Simple and universal model for electron-impact ionization of complex biomolecules

We present a simple and universal approach to calculate the total ionization cross section (TICS) for electron impact ionization in DNA bases and other biomaterials in the condensed phase. Evaluating the electron impact TICS plays a vital role in ion-beam radiobiology simulation at the cellular level, as secondary electrons are the main cause of DNA damage in particle cancer therapy. Our method is based on extending the dielectric formalism. The calculated results agree well with experimental data and show a good comparison with other theoretical calculations. This method only requires information of the chemical composition and density and an estimate of the mean binding energy to produce reasonably accurate TICS of complex biomolecules. Because of its simplicity and great predictive effectiveness, this method could be helpful in situations where the experimental TICS data are absent or scarce, such as in particle cancer therapy.

Figure 1

Theoretical calculation and fitting of the mean binding energy of (a) adenine, (b) thymine, (c) cytosine, and (d) guanine at different energy of incident electrons. The red dots show the mean binding energy calculated by using Eqs. (11) and (12) with various incident energy of the electrons. The solid lines show the best fit lines with formula expressed in Eq. (10).

Figure 2

Comparison of the theoretical TICSs under different assumptions in the extended model with experimental data of the four DNA bases of (a) adenine, (b) thymine, (c) cytosine, and (d) guanine. The gray triangles are the experimental measurement data adapted from Ref. [33].

Figure 3

Comparison of the TICSs calculated using the new semiempirical method with other theoretical calculations and experimental data for (a) adenine, (b) thymine, (c) cytosine, and (d) guanine. The solid line represents the calculation derived in this paper. The theoretical data of green, red, and blue squares are adapted from Refs. [38], [39], and [40], respectively. The empty squares are experimental measurement data adapted from Ref. [33].

Figure 4

Comparison of theoretical calculations of the TICSs with experimental data of three different organic compounds—benzene, phenol, and toluene. (a) The solid red line represents the TICS of benzene using our extended electron-impact model. The blue circles and dotted purple line are theoretical calculation from Refs. [41] and [42], respectively. The cyan inverted triangles are experimental data adapted from Ref. [43]. (b) The red solid line represents the TICS of phenol using our model and the blue diamonds are the theoretical calculation from Ref. [41]. (c) The red solid line is the TICS of toluene using our model and blue squares represent the theoretical calculation in Ref. [36]. The black triangles are experimental data from Ref. [44].

Figure 5

(a) The solid lines show the calculated TICSs for different DNA bases (adenine, thymine, cytosine, and guanine), DNA backbones, and uracil. The solid squares are the calculated TICS data of uracil adapted from Ref. [40]. (b) The solid lines show the calculated TICSs for different biological molecules. The solid circles, squares, inverted triangles, and hexagons are the experimental measurements of the TICSs in water adapted from Refs. [40, 50, 51, 52]. The experimental measurements were all made in gaseous phase, while our calculations were assumed with condensed phase of these biomolecules.

Figure 6

Sensitivity of the TICSs with the uncertainty of the parameters (a) $B_0$, (b) $k$, and (c) $\rho$. The horizontal axis represents different incident electron energy and the vertical axis represents various values of the parameters, respectively while keeping other parameters constant. The color scale represents the TICS value in the unit of ${\AA }^2$.