Independent Reaction Times Method Research Articles

GEANT4-DNA simulation of temperature-dependent and pH-dependent yields of chemical radiolytic species

Objective. GEANT4-DNA can simulate radiation chemical yield (G-value) for radiolytic species such as the hydrated electron () with the independent reaction times (IRT) method, however, only at room temperature and neutral pH. This work aims to modify the GEANT4-DNA source code to enable the calculation of G-values for radiolytic species at different temperatures and pH values. Approach. In the GEANT4-DNA source code, values of chemical parameters such as reaction rate constant, diffusion coefficient, Onsager radius, and water density were replaced by corresponding temperature-dependent polynomials. The initial concentration of hydrogen ion (H+)/hydronium ion (H3O+) was scaled for a desired pH using the relationship pH = –log10 [H+]. To validate our modifications, two sets of simulations were performed. (A) A water cube with 1.0 km sides and a pH of 7 was irradiated with an isotropic electron source of 1 MeV. The end time was 1 μs. The temperatures varied from 25 °C to 150 °C. (B) The same setup as (A) was used, however, the temperature was set to 25 °C while the pH varied from 5 to 9. The results were compared with published experimental and simulated work. Main results. The IRT method in GEANT4-DNA was successfully modified to simulate G-values for radiolytic species at different temperatures and pH values. Our temperature-dependent results agreed with experimental data within 0.64%–9.79%, and with simulated data within 3.52%–12.47%. The pH-dependent results agreed well with experimental data within 0.52% to 3.19% except at a pH of 5 (15.99%) and with simulated data within 4.40%–5.53%. The uncertainties were below ±0.20%. Overall our results agreed better with experimental than simulation data. Significance. Modifications in the GEANT4-DNA code enabled the calculation of G-values for radiolytic species at different temperatures and pH values.

DNA damage modeled with Geant4-DNA: effects of plasmid DNA conformation and experimental conditions

The chemical stage of the Monte Carlo track-structure (MCTS) code Geant4-DNA was extended for its use in DNA strand break (SB) simulations and compared against published experimental data. Geant4-DNA simulations were performed using pUC19 plasmids (2686 base pairs) in a buffered solution of DMSO irradiated by 60Co or 137Cs γ-rays. A comprehensive evaluation of SSB yields was performed considering DMSO, DNA concentration, dose and plasmid supercoiling. The latter was measured using the super helix density value used in a Brownian dynamics plasmid generation algorithm. The Geant4-DNA implementation of the independent reaction times method (IRT), developed to simulate the reaction kinetics of radiochemical species, allowed to score the fraction of supercoiled, relaxed and linearized plasmid fractions as a function of the absorbed dose. The percentage of the number of SB after •OH + DNA and H• + DNA reactions, referred as SSB efficiency, obtained using MCTS were 13.77% and 0.74% respectively. This is in reasonable agreement with published values of 12% and 0.8%. The SSB yields as a function of DMSO concentration, DNA concentration and super helix density recreated the expected published experimental behaviors within 5%, one standard deviation. The dose response of SSB and DSB yields agreed with published measurements within 5%, one standard deviation. We demonstrated that the developed extension of IRT in Geant4-DNA, facilitated the reproduction of experimental conditions. Furthermore, its calculations were strongly in agreement with experimental data. These two facts will facilitate the use of this extension in future radiobiological applications, aiding the study of DNA damage mechanisms with a high level of detail.

Assessment of DNA damage with an adapted independent reaction time approach implemented in Geant4-DNA for the simulation of diffusion-controlled reactions between radio-induced reactive species and a chromatin fiber.

PurposeSimulation of indirect damage originating from the attack of free radical species produced by ionizing radiation on biological molecules based on the independent pair approximation is investigated in this work. In addition, a new approach, relying on the independent pair approximation that is at the origin of the independent reaction time (IRT) method, is proposed in the chemical stage of Geant4‐DNA.MethodsThis new approach has been designed to respect the current Geant4‐DNA chemistry framework while proposing a variant IRT method. Based on the synchronous algorithm, this implementation allows us to access the information concerning the position of radicals and may make it more convenient for biological damage simulations. Estimates of the evolution of free species as well as biological hits in a segment of DNA chromatin fiber in Geant4‐DNA were compared for the dynamic time step approach of the step‐by‐step (SBS) method, currently used in Geant4‐DNA, and this newly implemented IRT.ResultsResults show a gain in computation time of a factor of 30 for high LET particle tracks with a better than 10% agreement on the number of DNA hits between the value obtained with the IRT method as implemented in this work and the SBS method currently available in Geant4‐DNA.ConclusionOffering in Geant4‐DNA more efficient methods for the chemical step based on the IRT method is a task in progress. For the calculation of biological damage, information on the position of chemical species is a crucial point. This can be achieved using the method presented in this paper.

Independent reaction times method in Geant4‐DNA: Implementation and performance

The simulation of individual particle tracks and the chemical stage following water radiolysis in biological tissue is an effective means of improving our knowledge of the physico-chemical contribution to the biological effect of ionizing radiation. However, the step-by-step simulation of the reaction kinetics of radiolytic species is the most time-consuming task in Monte Carlo track-structure simulations, with long simulation times that are an impediment to research. In this work, we present the implementation of the independent reaction times (IRT) method in Geant4-DNA Monte Carlo toolkit to improve the computational efficiency of calculating G-values, defined as the number of chemical species created or lost per 100eV of deposited energy. The computational efficiency of IRT, as implemented, is compared to that from available Geant4-DNA step-by-step simulations for electrons, protons and alpha particles covering a wide range of linear energy transfer (LET). The accuracy of both methods is verified using published measured data from fast electron irradiations for • OH and for time-dependent G-values. For IRT, simulations in the presence of scavengers irradiated by cobalt-60 γ-ray and 2MeV protons are compared with measured data for different scavenging capacities. In addition, a qualitative assessment comparing measured LET-dependent G-values with Geant4-DNA calculations in pure liquid water is presented. The IRT improved the computational efficiency by three orders of magnitude relative to the step-by-step method while differences in G-values by 3.9% at 1μs were found. At 7ps, • OH and yields calculated with IRT differed from recent published measured data by 5%±4% and 2%±4%, respectively. At 1μs, differences were 9%±5% and 6%±7% for • OH and , respectively. Uncertainties are one standard deviation. Finally, G-values at different scavenging capacities and LET-dependent G-values reproduced the behavior of measurements for all radiation qualities. The comprehensive validation of the Geant4-DNA capabilities to accurately simulate the chemistry following water radiolysis is an ongoing work. The implementation presented in this work is a necessary step to facilitate performing such a task.

Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations

Ionizing radiation interacts with the water molecules of the tissues mostly by ionizations and excitations, which result in the formation of the radiation track structure and the creation of radiolytic species such as H.,.OH, H2, H2O2, and e-aq. After their creation, these species diffuse and may chemically react with the neighboring species and with the molecules of the medium. Therefore radiation chemistry is of great importance in radiation biology. As the chemical species are not distributed homogeneously, the use of conventional models of homogeneous reactions cannot completely describe the reaction kinetics of the particles. Actually, many simulations of radiation chemistry are done using the Independent Reaction Time (IRT) method, which is a very fast technique to calculate radiochemical yields but which do not calculate the positions of the radiolytic species as a function of time. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time-consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. The SBS and IRT methods are both based on the Green's functions of the diffusion equation (GFDE). In this paper, several sampling algorithms of the GFDE and for the IRT method are presented. We show that the IRT and SBS methods are exactly equivalent for 2-particles systems for diffusion and partially diffusion-controlled reactions between non-interacting particles. We also show that the results obtained with the SBS simulation method with periodic boundary conditions are in agreement with the predictions by classical reaction kinetics theory, which is an important step towards using this method for modelling of biochemical networks and metabolic pathways involved in oxidative stress. Finally, the first simulation results obtained with the code RITRACKS (Relativistic Ion Tracks) are presented.

A Monte–Carlo step-by-step simulation code of the non-homogeneous chemistry of the radiolysis of water and aqueous solutions. Part I: theoretical framework and implementation

The importance of the radiolysis of water in irradiation of biological systems has motivated considerable theoretical and experimental work in the radiation chemistry of water and aqueous solutions. In particular, Monte-Carlo simulations of radiation track structure and non-homogeneous chemistry have greatly contributed to the understanding of experimental results in radiation chemistry of heavy ions. Actually, most simulations of the non-homogeneous chemistry are done using the Independent Reaction Time (IRT) method, a very fast technique. The main limitation of the IRT method is that the positions of the radiolytic species are not calculated as a function of time, which is needed to simulate the irradiation of more complex systems. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. In the present paper, the first of a series of two, the SBS method is reviewed in detail. To these ends, simulation of diffusion of particles and chemical reactions in aqueous solutions is reviewed, and implementation of the program is discussed. Simulation of model systems is then performed to validate the adequacy of stepwise diffusion and reaction schemes. In the second paper, radiochemical yields of simulated radiation tracks calculated by the SBS program in different conditions of LET, pH, and temperature are compared with results from the IRT program and experimental data.

On the validity of the independent reaction times approximation for the description of the nonhomogeneous kinetics of liquid water radiolysis

The validity of using the independent reaction times (IRT) method to describe the nonhomogeneous reaction kinetics of complex and spatially correlated systems, such as ionising radiation track segments in liquid water, is tested. The time-dependent yields of various radiolytic species obtained with the IRT method are shown to compare well to those of a full step-by-step Monte Carlo simulation code. The good agreement between the two methods still holds as the linear energy transfer of the radiation is increased from 0.3 to 45 keV μm −1.

Simulation of ion recombination in low permittivity solvents: Extended clusters

Ion recombination in spatially extended multi-pair cation-anion (C +/A −) and cation-electron (C +/e −) systems in low permittivity solvents has been modeled using random flights simulation and the independent reaction times method, in order to investigate the effects of the spatial distribution of the reactants on the recombination kinetics. The kinetics are found to depend on the separations between adjacent C +s, the C +-C +-C + angle, and the cation and anion diffusion coefficients. The long-time yields predicted by the two simulation methods are in good agreement, however, the short-time dependence of the decay kinetics simulated by the IRT model is slower than that of the more realistic random flights method when the inter-cation distances are small, because of the cumulative effects of the Coulomb inter-ion forces. Some other small and subtle effects of initial distribution are presented, which are not recognized by the IRT method.

On the reactions of hydrated electrons with OH⋅ and H3O+. Analysis of photoionization experiments

With the help of Monte Carlo simulation techniques, we study the recombination kinetics of hydrated electrons (e−aq) with H3O+ and OH⋅ which results from the photoionization of pure water with femtosecond pulsed lasers. A full description of the simulation procedure is given and various comparisons are made with analytical formulations of the reaction kinetics. Particular attention is given to the reaction of e−aq with H3O+, which is only partially diffusion controlled and which involves a Coulombic interaction with dielectric saturation effects. We find that the probability of reaction per e−aq –H3O+ encounter is small (∼6%) and that the encounter duration can be of the order of a few picoseconds. The competition between the reaction of e−aq with H3O+ and with OH⋅ is analyzed with the simulations and with the independent reaction times method. Both approaches indicate that the e−aq decay is largely dominated by the reaction of e−aq with OH⋅. The effect of neighboring ionization sites on the e−aq decay kinetics is also included in the simulations to account for different possible densities of ionization sites. The initial separation between the reactants is found to be about 1 nm, in agreement with previous determinations. The significance of this last value and the constraints that it puts on the initial kinetic energy of the photoelectrons is discussed.

Stochastic modeling of fast kinetics in a radiation track

A method is presented for calculating the time-dependent G values and product yields formed in a fast electron track. The calculations are based on an efficient stochastic simulation technique--the independent reaction times (IRT) method--which has previously been developed and validated in detail. The IRT method combines the reactants in pairs and selects reaction times randomly from the appropriate marginal reaction time distributions. Reactions are counted sequentially, starting with the shortest reaction time and limiting subsequent consideration to pairs in the set of remaining particles. The technique is efficient and accurate and is capable of dealing with ionic species, partially diffusion-controlled reactions, and reactive products. Our previous calculations based on the IRT method have considered only reactions of small numbers of particles in isolated spurs. A new simulation protocol is presented that efficiently handles the extended distribution and the large number of reactive particles encountered in a radiation track while making use of any isolation that exists on appropriate timescales. The simulated G values at zero time and 0.1 {mu}s for a model 22-MeV electron track differ significantly from experimental values, and the discrepancy is ascribed to deficiencies in the initial distribution.

Stochastic models of diffusion-controlled ionic reactions-induced spurs. 2. Low-permittivity solvents

The diffusion-controlled recombination of small clusters of ions in low-permittivity solvents is considered. A Monte Carlo simulation technique used previously for high-permittivity solvents is introduced and discussed briefly. The independent reaction times (IRT) simulation method is described, and its implementation for the kinetics of ion clusters is detailed. The IRT approximation is tested against the full Monte Carlo simulation for a variety of random and nonrandom initial configurations and against alternative analytic theories. We find the IRT method to be surprisingly accurate under these stringent conditions.