Acid spike effect in spurs/tracks of the low/high linear energy transfer radiolysis of water: potential implications for radiobiology

Abstract

Monte Carlo track chemistry simulations have been used to calculate the yields of hydronium ions (H₃O⁺) that are formed within spurs/tracks of the low/high linear energy transfer (LET) radiolysis of pure, deaerated water during and shortly after irradiation. The in situ formation of H₃O⁺ renders the spur/track regions temporarily more acidic than the surrounding medium. Although experimental evidence for an acidic spur has already been reported, there is only fragmentary information on its magnitude and time dependence. Here, spur/track H₃O⁺ concentrations and the corresponding pH values are obtained from our calculated yields of H₃O⁺ as a function of time (in the interval of ∼1 ps to 1 ms). We selected four impacting ions and we used two different spur/track models: (1) an isolated “spherical” spur model characteristic of low-LET radiation (such as 300 MeV protons, which mimic ⁶⁰Co γ/fast electron irradiation, LET ∼ 0.3 keV μm⁻¹) and (2) an axially homogeneous “cylindrical” track model for high-LET radiation (such as 150 keV protons, LET ∼ 70 keV μm⁻¹; 1.75 MeV per nucleon helium ions, LET ∼ 70 keV μm⁻¹; and 0.6 MeV per nucleon helium ions, LET ∼ 146 keV μm⁻¹). Very good agreement is found between our calculated time evolution of G(H₃O⁺) in the radiolysis of pure, deaerated water by 300 MeV incident protons and the available experimental data at 25 °C. For all cases studied, an abrupt transient acid pH effect is observed at times immediately after the initial energy release. This effect, which we call an “acid spike”, is found to be greatest for times shorter than ∼1 ns in isolated spurs. In this time range, the pH remains nearly constant at ∼3.3. For cylindrical tracks, the acid spike response to ionizing radiation is far more intense than that for the spherical spur geometry. For the three high-LET irradiating ions considered, the pH is around 0.5 on a time scale of ∼100 ps. At longer times, the pH increases gradually for all cases, ultimately reaching a value of 7 (neutral pH) at ∼1 μs for the spherical geometry and ∼0.1 ms for the cylindrical geometry. It does not appear that the transient acid spike effect described here has been explored in water or in a cellular environment subject to the action of ionizing radiation, especially high-LET radiation. In this regard, this work raises a number of questions about the potential implications of this effect in radiobiology, some of which are briefly evoked.

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1. Introduction

All biological systems are damaged by ionizing radiation. Since living cells and tissues consist mainly of water (∼70–85% by weight), a thorough knowledge of the radiation chemistry of water is critical to our understanding of the early stages in the complicated chain of radiobiological events that follow the absorption of radiation. Indeed, in a cellular environment, reactive species generated by water radiolysis are likely to cause chemical modifications and changes in cells, which subsequently may act as triggers of signaling or damaging effects.^1–3 Ultimately, this can lead to observable biological responses.

Although damage can be randomly induced in all biomolecules (e.g., DNA, membrane lipids, and proteins), DNA and its associated water molecules are considered to be the critical target in defining the radiobiological response. Exposure to ionizing radiation is known to cause a plethora of DNA damage. This includes single- and double-strand breaks, base damage, abasic sites, destruction of sugars, tandem lesions, cross-links, defects in mitochondrial functions, and clustered damage.^4–15 Clustered damage is the most biologically-relevant DNA damage induced by radiation because it is less readily repaired by the cell. Damage is caused either directly or indirectly through chemical attack by radiolytic products as the radiation track passes through and deposits energy near to (mostly bulk water) or in the DNA. If unrepaired or mis-repaired, this damage may lead to mutations and promote tumorigenesis, cell death, or long-term stressful effects in surviving cells. A goal of radiobiology research is to understand how radiation exposure deregulates molecular pathways that are important in maintaining genomic integrity.

It is noteworthy that the extent and nature of cellular radiobiological damage depends not only on the absorbed dose but also on the quality of radiation. The “linear energy transfer” (LET) (also called “stopping power” by physicists) represents, to a first approximation, the nonhomogeneity of energy deposition on a sub-microscopic scale. High-LET radiation (e.g., α-particles, high-energy charged nuclei) has a high potential to kill cells with little oxygen and cell cycle dependence. It is thought that the enhanced biological severity of high-LET heavy ions reflects the increased ionization density of high-LET radiation. Therefore, a full understanding is essential of (1) the early physicochemical track structure (i.e., the physical and chemical events that occur in the “native” radiation track) and (2) the spatio-temporal development of the track. Using this information, we can develop a realistic description of all the reactive fragment species created at early times and involved as precursors to radiobiological damage.^{1,3,7,10,16–18} It is also important to know how the initial, spatially nonhomogeneous distribution of reactive species relaxes in time toward a homogeneous distribution. This knowledge is critical to unravel the fundamental biochemical mechanisms leading to the biological consequences of ionizing radiation.

While fundamental biological processes are numerous and complex, they are triggered in aqueous environments. Low-LET, sparsely ionizing radiation includes γ-rays from ⁶⁰Co and ¹³⁷Cs, hard X-rays, and high-energy charged particles, such as fast electrons or ∼300 MeV protons (LET ∼ 0.3 keV μm⁻¹). From the viewpoint of pure aqueous radiation chemistry, tracks are formed initially by well-separated clusters of reactive species. These are commonly known as “spurs”^19,20 (spherical in shape). During the physicochemical stage of radiation action in Platzman's classification^21,22 (from ∼10⁻¹⁶ to 10⁻¹² s after the initial energy deposition), the radiolysis of water can be described by the following reactions:^17,23–25

H₂O [long arrow, wavy then straight] H₂O˙⁺ + e⁻ (ionization) (1)

H₂O [long arrow, wavy then straight] H₂O* (excitation) (2)

H₂O˙⁺ + H₂O → H₃O⁺ + ˙OH (proton transfer reaction, ∼200 fs)²⁶ (3)

H₂O˙⁺ + M → M˙⁺ + H₂O (scavenging of the radical cation H₂O˙⁺ in highly concentrated solutions)²⁷ (4)

e⁻ → e_sub⁻ → e_th⁻ → e_tr⁻ → e_aq⁻ (∼240 fs to 1 ps)^28,29 (slowing down to subexcitation energies (<7.3 eV), thermalization, trapping and hydration)³⁰ (5)

e⁻ + H₂O˙⁺ → H₂O* (electron-cation geminate recombination)^31–33 (6)

e⁻ + H₂O → H₂O˙⁻ → H⁻ + ˙OH (resonant dissociative electron attachment, or DEA process)^33–37 (7)

followed by

H⁻ + H₂O → H₂ + OH⁻ (8)

{e⁻, e_sub⁻, e_th⁻ or e_tr⁻} + M → M˙⁻ (“dry” or “pre-hydrated” electron capture by a suitable scavenger in sufficiently high concentrations)^38–42 (9)

H₂O* → e_aq⁻ + H₂O˙⁺ (threshold at ∼6.5 eV)⁴³ (10)

H₂O* → H˙ + ˙OH (11)

H₂O* → H₂ + O(¹D) (oxygen atom in its singlet ¹D first excited state) (12)

followed by

O(¹D) + H₂O → H₂O₂ (or possibly also 2˙OH)⁴⁴ (13)

H₂O* → 2H˙ + ˙O˙(³P) (oxygen atom in its triplet ³P ground state, rather inert to water but reacts with most additives)⁴⁵ (14)

By ∼1 ps, the various “initial” radiolysis products are the hydrated electron (e_aq⁻), H˙, ˙OH, H₂, H₂O₂, H⁺ (or equivalently, H₃O⁺ or H_aq⁺), OH⁻, O₂˙⁻ [or HO₂˙, depending on the pH; pK_a (HO₂˙/O₂˙⁻) = 4.8 in water at 25 °C],⁴⁶ ˙O˙(³P), etc.^17,23–25 At this time, these species begin to diffuse away from the site where they were originally produced. The result is that a fraction of them react together within the spurs as they develop in time while the remainder escape into the bulk solution. At ambient temperature, the spur expansion is essentially complete by ∼0.2 μs.⁴⁷ At this time, the species that have escaped from spur reactions become homogeneously distributed throughout the bulk of the solution (i.e., the system at large) and the radiation track structure no longer exists.^1,48

The yields per 100 eV of absorbed energy of the species, which emerge from the spurs at the end of the nonhomogeneous chemical stage,^21,22 are the so-called “primary” (or “escape”) yields. They are denoted by g(e_aq⁻), g(H˙), g(˙OH), g(H₂), g(H₂O₂), etc.^{17,23–25,49,50} For ⁶⁰Co γ-irradiated neutral solution at 25 °C, g(e_aq⁻) = 2.65, g(H˙) = 0.6, g(˙OH) = 2.8, g(H₂) = 0.45, and g(H₂O₂) = 0.68 molecules per 100 eV.^50,51 The radical and molecular products are then available for reaction with dissolved solutes (if any) present (in low or moderate concentrations) at the time of irradiation. In the presence of air or oxygen, e_aq⁻ and H˙ atoms are rapidly converted to superoxide anion (O₂˙⁻)/hydroperoxyl (HO₂˙) radicals, according to:

e_aq⁻ + O₂ → O₂˙⁻, k₁₅ = 2.11 × 10¹⁰ M⁻¹ s⁻¹ (15)

H˙ + O₂ → HO₂˙, k₁₆ = 1.2 × 10¹⁰ M⁻¹ s⁻¹ (16)

where k₁₅ and k₁₆ are the rate constants for the two individual reactions.⁵⁰ Thus, in an aerobic cellular environment at pH 7, the major reactive species at homogeneity (∼0.2 μs) include O₂˙⁻, ˙OH, and H₂O₂.³

In biological systems, ionizing radiation can also stimulate inducible nitric oxide synthase activity in hit cells,⁵² thereby generating large amounts of nitrogen monoxide (or “nitric oxide”, ˙NO). Although ˙NO is chemically inert toward most cellular constituents (except for heme), it reacts with O₂˙⁻ to form the peroxynitrite anion (ONOO⁻) with a rate constant (1.9 × 10¹⁰ M⁻¹ s⁻¹) that is larger than that for the copper/zinc-superoxide dismutase (SOD)-catalyzed disproportionation of O₂˙⁻.⁵³ Like ˙OH radicals, ONOO⁻ and its conjugate acid, peroxynitrous acid ONOOH (pK_a = 6.8 at 37 °C),⁵⁴ are powerful oxidizing agents. They are capable of attacking a wide range of cellular targets, including lipids, thiols, proteins, and DNA bases.^3,53–55

The yield of all the radiolytic species and free radical intermediates and their initial geometric distributions along the tracks are strongly dependent on the radiation type and energy. For the chemical properties of spurs, the predominant effect of ⁶⁰Co γ/fast electron radiolysis is radical production.^23–25 However, the chemistry of water and aqueous solutions is very different after irradiation with high-LET, densely ionizing radiation.^{1,17,48,56,57} Indeed, with increasing LET, the mean separation distance between the spurs decreases. Further, the isolated spur structure changes to a situation in which the spurs eventually overlap and form (initially) a dense continuous column (cylindrical in shape) of species.^1,30,58,59 This leads to an increased amount of intra-track chemistry, favoring radical–radical reactions in the diffusing tracks. Under these conditions, the free-radical yields tend to diminish as the LET is increased, whereas the molecular yields increase.^17,24,25,56

Herein, we present simple space-time model calculations. They quantitatively show that the formation of H₃O⁺ in reaction (3), during the initial radiolytic processes in irradiated water, renders the spur/track regions temporarily more acid than the body of the solution. Although experimental evidence for this transient acid pH effect has already been reported,^24,60,61 there is only fragmentary information on its magnitude and time dependence following energy deposition. In this work, we use Monte Carlo track chemistry simulations to calculate, at 25 °C, the yields of H₃O⁺ produced by water radiolysis as a function of time from ∼1 ps to 1 ms. We carry out simulations for four different impacting ions: (1) 300 MeV protons (which mimic ⁶⁰Co γ/fast electron irradiation; LET ∼ 0.3 keV μm⁻¹); (2) 150 keV protons (LET ∼ 70 keV μm⁻¹); (3) 1.75 MeV per nucleon helium ions (LET ∼ 70 keV μm⁻¹); and (4) 0.6 MeV per nucleon helium ions (LET ∼ 146 keV μm⁻¹). The results are compared with available experimental data. The concentrations of H₃O⁺ and the corresponding pH values for each ion considered are obtained from our calculated yields of H₃O⁺ using a “spherical” spur model for low-LET radiation and a “cylindrical” track model for high-LET radiation.

A brief preliminary report of this work has been presented elsewhere.⁶²

2. Monte Carlo track chemistry simulations of water radiolysis

Monte Carlo simulation methods are well suited to take into account the stochastic nature of the complex sequence of events that are generated in aqueous systems following the absorption of ionizing radiation. Simulations allow the reconstruction of the intricate action of radiation. This is a powerful tool for studying the relationship between the initial radiation track structure, the ensuing chemical processes, and the stable end products formed by radiolysis. In previous studies,^{17,33,63–66} we provided a detailed description of our IONLYS-IRT Monte Carlo code. This program simulates, in a 3D geometrical environment, the nonhomogeneous distribution of reactive species initially produced by the absorption of incident radiation and all of the energetic secondary electrons, as well as the subsequent diffusion and chemical reactions of these species. Briefly, the IONLYS step-by-step simulation program covers the early physical and physicochemical stages of radiation action up to ∼1 ps in track development. It models all the basic physical interactions (energy deposition). It also models the subsequent conversion of the physical products created locally into the various initial radical and molecular products of radiolysis [see reactions (1)–(14)], which are distributed in a highly nonhomogeneous track structure. The complex spatial distribution of reactants at the end of the physicochemical stage is provided as an output of the IONLYS program. It is then used directly as the starting point for the subsequent nonhomogeneous chemical stage.^21,22 The different species now diffuse randomly at rates determined by their diffusion coefficients. They react, or compete, with one another as well as with any added solutes present at the time of irradiation until all spur/track reactions are complete (typically, on the time scale from ∼1 ps to ∼0.2–1 μs). We simulate this stage using the “independent reaction times” (IRT) method.^64,67,68 This is a computer-efficient stochastic simulation technique that is used to simulate reaction times without having to follow the trajectories of the diffusing species. The IRT method relies on the approximation that the reaction time of each pair of reactants is independent of the presence of other reactants in the system. Its implementation has been described in detail previously.⁶⁴ The IRT method gives accurate time-dependent chemical yields over a wide range of irradiation conditions. This has been well validated by comparison with full random flight Monte Carlo simulations, which do follow the reactant trajectories on an event-by-event basis.^69,70 This IRT program can also be used to efficiently describe the reactions that occur in the bulk solution during the homogeneous chemical stage^21,22 (i.e., in the time domain beyond a few microseconds).

The reaction scheme and reaction parameters used in our IRT program for pure liquid water at 25 °C are the same as used previously (see Table 1 of ref. 71). This set of reactions, initially compiled in ref. 17 and 44, now includes some newly measured or recently re-assessed reaction rates by Elliot and Bartels.⁵⁰ Values for the diffusion coefficients of the various reactive species involved in the simulations are listed in Table 6 of ref. 72.

To reproduce the effects of ⁶⁰Co γ/fast electron radiolysis, we used short segments of 300 MeV incident proton tracks (see Fig. 1, panel a, of ref. 62 and 73). The average LET value obtained in the simulations was nearly constant and equal to ∼0.3 keV μm⁻¹ at 25 °C. Such model calculations thus gave “track segment” yields at a well-defined LET.^56,64,74 The influence of the LET of the radiation on the H₃O⁺ yields was investigated by performing a series of similar simulations, but using different types of impacting ions of various initial energies. In this study, we limited ourselves to the following cases: (1) 150 keV protons and 1.75 MeV per nucleon helium ions, which have the same LET (∼70 keV μm⁻¹),¹ and (2) 0.6 MeV per nucleon helium ions, corresponding to a LET value of ∼146 keV μm⁻¹.⁷⁵ In these cases, spurs are formed so close to each other along the path of the irradiating ions that they merge to form a cylindrical region of high LET (see below). At low dose rates (so that no track overlap occurs), each spherical spur or cylindrical track can be treated independently from the others.

Fig. 1 Time evolution of G(H₃O⁺) (in molecule per 100 eV) for the radiolysis of pure, deaerated liquid water by 300 MeV incident protons (LET ∼ 0.3 keV μm⁻¹) at 25 °C from ∼1 ps to 1 ms. The red solid line shows the hydrogen ion yield values obtained from our Monte Carlo simulations (see text). Experimental data for ⁶⁰Co γ/fast electron irradiation are: () ref. 76, () ref. 77, () ref. 78, () ref. 79, and () ref. 80. For the sake of reference, our simulated time-dependent yields of e_aq⁻ and ˙OH (see ref. 81), H˙ and OH⁻ are also included in the figure. Note that the hydroxide ion OH⁻, which is formed largely by the reaction: e_aq⁻ + ˙OH → OH⁻ (k = 3.55 × 10¹⁰ M⁻¹ s⁻¹) as the spur expands, contributes to an alkaline spur and consequently counteracts the acid spike effect discussed in this work. However, as we can see from the figure, G(OH⁻) remains much smaller than G(H₃O⁺) over the time range of interest. As a result, its effect only slightly modifies the quantitative features of the pH and can be ignored to a good approximation. Finally, the (dotted) line shown at ∼0.2 μs indicates the end of spur expansion (ref. 47), i.e., the time required to observe the transition from nonhomogeneity to homogeneity in the distribution of the radiolytic species.

The simulations consist of following the transport and energy loss of the incident ion (proton or helium ion) until it has penetrated the chosen length (∼1–150 μm) of the track segment into the medium. At the incident ion energies considered here, interactions involving electron capture and loss by the moving ion (charge-changing collisions) have been neglected. Due to its large mass, the impacting ion is almost not deflected by collisions with the target electrons.^1,17,63 Typically, about 5000 to 10⁵ reactive chemical species are generated in these simulated track segments (depending on the type and energy of the irradiating ions). This ensures only small statistical fluctuations in the determination of averaged chemical yields.

3. Results and discussion

Fig. 1 shows the time evolution of G(H₃O⁺) as obtained from our simulations of the radiolysis of pure, deaerated liquid water by 300 MeV incident protons (LET ∼ 0.3 keV μm⁻¹) at ambient temperature, over the interval of ∼1 ps to 1 ms. For comparison, experimental data obtained by several groups^76–80 for ⁶⁰Co γ/fast electron irradiation are also shown in the figure. As can be seen, our computed values (red solid line) are in very good agreement with the measured H₃O⁺ yields.

The sharp decrease of G(H₃O⁺) observed at times longer than ∼10 μs for 300 MeV irradiating protons is mainly due to H₃O⁺ reacting with OH⁻ and, to a lesser extent, with the hydrated electrons escaping the spurs, according to:

H₃O⁺ + OH⁻ → 2H₂O, k₁₇ = 1.18 × 10¹¹ M⁻¹ s⁻¹ (17)

H₃O⁺ + e_aq⁻ → H˙ + H₂O, k₁₈ = 2.13 × 10¹⁰ M⁻¹ s⁻¹ (18)

where k₁₇ and k₁₈ are the rate constants for the two individual reactions.^17,71 This is clearly seen in Fig. 2 where we show the time profiles of ΔG(H₃O⁺) for each of the reactions that contribute to G(H₃O⁺), calculated from our Monte Carlo simulations in the time interval ∼1 ps to 1 ms.

Fig. 2 Time dependence of the extents ΔG(H₃O⁺) (in molecule per 100 eV) of the different reactions that are involved in the decay of H₃O⁺, calculated from our Monte Carlo simulations of the radiolysis of pure, deaerated water by 300 MeV incident protons (LET ∼ 0.3 keV μm⁻¹) at 25 °C, in the interval of ∼1 ps to 1 ms. Other reactions, such as H₃O⁺ + O˙⁻ → ˙OH + H₂O (k = 5 × 10¹⁰ M⁻¹ s⁻¹) and H₃O⁺ + HO₂⁻ → H₂O₂ + H₂O (k = 5 × 10¹⁰ M⁻¹ s⁻¹), contribute only little to the decay of G(H₃O⁺). The (dotted) line shown at ∼0.2 μs indicates the end of spur expansion (ref. 47).

Fig. 3 shows the effect of LET on the temporal variation of the yield of H₃O⁺ at 25 °C for pure, deaerated liquid water irradiated by 300 MeV (LET ∼ 0.3 keV μm⁻¹) and 150 keV (LET ∼ 70 keV μm⁻¹) incident protons, and with 1.75 MeV per nucleon (LET ∼ 70 keV μm⁻¹) and 0.6 MeV per nucleon (LET ∼ 146 keV μm⁻¹) helium ions. As can be seen, the decrease in G(H₃O⁺) in high-LET ion tracks occurs as early as ∼100 ps up to microseconds, which is clearly different from what is observed for irradiation with 300 MeV incident protons (which mimic ⁶⁰Co γ/fast electron irradiation). As expected on physical grounds, this is consistent with differences in the initial spatial distribution of primary transient species (i.e., in the track structure). As mentioned earlier, in the track (cylindrical) geometry of the three high-LET irradiating ions used, the reactive intermediates are formed locally in much closer initial proximity than in the spur (spherical) geometry. This favors, at shorter time scales, an increased amount of intervening intra-track reactions. In this case, the results in Fig. 3 show that, as the LET is increased, the decrease in G(H₃O⁺) becomes more pronounced as a function of time, and begins at shorter times. It is also shown that the temporal variations of G(H₃O⁺) for 150 keV protons and 1.75 MeV per nucleon helium ions, which have nearly equal LET (∼70 keV μm⁻¹), are little affected by the differences in track structure between these two irradiating ions.¹ To our knowledge, there is no experimental information available in the literature, unfortunately, with which to compare our results on the time dependences of the yield of H₃O⁺ at high LET.

Fig. 3 Time dependences of H₃O⁺ yields (in molecule per 100 eV) calculated from our Monte Carlo simulations of the radiolysis of pure, deaerated liquid water at 25 °C and in the interval of ∼1 ps to 1 ms, for impacting 300 MeV (∼0.3 keV μm⁻¹) and 150 keV (∼70 keV μm⁻¹) protons, and 1.75 MeV per nucleon (∼70 keV μm⁻¹) and 0.6 MeV per nucleon (∼146 keV μm⁻¹) ⁴He²⁺ ions. It is worth noting here that G(OH⁻), in all high-LET ion tracks considered, remains at a nearly constant level well below 1 G-unit, and therefore much smaller than G(H₃O⁺), during the lifetime of the tracks (not shown in the figure). Consequently, as mentioned in the caption of Fig. 1, the formation of OH⁻ ions only slightly modifies the quantitative features of the pH and can simply be ignored.

With the objective of calculating the pH values prevailing in the spur or track regions, we now need to estimate the concentrations of H₃O⁺ generated in situ in these regions as a function of time. Two simple models are considered here depending on the quality (or LET) of the radiation.

(1) For 300 MeV incident protons (LET ∼ 0.3 keV μm⁻¹), we assume that the hydronium ions are produced evenly in an isolated spherical spur. The spur's initial radius r_o, prior to spur expansion, is equal to the average electron thermalization distance obtained from our simulations (r_o ∼ 11.7 nm).^31,33,82 The low-LET spur concentrations of H₃O⁺ are derived from^62,83

where the mean energy loss in a single energy deposition event (i.e., the mean energy deposited in a spur) in liquid water is taken to be ∼47 eV (ref. 63, 71, 84 and 85) and

r(t)² = r_o² + 6Dt (20)

represents the change with time of r_o due to the three-dimensional diffusive expansion of the spur. Here, t is time and D is the diffusion coefficient of H₃O⁺ in water (D = 9.46 × 10⁻⁹ m² s⁻¹ at 25 °C).⁶⁴

Using a consistent set of units,⁸³ eqn (19) and (20) readily give the concentration of H₃O⁺ as a function of time. The pH in the corresponding spur region is then simply given by the negative logarithm (to the base 10) of [H₃O⁺]:

pH(t) = −log{[H₃O⁺](t)}. (21)

The time evolution of the pH values calculated for 300 MeV incident protons in pure, deaerated liquid water (LET ∼ 0.3 keV μm⁻¹) using the spherically symmetric spur model is shown by the solid curve in Fig. 4. As can be seen, there is an abrupt transient acid pH effect at times immediately after the initial energy release. This “acid spike” is greatest for times shorter than ∼1 ns. The “acid spike” term arises from an analogy with the “thermal spike” used in radiation chemistry to describe the formation of a transient excess temperature region around the high-LET tracks of heavy ions in water.^56,86–88 In this time range, the pH remains nearly constant, equal to ∼3.3. Beyond ∼1 ns, the pH increases gradually, ultimately reaching a value of 7 (neutral pH) at ∼1 μs (i.e., slightly longer than the end of spur expansion and the beginning of homogeneous chemistry).^17,23–25 Fig. 4 also shows the sensitivity of our calculated pH results to the choice of the radius of the initial spatial distribution of e_aq⁻(r_o), which is not precisely known. Using a smaller value of r_o (∼8.3 nm instead of 11.7 nm)⁸² results in an increased acid spike effect at early times (pH ∼2.8 instead of 3.3), but has little impact on the temporal variation of the pH beyond ∼1 ns (dashed curve in Fig. 4). This is expected since a decrease in the spur radius, all other parameters being constant, leads to an increase in the concentration of H₃O⁺ ions formed in the spur and, hence, to a more acidic pH response.

Fig. 4 Time evolution of pH in a spur calculated for 300 MeV incident protons in pure, deaerated liquid water (LET ∼ 0.3 keV μm⁻¹) using the isolated “spherical” spur model, characteristic of low-LET radiation, at 25 °C (see text). The solid and dashed lines show the pH values obtained for two different spur radii r_o = 11.7 and 8.3 nm, respectively. The (dotted) line shown at ∼0.2 μs indicates the end of spur expansion (ref. 47).

(2) For high-LET radiation, we consider the track as being an axially homogeneous cylinder, of length L = 1 μm and initial radius r_c equal to the radius of the physical track “core”. The core corresponds to the tiny radial region within the first few nanometers around the impacting ion trajectory. In this region the energy density of deposition is very high.^16,17,30,59 For the sake of illustration, Fig. 5–7 show typical two-dimensional representations of 1 μm track segments of, respectively, a 150 keV (LET ∼ 70 keV μm⁻¹) proton, a 1.75 MeV per nucleon (LET ∼ 70 keV μm⁻¹) helium ion, and a 0.6 MeV per nucleon (LET ∼ 146 keV μm⁻¹) helium ion in liquid water at 25 °C. They were calculated (at ∼10⁻¹³ s) with our IONLYS Monte Carlo simulation code. In this case, the high-LET track concentrations of H₃O⁺ can be obtained from^17,62,83

where⁵⁹

r(t)² = r_c² + 4Dt (23)

represents the change with time of r_c due to the two-dimensional diffusive expansion of the track. Here, r_c was estimated directly from our simulations (see Fig. 5–7).

Fig. 5 Simulated track history (at ∼10⁻¹³ s, projected into the XY plane of figure) of a 150 keV proton (LET ∼ 70 keV μm⁻¹) traversing through liquid water at 25 °C. The irradiating proton is generated at the origin and starts traveling along the Y axis. Dots represent the energy deposited at points where an interaction occurred. The track can be described as two coaxial cylindrical volumes centered on the path of the proton. The inner cylindrical volume (i.e., the region adjacent to the trajectory) is the track “core” with radius r_c. Surrounding the core is a much larger region called the “penumbra” where all of the energy is deposited by energetic secondary electrons (δ-rays) created in knock-on collisions by the primary proton. The total time for penumbra formation may be as long as ∼1 ps, and its radius extends to the limit of the range of knock-on electrons.

Fig. 6 Simulated track history (at ∼10⁻¹³ s, projected into the XY plane of figure) of a 1.75 MeV per nucleon helium ion (LET ∼ 70 keV μm⁻¹) incident on liquid water at 25 °C. Irradiating conditions are the same as in Fig. 5.

Fig. 7 Simulated track history (at ∼10⁻¹³ s, projected into the XY plane of figure) of a 0.6 MeV per nucleon helium ion (LET ∼ 146 keV μm⁻¹) incident on liquid water at 25 °C. Irradiating conditions are the same as in Fig. 5.

Using eqn (22) and (23) readily gives the concentrations of H₃O⁺ as a function of time for axially homogeneous, cylindrically symmetric tracks. The pH in the corresponding track regions is then simply given by eqn (21).

Fig. 8 shows the time evolution of the pH values calculated as indicated above for 150 keV incident protons in pure, deaerated liquid water (LET ∼ 70 keV μm⁻¹) using the cylindrical track model at 25 °C for different values of r_c in the range of 2–25 nm. Quite similarly to the spherical spur case for low-LET radiation, there is an abrupt temporary acid pH effect at early times. Its magnitude and duration strongly depend on the value chosen for r_c. If we adopt r_c = 2 nm (which is the most pertinent value for r_c according to Fig. 5), the pH is equal to ∼0.35 at times less than ∼100 ps and then increases gradually with time. Ultimately, it reaches a value of 7 (pH of the body of the solution) at ∼100 μs.

Fig. 8 Variation of pH with time calculated for 150 keV incident protons (LET ∼ 70 keV μm⁻¹) using the axially homogeneous cylindrical track model, characteristic of high-LET radiation, for different physical core radii between 2 and 25 nm, at 25 °C from ∼1 ps to 1 ms (see text).

However, even if the curves shown in Fig. 8 have shapes closely resembling those of Fig. 4, the acid spike for the cylindrical track is clearly far more intense than that found for isolated spherical spurs. This is also well illustrated in Fig. 9, where we show the effect of LET of the incident radiation on the variation of pH with time. Calculations were carried out for pure, deaerated liquid water irradiated by four impacting ions: (1) 300 MeV protons (which mimic ⁶⁰Co γ/fast electron irradiation; LET ∼ 0.3 keV μm⁻¹); (2) 150 keV protons (LET ∼ 70 keV μm⁻¹); (3) 1.75 MeV per nucleon helium ions (LET ∼ 70 keV μm⁻¹); and (4) 0.6 MeV per nucleon helium ions (LET ∼ 146 keV μm⁻¹). The different curves were obtained by using eqn (19)–(21) for the spherical spur model (low-LET radiation) and eqn (21)–(23) for the cylindrical track model (high-LET radiation) along with our calculated yields of H₃O⁺ shown in Fig. 3.

Fig. 9 Variation of pH with time calculated for pure, deaerated liquid water at 25 °C and in the interval of ∼1 ps to 1 ms, for irradiating 300 MeV protons (LET ∼ 0.3 keV μm⁻¹) (dotted line) using the isolated spherical spur model (characteristic of low-LET radiation) and for impacting 150 keV protons (LET ∼ 70 keV μm⁻¹), and 1.75 MeV per nucleon (LET ∼ 70 keV μm⁻¹) and 0.6 MeV per nucleon (LET ∼ 146 keV μm⁻¹) helium ions using the axially homogeneous cylindrical track model (characteristic of high-LET radiation) (see text).

To the best of our knowledge, the early-time, acid spike effect described above has never been explored in water or in living cells subject to ionizing radiation, especially high-LET radiations (e.g., α-particles, high charge and high energy particles). In this context, this work prompts a number of important questions not only in radiation chemistry, but also in radiation- and free-radical-biology^2,62,89 as many cellular processes critically depend on pH.^90–92 Any significant change in the early time, transient kinetics/chemistry would provoke important new insights into our understanding of many aspects of the biological action of radiation. This should stimulate novel predictions that can then be tested through new measurements. We mention a few of these questions below.

For example, in radiation chemistry, does the generation of strongly acidic regions, which extend over spatial dimensions of the order of tens of nanometers, have any noticeable influence on final product formation by affecting all pH-dependent species, protonation/deprotonation reactions, and reaction rates?^11,51,93 In radiation- and free-radical-biology, is this transient acid pH, which is well outside the physiological range, toxic to cells (e.g., by attacking DNA, by causing oxidative injury, by modifying normal biochemical reactions, or by triggering different signaling cascades that respond to these stress conditions).³ Moreover, could these in situ changes in acidity contribute to the initial events that lead to cell damage, enhanced lethality, “bystander” responses (where stressful effects are propagated from irradiated cells to non-targeted neighbors),^94–97 or genomic instability in progeny of irradiated cells and their neighboring bystanders?^98,99 In the development of effective therapies for malignant diseases, do these spikes of acidity have any adverse effect on the response of cells to conventional anticancer drugs and possibly influence the outcome of tumor therapy?⁹⁰

Finally, it has been demonstrated that cells in an acid pH environment are more sensitive to the lethal effect of heat (in the clinically relevant temperature range of 39–45 °C).^12,100 We have described the highly acidic environment that is generated temporarily in the spurs/tracks of the radiation. Thus, could this phenomenon explain, at least partly, why the combination of hyperthermia with radiotherapy (“thermoradiotherapy”) is synergistic (or, in other words, why hyperthermia is a very effective radiation sensitizer) and works best when the two are applied simultaneously.^90,100–103

4. Conclusion

In this work, Monte Carlo track chemistry simulations have been used in an attempt to quantify the “acid spike” effect that is generated in situ in spurs/tracks in the radiolysis of pure, deaerated water during and shortly after irradiation. Two track models were considered depending on the quality (LET) of the radiation: (1) an isolated “spherical” spur model associated with low-LET radiation, such as ∼300 MeV irradiating protons (LET ∼ 0.3 keV μm⁻¹) and (2) an axially homogeneous “cylindrical” track model associated with high-LET radiation, such as 150 keV protons (LET ∼ 70 keV μm⁻¹), 1.75 MeV per nucleon helium ions (LET ∼ 70 keV μm⁻¹), and 0.6 MeV per nucleon helium ions (LET ∼ 146 keV μm⁻¹). For times shorter than ∼1 ns, the pH was found to be nearly constant and equal to ∼3.3 in isolated spurs. For cylindrical tracks, however, the acid spike response to the ionizing radiation was far more intense than that for the spherical spur geometry. Indeed, on a time scale of ∼100 ps, the pH was found to be around 0.5 for the three cases of high-LET radiation considered. At longer times, the pH increased gradually for all cases, ultimately reaching a value of 7 (neutral pH) at ∼1 μs for the spherical geometry and ∼0.1 ms for the cylindrical geometry.

We should also emphasize here the very good agreement of our calculated time evolution of G(H₃O⁺) in the radiolysis of pure, deaerated water by 300 MeV incident protons (which mimic ⁶⁰Co γ/fast electron irradiation) with available experimental data at 25 °C.

The transient acid pH effect that we have described does not appear to have been explored in water or in a cellular environment subject to the action of ionizing radiation, especially high-LET radiation. In this regard, this work raises a number of questions about the potential implications of this effect in radiobiology, some of which have been briefly evoked.

Acknowledgements

We thank Professor Edouard I. Azzam (New Jersey Medical School Cancer Center, USA) and Professor Yusa Muroya (Osaka University, Japan) for valuable comments. The financial assistance of the Natural Sciences and Engineering Research Council of Canada (RGPIN-2015-06100) is gratefully acknowledged.

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