the bond potential energy described by the Morse potential. The potential $U\left(r\right)$, Eq. (46), is shown by solid red line. $\mathrm{\Delta }E$ is the energy barrier for bond rupture by the shock-wave-induced thermomechanical stress. See the main text for details.

Figure 11

The threshold distance $R_{\mathrm{SW}}$ for cleavage of the ${\mathrm{C}}_3^{\prime }$–O, ${\mathrm{C}}_4^{\prime }$–${\mathrm{C}}_5^{\prime }, {\mathrm{C}}_5^{\prime }$–O, and P–O bonds by the shock-wave-induced thermomechanical stress by the five studied ions at the Bragg peak region. The $R_{\mathrm{SW}}$ values are calculated according to Eq. (65) (symbols). The coefficient $b$, Eq. (66), varies in the range $(0.072–0.081){\mathrm{nm}}^{4/3}$ ${\mathrm{eV}}^{-1/3}$ for the four bonds considered. Dashed line shows the $R_{\mathrm{SW}}=b{S}_e^{1/3}$ dependence with the average value $b=0.077{\mathrm{nm}}^{4/3}$ ${\mathrm{eV}}^{-1/3}$.

Figure 12

Average number of simple lesions per DNA double twist due to a single carbon ion (a) and iron ion (b) at their Bragg peak energies, as a function of radial distance from the ion's path. ${\mathcal{N}}_{\mathrm{e}}\left(r\right)$ and ${\mathcal{N}}_{\mathrm{r}}\left(r\right)$ are the numbers of simple lesions produced by secondary electrons and free radicals, respectively. ${\mathcal{N}}_{\mathrm{SW}}\left(r\right)$ is the average number of lesions produced due to direct thermomechanical damage by the ion-induced shock wave. The value ${\mathcal{N}}_{\mathrm{SW}}=5.4$ at $r\le R_{\mathrm{SW}}=0.4$ nm was obtained from MD simulations, as summarized in Fig. 4 and Table 3. See the text for further details.

Figure 13

Probability for producing lethal lesions in a DNA double twist as a function of radial distance from the ion's path for irradiation with a carbon ion (a) and with an iron ion (b) in the vicinity of the corresponding Bragg peaks. Solid gray, solid black and dashed red curves show, respectively, the contribution of only secondary electrons, secondary electrons and free radicals, as well as these agents together with the shock-wave-induced thermomechanical stress of the DNA.

Figure 14

Survival probability as a function of deposited dose for the normal tissue human fibroblast cell lines, NB1RGB and M/10, irradiated with carbon ions. Survival probabilities calculated within the MSA using Eqs. (19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32) at the indicated values of LET are shown with lines. Experimental data for the NB1RGB [74] and M/10 [75] cells measured at a specific dose are shown by symbols.

Figure 15

Survival probability as a function of deposited dose for normal rodent cells, V79 and CHO, irradiated with iron ions at the indicated values of LET in the vicinity of the Bragg peak. Solid red lines show the probabilities calculated within the MSA framework with accounting for the shock-wave-induced thermomechanical damage. Shaded areas illustrate variation of cell survival probabilities due to variation in the cell nucleus area (see text for details). Dashed lines show the cell survival probabilities calculated with accounting for the DNA damage produced only by secondary electrons and free radicals. Symbols denote experimental data for irradiation of the V79 [76] and CHO [77] cells.