TOPAS-nBio validation for simulating water radiolysis and DNA damage under Low-LET irradiation

Abstract

The chemical stage of the Monte Carlo track-structure simulation code Geant4-DNA has been revised and validated. The root-mean-square (RMS) empirical parameter that dictates the displacement of water molecules after an ionization and excitation event in Geant4-DNA has been shortened to better fit experimental data. The pre-defined dissociation channels and branching ratios were not modified, but the reaction rate coefficients for simulating the chemical stage of water radiolysis were updated. The evaluation of Geant4-DNA was accomplished with TOPAS-nBio. For that, we compared predicted time-dependent G values in pure liquid water for ^•OH, e⁻_aq, and H₂ with published experimental data. For H₂O₂ and H^•, simulation of added scavengers at different concentrations resulted in better agreement with measurements.

In addition, DNA geometry information was integrated with chemistry simulation in TOPAS-nBio to realize reactions between radiolytic chemical species and DNA. This was used in the estimation of the yield of single-strand breaks (SSB) induced by ¹³⁷Cs γ-ray radiolysis of supercoiled pUC18 plasmids dissolved in aerated solutions containing DMSO. The efficiency of SSB induction by reaction between radiolytic species and DNA used in the simulation was chosen to provide the best agreement with published measurements.

An RMS displacement of 1.24 nm provided agreement with measured data within experimental uncertainties for time-dependent G values and under the presence of scavengers. SSB efficiencies of 24% and 0.5% for ^•OH and H^•, respectively, led to an overall agreement of TOPAS-nBio results within experimental uncertainties. The efficiencies obtained agreed with values obtained with published non-homogeneous kinetic model and step-by-step Monte Carlo simulations but disagreed by 12% with published direct measurements. Improvement of the spatial resolution of the DNA damage model might mitigate such disagreement.

In conclusion, with these improvements, Geant4-DNA/TOPAS-nBio provides a fast, accurate, and user-friendly tool for simulating DNA damage under low LET irradiation.

1. Introduction.

A reliable way to study the underlying channels of radiobiological damage is mechanistic modeling. The modeling task is accomplished with Monte Carlo track-structure (MCTS) codes that have the capability of combining complex DNA geometry models with the stochastic processes of the interaction of ionizing radiation with matter and the subsequent non-homogeneous chemistry processes to produce initial DNA damage. MCTS codes specific for radiobiological applications include KURBUC (Nikjoo et al 2016), PARTRAC (Dingfelder et al 1999), Geant4-DNA (Incerti et al 2010a, 2010b, Bernal et al 2015), RITRACKS (Plante and Devroye 2017), RADAMOL (Štěpán and Davídková 2014), and TOPAS-nBio (Schuemann et al 2018). The reported results obtained with such codes demonstrate the usability of the Monte Carlo method to quantify DNA damage-induced at early stages following irradiation from first principles.

MCTS codes, being flexible mechanistic tools initially developed for liquid water calculations, have demonstrated acceptable accuracy in estimating DNA damage induced by ionizing radiation from first principles. However, many radiobiology-oriented MCTS codes overestimate the yields of ^•OH radical produced by fast electrons in liquid water within the nanosecond time scale (Kreipl et al 2009, Uehara and Nikjoo 2006, Ramos-Méndez et al 2018, Boscolo et al 2018). This inaccuracy might potentially mislead the interpretation of calculated DNA damage yields and hence requires benchmarking. In this work, we aim to reconcile MCTS by comparing simulated with experimentally measured yields from the literature for radiolytic species produced by fast electrons at the earliest times.

Experimental validation is paramount to determine the accuracy of the Monte Carlo method. A common approach among MCTS codes assumes that, from the physics perspective, liquid water is sufficient to represent biological tissue (Friedland et al 2017, Nikjoo et al 2016, Sakata et al 2019, Zhu et al 2020b). For this reason, MCTS validation relies upon the comparison between calculated quantities with measurements performed in gas or liquid water (see e.g., (Burigo et al 2016, Kreipl et al 2009, Pimblott and LaVerne 1997)). Under low linear energy transfer (LET) irradiation, e.g., 0.4 keV/μm track-averaged LET for ¹³⁷Cs (Bruce et al 1963), the highest contribution to DNA lethal damage is caused by reactions with hydroxyl radicals produced in the radiolysis of water (e.g. > 70% for ⁶⁰Co, estimated with DNA plasmids pBR322 at scavenging capacities below ~5 × 10⁸ s⁻¹) (Klimczak et al 1993). Therefore, thorough validation of the models used by MCTS to simulate the chemical stage in the radiolysis in water is crucial. This task has been accomplished typically by comparing calculated time-dependent yields in pure liquid water with measurements performed in solutes at different scavenging capacities. Subsequently, MCTS codes have been tuned to match the experimental yields at the earliest times available to date.

The accuracy of experimental measurements of radiolytic yields continuously improves. Nowadays, the most accurate picosecond-level measurements of radiolytic yields produced in liquid water by fast electrons have been performed with electron pulse radiolysis. The most recent measurements have determined reference G values (number of chemical species created or lost per 100 eV of energy deposit) for hydroxyl radicals (^•OH) of 4.8 ± 0.2 molec./100 eV and solvated electron (e⁻_aq) yields of 4.2±0.2 molec./100 eV after just 7 ps (El Omar et al 2011) (Wang et al 2018). These values are significantly lower than previous values used to calibrate Monte Carlo simulations (see e.g., (Tomita et al 1997, Kreipl et al 2009, Pimblott et al 1996, Uehara and Nikjoo 2006) and call for revisiting the input parameters of MCTS codes. A re-evaluation of such parameters has been mentioned for the radiation chemistry code IONLYS-IRT (Sanguanmith et al 2013, Sultana et al 2020); however, specific details of parameter adjustment were not reported.

On the other hand, to verify the accuracy of MCTS for radiobiology applications, sophisticated DNA models have been developed based on the whole cellular nucleus to identify and quantify clustered DNA strand breaks sites (Nikjoo et al 2016, Friedland et al 2017, Štěpán and Davídková 2014, Meylan et al 2017, Lampe et al 2018b, Sakata et al 2019, Zhu et al 2020a). The spatial resolution of experimental measurements at the cellular level is insufficient to validate Monte Carlo simulation outputs directly; for example, experimental techniques can still not resolve spatial distributions of individual DNA single-strand breaks (SSB) and double-strand breaks (DSB), and there is insufficient data about the structure and the radiation chemistry of chromatin. Thus, different assumptions have been made by different research groups to reconcile their MCTS results with experimental data, which impacts the accuracy of the codes. In particular, the scavenging capacity of the biological environment has been mimicked by limiting the time domain to a few nanoseconds. Moiseenko et al. (Moiseenko et al 1998) showed that this approach introduces 20%−30% differences in strand break yields compared to the explicit simulation of scavenger molecules uniformly distributed around the radiation spurs. Besides, the simulation of the chemical and biological mechanisms occurring within a cell is not a trivial task (Wardman 2020), and MCTS simulations have not yet utilized the corresponding models to simulate more reliable cellular conditions.

The selection of a less complex biological system than a cell would assist in providing relevant data to evaluate the accuracy of MCTS. Plasmids of DNA are a convenient example. Experiments consisting of the irradiation of plasmids can be performed in a well-controlled environment with solutes of various scavenging capacities (Milligan et al 1996). Thus, under low LET irradiation, direct comparison with plasmid experiments provides a suitable way to validate directly MCTS radiochemistry capabilities. Comparison of MCTS with plasmid experiments considering direct and indirect damages has been performed in the past (Tomita et al 1998) (Fulford et al 2001) (Edel et al 2006).

In this work, we focus on the comparison of calculated versus published measured data to evaluate the accuracy of TOPAS-nBio. Parameters for modeling the radiation chemistry process of TOPAS-nBio were revisited, driven by the latest published experimental measurements of G values of radiation yield for fast electrons at the picosecond level. In that way, a reconciliation between measured and Monte Carlo modeled G values in liquid water was achieved. Then, we validated TOPAS-nBio for simulation of indirect damage of DNA. To this end, experimental setups of plasmids under low-LET irradiation reported in the literature were replicated with our validated Monte Carlo track-structure tool. Our benchmarked code provides a tool over which extended features regarding effects of temperature, compaction of DNA, oxygen concentration and other radiation chemistry processes may be implemented and evaluated.

2. Materials and methods.

The physics list comprises models describing the discrete transport of electrons in liquid water with no production cuts for secondary electrons, and all the interaction events are explicitly simulated. The selected models have been described extensively elsewhere (Incerti et al 2018, Shin et al 2019, Ramos‐Méndez et al 2020). In brief, the physics list, encapsulated in the “G4EmDNAPhysics_option2” constructor, includes an elastic scattering model based on the partial wave theory and an inelastic scattering model based on the formalism of the complex dielectric response function of liquid water. For the latter model, four ionization shells and five discrete electronic excitation states are considered. In Geant4-DNA, after an ionization has taken place, the energy of the emitted secondary electron is calculated from the differential (in energy transfer) ionization cross section, which is described by the so-called Born ionization model. This model applies to weakly bound electrons in the liquid water molecule and adopts the dielectric response function formalism. In the case of K-shell ionization (of the oxygen atom), the atomic model Binary-encounter-Approximation-with-Exchange (BEAX) is used. Both models are described in more detail in Incerti et al (2018) and references therein. Models to simulate vibrational excitation and electron attachment processes are also included in the constructor.

The reaction kinetics is calculated with the independent reaction times method, IRT (Tachiya 1983, Clifford et al 1986, Green et al 1990, Pimblott et al 1991). The implementation in TOPAS-nBio is described elsewhere (Schuemann et al 2018, Ramos-Méndez et al 2020). The simulation of scavengers is performed with the continuum approximation (Pimblott et al 1991) where it is assumed that the scavenging molecules are uniformly distributed in the background. Then, the probability of chemical species potentially reacting with the background at time t is described by an exponential distribution given by 1 – exp(−k[B] t), where the product of reaction rate k and scavenger concentration [B], k[B], is the scavenging capacity of the background. Instantaneous scavenging within reaction distance R, at the time of chemical species creation, is performed with a probability given by exp(−4πR³[B]/2) (Pimblott et al 1991). The reactions and rate constants used in this work are presented in table 1, obtained from (Pimblott 1992). These values originated from the National Institute of Standards and Technology (NIST) database (Buxton et al 1988), where each rate constant was evaluated for accuracy and consistency.

Table 1.

List of reaction rate constants used for the simulation of G values obtained from (Buxton et al 1988) (Milligan et al 1996) (Pastina and LaVerne 1999) and (Huerta Parajon et al 2008)

Reactions for simulation of radiolysis in pure liquid water.			Reactions with scavengers for DNA damage simulation.
Reaction	kobs (/M/s)
e−aq + e−aq → H2 + OH−	5.5 × 109		Reaction	kobs (/M/s)
e−aq + H3O+ → H•	2.3 × 1010		e−aq + O2 → O2−	1.9 × 1010
e−aq + H• → H2 + OH−	2.5 × 1010		H• + O2 → HO2	2.1 × 1010
e−aq + •OH → OH−	3.0 × 1010		•OH + DMSO	7.1 × 109
e−aq + H2O2 → OH− + •OH	1.1 × 1010		H• + DMSO	2.7 × 106
H3O+ + OH− → H2O	14.3 × 1010		e−aq + DMSO	3.8 × 106
H• + H• → H2	7.8 × 109
H• + •OH → H2O	1.55 × 1010
H• + H2O2 → •OH + H2O	9.0 × 107		Reactions for calculating G(H2O2)
•OH + •OH → H2O2	5.5 × 109		Reaction	kobs (/M/s)
			CH3OH + •OH → •CH2OH + H2O	9.7 × 108
			NO3− + eaq− → •NO32–	9.7 × 109
			NO3− + •H → •NO32–	1.4 × 106
Reactions with DNA			Reactions for calculating G(H • )
Reaction	kobs (/M/s)		Reaction	kobs (/M/s)
•OH + DNA	Variable		•H + HCO2−→ H2 +•CO2−	2.1 × 108
H• + DNA	0.03 × 109		e−aq + NO3− → NO32−	9.7 × 109
e−aq + DNA	0.01 × 109		Br + •OH →	1.1 × 1010

2.1. Validation of TOPAS-nBio for water radiolysis simulations for fast electrons.

To validate TOPAS-nBio, we revisit Geant4-DNA (version 10.6.p03) parameters for the simulation of the pre-chemical stage of water radiolysis previously reported (Kreipl et al 2009, Karamitros et al 2011, Ramos-Méndez et al 2018, Shin et al 2019). Prior to the dissociation of the ionized water molecules (H₂O⁺), hole migration by electron correlation and electron relaxation (charge migration) results in a displacement of these molecules and their dissociation products from the place of energy transfer (Ogura and Hamill 1973, Despré et al 2015, Kuleff et al 2016). In Geant4-DNA, this process is considered by adding an isotropic displacement from where the ionization event occurred. The distance is sampled from a normal distribution with a given root-mean-square deviation (RMS). Due to the lack of measured data at the pre-chemical stage, the root-mean square (RMS) values (inherited from the PARTRAC code) are set to match measured yields of ^•OH radical available in 2009 (Kreipl et al 2009). In Table 2, the distances used in Geant4-DNA are described. In this work, the selection of empirical values $RM{S}^{H_2{O}^{+}}$ and $RM{S}^{H_2{O}^{*}}$ is driven by experimental G values for ^•OH radicals obtained at the picosecond time range for fast electrons reported in (Wang et al 2018). We increased the displacement distance in multiples of the mean separation between water molecules, 0.31 nm (Perkins 1986), to minimize the discrepancy with measured data. The branching ratios are kept unchanged, as reported in table 4 in (Shin et al 2019) and originally reported in (Kreipl et al 2009).

Table 2.

Displacements of physical and dissociation products implemented in Geant4-DNA.

Physical product	Dissociation products	$RM{S}^{H_2{O}^{+}}$ or $RM{S}^{H_2{O}^{*}}$	Displacement
H2O+	H3O+ + •OH(1)	2.0 nm	H3O+ •OH	0 or 0.8 nm(2) 0.8 or 0 nm(2)
H2O*	H• + •OH	2.4 nm	H• •OH	17/18 $RM{S}^{H_2{O}^{*}}$ 1/18 $RM{S}^{H_2{O}^{*}}$
	H2 + 2 •OH	0.8 nm	H2 •OH •OH	2/18 $RM{S}^{H_2{O}^{*}}$ 16/18 $RM{S}^{H_2{O}^{*}}$ + 0.55 nm 16/18 $RM{S}^{H_2{O}^{*}}$ + 0.55 nm (3)
	H2 + •OH + OH−	0.8 nm	H2 •OH OH−	2/18 $RM{S}^{H_2{O}^{*}}$ 16/18 $RM{S}^{H_2{O}^{*}}$ + 0.55 nm 16/18 $RM{S}^{H_2{O}^{*}}$ + 0.55 nm(3)

⁽¹⁾If e⁻_aq are produced after an autoionization event, then its position is sampled using the one-step thermalization model. See the text.

⁽²⁾Either value is selected randomly with 50% probability.

⁽³⁾Positioned in the opposite direction from the first ^•OH

The thermalization of sub-excited electrons is simulated using a “one-step model” with displacement parameters obtained from the literature. The transport of each individual sub-excited electron is stopped once its kinetic energy is reduced to <10 eV. Later, in this one-step model, a solvated electron is placed at a distance (around the last interaction point) randomly sampled from a Gaussian distribution, with a standard deviation given by the data reported in (Ritchie et al 1994), with the correction factor described in (Shin et al 2019). The data from Ritchie et al, 1994, provided the best agreement with measured data of the time-dependent G-values for solvated electrons from (El Omar et al 2011) when using the physics list selected in this work. This model and other approaches to simulate the thermalization of solvated electrons have been discussed in detail elsewhere (Shin et al 2019).

The simulation setup consists of a homogenous liquid water box (1 g/cm³ density) irradiated with monoenergetic electrons of 1 MeV. This setup is commonly used to simulate MCTS codes for fast electrons, as reported elsewhere (Pimblott and LaVerne 1997, Uehara and Nikjoo 2006, Ramos-Méndez et al 2018). Specifically, an isotropic electron source is positioned in the center of a cubic water phantom of 1 cm side. When the primary electron has lost more than 10 keV, the tracking of the electron is stopped, and it is removed from the simulation. The secondary electrons are then followed until their kinetic energy is reduced at or below 10 eV, the low energy limit of the ELSEPA model (Shin et al 2018). After that, thermalization is simulated with the one-step model. The total energy deposited in the aqueous medium thus corresponds to the energy lost by the primary electron, which is at least 10 keV (Karamitros 2012). Immediately, the pre-chemical stage takes place, and the initial position of radiolytic products are obtained and input to the IRT method for the simulation of the chemical stage up to 10 μs.

A comparison with reference data for H₂, H^•, and H₂O₂ was performed. For H₂, data was obtained from (Pastina et al 1999). The authors stated that reported G values are suitable for direct comparison with Monte Carlo simulations without scavengers. For H₂O₂ and H^•, the scavenger system used in the experiments was replicated in our simulations. G values of H₂O₂ measured in solutions containing NO₃⁻ at a concentration of 25 mM, and CH₃OH at concentrations ranging from 10^–3 – 10 M, were obtained from (Hiroki et al 2002). For H^•, measured G values in solutions containing 1 mM of Br, 1 mM of NO₃⁻ and HCO₂⁻ at a concentration ranging from 10^–2 – 1 M were obtained from (Huerta Parajon et al 2008). For the latter set of data, replicating the experiment, the calculated yield of H^• was estimated from the total yield of H₂ calculated with HCO₂⁻ subtracted from the total yield of H₂ calculated without HCO₂⁻ (Huerta Parajón 2010). The reactions used for simulations in the presence of scavengers are shown in table 1. The irradiation setup was the same as that used for pure liquid water simulations.

2.2. Validation of TOPAS-nBio for damage in supercoiled DNA plasmid.

The validation of DNA damage under low-LET irradiation was performed for the experimental conditions from plasmid DNA in aerobic aqueous solution irradiated with ¹³⁷Cs γ-rays, as reported in (Milligan et al 1993, Milligan and Ward 1994). A two-stage simulation was performed using condensed-history and track-structure Monte Carlo with TOPAS and TOPAS-nBio, respectively, as described below.

The first stage was used to determine the energy spectrum, at electronic equilibrium conditions, of secondary electrons set in motion by ¹³⁷Cs γ-rays interacting in a water phantom. For that, the TOPAS tool (Perl et al 2012, Faddegon et al 2020) version 3.5 was used to simulate a concentric system of two homogenous spherical water phantoms of 5 cm and 10 cm radius, respectively. The physics list used the constructor “G4EmStandardPhysics_option4” with a production cut for secondary electrons of 0.05 mm, extensively benchmarked for applications in medical physics (Arce et al 2021). An isotropic point source of monoenergetic γ-rays (662 keV) was positioned at the center, as shown in figure 1. We obtained the vertex kinetic energy spectrum (at the position of creation) of those secondary electrons that reached a phase space tallied on the surface of a 5 cm radius sphere. In total, 4 × 10⁸ γ-rays were simulated.

Figure 1.

Setup showing a two-stage simulation. The condensed-history MC simulation setup used to retrieve the secondary electron spectrum is shown on the left side. The track-structure MC simulation setup used to calculate SSB and DSB yields using supercoiled plasmid DNA is shown on the right side. Red lines correspond to few electron tracks. For more details, see the text.

The second stage consists of track-structure Monte Carlo simulations with TOPAS-nBio. The following assumptions are made for simulating the interactions of secondary electrons and reactions of chemical species with DNA molecules. All the medium, including the region occupied by the DNA geometry is made of liquid water. For biological targets, a canonical double helix B-DNA configuration is considered. The DNA sugar-phosphate groups and nucleobases, represented as cut spheres in figure 1, are the main target of the radiation or chemical species to cause DNA damage. The spatial coordinates of the centroids of the semi-spheres corresponding to sugar-phosphate groups are included in the IRT method for the realization of reactions with the chemical species produced in the water radiolysis process. The coordinates are determined by the supercoiled path, which defines the plasmid DNA model (see below). DNA nucleobases are not included in the reaction kinetics because observed rate constants between chemical species and DNA are used (Tomita et al 1998, Perry et al 2020), but they are present for ionization/excitation interactions (see below). For the simulated time domain of the chemical stage (10⁻¹²–10⁻⁴ s), the plasmid DNA model is assumed static. Accumulation of energy deposition of at least 17.5 eV in the sugar-phosphate volumes is considered to register an SSB from direct physical interactions (see (Lampe et al 2018a, Zhu et al 2020b) and references therein). Chemical species originated from radiolysis occurring within the regions occupied by the DNA semi-spheres are not included in the reaction kinetics and are eliminated upon creation, i.e., no DNA radiolysis is simulated.

For modeling indirect damage, a SSB is registered with specific efficiency after the reaction between ^•OH and DNA (as a whole) occurred (Önal et al 1988, Milligan et al 1993, Klimczak et al 1993). The reaction rate coefficient for the •OH+DNA reaction (table 1) depends on the scavenging capacity of the irradiated environment and is obtained from measured data reported elsewhere (Milligan et al 1996). For H^• and e⁻_aq, constant reaction rates are used as obtained from (Buxton et al 1988). We estimate the DNA strand break efficiencies of ^•OH and H^• by minimization. We compare calculated to measured data applying a minimization algorithm using the Nelder-Mead method (Nelder and Mead 1965) to find the best efficiency values. For e⁻_aq, no strand breaking in DNA is counted as it has not been observed experimentally (Jones and O’Neill 1991), but reactions with DNA are included as e⁻_aq binds efficiently with nucleobases (Kumar et al 2019).

The DNA model is wrapped around supercoiled paths to reconstruct pUC18 plasmids (length of 2686 base-pairs length) utilizing DNAfabric (Meylan et al 2015). In a separate simulation, the geometric model of the pUC18 plasmid (Yanisch-Perron et al 1985) is constructed by the worm-like chain method and subsequent smoothing to base-pair level. First, the supercoiling of a circular plasmid represented by 91 linear segments is modeled using the elastic worm-like chain code developed by the group of A. Vologodskii (Vologodskii and Cozzarelli 1994, Huang et al 2001). The temperature is set to 298 K, the superhelical density to −0.06, and the step length to 500 ps. Resulting coarse configurations are converted to sets of 2686 equidistant points along a smooth path using an in-house code implementing the approach of Kümmerle and Pomplun (Kümmerle and Pomplun 2005). One sample supercoiled plasmid configuration is selected for the Monte Carlo simulation of DNA damage.

The plasmid is positioned multiple times inside a spherical water phantom of 0.5 μm radius. The positions and orientations of the plasmids are uniformly random. The sphere is centered in a cubic water box of 2 μm side. A volumetric electron source is uniformly distributed in the cubic box, including the sphere. The initial electron spectrum is calculated in the first stage using a condensed-history Monte Carlo, where the initial directions are set to be isotropic (figure 1). In the experiment (Milligan et al 1993), the DNA is dissolved in an aerated solution containing DMSO. Thus, we simulated the scavenging behavior of that solution using the reaction rates shown in Table 1 for e⁻_aq and H^• with O₂, using a concentration of 21% O₂ (0.27 × 10^–3 mol dm^–3). We report the G value of SSBs using the same units of the experimental data (μmol J^–1) as a function of scavenging capacity for DMSO. In this way, measured results from (Perry et al 2021) performed with different scavenger can be included. The DMSO concentrations range from 0.5 × 10^–4 to 1 mol dm^–3 and the DNA concentration is 50 μg mL^–1. We estimated that nine pUC18 plasmids in the spherical phantom of 0.5 μm radius are equivalent to approximately 50 μg mL^–1 of DNA concentration (50 × 10^–6 g mL⁻¹ × 10³ L^–1 × mL /(2686 bp × 650 g mol^–1 bp^–1)] × N_av × 5.24 × 10^–16 L ≈ 9). Results for calculated SSB yields as a function of DNA concentration (from 10 – 200 μg mL^–1) for a concentration of 10^–3 mol dm^–3 DMSO are also reported. Finally, the yield of SSB and DSB as a function of ^•OH scavenging capacity (from 7.1 × 10⁵ – 7.1 × 10⁹ s^–1) are reported. A DSB was scored when there was no more than a 10 base-pair distance between at least two SSB’s occurring in opposite DNA strands. The total number of simulation jobs with independent random number seeds were 200 to 500, achieving statistical uncertainties from 0.7% to 5% (one standard deviation) for the simulation with the lowest and highest DMSO concentration, respectively. On average, 1150±80 primary histories are generated in each simulation job to achieve an absorbed dose of 30 Gy in the spherical phantom. In a systematic study (not shown) we found that 30 Gy absorbed dose provided a reasonable computing memory and speed, resulting from the number of primary yields used in the IRT and their processing time. The simulations take between 3 to 6 minutes to complete on a single core of a 2.7 GHz 12-Core Intel Xeon E4.

3. Results.

3.1. Time-dependent G values for fast electrons.

It was found that a distance of four water molecule’s mean separation distances, 1.24 nm, for both $RM{S}^{H_2{O}^{+}}$ and $RM{S}^{H_2{O}^{*}}$ reproduced the measured time-dependent G values for ^•OH radicals. The G values using that value are shown in figure 2. In the top row of the figure, the calculated G value in pure liquid water for ^•OH, e⁻_aq and H₂ are displayed in individual panels, along with experimental data. The agreement for the three sets of data along all the time domains was within one standard deviation of experimental measurements. In the bottom row of figure 2, the G value for H₂O₂ and H^• is displayed in each panel. As depicted, the time-dependent G values calculated in pure liquid water (solid line) did not reproduce the behavior of the experimental yields for H₂O₂ (empty circles) and H^• (filled triangles). However, the simulations considering the scavengers used in the experiments (squares connected by dashed lines) agreed within one standard deviation of the experimental data.

Figure 2.

Time-dependent G values for fast electrons (1 molec./100 eV = 1.036×10^–7 mol J^–1). TOPAS-nBio/Geant4-DNA simulated data: (solid line) pure liquid water calculations; (blue squares connected with dashed lines) simulations of scavenger systems for H₂O₂ and H^• as shown in table 1. Error bars represent statistical uncertainties, one standard deviation. Measured data: black and grey solid lines (Ma et al 2015); ☐ (Wang et al 2018); △ (Laverne 2000); ■ (Bartels et al 2000); ◇ (Shiraishi et al 1988); ✕ and ◆ (Pastina et al 1999); ○ (Hiroki et al 2002); ▲ (Huerta Parajon et al 2008).

3.2. DNA damage in plasmid geometries.

In figure 3, calculated and measured SSB yields as a function of ^•OH scavenging capacity are shown. The estimated efficiencies for ^•OH and H^• are 24% and 0.5%, respectively. These values are used in all the following results. As depicted, the calculated SSB yields reproduced the measured data from pUC18 irradiations along with the considered DMSO concentrations reasonably well. The yields included the G(SSB) produced by direct effects, which resulted in 1.77±0.01 × 10⁻⁶ μmol/J for the geometrical DNA model used in this work. Figure 4 shows G(SSB) as a function of the DNA concentration. The slopes of linear regression fitting to both calculated and measured data agreed within 1%±0.8%. Finally, calculated DBS as a function of ^•OH scavenging capacity reproduced the behavior of measured yields well as shown in figure 5.

Figure 3.

Total calculated SSB yields (direct plus indirect) as a function of ^•OH scavenging capacity (solid lines). Measured data for pUC18 is from ■ (Milligan et al 1993), ◆ (Milligan and Ward 1994), and ● (Milligan et al 1996). Measured data for pUC19 ▲ is from (Perry et al 2021). Percentage differences (☐) between calculated to measured data are shown in the bottom figure. The dotted lines are margins from experimental uncertainty. Error bars are displayed when bigger than the symbol, represent statistical uncertainties from Monte Carlo simulations, one standard deviation.

Figure 4.

Calculated G(SSB) as a function of the DNA concentration (■ connected with solid line). Error bars, smaller than the symbols, represent statistical uncertainties, one standard deviation. Measured data is from (Milligan et al 1993): pUC18 (○); pEC (△); and SV40 (◆).

Figure 5.

Calculated single and double-strand break yields as a function of hydroxyl radical scavenging capacity. Error bars represent statistical uncertainties, one standard deviation. Measured data: ○ pBR322 (Klimczak et al 1993), ∇ pBR322 (Tomita et al 1995).

4. Discussion.

In this work, TOPAS-nBio was applied to simulate water radiolysis and DNA damage under low-LET irradiation. The simulation of the reaction kinetics was performed with the IRT method, providing a fast and reliable tool to assist in investigating the biological effect of the interaction of ionizing radiation at the early stages.

Calculated G values at the picosecond stage agreed within experimental errors of published direct measurements of ^•OH and e⁻_aq performed in pure liquid water. The temporal evolution of the G values simulated up to the microsecond time stage was also well reproduced by TOPAS-nBio for ^•OH, e⁻_aq, and H₂. To obtain such an agreement we adjusted the RMS of the displacement of ionized and excited water molecules caused by charge migration. Oscillating charge migration is expected to happen a few femtoseconds after an energy transfer event, hence challenging its experimental observation given the short period of time (Kuleff et al 2016). Thus, RMS values have been empirically adjusted in other Monte Carlo track-structure codes due to the lack of corresponding measured data (Kreipl et al 2009, Cobut et al 1998, Tomita et al 1997, Uehara and Nikjoo 2006). The RMS obtained in this work (1.24 nm), shorter than Geant4-DNA’s default value (2 nm), increased the chance of contact reactions at the earliest times producing lower yields of ^•OH radical. For ^•OH radicals at 7 ps, this modification represented a reduction from 5.0 molecules per 100 eV (Ramos-Mendez et al., 2020) to 4.7 molecules per 100 eV (the measure data show 4.7±0.2 molecules per 100 eV (Wang et al 2018)). Geant4-DNA being a radiation transport code is not currently capable of simulating molecular dynamics of water molecules. Thus, effects like the binding of water molecules to biomolecules (DNA, proteins or lipids) that in principle affect the RMS displacement (see e.g., Shweta and Sen 2018), cannot be studied in detail at this point with our code. For e⁻_aq, this parameter had a negligible effect as the products of auto-ionization that followed a dissociation event were handled by the one-step thermalization method (Shin et al 2019).

While it is a common practice, the comparison between time-dependent product yields calculated in pure liquid water and measured data under the presence of scavengers deviated from each other and should be avoided. In this work, two sets of data were selected to demonstrate this point. The temporal evolution of H₂O₂ and H^• reproduced the measured data within experimental errors only when the yields were calculated in the presence of scavengers. However, a more comprehensive evaluation of TOPAS-nBio under a wide range of scavengers, scavenger concentrations, and radiation qualities was outside the scope of this work and it is the subject of future work. A selection of radiobiologically relevant scavengers should precede that task given the scope of TOPAS-nBio.

On the other hand, for DNA damage simulations an encouraging agreement was found between calculated yields of SSB and DSB with measured data for low-LET radiation on a base-pair level. A limitation of the applicability of IRT for smaller scales (e.g., including adenine, thymine, cytosine, and guanine nucleobases or atomic components) could be expected. Bluett and Green demonstrated (Bluett and Green 2006) that at such proximity, multiple reactive centers in the sugar-base system might occur, so the reaction rate between a reaction pair is affected by the presence of static neighboring species. The IRT method assumes that reactions between pairs occur in isolation, thus, the IRT method may give inaccurate results. Nevertheless, the use of observed reaction rates in this work provided a base-pair level resolution, which resulted in a general agreement within experimental uncertainties.

The estimated SSB efficiencies from the Monte Carlo data included a highly detailed plasmid DNA geometrical model. The estimated efficiency of 24% for SSB induction for ^•OH was within previously reported values between 24% to 44% obtained with cylindrical non-homogeneous kinetic model (Milligan et al 1993, Udovičić et al 1994, Klimczak et al 1993). In that model, however, a homogenous cylindrical model representing a straight DNA segment was considered, which differed from the more detailed supercoiling DNA representation facilitated by TOPAS-nBio. For H^•, the efficiency of 0.5% provided the best agreement at higher scavenger concentrations. This value was close to the 0.81% calculated by (Aydogan et al 2008). The differences are subtle and could be attributed to the different Monte Carlo codes used used by these authors. In their model, the authors used a straight linear DNA segment of 38 bp, with atomic resolution and multiple reactions sites on a base pair. However, our calculated efficiency was 12% higher than that measured experimentally (Milligan et al 1993). This difference may be due to the limited resolution of our model, justified by the use of the variable rate coefficient for ^•OH + DNA, which disregards the individual reactions with nucleobases and other components. The reaction of ^•OH with nucleobases is in general several times faster than the reaction of ^•OH with deoxyribose (Buxton et al 1988). Thus, by including reactions with DNA bases, an increment in the number of ^•OH reactions is expected, which might lead to a lower SSB efficiency. For that, reaction rate constants obtained in a B-DNA structure instead of an aqueous solution of DNA are needed. From the computational point of view, an effort of our group to find ways to extend the IRT method to handle DNA bases was reported in (Tran et al 2021). On the other hand, our estimation of the direct effect assumed an energy threshold for accumulated energy depositions of at least 17.5 eV, which produced 28% fewer SSB compared to, e.g., the 5–37.5 eV linear ramp threshold shown elsewhere (Zhu et al 2020b). A more suitable selection of the energy threshold must consider the transport of low energy electrons below 15 eV (avoiding the one-step thermalization model), which can induce DNA damage, as shown experimentally by (Alizadeh et al 2015). In that regard, an extended physics package which improves the detail in the pre-chemical stage for handling Auger electrons and electron capture will be soon made available in Geant4 (Shin et al., 2021 under review). Experimentally, a dependence with the scavenging capacity of the SSB induction efficiency was further observed (Önal et al 1988). Even though we used a single constant value as a first approach, the assumptions made in this work were sufficient to reproduce the behavior of scavenging dependence of DSB yields measured for different plasmids.

5. Conclusions.

In this work, TOPAS-nBio was validated for simulating water radiolysis in liquid water and DNA damage for plasmids at low LET irradiation. Satisfactory agreement within experimental uncertainties was obtained, reconciling Monte Carlo calculations of water radiolysis from ^•OH and e⁻_aq yields at the picosecond level. For pUC18 plasmids irradiated by ¹³⁷Cs γ-rays, calibration via the SSB induction efficiency was consistent with published efficiency values, leading to agreement with measure data within experimental uncertainties. TOPAS-nBio facilitated the implementation of experimental conditions of DNA irradiations including DNA geometry, source quality, prescribed dose, chemical parameters, and scavengers, exploiting the full potential of Geant4-DNA. As a result, an accurate, fast, and user-friendly Monte Carlo framework is provided by TOPAS-nBio/Geant4-DNA to evaluate DNA damage from first principles.