Free-electron production from nucleotides upon collision with charged carbon ions

Ion-beam cancer therapy has become increasingly favored worldwide in treatment of certain types of cancer over the last decade. Whereas the clinical effects of the therapy are well documented, the understanding of the underlying physical mechanisms is somewhat incomplete. The problem arises due to the multiscale nature of the effects involved in ion-beam cancer therapy, as the effects range from quantum-mechanical to macroscopic scales. The present study investigates the production of free electrons in the vicinity of the Bragg peak through quantum-mechanical simulations of the collision between a ${\mathrm{C}}^{4+}$ ion with a cytosine-guanine nucleotide pair taken from a DNA double helix. Time-dependent density-functional theory was employed using the octopus 6.0 software. The results show that such a collision triggers the release of a large amount of electrons into the cellular environment, as only a fraction is captured by the ${\mathrm{C}}^{4+}$ ion. Furthermore, it is demonstrated that the impact angle and projectile kinetic energy have much more influence on the number of ejected electrons than the impact parameter.

Figure 1

A beam of carbon ions hits a piece of DNA in a cancer tumor (a). In this study the focus is on examining how electron release, electron capture, and energy deposition is affected by the collision between a highly charged carbon ion from the beam and a piece of a DNA strand (b). Here, a cytosine (CYT)-guanine (GUA) pair is chosen as a representative target (c).

Figure 2

System setup used in the simulations. The impact parameter $d$ is shown together with the impact angle $\theta$. $d$ is varied along the red thick vector whose projection on the plane of the CYT+GUA pair is indicated by a thin red line. $d=0$ corresponds to collisions close to the center of mass of the CYT+GUA pair, while the directions of the ${\mathrm{C}}^{4+}$ ion motion for other values of $d$ are indicated by cyan arrows. The impact angle ${\theta }_{\mathrm{start}}<\theta <{\theta }_{\mathrm{end}}$ is defined as the angle between the CYT+GUA pair normal vector $\vec{n}$ and the ${\mathrm{C}}^{4+}$ ion shooting direction indicated by the gray vectors for the outermost cases characterized through ${\theta }_{\mathrm{start}}$ and ${\theta }_{\mathrm{end}}$, where ${\theta }_{\mathrm{start}}={18}^{\circ }$ and ${\theta }_{\mathrm{end}}={158}^{\circ }$. $\theta ={90}^{\circ }$ represents an in-plane collision.

Figure 3

Quantifying the collision process. Visual representation of how the electronic densities were integrated in the cubecat analysis software, see SM [25]. It is reasoned that the mismatch between the cumulative electronic densities localized around the ${\mathrm{C}}^{4+}$ ion, the CYT+GUA pair, and the total amount of electrons in the system indicates that a number of free electrons are released upon collision.

Figure 4

Computational setup of the ${\mathrm{C}}^{4+}$ central collision. The ${\mathrm{C}}^{4+}$ ion travels through the center of mass of the CYT+GUA pair at an impact angle of $\theta ={23}^{\circ }$ with respect to the normal vector $\vec{n}$ of the molecular plane. When the ${\mathrm{C}}^{4+}$ ion travels $20\AA$ after passing the target, the collision event is considered completed, and this point is used as a reference for calculation and comparison of electronic density changes in the system. Note that for the initial kinetic energies of $E_{\mathrm{kin}}=0.006\mathrm{MeV}$ and $E_{\mathrm{kin}}=0.036\mathrm{MeV}$ the collision is considered complete at shorter distances after passing the CYT+GUA pair.

Figure 5

Electronic density change of the CYT+GUA pair. (a) The change in electronic density $\mathrm{\Delta }{\rho }_e$ around the CYT+GUA pair during collision, see Fig. 3. Each plot corresponds to a different value of the initial kinetic energy of the ${\mathrm{C}}^{4+}$ ion, given in units of MeV. The disturbance of the electronic density starts when the ${\mathrm{C}}^{4+}$ ion approaches the target, and the electronic density surrounding the nucleotide pair starts to drop after the ${\mathrm{C}}^{4+}$ ion has left the target. The interaction is initiated earlier for lower kinetic energies of the ${\mathrm{C}}^{4+}$ ion. (b) The change of the electronic densities of the ${\mathrm{C}}^{4+}$ ion (dots) and the CYT+GUA pair (squares) after the collision is displayed as a function of initial kinetic energy of the projectile. The disturbance of the electronic density during the ion's passage through the molecule increases for smaller energies. (c) Electronic density corresponding to the free electrons released into the system during collision, i.e., the electronic density not localized around either the CYT+GUA pair or the ${\mathrm{C}}^{4+}$ ion. The curve peaks at around $1.21\mathrm{MeV}$.

Figure 6

Electronic density change is influenced by the impact parameters. (a) Varying the impact parameter $d$ (see Fig. 2) has relatively little effect on the change in the electronic densities, both around the projectile and the target. (b) Electronic density changes around the projectile ion and the target molecule are perturbed significantly as the impact angle $\theta$ (see Fig. 2) changes, peaking around the impact angle of ${90}^{\circ }$, corresponding to the longest ${\mathrm{C}}^{4+}$ ion passage distance through the CYT+GUA pair. (c) Electronic density representing the electrons released into the system and thereby not located around either the CYT+GUA pair or the ${\mathrm{C}}^{4+}$ ion for the studied impact parameter, $d$. (d) Electronic density of electrons released into the system peaks around an impact angle of $\theta ={90}^{\circ }$ mirroring the disturbance of the electronic density surrounding the CYT+GUA pair depicted in (b). Prediction for electron loss in water with a penetration depth of 1 nm for $E_{\mathrm{kin}}=1.2\mathrm{MeV}$ are illustrated by red stars, corresponding to the angle with a similar penetration depth in the nucleotide pair [7]. All density changes have been computed for two values of the initial kinetic energies $E_{\mathrm{kin}}=3.6\mathrm{MeV}$ (blue, violet) and $E_{\mathrm{kin}}=1.21\mathrm{MeV}$ (green, yellow).

Figure 7

Stopping power of the ${\mathrm{C}}^{4+}$ ion. Comparison of the stopping power of the ${\mathrm{C}}^{4+}$ ion in the CYT+GUA pair collisions (squares) with the stopping power of ${\mathrm{C}}^{3+}$ ion in water (orange line) [27]. The effective interaction distance of the ${\mathrm{C}}^{4+}$ ion with the CYT+GUA pair is assumed to be $2\pm 0.5\AA$ based on the van der Waals radius, leading to a spread out distribution highlighted by a green color. The maximum stopping power for the ${\mathrm{C}}^{4+}$ ion in the CYT+GUA pair collision and for the ${\mathrm{C}}^{3+}$ ion in water is indicated by the blue and the orange arrows, respectively.

Figure 8

The root-mean-square deviation (RMSD) of the atoms in the nucleotide pair. The RMSD values for various initial kinetic energies of the ${\mathrm{C}}^{4+}$ ion. Each line corresponds to a different value of the initial kinetic energy of the ${\mathrm{C}}^{4+}$ ion, given in units of MeV color coded in the legend. The simulation time instance of $0.0$ fs corresponds to the collision, i.e., a point when the projectile ion hits the center of the target CYT+GUA pair. Linearly extrapolating the line for $0.006\mathrm{MeV}$ suggests that an RMSD of $\sim 1\AA$ is reached at around 3 fs.