Computational demonstration of multiple DNA damages produced by the radiolytic chemical species in an aqueous DNA solution

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The critical size and the chemical lesion types constituting the damage site have not been fully elucidated. We challenged this long-term issue by developing a dynamic Monte Carlo code for the chemical process. The reaction probabilities and the spatial distribution of lesions were theoretically solved as a function of the spur radius and distance between DNA and the initial ionisation position. The results showed that a hydroxyl radical and a hydrated electron from a single spur can concomitantly react within a 10 base pairs DNA to induce a multiple DNA damage site comprising a DNA single-strand break and reductive nucleobase damage; however, the reaction probability is 0.4% or less. Once this combination arises, it strongly compromises the activity of nucleobase excision repair enzymes. The efficiency is comparable to that of DNA double-strand breaks, which have been thought to be a significant cause of cell death. However, a single-spur reaction could be a source of damaged nucleobase misrepair, leading to point mutations in the genome. Physical sciences/Chemistry/Chemical biology/DNA Biological sciences/Biochemistry/DNA Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Water radiolysis in a living system results in chemically irreversible deoxyribonucleic acid (DNA) damage, such as DNA strand breaks, nucleobase lesions and apurinic/apyrimidinic (AP) sites. DNA repair enzymes recover most DNA lesions in vivo. However, when multiple lesions are within 1–2 helical turns (10–20 base pairs (bps)) of DNA, the lesions are less likely to be repaired, leading to cell death or mutations. These DNA damage configurations are called multiple damage sites or clustered damage 1,2 . They are formed by the direct action of ionisation/excitation with DNA, referred to as the direct effect, and indirect actions of water radiolytic species, categorised as indirect effects. The latter effect occurs via thermal diffusion and chemical reactions with the water radiolytic species, typically a hydroxyl radical ( • OH) and hydrated electron (e − aq ). A previous study using a plasmid as a simple model DNA exposed to X-rays or carbon ion beams showed that the indirect action induced strand breaks, nucleobase lesions and AP sites in vitro , even at the cell mimetic scavenging condition 3 . Computer simulations assuming the radical scavenging environment in cells indicated that the direct-to-indirect effect ratio is approximately 1:3 4,5 ; however, the contributions to cluster damage generation of the direct and indirect effects remain unclear experimentally. The reason is that biochemical or analytical chemistry methods for DNA damage detection have insufficient spatial resolution to determine the DNA lesion types and damage distributions within a few ten bps; thus, advanced computer simulation is the only approach. So far, Monte Carlo (MC) simulation allows quantitatively estimating clustered DNA damage yields by simulating the physical, physicochemical and chemical processes 6 . The physical process identifies the ionisation and electronic excitation sites induced in water 7,8 . In the physicochemical process, the radiolytic chemical species of water are identified 6,9 ; however, the MC codes should adjust for the initial yield of the chemical species to reproduce the experimental results of the time-dependent yields in the chemical process 6,9 . The diffusion and the reactions of the chemical species in water are simulated during chemical processes. The spatial distributions of DNA damage are estimated based on these ionisation, electronic excitation, and chemical reaction sites based on water radiolysis 4 . The efficiencies of the enzymatic repair of the clustered damage could be strongly affected by individual lesions comprising clustered damage sites and their spatial distributions 10,11 . These depend on the initial damage processes, namely direct or indirect effects. Thus, we have previously developed a dynamic MC code for the physical process (dmcc_phys) comprising a time-evolving MC and molecular dynamics (MD) 12–20 . Using this code, we succeeded in quantitatively evaluating DNA damage clustering via the direct effect 17 . Secondary electron deceleration in water was also investigated to demonstrate the initial yields 18 and the spatial distributions 19,20 of e − aq using dmcc_phys. These findings help estimate DNA damage. We newly developed a dynamic MC code for the chemical process (dmcc_chem) to quantitatively demonstrate the yields of DNA damage clustering via the indirect effect as an initial step of radiobiological phenomena, such as cell lethality or mutation induction. The rate constants 21 between the chemical species and nucleotides (adenosine monophosphate (AMP), cytidine monophosphate (CMP), guanosine monophosphate (GMP) and thymidine monophosphate (TMP)), whose sequences in DNA are the genetic information of an organism, were used for code development. This study aimed to reveal whether the single-spur comprising a hydronium ion (H 3 O + ), • OH and e − aq originating from the single ionisation of a water molecule, the most fundamental process of the indirect effect, potentially causes clustered lesions in DNA. We investigated the time evolution of spur broadening. The effects of the initial ionisation distance from DNA and the radical scavengers on the probabilities of their chemical reactions were also quantified. Formed complex damage site impairs enzymatic DNA repair processes, leading to deleterious genomic damage. Results First, we summarise the simulation geometry setup and code validation. Chemical species in a single spur could contact the DNA and a certain population of the species escapes from DNA. Therefore, we evaluated the diffusion coefficient of the chemical species migrating in DNA. The calculated results for their diffusion reactions are shown, and the reaction probabilities of the species under the conditions with and without radical scavengers are presented. Simulation geometry setup Figure 1 (a) shows the simulation geometry used in this study. The 10 bps DNA was modelled as a cylinder with a 1 nm radius and a length of 3.4 nm. The DNA model extended towards the z-axis; its centre was at the origin. The mol concentration of nucleotide units in the DNA model was 3.02 × 10 − 3 mol L − 1 . This determination referred to the enhanced green fluorescent protein plasmid-C1 (pEGFP-C1). When the chemical species enter the DNA model, the reaction between the DNA and the chemical species is determined with P (Δ t ) = 1 − exp (− k [B] Δ t ) 22 , where k is the rate constant between the chemical species and nucleotides, [B] is the DNA mol concentration, Δ t is time step of 100 fs. In this study, the energy deposition site ( x , 0, 0) and the spur radius ( a ) are free parameters. Therefore, H 3 O + and • OH are at ( x , 0, 0) and e − aq with a spur radius ( a ) exists in a Gaussian centred at ( x , 0, 0). The radicals could be scavenged in a living system. This study also considers this effect. The radical scavenging is determined with P (Δ t ) = 1 − exp (− k ' [B'] Δ t ) 22 , where k ' [B'] is the scavenging capacity (s − 1 ) and we investigated the DNA damage yields in a living system under the scavenging capacity from 10 7 (s − 1 ) to 10 9 (s − 1 ). Figure 1 (b) shows a flowchart of our code. Code validation As a code validation, we focused on the e − aq yields in water photolysis, for which many experimental and analytical results have been reported 23–28 . Figure 2 (a) shows the experimental values of e − aq 28 and the calculated results of our code at deposition energies 8.3 and 12.4 eV. In the experiments, the two-photon absorption of the laser generates e − aq and its time evolution yield during 1 ns was measured 28 . In this analysis, the spur radius ( a ) is the only free parameter 23–28 . The experimental values were almost entirely reproduced at a deposition energy of 8.3 eV, assuming a Gaussian of e − aq and a spur radius of 0.78 nm. The experimental values were reproduced at a deposition energy of 12.4 eV, assuming a spur radius of 3.8 nm in this study. Figure 2 (b) shows the spur radius ( a ) dependence as a function of the deposition energy. The spur radii for various deposition energies were determined using the parameter analysis based on previous experimental studies (Fig. 2 (a)). Since the spur radius was assumed to be Gaussian and exponential distributions in a previous study 28 , these two calculations were performed in this study. Our results well reproduced the experimental results previously reported, validating our code. Diffusion coefficient of chemical species in a DNA molecule In this study, we noted the diffusion coefficients of chemical species in water (or DNA) as D water (or D DNA ). When the chemical species contact the DNA, it will slowly migrate on the DNA surface. The chemical species will react with or escape DNA. The diffusion coefficient of the chemical species in contact with the DNA will differ from the diffusion coefficient in water. However, the diffusion coefficients D DNA of • OH and e − aq migrating on the DNA surface are yet to be reported. Here, we estimated the diffusion coefficients, D DNA , by assuming they were significantly smaller than D water . Here, we introduce a slowing down parameter ( S ) for the diffusion coefficient on the DNA surface. We assumed D DNA as D water / S ; then, we calculated the reaction probabilities of DNA with • OH and e − aq near S from 10 to 1000 (Fig. 3 (a)). The simulation conditions were x = 1.2 nm and a = 2 nm. When S is 10, the reaction probabilities are too small to ensure the reaction of • OH with DNA. Near ratios above S = 100, a specific amount of the chemical species could react with DNA, whereas others escape. For S = 1,000, under a very slight diffusion condition for the chemical species, most • OH and e − aq that reach the DNA react with it. Figure 3 (b) shows these representative illustrations of the reaction between • OH and DNA. We assumed that S = 10, 100 and 1000 correspond to the DNA and • OH rate constants or DNA and e − aq of much less than 10 9 , ~10 9 and much greater than 10 9 L mol − 1 s − 1 . The rate constant in an aqueous DNA solution is ~ 10 9 L mol − 1 s − 1 21 , showing that • OH and e − aq could react with or escape from the DNA. We estimated that the D DNA for • OH and e − aq moving in the DNA region is approximately D water /100 in water. Henceforth, we assumed that the D DNA equals to D water /100. Diffusion and reaction of chemical species Figure 4 (a) shows the calculated relative distance between • OH and e − aq after 10 ns without radical scavengers. Here, three calculation conditions were employed: ( 1 ) x = 1.2 nm, a = 2 nm; ( 2 ) x = 2 nm, a = 2 nm; and ( 3 ) x = 6 nm, a = 2 nm. The results of ( 1 ) and ( 2 ) show a peak structure at a few nm, but no structure was observed in ( 3 ). This peak structure indicates that a specific number of e − aq was present in the 10 bps of the DNA region under the initial calculation conditions. Figure 4 (a) also shows that • OH and e − aq are considerably separated by a few 10 nm. In this case, the chance of multiple reactions between the DNA and the two species is scarce and each species could cause isolated lesions in the DNA. Time-dependent yield changes of the chemical species Figure 4 (b) shows the time evolution yields for each chemical species in the conditions without radical scavengers. The computational conditions are x = 1.2 nm and a = 2 nm. We compared the calculated results with and without the DNA model (shown in Fig. 1 (a)). The result indicates that H 3 O + does not significantly decrease, which might be attributed to a small reaction probability between H 3 O + and e − aq of 3.8%. In liquid water without the DNA model, the e − aq yield is slightly lower than that of • OH because e − aq can also react with H 3 O + . The decrements in the • OH and e − aq yields become more pronounced at 100 ps or later under this condition. When the DNA structure is considered a simple cylinder (shown in Fig. 1 (a)), the chemical reaction rates are slower than without the DNA model during a few ns. This result is because the rate constants between the chemical species (~ 10 10 L mol − 1 s − 1 ) 21 in water are higher than those in DNA component nucleotides molecules with H 3 O + , • OH and e − aq (~ 10 9 L mol − 1 s − 1 ) 21 . The • OH yield is less than that of e − aq after 10 ns because the rate constants between • OH and nucleotides (AMP: 4.1 × 10 9 L mol − 1 s − 1 , CMP: 4.7 × 10 9 L mol − 1 s − 1 , GMP: 4.7 × 10 9 L mol − 1 s − 1 and TMP: 5.2 × 10 9 L mol − 1 s − 1 ) are mostly greater than that between e − aq and nucleotides (AMP: 3.8 × 10 9 L mol − 1 s − 1 , CMP: 6.8 × 10 9 L mol − 1 s − 1 , GMP: 1.5 × 10 9 L mol − 1 s − 1 and TMP: 1.5 × 10 9 L mol − 1 s − 1 ) 21 . Furthermore, the diffusion coefficient of • OH (2.2 × 10 − 9 m 2 /s) is less than half of that for e − aq (4.9 × 10 − 9 m 2 /s) 29 . This result indicates that • OH reacts with DNA more readily than e − aq , and • OH stays around the DNA for a long time, resulting in high reactivity. In general, the chemical reactions to produce stable products, such as DNA damage, begin to converge after approximately 100 ns. Estimating DNA damage Figure 5 (a) shows the calculated results of the sum of probabilities of the reactions of e − aq with • OH and e − aq with H 3 O + . The results depend on parameter ( a ) but not parameter ( x ). When the spur radius (the distance between e − aq and • OH or H 3 O + ) is approximately 2 nm, corresponding to deposition energy 10 eV (see Fig. 2 (b)), the chemical species react with each other with a high probability of several 10%. When the spur radius is approximately 8 nm, corresponding to water radiolysis 18 , the chemical species react with each other with a probability of 10%. Figure 5 (b) shows the probabilities of the reaction between DNA and • OH, indicating a slight dependence on parameter ( a ) and a strong dependence on parameter ( x ). When • OH is generated near the DNA, it reacts with the DNA with a high probability of several 10%; however, the probability decreases to a few % at the condition of x = 10 nm. Note that the DNA length is limited to 10 bps in this case. Figure 5 (c) shows the probabilities of e − aq reacting with DNA, indicating a slight dependence on parameters ( a ) and ( x ). When radiation deposits the energy near the DNA, e − aq reacts with the DNA and the reaction probability is less than a few %. Figure 5 (d) shows the multiple reaction probabilities of DNA with • OH and e − aq within 10 bps, namely, the production of a clustered DNA damage site. Note that the results of Fig. 5 (d) are not the sum of the results of Fig. 5 (b) and Fig. 5 (c). The results show a slight dependence on ( a ) and a strong dependence on ( x ), although the probabilities are 0.6% or less. Figure 6 shows the calculated results under the condition with radical scavengers. Figure 6 (a) shows the probabilities of • OH scavenging when a = 2 nm. The • OH scavengers, such as dimethyl sulfoxide (DMSO) and tris(hydroxymethyl) aminomethane (Tris), with a scavenging capacity in mammalian cells of ~ 3 × 10 8 (s − 1 ) 30 , are assumed here. The • OH scavenging probabilities are higher than 60% above a scavenging capacity of 3 × 10 8 (s − 1 ), typically in a living system. Figure 6 (b) shows the reaction probabilities between DNA and • OH, indicating a strong dependence on parameter ( x ). When • OH is generated near the DNA, it reacts with the DNA with a high probability of approximately 10%. However, as shown in Fig. 6 (c), the probabilities of the e − aq reaction with DNA do not significantly depend on parameters ( a ) and ( x ), and even when e − aq is distributed around the DNA, the probability would be a few %. Figure 6 (d) shows the probability of producing a clustered damage site by multiple reactions with • OH and e − aq within 10 bps. Although the damage clustering is not very frequent (0.4% or less), the radiation energy deposition proximately to DNA causes two DNA lesions originating from reactions with • OH and e − aq , inducing oxidative and reductive damage within a localised region of 10 bps, respectively. The important point is that • OH proximately arising around the DNA within a few nm or less could react with DNA before it encounters radical scavengers. Discussion The correlation between the single-spur fate and DNA damage clustering was revealed for the first time using the newly developed dynamic MC code for chemical processes (dmcc_chem). To quantitatively calculate the indirect effect of each water radiolysis species on DNA damage induction, the diffusion coefficients of • OH and e − aq in DNA were newly estimated and the rate constants for the reactions of the species with nucleotides were considered to calculate the chemical reaction probabilities of chemical species constituting a spur. The primary findings from this study on the three-body single spur and DNA damage clustering are as follows: (i) The spur centre is produced within 1.5 nm from the DNA. Assuming that the diffusion coefficients D DNA of • OH and e − aq in the DNA molecule were D water /100, indicating that • OH and e − aq arising near the DNA could cause localised damage. (ii) The • OH and e − aq yields decrease following specific kinetic curves until 100 ns, contrasting with the independence observed for H 3 O + . (iii) The probability of 10% for • OH reacting with DNA decreases with the increasing distance ( x ) of the spur centre from the DNA to 1%, irrespective of the spur radius. However, for an e − aq of a few %, the spur centre distance and spur radius do not significantly change. (iv) Interestingly, radical scavengers do not significantly quench • OH proximately arising around the DNA and do not affect the e − aq yield, indicating that the radical scavengers do not significantly impact the damage clustering efficiency. The obtained evidence establishes that the DNA damage clustering arises from the reactions with a single spur and not an accumulation of multiple spurs arising from more than one radiation track. This aspect is fundamental in forming multiple damaged sites, which is a normal event at the end of the radiation track. The yields of DNA single-strand breaks (SSBs) or isolated base lesions are 1–3% of the total ionisation events in the nucleus of a living cell. The double-strand break (DSB) yield is much less than approximately 0.05% 31 . Compared to the reported damage yields, our result on the probabilities below 1% for concomitant reactions of • OH and e − aq with 10 bps of DNA is consistent with the reported values. We revealed that the three species constituting the spur (H 3 O + , • OH, and e − aq ) behaved differently in the spur’s lifetime. The different dynamics of the three species is strongly involved in the chemical structure of clustered damage sites. The chemical species in the spur, proximately arising within 1.5 nm from the DNA, could react with the DNA. The water molecules surrounding the DNA with an approximate 1 nm thickness called a hydration layer specifically contribute to oxidative or reductive base damage induction 32 . A hole created in a water molecule in the hydration layer might be transferred to the DNA through the hydrogen-bonded water networks. The positive charge migrates on the DNA strand and finally stabilises at the lowest oxidative potential nucleobase, guanine as an electronless centre (cation radical) and a low probability of strand break induction 33 . Thus, the H 3 O + in the spur would be a source of oxidised guanine, such as 7,8-dihydro-8-oxo-2’-deoxyguanine (8-oxo-G) or 2,6-diamino-4-hydroxy-5- N -methylformamidopyrimidine (Fapy). A typical inducer of the indirect effect, • OH, causes an SSB by abstracting a hydrogen atom from the deoxyribose moiety in the DNA 34 and oxidised base damage, such as 8-oxo-G or 8-oxo-adenine 35 . However, e − aq could be a source of the electron gain process (anion radical formation). The primary product of the reductive base is dihydrothymine (DHT) because DHT generation is enhanced under an anaerobic condition 36 or much more pronounced with the presence of radical scavengers compared to oxidative lesions 37 . The reaction probability of • OH with DNA significantly depends on the distance ( x ) of the spur centre from the DNA, and is a couple of times larger than the reaction of e − aq , irrespective of ( x ). Interestingly, when the spur arises beyond 4 nm from the DNA, the reaction probability of e − aq with DNA surpasses that of • OH under the scavenging capacity of approximately 3 × 10 8 (s − 1 ) (Fig. 6 (b) and 6(c)). These results indicate that the interaction of single spurs could realise various lesion combinations. Heterogeneous lesions, not specific or homogeneous lesions, likely constitute the clustered DNA damage site by reacting with a single spur. Conclusions The dmcc_chem demonstrated the indirect effects of a single-spur comprising H 3 O + , • OH, and e − aq on damage clustering in DNA. The rate constants of each radiolytic chemical species reacting with nucleotides were considered for the calculations. The results showed that the three bodies spur can concomitantly react within a 3.4 nm range of DNA length (10 base pairs) to induce a multiple DNA damage site, presumably comprising SSB, oxidative or reductive nucleobase damage. The reaction probability was 0.4% or less, consistent with the experimental values previously reported. The efficiency is comparable to that of DSBs. The energy deposition to the water layer near DNA from ionising radiation causes a critical effect on living system. This aspect contributes to a much better understanding of low dose radiation risk. Methods We developed the dmcc_chem to analyse the radio- or photo-chemical process. Here, we applied the dmcc_chem to aqueous DNA solution systems with and without radical scavengers and aimed to extend it to various solvents. First, we note the features of the dmcc_chem by briefly describing diffusion and reaction, dielectric response and the dynamic MC method. Diffusion and reaction This study assumed a three-body single spur formed by water photolysis or radiolysis 23–28 . Figure 7 (a) shows the diffusion reaction of H 3 O + and e − aq . The diffusion coefficients of H 3 O + and e − aq are 9.5 × 10 − 9 m 2 /s and 4.9 × 10 − 9 m 2 /s, respectively 29 . The reaction radius and probability of H 3 O + and e − aq are 0.75 nm and 3.8%, respectively 22 . When both react chemically, they form H 3 O, which becomes H 2 O + H • 22 . An escape distance was introduced if the chemical reaction did not occur (96.2%) 22 . The escape distance is derived from the reaction radius and separation distance (0.3 nm) 22 . Those diffusion motions are continuously calculated when H 3 O + and e − aq enter the reaction radius (0.75 nm). They completely escape in one contact at an escape distance of 1.05 nm. Figure 7 (b) shows the diffusion reaction of • OH and e − aq . The diffusion coefficient of • OH is 2.2 × 10 − 9 m 2 /s 29 and the reaction radius and probability of OH • and e − aq are 0.72 nm and 49%, respectively 22 . When both react chemically, OH − is formed 22 . If the chemical reactions do not occur (51%), the escape distance of 1.02 nm is used to determine the separation in one contact event. Dielectric response The dmcc_phys that has been developed so far comprises MD and MC. It calculates the delocalisation and relocalisation of secondary electrons generated by water photolysis and radiolysis 18–20 . In the MD calculations of secondary electrons, the Coulombic interaction between the secondary electrons and the parent cation is considered 19 . Electronic (a few fs), phonon (from 10 fs to several 100 fs) and orientation polarisations (after several 100 fs) shield this Coulombic force with time evolution 19 . These shielding effects were evaluated using the dielectric response, which is the time evolution of the relative dielectric constant 19 . Using the dielectric response, we simulated the hydration of charged particles 19 . The present dmcc_chem also uses this dielectric response. Dynamic MC method The Smolchowski–Debye equation describes the thermal diffusion motion of chemical species in a solution 38 . The MC method is typically used because this equation is challenging to solve. Here, the step-by-step method accounts for the dielectric response. The chemical species thermally diffuse at each time step and a chemical reaction is decided when two chemical species enter the reaction radius 22 . The thermal diffusion motion of each chemical species per time step is determined by sampling from Eq. (1) 22 , $${\mathbf{r}}_{i}\left(t+\varDelta t\right) = {\mathbf{r}}_{i}\left(t\right)+\sqrt{2{D}_{i}\varDelta t}\left({N}_{i,x}{\mathbf{e}}_{x}+{N}_{i,y}{\mathbf{e}}_{y}+{N}_{i,z}{\mathbf{e}}_{z}\right)+\frac{{D}_{i}}{{k}_{\text{B}}T}{\mathbf{F}}_{i}\varDelta t$$ 1 where r i ( t ) is the three-dimensional spatial coordinate of the i -th chemical species at time t . The second term is the thermal diffusion term and D i is the diffusion coefficient of the i -th chemical species. Δ t was 100 fs to ensure timestep convergence. ( N i,x , N i,y , and N i,z ) are the x , y and z components of the thermal diffusion direction, respectively, determined from uniform random numbers. The third is the Coulombic force term, where k B and T are the Boltzmann constant and water temperature (300 K), respectively. The Coulombic force F i involved in the i -th chemical species is expressed by $${\mathbf{F}}_{i} = \sum _{j\ne i}\frac{{Z}_{i}{Z}_{j}{e}^{2}}{4\pi {\epsilon }_{0}{\epsilon }_{\text{r}}\left(t\right)}\frac{{\varvec{r}}_{i}-{\varvec{r}}_{j}}{{\left|{\varvec{r}}_{i}-{\varvec{r}}_{j}\right|}^{3}}$$ 2 where Z i and Z j are the valences of the i -th and j -th chemical species, respectively, e is the elementary charge, ε 0 is the dielectric constant of the vacuum and ε r ( t ) is the dielectric response 19 . Consequently, the Coulombic force between the charged chemical species decreases with time. This Coulombic force term can be expressed in terms of the Onsager distance 39 as $$\frac{{D}_{i}}{{k}_{\text{B}}T}{\mathbf{F}}_{i}\varDelta t = -{D}_{i}\varDelta t\sum _{j\ne i}{r}_{\text{c},ij}\left(t\right)\frac{{\varvec{r}}_{i}-{\varvec{r}}_{j}}{{\left|{\varvec{r}}_{i}-{\varvec{r}}_{j}\right|}^{3}},$$ 3 where $${r}_{\text{c},ij}\left(t\right) = -\frac{{{Z}_{i}{Z}_{j}e}^{2}}{4\pi {\epsilon }_{0}{\epsilon }_{\text{r}}\left(t\right){k}_{\text{B}}T} ,$$ is the time-dependent Onsager distance. When the target is water, the dielectric response is completed in a few 10 ps 19 . Therefore, after a few 10 ps from charge generation, the time-dependent Onsager distance converges to 0.7 nm, with a relative dielectric constant of 80. Declarations Acknowledgements This work was supported by the Japan Society for the Promotion of Science KAKENHI (Grant nos. 22K04993, 22K14631, 22H03744, 22K14630, and 22K03549). Author contributions Conceptualisation: TK, TT, and AY; Methodology: TK, TT, and YM; Investigation: TK, TT, YM, UH, HT, and YI; Visualisation: TK; Funding acquisition: TK, TT, YM, UH, and HT; Project administration: TK; Supervision: AY; Writing–original draft: TK; Writing–review & editing: TK, YM, and AY Competing interests The authors declare no competing interests. Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Correspondence and requests for materials should be addressed to Takeshi Kai. References Ward, J. F. DNA damage produced by ionizing radiation in mammalian cells: identities, mechanisms of formation, and reparability. Prog . Nucl. Acid. Res. Mol. Biol . 35, 95–125 (1988). Goodhead, D. T. 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Initial yield of hydrated electron production from water radiolysis based on first-principles calculation. RSC adv. 13, 7076–7086 (2023). Kai, T., Toigawa, T., Ukai, M., Fujii, K., Watanabe, R. & Yokoya, A. Nature of the physicochemical process in water photolysis uncovered by a computer simulation. J. Chem. Phys. 158, 164103 (2023). Kai, T., Toigawa, T., Matsuya, Y., Hirata, Y., Tezuka, T., Tsucida, H. & Yokoya, A. RSC adv. 13, 32371 (2023). Buxton, G. V., Greenstock, C. L., Helman, W. P. & Ross, A. B. Critical Review of rate constants for reactions of hydrated electrons, hydrogen atoms and hydroxyl radicals (•OH/•O – ) in Aqueous Solution. J. Phys. Chem. Ref. Data 17, 513–886 (1988). Plante, I. A. A review of simulation codes and approaches for radiation chemistry. Phys. Med. Biol. 66, 03TR02 (2021). Sander, M. U., Gudiksen, M. S., Luther, K. & Troe, Liquid water ionization: mechanistic implications of the H/D isotope effect in the geminate recombination of hydrated electrons, J. Chem. Phys. 258, 257 (2000). Thomsen, C. L., Madsen, D., Keiding, S. R., Thogersen, J. & Christiansen, O. Two-photon dissociation and ionization of liquid water studied by femtosecond transient absorption spectroscopy, J. Chem. Phys. 110, 3453 (1999). Madsen, D., Thomsen, C. L., Thogersen, J. & Keiding, S. R. Temperature dependent relaxation and recombination dynamics of the hydrated electron, J. Chem. Phys. 113, 1126 (2000). Kloepfer, J. A., Vilchiz, V. H., Lenchenkov, V. A., Germaine, A. C. & Bradforth, S.E. The ejection distribution of solvated electrons generated by the one-photon photodetachment of aqueous I – and two-photon ionization of the solvent, J. Chem. Phys. 113, 6288 (2000). Crowell, R. A. & Bartels, D. M. Multiphoton Ionization of Liquid Water with 3.0 – 5.0 eV Photons, J. Phys. Chem. 100, 17940 (1996). Elles, C. G., Jailaubekov, A. E., Crowell, R. A. & Bradforth, S. E. Excitation-energy dependence of the mechanism for two-photon ionization of liquid H 2 O and D 2 O from 8.3 to 12.4 eV, J. Chem. Phys. 125, 044515 (2006). Frongillo, Y., Goulte, T., Fraser, M.-J., Cobut, V., Patau, J. P. & Jay-Gerin, J.-P. Monte Carlo simulation of fast electron and proton tracks in liquid water—II. Nonhomogeneous chemistry. Radiat. Phys. Chem. 51, 245–254 (1998). Fulford, J., Nikjoo, H., Goodhead, D. T., O’Neill, P. Yields of SSB and DSB induced in DNA by AlK ultrasoft X-rays and α-particles: comparison of experimental and simulated yields. Int. J. Radiat. Biol. 77, 1053–1066 (2001). von Sonntage C. Chapter 12 DNA and double stranded oligonucleotides, Free-radical-induced DNA damage and its repair . Springer, Germany, 359–360 (2005). Yokoya, A., Cunniffe, S. M. T. & O’Neill, P. Effect of Hydration on the Induction of Strand Breaks and Base Lesions in Plasmid DNA Films by γ-Radiation. J. Am. Chem. Soc. 124, 8859–8866 (2002). Melvin, T., Cunniffe, S. M. T., O’Neill, P., Parker, A. W. & Roldan-Aujona, T. Guanine is the target for direct ionisation damage inDNA, as detected using excision enzymes. Nucleic Acids Res. 26, 4935–4942 (1998). B. Balasubramanian, Pogozelski, W. K. & Tullius, T. D. DNA strand breaking by the hydroxyl radical is governed by the accessible surface areas of the hydrogen atoms of the DNA backbone. Proc. Natl. Acad. Sci. USA 95, 9738 – 9743 (1998). Chatgilialoglu, C., Ferreri, C., Krokidis, M. G., Masi, A. & Terzidis M. A. On the relevance of hydroxyl radical to purine DNA damage. Free Radic. Res. 55, 384–404 (2021). Schroder, E., Budzinski, E.E., Wallace, J.C., Zimbrick, J. D. & Box, H.C. Radiation Chemistry of D(ApCpGpT). Int. J. Radiat. Biol. 68, 509–523 (1995). Yu, H., Kondo, Y., Fujii, K., Yokoya, A. & Yamashita, S. Establishment of a Method for Investigating Direct and Indirect Actions of Ionizing Radiation Using Scavenger-free Plasmid DNA, Radiat. Res. 197, 594–604 (2022). Debye, P. Reaction Rates In Ionic Solutions, Transactions of The Electrochemical Society, 82, 265–272 (1942). Onsager, L. Initial Recombination of Ions, Phys. Rev. 54, 554–557 (1938). Additional Declarations There is NO Competing Interest. Supplementary Files codedata1.zip Code and dataset 1 codedata2.zip Code and dataset 2 codedata3.zip Code and dataset 3 codedata4.zip Code and dataset 4 Cite Share Download PDF Status: Published Journal Publication published 06 Mar, 2025 Read the published version in Communications Chemistry → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4596630","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":315814507,"identity":"d7b08968-fbcf-4ba6-968a-1c7ffab51017","order_by":0,"name":"Takeshi Kai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYBACCQbGBiCVAGQxNj6QQAgT0HIAoqXZgEgtQADRwsCGTyECSLYfbmD+UJMmJz+7ua3CosZGnoF/8QEGyx24tUjzJAIddizH2ODOwbYbEsfSDBskniUwSJ7BrUWOAaSFrSJxg0QiUAvbYcYGiTMGDJJteLTwPwRq+VdRP39GYluBxL//9gS1SEsAbTnYlpPAcCOxDajyQGIDfw9+LZIzHjYcONuXZrjhRmKzhGRfcnKbBFvCAXx+kTif/vBBxbdkefkZ6Q8/S3yzs+3nP3zwsSSeEAOBAzAGMyhi2CQSGA5LNuDXAgeMH0Ak/wEGxo/EahkFo2AUjIKRAADqGVWRPBONVQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-0538-7844","institution":"Japan Atomic Energy Agency","correspondingAuthor":true,"prefix":"","firstName":"Takeshi","middleName":"","lastName":"Kai","suffix":""},{"id":315814508,"identity":"fc468d1a-b93a-4b3f-a5d3-e0b922097253","order_by":1,"name":"Tomohiro Toigawa","email":"","orcid":"","institution":"Japan Atomic Energy Agency","correspondingAuthor":false,"prefix":"","firstName":"Tomohiro","middleName":"","lastName":"Toigawa","suffix":""},{"id":315814509,"identity":"35a2ddc1-a0e4-4898-8ae8-e136497d6fbe","order_by":2,"name":"Yusuke Matsuya","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yusuke","middleName":"","lastName":"Matsuya","suffix":""},{"id":315814510,"identity":"dc2a9a2f-d567-423d-b1c2-3820d5a22ca3","order_by":3,"name":"Yuho Hirata","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yuho","middleName":"","lastName":"Hirata","suffix":""},{"id":315814511,"identity":"d150dcf5-0c2f-4ff6-b90c-001ccdbd1423","order_by":4,"name":"Hidetsugu Tsuchida","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Hidetsugu","middleName":"","lastName":"Tsuchida","suffix":""},{"id":315814512,"identity":"cfc1bc8b-bf68-43cb-8c16-b3a1ba3ddfbd","order_by":5,"name":"Yuma Ito","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yuma","middleName":"","lastName":"Ito","suffix":""},{"id":315814513,"identity":"4cc27fb6-2871-4790-8498-8e8cfbe68f8b","order_by":6,"name":"Akinari Yokoya","email":"","orcid":"","institution":"National Institutes for Quantum and Radiological Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Akinari","middleName":"","lastName":"Yokoya","suffix":""}],"badges":[],"createdAt":"2024-06-18 02:00:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4596630/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4596630/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s42004-025-01453-x","type":"published","date":"2025-03-06T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":59564996,"identity":"9c571053-cd68-4d70-8c70-23a347f4a6da","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":322649,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eSimulation geometry in this study, \u003cstrong\u003e(b)\u003c/strong\u003eflowchart of the dmcc_chem\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/9b0fba273e729c8e2c421e3f.jpeg"},{"id":59565694,"identity":"0eb8bb3f-4b45-474e-9cee-557b788fbd63","added_by":"auto","created_at":"2024-07-03 09:07:12","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":287008,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eThe time-dependent yields of e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e comparing the calculated results of our code with the experimental values\u003csup\u003e27\u003c/sup\u003e at deposition energies 8.3 and 12.4 eV; \u003cstrong\u003e(b)\u003c/strong\u003e the spur radius (\u003cem\u003ea\u003c/em\u003e) dependence as a function of deposition energy from 8 to 12.4 eV; we compared our calculated results with the experimental values\u003csup\u003e22-27\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/7d404d6f4dd747dc6476c78f.jpeg"},{"id":59564994,"identity":"c82406a2-fab9-4b9a-bc33-bcd60bb0ecfb","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":282379,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eProbabilities of the DNA reaction with \u003csup\u003e•\u003c/sup\u003eOH or e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e during 100 ns; the computational conditions were \u003cem\u003ex\u003c/em\u003e = 1.2 nm and \u003cem\u003ea\u003c/em\u003e = 2 nm; the horizontal axis shows the slowing down parameter (\u003cem\u003eS\u003c/em\u003e) for the \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e = \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e/\u003cem\u003eS\u003c/em\u003e; \u003cstrong\u003e(b)\u003c/strong\u003e an illustration for the diffusions and reactions of the chemical species with the DNA model\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/acad4782a8c9b46efa6ab4ae.jpeg"},{"id":59565693,"identity":"16e90051-8f8b-4ee2-b4d8-c91b6625f1f7","added_by":"auto","created_at":"2024-07-03 09:07:12","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":424199,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Probability of the\u003cstrong\u003e \u003c/strong\u003erelative distance between \u003csup\u003e•\u003c/sup\u003eOH and e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e at 10 ns; \u003cstrong\u003e(b)\u003c/strong\u003e the time evolution yields for each chemical species (H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e, \u003csup\u003e•\u003c/sup\u003eOH, and e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e) during 100 ns\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/202cd8ac53cb1d19fdd47f4c.jpeg"},{"id":59565696,"identity":"56e07abc-8380-44e4-a1c1-658f7e23a5c8","added_by":"auto","created_at":"2024-07-03 09:07:12","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":486916,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eThe sum of the reaction probabilities of e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e with \u003csup\u003e•\u003c/sup\u003eOH or H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e without radical scavengers; \u003cstrong\u003e(b)\u003c/strong\u003e the reaction probabilities of \u003csup\u003e•\u003c/sup\u003eOH with DNA without radical scavengers; \u003cstrong\u003e(c)\u003c/strong\u003e the reaction probabilities of e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e with DNA without radical scavengers; \u003cstrong\u003e(d)\u003c/strong\u003e the reaction probabilities of DNA with \u003csup\u003e•\u003c/sup\u003eOH and e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e without radical scavengers\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/9405281cc6f4270ecd5213ed.jpeg"},{"id":59564999,"identity":"96566874-d5ab-4ddc-99cd-7c3f6af66ae7","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":547127,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eThe radical scavenging probabilities of \u003csup\u003e•\u003c/sup\u003eOH in the presence of radical scavengers; \u003cstrong\u003e(b)\u003c/strong\u003e the reaction probabilities of \u003csup\u003e•\u003c/sup\u003eOH with DNA in the presence of radical scavengers; \u003cstrong\u003e(c)\u003c/strong\u003e the reaction probabilities of e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e with DNA in the presence of radical scavengers; \u003cstrong\u003e(d)\u003c/strong\u003e the probability that DNA and \u003csup\u003e•\u003c/sup\u003eOH as well as DNA and e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e react together in the presence of radical scavengers\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/b3d2ddd629552c8d1d36e828.jpeg"},{"id":59565002,"identity":"e2322025-e495-4c3c-a1cb-bb275d1c3b9b","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":274445,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eDiffusion and reaction of H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e in liquid water; \u003cstrong\u003e(b)\u003c/strong\u003e diffusion and reaction of \u003csup\u003e•\u003c/sup\u003eOH and e\u003csup\u003e−\u003c/sup\u003e\u003csub\u003eaq\u003c/sub\u003e in liquid water\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/5ed4530ff95aba35692e8dcc.jpeg"},{"id":77955970,"identity":"9c5d3f18-2774-4ae8-ad3e-dd45fac2050a","added_by":"auto","created_at":"2025-03-07 08:09:57","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3497469,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/276089d9-0918-4f23-89fd-d035a41e51e1.pdf"},{"id":59565695,"identity":"ad862828-a733-42b1-904b-c3cb77e844ed","added_by":"auto","created_at":"2024-07-03 09:07:12","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":26856519,"visible":true,"origin":"","legend":"\u003cp\u003eCode and dataset 1\u003c/p\u003e","description":"","filename":"codedata1.zip","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/d2130c8c42eae7e1f515a50e.zip"},{"id":59565000,"identity":"35f7aeed-4ed2-4722-8b39-13b1ec16c09a","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"zip","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":21667091,"visible":true,"origin":"","legend":"\u003cp\u003eCode and dataset 2\u003c/p\u003e","description":"","filename":"codedata2.zip","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/4f06daa32ac60ed0c2b06f41.zip"},{"id":59564998,"identity":"511f993e-f07f-4a1b-841e-7eed882746af","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"zip","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":4883853,"visible":true,"origin":"","legend":"\u003cp\u003eCode and dataset 3\u003c/p\u003e","description":"","filename":"codedata3.zip","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/0fe9b18d5e58879d3fe3d8bb.zip"},{"id":59565003,"identity":"3b87d275-2c56-4bff-8a4b-492d65318e18","added_by":"auto","created_at":"2024-07-03 08:59:12","extension":"zip","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":18341408,"visible":true,"origin":"","legend":"\u003cp\u003eCode and dataset 4\u003c/p\u003e","description":"","filename":"codedata4.zip","url":"https://assets-eu.researchsquare.com/files/rs-4596630/v1/9e9c435ae64a4d11f7db3097.zip"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Computational demonstration of multiple DNA damages produced by the radiolytic chemical species in an aqueous DNA solution","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWater radiolysis in a living system results in chemically irreversible deoxyribonucleic acid (DNA) damage, such as DNA strand breaks, nucleobase lesions and apurinic/apyrimidinic (AP) sites. DNA repair enzymes recover most DNA lesions in vivo. However, when multiple lesions are within 1\u0026ndash;2 helical turns (10\u0026ndash;20 base pairs (bps)) of DNA, the lesions are less likely to be repaired, leading to cell death or mutations. These DNA damage configurations are called multiple damage sites or clustered damage\u003csup\u003e1,2\u003c/sup\u003e. They are formed by the direct action of ionisation/excitation with DNA, referred to as the direct effect, and indirect actions of water radiolytic species, categorised as indirect effects. The latter effect occurs via thermal diffusion and chemical reactions with the water radiolytic species, typically a hydroxyl radical (\u003csup\u003e\u0026bull;\u003c/sup\u003eOH) and hydrated electron (e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e). A previous study using a plasmid as a simple model DNA exposed to X-rays or carbon ion beams showed that the indirect action induced strand breaks, nucleobase lesions and AP sites \u003cem\u003ein vitro\u003c/em\u003e, even at the cell mimetic scavenging condition\u003csup\u003e3\u003c/sup\u003e. Computer simulations assuming the radical scavenging environment in cells indicated that the direct-to-indirect effect ratio is approximately 1:3\u003csup\u003e4,5\u003c/sup\u003e; however, the contributions to cluster damage generation of the direct and indirect effects remain unclear experimentally. The reason is that biochemical or analytical chemistry methods for DNA damage detection have insufficient spatial resolution to determine the DNA lesion types and damage distributions within a few ten bps; thus, advanced computer simulation is the only approach.\u003c/p\u003e \u003cp\u003eSo far, Monte Carlo (MC) simulation allows quantitatively estimating clustered DNA damage yields by simulating the physical, physicochemical and chemical processes\u003csup\u003e6\u003c/sup\u003e. The physical process identifies the ionisation and electronic excitation sites induced in water\u003csup\u003e7,8\u003c/sup\u003e. In the physicochemical process, the radiolytic chemical species of water are identified\u003csup\u003e6,9\u003c/sup\u003e; however, the MC codes should adjust for the initial yield of the chemical species to reproduce the experimental results of the time-dependent yields in the chemical process\u003csup\u003e6,9\u003c/sup\u003e. The diffusion and the reactions of the chemical species in water are simulated during chemical processes. The spatial distributions of DNA damage are estimated based on these ionisation, electronic excitation, and chemical reaction sites based on water radiolysis\u003csup\u003e4\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe efficiencies of the enzymatic repair of the clustered damage could be strongly affected by individual lesions comprising clustered damage sites and their spatial distributions\u003csup\u003e10,11\u003c/sup\u003e. These depend on the initial damage processes, namely direct or indirect effects. Thus, we have previously developed a dynamic MC code for the physical process (dmcc_phys) comprising a time-evolving MC and molecular dynamics (MD)\u003csup\u003e12\u0026ndash;20\u003c/sup\u003e. Using this code, we succeeded in quantitatively evaluating DNA damage clustering via the direct effect\u003csup\u003e17\u003c/sup\u003e. Secondary electron deceleration in water was also investigated to demonstrate the initial yields\u003csup\u003e18\u003c/sup\u003e and the spatial distributions\u003csup\u003e19,20\u003c/sup\u003e of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e using dmcc_phys. These findings help estimate DNA damage.\u003c/p\u003e \u003cp\u003eWe newly developed a dynamic MC code for the chemical process (dmcc_chem) to quantitatively demonstrate the yields of DNA damage clustering via the indirect effect as an initial step of radiobiological phenomena, such as cell lethality or mutation induction. The rate constants\u003csup\u003e21\u003c/sup\u003e between the chemical species and nucleotides (adenosine monophosphate (AMP), cytidine monophosphate (CMP), guanosine monophosphate (GMP) and thymidine monophosphate (TMP)), whose sequences in DNA are the genetic information of an organism, were used for code development. This study aimed to reveal whether the single-spur comprising a hydronium ion (H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e), \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e originating from the single ionisation of a water molecule, the most fundamental process of the indirect effect, potentially causes clustered lesions in DNA. We investigated the time evolution of spur broadening. The effects of the initial ionisation distance from DNA and the radical scavengers on the probabilities of their chemical reactions were also quantified. Formed complex damage site impairs enzymatic DNA repair processes, leading to deleterious genomic damage.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eFirst, we summarise the simulation geometry setup and code validation. Chemical species in a single spur could contact the DNA and a certain population of the species escapes from DNA. Therefore, we evaluated the diffusion coefficient of the chemical species migrating in DNA. The calculated results for their diffusion reactions are shown, and the reaction probabilities of the species under the conditions with and without radical scavengers are presented.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSimulation geometry setup\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) shows the simulation geometry used in this study. The 10 bps DNA was modelled as a cylinder with a 1 nm radius and a length of 3.4 nm. The DNA model extended towards the z-axis; its centre was at the origin. The mol concentration of nucleotide units in the DNA model was 3.02 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e mol L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. This determination referred to the enhanced green fluorescent protein plasmid-C1 (pEGFP-C1). When the chemical species enter the DNA model, the reaction between the DNA and the chemical species is determined with \u003cem\u003eP\u003c/em\u003e(Δ\u003cem\u003et\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;1\u0026thinsp;\u0026minus;\u0026thinsp;exp (\u0026minus;\u0026thinsp;\u003cem\u003ek\u003c/em\u003e [B] Δ\u003cem\u003et\u003c/em\u003e)\u003csup\u003e22\u003c/sup\u003e, where \u003cem\u003ek\u003c/em\u003e is the rate constant between the chemical species and nucleotides, [B] is the DNA mol concentration, Δ\u003cem\u003et\u003c/em\u003e is time step of 100 fs. In this study, the energy deposition site (\u003cem\u003ex\u003c/em\u003e, 0, 0) and the spur radius (\u003cem\u003ea\u003c/em\u003e) are free parameters. Therefore, H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and \u003csup\u003e\u0026bull;\u003c/sup\u003eOH are at (\u003cem\u003ex\u003c/em\u003e, 0, 0) and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e with a spur radius (\u003cem\u003ea\u003c/em\u003e) exists in a Gaussian centred at (\u003cem\u003ex\u003c/em\u003e, 0, 0). The radicals could be scavenged in a living system. This study also considers this effect. The radical scavenging is determined with \u003cem\u003eP\u003c/em\u003e(Δ\u003cem\u003et\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;1\u0026thinsp;\u0026minus;\u0026thinsp;exp (\u0026minus;\u0026thinsp;\u003cem\u003ek\u003c/em\u003e' [B'] Δ\u003cem\u003et\u003c/em\u003e)\u003csup\u003e22\u003c/sup\u003e, where \u003cem\u003ek\u003c/em\u003e' [B'] is the scavenging capacity (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and we investigated the DNA damage yields in a living system under the scavenging capacity from 10\u003csup\u003e7\u003c/sup\u003e (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) to 10\u003csup\u003e9\u003c/sup\u003e (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b) shows a flowchart of our code.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eCode validation\u003c/h2\u003e \u003cp\u003eAs a code validation, we focused on the e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e yields in water photolysis, for which many experimental and analytical results have been reported\u003csup\u003e23\u0026ndash;28\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) shows the experimental values of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e\u003csup\u003e28\u003c/sup\u003e and the calculated results of our code at deposition energies 8.3 and 12.4 eV. In the experiments, the two-photon absorption of the laser generates e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e and its time evolution yield during 1 ns was measured\u003csup\u003e28\u003c/sup\u003e. In this analysis, the spur radius (\u003cem\u003ea\u003c/em\u003e) is the only free parameter\u003csup\u003e23\u0026ndash;28\u003c/sup\u003e. The experimental values were almost entirely reproduced at a deposition energy of 8.3 eV, assuming a Gaussian of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e and a spur radius of 0.78 nm. The experimental values were reproduced at a deposition energy of 12.4 eV, assuming a spur radius of 3.8 nm in this study. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b) shows the spur radius (\u003cem\u003ea\u003c/em\u003e) dependence as a function of the deposition energy. The spur radii for various deposition energies were determined using the parameter analysis based on previous experimental studies (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a)). Since the spur radius was assumed to be Gaussian and exponential distributions in a previous study\u003csup\u003e28\u003c/sup\u003e, these two calculations were performed in this study. Our results well reproduced the experimental results previously reported, validating our code.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eDiffusion coefficient of chemical species in a DNA molecule\u003c/h2\u003e \u003cp\u003eIn this study, we noted the diffusion coefficients of chemical species in water (or DNA) as \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e (or \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e). When the chemical species contact the DNA, it will slowly migrate on the DNA surface. The chemical species will react with or escape DNA. The diffusion coefficient of the chemical species in contact with the DNA will differ from the diffusion coefficient in water. However, the diffusion coefficients \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e migrating on the DNA surface are yet to be reported. Here, we estimated the diffusion coefficients, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e, by assuming they were significantly smaller than \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e. Here, we introduce a slowing down parameter (\u003cem\u003eS\u003c/em\u003e) for the diffusion coefficient on the DNA surface. We assumed \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e as \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e/\u003cem\u003eS\u003c/em\u003e; then, we calculated the reaction probabilities of DNA with \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e near \u003cem\u003eS\u003c/em\u003e from 10 to 1000 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a)). The simulation conditions were \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.2 nm and \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm. When \u003cem\u003eS\u003c/em\u003e is 10, the reaction probabilities are too small to ensure the reaction of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH with DNA. Near ratios above \u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;100, a specific amount of the chemical species could react with DNA, whereas others escape. For \u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1,000, under a very slight diffusion condition for the chemical species, most \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e that reach the DNA react with it. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b) shows these representative illustrations of the reaction between \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and DNA. We assumed that \u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10, 100 and 1000 correspond to the DNA and \u003csup\u003e\u0026bull;\u003c/sup\u003eOH rate constants or DNA and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e of much less than 10\u003csup\u003e9\u003c/sup\u003e, ~10\u003csup\u003e9\u003c/sup\u003e and much greater than 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The rate constant in an aqueous DNA solution is ~\u0026thinsp;10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1 21\u003c/sup\u003e, showing that \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e could react with or escape from the DNA. We estimated that the \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e for \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e moving in the DNA region is approximately \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e/100 in water. Henceforth, we assumed that the \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e equals to \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e/100.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eDiffusion and reaction of chemical species\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) shows the calculated relative distance between \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e after 10 ns without radical scavengers. Here, three calculation conditions were employed: (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.2 nm, \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm; (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm, \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm; and (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6 nm, \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm. The results of (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) and (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) show a peak structure at a few nm, but no structure was observed in (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). This peak structure indicates that a specific number of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e was present in the 10 bps of the DNA region under the initial calculation conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) also shows that \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e are considerably separated by a few 10 nm. In this case, the chance of multiple reactions between the DNA and the two species is scarce and each species could cause isolated lesions in the DNA.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eTime-dependent yield changes of the chemical species\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b) shows the time evolution yields for each chemical species in the conditions without radical scavengers. The computational conditions are \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.2 nm and \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm. We compared the calculated results with and without the DNA model (shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a)). The result indicates that H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e does not significantly decrease, which might be attributed to a small reaction probability between H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e of 3.8%. In liquid water without the DNA model, the e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e yield is slightly lower than that of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH because e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e can also react with H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e. The decrements in the \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e yields become more pronounced at 100 ps or later under this condition. When the DNA structure is considered a simple cylinder (shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a)), the chemical reaction rates are slower than without the DNA model during a few ns. This result is because the rate constants between the chemical species (~\u0026thinsp;10\u003csup\u003e10\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) \u003csup\u003e21\u003c/sup\u003e in water are higher than those in DNA component nucleotides molecules with H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e, \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e (~\u0026thinsp;10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003csup\u003e21\u003c/sup\u003e. The \u003csup\u003e\u0026bull;\u003c/sup\u003eOH yield is less than that of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e after 10 ns because the rate constants between \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and nucleotides (AMP: 4.1 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, CMP: 4.7 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, GMP: 4.7 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and TMP: 5.2 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) are mostly greater than that between e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e and nucleotides (AMP: 3.8 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, CMP: 6.8 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, GMP: 1.5 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and TMP: 1.5 \u0026times; 10\u003csup\u003e9\u003c/sup\u003e L mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003csup\u003e21\u003c/sup\u003e. Furthermore, the diffusion coefficient of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH (2.2 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s) is less than half of that for e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e (4.9 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s)\u003csup\u003e29\u003c/sup\u003e. This result indicates that \u003csup\u003e\u0026bull;\u003c/sup\u003eOH reacts with DNA more readily than e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e, and \u003csup\u003e\u0026bull;\u003c/sup\u003eOH stays around the DNA for a long time, resulting in high reactivity. In general, the chemical reactions to produce stable products, such as DNA damage, begin to converge after approximately 100 ns.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eEstimating DNA damage\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a) shows the calculated results of the sum of probabilities of the reactions of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e with \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e with H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e. The results depend on parameter (\u003cem\u003ea\u003c/em\u003e) but not parameter (\u003cem\u003ex\u003c/em\u003e). When the spur radius (the distance between e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e and \u003csup\u003e\u0026bull;\u003c/sup\u003eOH or H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e) is approximately 2 nm, corresponding to deposition energy 10 eV (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b)), the chemical species react with each other with a high probability of several 10%. When the spur radius is approximately 8 nm, corresponding to water radiolysis\u003csup\u003e18\u003c/sup\u003e, the chemical species react with each other with a probability of 10%. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b) shows the probabilities of the reaction between DNA and \u003csup\u003e\u0026bull;\u003c/sup\u003eOH, indicating a slight dependence on parameter (\u003cem\u003ea\u003c/em\u003e) and a strong dependence on parameter (\u003cem\u003ex\u003c/em\u003e). When \u003csup\u003e\u0026bull;\u003c/sup\u003eOH is generated near the DNA, it reacts with the DNA with a high probability of several 10%; however, the probability decreases to a few % at the condition of \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10 nm. Note that the DNA length is limited to 10 bps in this case. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c) shows the probabilities of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e reacting with DNA, indicating a slight dependence on parameters (\u003cem\u003ea\u003c/em\u003e) and (\u003cem\u003ex\u003c/em\u003e). When radiation deposits the energy near the DNA, e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e reacts with the DNA and the reaction probability is less than a few %. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d) shows the multiple reaction probabilities of DNA with \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e within 10 bps, namely, the production of a clustered DNA damage site. Note that the results of Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d) are not the sum of the results of Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b) and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c). The results show a slight dependence on (\u003cem\u003ea\u003c/em\u003e) and a strong dependence on (\u003cem\u003ex\u003c/em\u003e), although the probabilities are 0.6% or less.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the calculated results under the condition with radical scavengers. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) shows the probabilities of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH scavenging when \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 nm. The \u003csup\u003e\u0026bull;\u003c/sup\u003eOH scavengers, such as dimethyl sulfoxide (DMSO) and tris(hydroxymethyl) aminomethane (Tris), with a scavenging capacity in mammalian cells of ~\u0026thinsp;3 \u0026times; 10\u003csup\u003e8\u003c/sup\u003e (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003csup\u003e30\u003c/sup\u003e, are assumed here. The \u003csup\u003e\u0026bull;\u003c/sup\u003eOH scavenging probabilities are higher than 60% above a scavenging capacity of 3 \u0026times; 10\u003csup\u003e8\u003c/sup\u003e (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), typically in a living system. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b) shows the reaction probabilities between DNA and \u003csup\u003e\u0026bull;\u003c/sup\u003eOH, indicating a strong dependence on parameter (\u003cem\u003ex\u003c/em\u003e). When \u003csup\u003e\u0026bull;\u003c/sup\u003eOH is generated near the DNA, it reacts with the DNA with a high probability of approximately 10%. However, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c), the probabilities of the e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e reaction with DNA do not significantly depend on parameters (\u003cem\u003ea\u003c/em\u003e) and (\u003cem\u003ex\u003c/em\u003e), and even when e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e is distributed around the DNA, the probability would be a few %. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(d) shows the probability of producing a clustered damage site by multiple reactions with \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e within 10 bps. Although the damage clustering is not very frequent (0.4% or less), the radiation energy deposition proximately to DNA causes two DNA lesions originating from reactions with \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e, inducing oxidative and reductive damage within a localised region of 10 bps, respectively. The important point is that \u003csup\u003e\u0026bull;\u003c/sup\u003eOH proximately arising around the DNA within a few nm or less could react with DNA before it encounters radical scavengers.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe correlation between the single-spur fate and DNA damage clustering was revealed for the first time using the newly developed dynamic MC code for chemical processes (dmcc_chem). To quantitatively calculate the indirect effect of each water radiolysis species on DNA damage induction, the diffusion coefficients of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e in DNA were newly estimated and the rate constants for the reactions of the species with nucleotides were considered to calculate the chemical reaction probabilities of chemical species constituting a spur.\u003c/p\u003e \u003cp\u003eThe primary findings from this study on the three-body single spur and DNA damage clustering are as follows: (i) The spur centre is produced within 1.5 nm from the DNA. Assuming that the diffusion coefficients \u003cem\u003eD\u003c/em\u003e\u003csub\u003eDNA\u003c/sub\u003e of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e in the DNA molecule were \u003cem\u003eD\u003c/em\u003e\u003csub\u003ewater\u003c/sub\u003e/100, indicating that \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e arising near the DNA could cause localised damage. (ii) The \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e yields decrease following specific kinetic curves until 100 ns, contrasting with the independence observed for H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e. (iii) The probability of 10% for \u003csup\u003e\u0026bull;\u003c/sup\u003eOH reacting with DNA decreases with the increasing distance (\u003cem\u003ex\u003c/em\u003e) of the spur centre from the DNA to 1%, irrespective of the spur radius. However, for an e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e of a few %, the spur centre distance and spur radius do not significantly change. (iv) Interestingly, radical scavengers do not significantly quench \u003csup\u003e\u0026bull;\u003c/sup\u003eOH proximately arising around the DNA and do not affect the e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e yield, indicating that the radical scavengers do not significantly impact the damage clustering efficiency. The obtained evidence establishes that the DNA damage clustering arises from the reactions with a single spur and not an accumulation of multiple spurs arising from more than one radiation track. This aspect is fundamental in forming multiple damaged sites, which is a normal event at the end of the radiation track. The yields of DNA single-strand breaks (SSBs) or isolated base lesions are 1\u0026ndash;3% of the total ionisation events in the nucleus of a living cell. The double-strand break (DSB) yield is much less than approximately 0.05%\u003csup\u003e31\u003c/sup\u003e. Compared to the reported damage yields, our result on the probabilities below 1% for concomitant reactions of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e with 10 bps of DNA is consistent with the reported values.\u003c/p\u003e \u003cp\u003eWe revealed that the three species constituting the spur (H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e, \u003csup\u003e\u0026bull;\u003c/sup\u003eOH, and e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e) behaved differently in the spur\u0026rsquo;s lifetime. The different dynamics of the three species is strongly involved in the chemical structure of clustered damage sites. The chemical species in the spur, proximately arising within 1.5 nm from the DNA, could react with the DNA. The water molecules surrounding the DNA with an approximate 1 nm thickness called a hydration layer specifically contribute to oxidative or reductive base damage induction\u003csup\u003e32\u003c/sup\u003e. A hole created in a water molecule in the hydration layer might be transferred to the DNA through the hydrogen-bonded water networks. The positive charge migrates on the DNA strand and finally stabilises at the lowest oxidative potential nucleobase, guanine as an electronless centre (cation radical) and a low probability of strand break induction\u003csup\u003e33\u003c/sup\u003e. Thus, the H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e in the spur would be a source of oxidised guanine, such as 7,8-dihydro-8-oxo-2\u0026rsquo;-deoxyguanine (8-oxo-G) or 2,6-diamino-4-hydroxy-5-\u003cem\u003eN\u003c/em\u003e-methylformamidopyrimidine (Fapy).\u003c/p\u003e \u003cp\u003eA typical inducer of the indirect effect, \u003csup\u003e\u0026bull;\u003c/sup\u003eOH, causes an SSB by abstracting a hydrogen atom from the deoxyribose moiety in the DNA\u003csup\u003e34\u003c/sup\u003e and oxidised base damage, such as 8-oxo-G or 8-oxo-adenine\u003csup\u003e35\u003c/sup\u003e. However, e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e could be a source of the electron gain process (anion radical formation). The primary product of the reductive base is dihydrothymine (DHT) because DHT generation is enhanced under an anaerobic condition\u003csup\u003e36\u003c/sup\u003e or much more pronounced with the presence of radical scavengers compared to oxidative lesions\u003csup\u003e37\u003c/sup\u003e. The reaction probability of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH with DNA significantly depends on the distance (\u003cem\u003ex\u003c/em\u003e) of the spur centre from the DNA, and is a couple of times larger than the reaction of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e, irrespective of (\u003cem\u003ex\u003c/em\u003e). Interestingly, when the spur arises beyond 4 nm from the DNA, the reaction probability of e\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026thinsp;\u003csub\u003eaq\u003c/sub\u003e with DNA surpasses that of \u003csup\u003e\u0026bull;\u003c/sup\u003eOH under the scavenging capacity of approximately 3 \u0026times; 10\u003csup\u003e8\u003c/sup\u003e (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b) and 6(c)). These results indicate that the interaction of single spurs could realise various lesion combinations. Heterogeneous lesions, not specific or homogeneous lesions, likely constitute the clustered DNA damage site by reacting with a single spur.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe dmcc_chem demonstrated the indirect effects of a single-spur comprising H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e, \u003csup\u003e•\u003c/sup\u003eOH, and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e on damage clustering in DNA. The rate constants of each radiolytic chemical species reacting with nucleotides were considered for the calculations. The results showed that the three bodies spur can concomitantly react within a 3.4 nm range of DNA length (10 base pairs) to induce a multiple DNA damage site, presumably comprising SSB, oxidative or reductive nucleobase damage. The reaction probability was 0.4% or less, consistent with the experimental values previously reported. The efficiency is comparable to that of DSBs. The energy deposition to the water layer near DNA from ionising radiation causes a critical effect on living system. This aspect contributes to a much better understanding of low dose radiation risk.\u003c/p\u003e "},{"header":"Methods","content":"\u003cp\u003eWe developed the dmcc_chem to analyse the radio- or photo-chemical process. Here, we applied the dmcc_chem to aqueous DNA solution systems with and without radical scavengers and aimed to extend it to various solvents. First, we note the features of the dmcc_chem by briefly describing diffusion and reaction, dielectric response and the dynamic MC method.\u003c/p\u003e\u003ch2\u003eDiffusion and reaction\u003c/h2\u003e\u003cp\u003eThis study assumed a three-body single spur formed by water photolysis or radiolysis\u003csup\u003e23–28\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) shows the diffusion reaction of H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e. The diffusion coefficients of H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e are 9.5 × 10\u003csup\u003e− 9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s and 4.9 × 10\u003csup\u003e− 9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s, respectively\u003csup\u003e29\u003c/sup\u003e. The reaction radius and probability of H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e are 0.75 nm and 3.8%, respectively\u003csup\u003e22\u003c/sup\u003e. When both react chemically, they form H\u003csub\u003e3\u003c/sub\u003eO, which becomes H\u003csub\u003e2\u003c/sub\u003eO + H\u003csup\u003e• 22\u003c/sup\u003e. An escape distance was introduced if the chemical reaction did not occur (96.2%)\u003csup\u003e22\u003c/sup\u003e. The escape distance is derived from the reaction radius and separation distance (0.3 nm)\u003csup\u003e22\u003c/sup\u003e. Those diffusion motions are continuously calculated when H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e enter the reaction radius (0.75 nm). They completely escape in one contact at an escape distance of 1.05 nm. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) shows the diffusion reaction of \u003csup\u003e•\u003c/sup\u003eOH and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e. The diffusion coefficient of \u003csup\u003e•\u003c/sup\u003eOH is 2.2 × 10\u003csup\u003e− 9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s \u003csup\u003e29\u003c/sup\u003e and the reaction radius and probability of OH\u003csup\u003e•\u003c/sup\u003e and e\u003csup\u003e−\u003c/sup\u003e \u003csub\u003eaq\u003c/sub\u003e are 0.72 nm and 49%, respectively\u003csup\u003e22\u003c/sup\u003e. When both react chemically, OH\u003csup\u003e−\u003c/sup\u003e is formed\u003csup\u003e22\u003c/sup\u003e. If the chemical reactions do not occur (51%), the escape distance of 1.02 nm is used to determine the separation in one contact event.\u003c/p\u003e\u003ch2\u003eDielectric response\u003c/h2\u003e\u003cp\u003eThe dmcc_phys that has been developed so far comprises MD and MC. It calculates the delocalisation and relocalisation of secondary electrons generated by water photolysis and radiolysis\u003csup\u003e18–20\u003c/sup\u003e. In the MD calculations of secondary electrons, the Coulombic interaction between the secondary electrons and the parent cation is considered\u003csup\u003e19\u003c/sup\u003e. Electronic (a few fs), phonon (from 10 fs to several 100 fs) and orientation polarisations (after several 100 fs) shield this Coulombic force with time evolution\u003csup\u003e19\u003c/sup\u003e. These shielding effects were evaluated using the dielectric response, which is the time evolution of the relative dielectric constant\u003csup\u003e19\u003c/sup\u003e. Using the dielectric response, we simulated the hydration of charged particles\u003csup\u003e19\u003c/sup\u003e. The present dmcc_chem also uses this dielectric response.\u003c/p\u003e\u003ch2\u003eDynamic MC method\u003c/h2\u003e\u003cp\u003eThe Smolchowski–Debye equation describes the thermal diffusion motion of chemical species in a solution\u003csup\u003e38\u003c/sup\u003e. The MC method is typically used because this equation is challenging to solve. Here, the step-by-step method accounts for the dielectric response. The chemical species thermally diffuse at each time step and a chemical reaction is decided when two chemical species enter the reaction radius\u003csup\u003e22\u003c/sup\u003e. The thermal diffusion motion of each chemical species per time step is determined by sampling from Eq.\u0026nbsp;(1) \u003csup\u003e22\u003c/sup\u003e,\u003c/p\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\mathbf{r}}_{i}\\left(t+\\varDelta t\\right) = {\\mathbf{r}}_{i}\\left(t\\right)+\\sqrt{2{D}_{i}\\varDelta t}\\left({N}_{i,x}{\\mathbf{e}}_{x}+{N}_{i,y}{\\mathbf{e}}_{y}+{N}_{i,z}{\\mathbf{e}}_{z}\\right)+\\frac{{D}_{i}}{{k}_{\\text{B}}T}{\\mathbf{F}}_{i}\\varDelta t$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cp\u003ewhere \u003cb\u003er\u003c/b\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e) is the three-dimensional spatial coordinate of the \u003cem\u003ei\u003c/em\u003e-th chemical species at time \u003cem\u003et\u003c/em\u003e. The second term is the thermal diffusion term and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the diffusion coefficient of the \u003cem\u003ei\u003c/em\u003e-th chemical species. Δ\u003cem\u003et\u003c/em\u003e was 100 fs to ensure timestep convergence. (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ei,x\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ei,y\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ei,z\u003c/em\u003e\u003c/sub\u003e) are the \u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e and \u003cem\u003ez\u003c/em\u003e components of the thermal diffusion direction, respectively, determined from uniform random numbers. The third is the Coulombic force term, where \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e and \u003cem\u003eT\u003c/em\u003e are the Boltzmann constant and water temperature (300 K), respectively. The Coulombic force \u003cb\u003eF\u003c/b\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e involved in the \u003cem\u003ei\u003c/em\u003e-th chemical species is expressed by\u003c/p\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${\\mathbf{F}}_{i} = \\sum _{j\\ne i}\\frac{{Z}_{i}{Z}_{j}{e}^{2}}{4\\pi {\\epsilon }_{0}{\\epsilon }_{\\text{r}}\\left(t\\right)}\\frac{{\\varvec{r}}_{i}-{\\varvec{r}}_{j}}{{\\left|{\\varvec{r}}_{i}-{\\varvec{r}}_{j}\\right|}^{3}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cp\u003ewhere \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e are the valences of the \u003cem\u003ei\u003c/em\u003e-th and \u003cem\u003ej\u003c/em\u003e-th chemical species, respectively, \u003cem\u003ee\u003c/em\u003e is the elementary charge, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the dielectric constant of the vacuum and \u003cem\u003eε\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e) is the dielectric response\u003csup\u003e19\u003c/sup\u003e. Consequently, the Coulombic force between the charged chemical species decreases with time. This Coulombic force term can be expressed in terms of the Onsager distance\u003csup\u003e39\u003c/sup\u003e as\u003c/p\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\frac{{D}_{i}}{{k}_{\\text{B}}T}{\\mathbf{F}}_{i}\\varDelta t = -{D}_{i}\\varDelta t\\sum _{j\\ne i}{r}_{\\text{c},ij}\\left(t\\right)\\frac{{\\varvec{r}}_{i}-{\\varvec{r}}_{j}}{{\\left|{\\varvec{r}}_{i}-{\\varvec{r}}_{j}\\right|}^{3}},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cp\u003ewhere\u003c/p\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${r}_{\\text{c},ij}\\left(t\\right) = -\\frac{{{Z}_{i}{Z}_{j}e}^{2}}{4\\pi {\\epsilon }_{0}{\\epsilon }_{\\text{r}}\\left(t\\right){k}_{\\text{B}}T} ,$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eis the time-dependent Onsager distance. When the target is water, the dielectric response is completed in a few 10 ps\u003csup\u003e19\u003c/sup\u003e. Therefore, after a few 10 ps from charge generation, the time-dependent Onsager distance converges to 0.7 nm, with a relative dielectric constant of 80.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Japan Society for the Promotion of Science KAKENHI (Grant nos. 22K04993, 22K14631, 22H03744, 22K14630, and 22K03549).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualisation: TK, TT, and AY; Methodology: TK, TT, and YM; Investigation: TK, TT, YM, UH, HT, and YI; Visualisation: TK; Funding acquisition: TK, TT, YM, UH, and HT; Project administration: TK; Supervision: AY; Writing–original draft: TK; Writing–review \u0026amp; editing: TK, YM, and AY\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u003c/strong\u003e and requests for materials should be addressed to Takeshi Kai.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWard, J. 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Res. 55, 384\u0026ndash;404 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchroder, E., Budzinski, E.E., Wallace, J.C., Zimbrick, J. D. \u0026amp; Box, H.C. Radiation Chemistry of D(ApCpGpT). Int. J. Radiat. Biol. 68, 509\u0026ndash;523 (1995).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYu, H., Kondo, Y., Fujii, K., Yokoya, A. \u0026amp; Yamashita, S. Establishment of a Method for Investigating Direct and Indirect Actions of Ionizing Radiation Using Scavenger-free Plasmid DNA, Radiat. Res. 197, 594\u0026ndash;604 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDebye, P. Reaction Rates In Ionic Solutions, Transactions of The Electrochemical Society, 82, 265\u0026ndash;272 (1942).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOnsager, L. Initial Recombination of Ions, Phys. Rev. 54, 554\u0026ndash;557 (1938).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4596630/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4596630/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMultiple DNA damage resulting from the single ionisation of a water molecule is the most fundamental process of the initial step of radiobiological effects. The critical size and the chemical lesion types constituting the damage site have not been fully elucidated. We challenged this long-term issue by developing a dynamic Monte Carlo code for the chemical process. The reaction probabilities and the spatial distribution of lesions were theoretically solved as a function of the spur radius and distance between DNA and the initial ionisation position. The results showed that a hydroxyl radical and a hydrated electron from a single spur can concomitantly react within a 10 base pairs DNA to induce a multiple DNA damage site comprising a DNA single-strand break and reductive nucleobase damage; however, the reaction probability is 0.4% or less. Once this combination arises, it strongly compromises the activity of nucleobase excision repair enzymes. The efficiency is comparable to that of DNA double-strand breaks, which have been thought to be a significant cause of cell death. However, a single-spur reaction could be a source of damaged nucleobase misrepair, leading to point mutations in the genome.\u003c/p\u003e","manuscriptTitle":"Computational demonstration of multiple DNA damages produced by the radiolytic chemical species in an aqueous DNA solution","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-03 08:59:07","doi":"10.21203/rs.3.rs-4596630/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-chemistry","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commschem","sideBox":"Learn more about [Communications Chemistry](http://www.nature.com/commschem/)","snPcode":"","submissionUrl":"","title":"Communications Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"91232ab4-4aec-4740-bab2-7d4e481d36a3","owner":[],"postedDate":"July 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":33396229,"name":"Physical sciences/Chemistry/Chemical biology/DNA"},{"id":33396230,"name":"Biological sciences/Biochemistry/DNA"}],"tags":[],"updatedAt":"2025-03-07T08:09:51+00:00","versionOfRecord":{"articleIdentity":"rs-4596630","link":"https://doi.org/10.1038/s42004-025-01453-x","journal":{"identity":"communications-chemistry","isVorOnly":false,"title":"Communications Chemistry"},"publishedOn":"2025-03-06 05:00:00","publishedOnDateReadable":"March 6th, 2025"},"versionCreatedAt":"2024-07-03 08:59:07","video":"","vorDoi":"10.1038/s42004-025-01453-x","vorDoiUrl":"https://doi.org/10.1038/s42004-025-01453-x","workflowStages":[]},"version":"v1","identity":"rs-4596630","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4596630","identity":"rs-4596630","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}