Introduction

A clustered DNA damage site (cluster) or a multiply damaged site, where more than two lesions exist within a few helical turns, is believed to cause irreversible biological effects such as cell death and carcinogenesis because the DNA cannot be repaired [1,2,3]. Densely ionizing radiation such as a heavy ion beam and a low-energy electron [4, 5] should produce a cluster and is responsible for mutagenesis [6,7,8,9,10]. In the past few decades, numerous experimental and computational studies have examined damage localization and the influence of different types of ionizing radiations (reviewed in [11,12,13]). The experimental approaches have mainly estimated single- and double-strand break yields using electrophoretic analyses of the irradiated plasmid, phage DNA [14,15,16,17], and genomic DNA extracted from the irradiated mammalian cells [18,19,20]. Moreover, the direct visualization in a cell using confocal microscopy [21, 22] and the single-molecule observations using atomic force microscopy [23, 24] were reported. These analyses are often performed in conjunction with the base excision repair enzymes (e.g., endonuclease III and formamido pyrimidine-N-glycosylase) in which oxidative base lesions are excised to bear an apurinic/apyrimidinic site (AP) followed by a strand break. Although various studies have reported mechanisms for DNA damage clustering and the cluster quality (i.e., the production frequency, types of constituent lesions), the cluster itself or its biological processing in a living cell has yet to be observed. However, γH2AX foci are regarded as evidence of double-strand break formation [25]. One difficulty in detecting a cluster in a cell is the structural and spatial diversity. To address this issue, we utilize Förster resonance energy transfer (FRET) to detect a cluster with two or more APs. Moreover, the FRET technique has a potential visualizing a cluster not only in a DNA molecule extracted from cells but also in a living cell.

FRET has been used in molecular and cell biology to investigate the interaction between biomolecules as a “nanometer ruler” [26, 27]. It is also applicable to visualize a cluster in a living cell. There are generally two categories of FRET: hetero-FRET and homo-FRET. Hetero- and homo-FRET evaluate the energy transfer phenomena between structurally different (a “donor”–“acceptor” (DA) pair) and the same dye molecules, respectively.

We previously reported that the hetero-FRET method can estimate the localization of DNA lesions by fluorescence spectroscopy of a labeled plasmid sample solution [28, 29]. However, its sensitivity is insufficient, in principle, mainly because all the clustered AP sites cannot be labeled with a DA pair (i.e., a clustered AP labeled with DD or AA pair is not detected as a cluster). Alternatively, we tried to apply the homo-FRET to compensate for this disadvantage [30]. The homo-FRET method is better suited than the hetero-FRET due to its sensitivity and simple experimental protocol. However, the FRET efficiency must be estimated by a fluorescence anisotropy measurement because the fluorescence intensities with and without FRET for a given emission wavelength are also the same. Here, we apply the homo-FRET method to estimate the AP localization in a plasmid DNA irradiated with carbon, helium ion beams, and 60Co γ-rays in the solid state.

Materials and methods

Chemicals

The pUC19 plasmid vector (2686 bp) was obtained from Bayou Biolabs (Metairie, LA, USA). A fluorescent dye (Alexa Fluor 488, AF488) with O-amino functional group was purchased from Thermo Fisher Scientific K. K. (Tokyo, Japan). AF488 was dissolved in dimethylsulfoxide (DMSO) to a concentration of 10 mM before use. Linearized pUC19 with blunt ends was prepared using SmaI (pUC19/SmaI) [28]. Tris(hydroxymethyl)aminomethane (Tris), ethylenediamine tetraacetic acid disodium salt (EDTA 2Na), glycerin, and all other chemicals were obtained from Nakalai Tesque, Inc. (Kyoto, Japan).

DNA sample for irradiation

For γ-irradiation, 200 μL of pUC19/SmaI aqueous solution (~ 2 g/L) was dropped onto a glass plate (6 × 25 × 1 mm) pretreated with 5 N NaOH for high wettability, and then dried in a draft chamber at room temperature. The sample plate was thoroughly dried under vacuum at r.t. for 12 h. Each sample plate was placed in a 1.5-mL plastic microtube, which was sealed in the atmosphere. The tube was placed on a wooden bar (10 mm thickness) to achieve secondary electron equilibrium.

For ion beam irradiation, 25 μL of pUC19/SmaI aqueous solution (2 g/L) was dropped onto an 8-mm ϕ area (0.5 cm2) of a glass slide pretreated with 5 N NaOH (25 × 70 × 1 mm, for six sample spots). The drying process was the same as described above. The resultant average surface density of the dry DNA layer was 0.1 mg/cm2.

60Co γ-irradiation

60Co γ-irradiation (1.17 and 1.33 MeV, ~ 0.2 keV/μm) of the dry DNA sample was performed at room temperature at the Co-60 Gamma-ray Irradiation Facility of Institute for Integrated Radiation and Nuclear Science, Kyoto University, according to the protocol previously reported [30]. The dose rates were 2–10 kGy/h. Each irradiated DNA sample was dissolved in ice-cold water, lyophilized, and stored at − 20 °C until use.

Ion beam irradiation

The irradiation of 4He2+ and 12C5+ beams to the dry DNA sample was performed at room temperature using the depth-tunable cell irradiation equipment [31] on a 3-MV tandem accelerator beam line of the Takasaki Advanced Radiation Research Institute, QST, as previously reported [29]. In brief, the ion particles were counted precisely using a CR-39 film track detector (HARZLAS (TNF-1); Fukuvi Chemical Industry, Fukui, Japan). The incident particle energy was controlled by changing the air layer thickness between the beam exit and the sample surface using the ELOSSM code [32]. The air layer thicknesses were set to 1 and 7 cm for 4He2+ of which the incident particle energies were 2.0 and 0.52 MeV/u, respectively. And that was set to 1 cm for 12C5+ with 0.37 MeV/u. They were able to penetrate the dry DNA layer (0.1 mg/cm2). Each linear energy transfer (LET) was ~ 70, ~ 150, and ~ 760 keV/μm, respectively, regarding the density of the dry DNA set as 1 (g/cm3). Each irradiated DNA sample was dissolved in water, lyophilized, and stored at − 20 °C until use.

Fluorimetry

The fluorimetry was performed using a spectrofluorometer (SPEX FluoroMAX-3, Horiba, Kyoto, Japan) equipped with dual polarizers (FL1044) and a 150-W xenon arc lamp (Model 1905-ORF), and a photon-counting signal detector (R928P), according to the previous report [30]. Briefly, in fluorescence intensity measurements of AF488 for quantifying the AP sites in a plasmid molecule, the excitation/emission wavelengths were set at 470 nm (band pass, 5 nm) and 525 nm (band path, 20 nm), respectively. The polarizers were set at the magic angle (excitation, 0°; emission, 55°), and a sharp cut filter (SCF-50S-50Y, Sigma-koki, Tokyo, Japan) was put in front of the emission monochromator. A quartz microcuvette (Type 23-3.45, 3 × 3 mm (internal length and width), Starna Scientific, Essex, UK) containing a plasmid sample solution was set into the cell holder (Type FCA3.3, Starna Scientific, Essex, UK) at room temperature. In addition, appropriate neutral density (ND) filters (AND-50S series, Sigma-koki, Tokyo, Japan) were used to weaken the excitation light.

The steady-state fluorescence emission anisotropy measurements were performed at 10.0 ± 0.2 °C measured by a resistance thermometer (Okazaki Manufacturing Co., Hyogo, Japan) under dry nitrogen flow (N2 Supplier Model 02, System Instruments, Co., Tokyo, Japan) to prevent dew condensation. To obtain the correct anisotropy, the IVV (see below) was maintained at around 150 cps using the ND filters for excitation light. The observed anisotropy, robs, is defined as

$$ {r}_{\mathrm{obs}}=\frac{I_{\mathrm{VV}}-G\cdotp {I}_{\mathrm{VH}}}{I_{\mathrm{VV}}+2G\cdotp {I}_{\mathrm{VH}}}, $$
(1)

where, for example, IVH are the horizontally polarized fluorescence intensities when excited by vertically polarized photons. G is the grating factor: IHV/IHH, which was measured at every instance of data acquisition.

Construction of theoretical relationship between fluorescence anisotropy and FRET efficiency

FRET efficiency (E) is given by

$$ E=\frac{1}{1+{\left(\frac{R}{R_0}\right)}^6}\kern0.5em , $$
(2)

where R is the distance between a couple of fluorophores and R0 is R at E = 0.5, referred to as Förster distance. Here, R0 is equal to be 4.4 nm in the present study as previously determined [28]. The observed fluorescence anisotropy, robs, is expressed as

$$ \frac{1}{r_{\mathrm{obs}}}\simeq \left(N-1\right)\left(\frac{1}{r_1}-\frac{1}{r_0}\right){E_N}^2+\left(N-1\right)\frac{1}{r_0}{E}_N+\frac{1}{r_1}, $$
(3)

based on a theory for analyzing protein oligomerization [33], where N is the number of fluorophores clustered in which each distance among them is all identical, EN is the averaged FRET efficiency dependent on N, r0 is the anisotropy without both FRET and rotational diffusion of the fluorophore, and r1 is that without FRET. These were previously determined to be 0.377 ± 0.003 and 0.343 ± 0.002, respectively [30]. Hence, EN is given by

$$ {E}_N\simeq \frac{\sqrt{{\left(N-1\right)}^2{r}_0^{-2}-4\left(N-1\right)\left({r}_1^{-1}-{r}_0^{-1}\right)\left({r}_1^{-1}-{r}_{\mathrm{obs}}^{-1}\right)}-\left(N-1\right){r}_0^{-1}}{2\left(N-1\right)\left({r}_1^{-1}-{r}_0^{-1}\right)}\kern0.5em . $$
(4)

When r1 is almost equal to r0 (i.e., fluorophores are not rotated), Eq. 3 can be simplified as

$$ \frac{1}{r_{\mathrm{obs}}}\simeq \frac{1}{r_0}\left\{\left(N-1\right){E}_N+1\right\}, $$
(3′)

hence,

$$ {E}_N\simeq \frac{1}{N-1}\left(\frac{r_0}{r_{\mathrm{obs}}}-1\right). $$
(4′)

Considering a double-stranded DNA with two lesions, there are dual FRET patterns at the same base separation, “i”: one is the case that two lesions place at the same strand, the other is that in opposing strands (Fig. 1a). Assuming that they have the same production probability, the observed Ei could be regarded as the average of the two cases.

$$ {E}_i=\frac{1}{2}\left({E}_{i,\mathrm{sam}}+{E}_{i,\mathrm{opp}}\right), $$
(5)

where Ei,sam and Ei,opp are the FRET efficiencies on the same and opposing strand(s), respectively. Given that a couple of dyes are fixed perpendicular to the side of B-form DNA “cylinder,” the distances between them (Ri,sam, Ri,opp) in nanometer are written as follows:

$$ {R}_{i,\mathrm{sam}}\simeq \sqrt{(0.33i)^2+2{\left(a+d\right)}^2\left\{1-\cos \left(\frac{\pi }{5}i\right)\right\}}, $$
(6)
$$ {R}_{i,\mathrm{opp}}\simeq \sqrt{(0.33i)^2+2{\left(a+d\right)}^2\left\{1+\cos \left(\frac{\pi }{5}i\right)\right\}}, $$
(7)

respectively [34], where d is the average length of AF488 fluorescent probe to be ~ 1 nm [28], and a is the radius of B-form DNA (~ 1 nm; distance from its central axis to an AP). Thus, we describe robs or Eobs as a function of i (bp) using Eqs. 27. Here, Eobs is expressed as

$$ {E}_{\mathrm{obs}}=<{E}_{N=2}>=\sum \limits_{i=0}^{2686}\left({E}_i{p}_i\right)\kern1em \left(\sum \limits_{i=0}^{2686}{p}_i=1\right), $$
(8)

where pi is the production probability of i. <EN = 2> is the weighted average of all Eis weighted by corresponding pi. Conversely, the “apparent” i value (iap) can be obtained from the Eobs (a solid line in Fig. 1b).

Fig. 1
figure 1

Theoretical curves of fluorescence anisotropy (a) and the corresponding FRET efficiency (b) as a function of base separation. The dotted, the dashed and, the solid lines indicate APs in opposing strands, those in one strand, and the average of the two, respectively

Labeling of irradiated DNA samples with fluorescent probes and FRET experiments

The labeling reaction to DNA samples with APs was performed as reported previously [30]. The aminooxy group (–ONH2) of AF488 molecule is known to covalently and selectively bind to the electrophilic aldehydes and ketones [35] produced in many kinds of APs derived from sugar hydrogen abstraction reactions [36]. In brief, 10 μL of plasmid sample solution (~ 2 μg/μL) was mixed with 10 μL of 0.1 M Tris-HCl buffer (pH 7.5) in a microtube on ice. Two microliters of DMSO solution of AF488 was added to the DNA solution and incubated at 35 °C for 24 h needed for saturating the labeling reaction. The reaction solution underwent ethanol precipitation three times. The crude-labeled DNA was purified using a Sephadex G50 pre-loaded spin column (ProbeQuant G50, GE Healthcare Japan, Tokyo) to remove traces of unreacted dye molecules. The purified sample was kept at − 20 °C until use.

Preparation of linear plasmid DNA (pUC19/SmaI)

We prepared a linear-form plasmid (form III) to avoid unexpected effects due to a topological change in DNA by induction of a lesion as previously reported [28, 30]. PUC19 was incubated in 10 mM Tris-HCl (pH 7.5), 7 mM MgCl2, 20 mM KCl, and 7 mM 2-mercaptoethanol with Sma I (144 units, 12 μL) added at 30 °C overnight (~ 1 mg of DNA/mL). The reaction mixture was subjected to phenol extraction to remove Sma I using a spin column, followed by ethanol precipitation. The purified DNA was dissolved in water to a final concentration of ~ 2 μg/μL, and the precise concentration was determined by measuring the absorbance at 260 nm of the 100× diluted TE.

Calculation of the averaged AP density: λ AP (average number of APs per base pair)

AF488-labeled AP-DNA solution (20 μL) was diluted with TE up to 165 μL. The AF488-labeled DNA concentration, CDNA, was calculated using the following equation:

$$ {C}_{\mathrm{DNA}}\left(\mathrm{g}/\mathrm{L}\right)=0.050\times \left({A}_{260}-\frac{\ {\varepsilon}_{260}}{\varepsilon_{470}}{A}_{470}\right), $$
(9)

where A260 and A470 are the absorbances at 260 nm and 470 nm, and ε260 and ε470 are the molar extinction coefficients of AF488 in TE buffer (pH.7.5) at 260 nm (22,500 M−1 cm−1) and 470 nm (37,600 M−1 cm−1), respectively. The solution was transferred into a quartz microcuvette (3 × 3 mm), followed by measuring the fluorescence intensity of AF488. The AF488 concentration, CAF488, was calculated from the fluorescence intensity using calibration curves of free AF488. Averaged AP density (average number of APs per base pair), λAP, was given by

$$ {\lambda}_{\mathrm{AP}}\left(/\mathrm{bp}\right)=630\ \left(\mathrm{g}/\mathrm{mol}/\mathrm{bp}\right)\times \frac{C_{\mathrm{AF}488}\left(\mathrm{mol}/\mathrm{L}\right)}{C_{\mathrm{DNA}}\left(\mathrm{g}/\mathrm{L}\right)}, $$
(10)

where 630 is the averaged molecular weight of a base pair without counter ions.

Sample preparation and anisotropy measurement

The fluorescence depolarization occurs due to a rotational diffusion and a directional difference between excitation/emission moments of a dye used as well as the energy transfer such as FRET [37]. Hence, the DNA sample was dissolved in a viscous buffered solution containing glycerin in order to minimize the contribution from the diffusion. One hundred sixty milligrams of glycerin, x mg (16.5 μL) of 1 M Tris-HCl-10 mM EDTA (pH 7.5), y mg of labeled DNA mother solution, and (40.0 − x − y) mg of water were added to a 0.5-mL microtube, followed by careful homogenization (finally, 80 wt.% glycerin, 0.1 M Tris-HCl (pH 7.5), 165 μL). Each y value was determined in reference to the corresponding A470 and CAF488 in Eqs. 9 and 10 to obtain the correct fluorescence intensities from AF488 molecules. The final DNA concentration was controlled to be less than 0.1 μg/μL to avoid an unexpected FRET among AF488-labeled DNA molecules.

Results and discussion

Previously, we demonstrated the advantages of the FRET method for a cluster estimation [28,29,30]. Herein we apply two features. One is the localization of chemically specific lesions. APs are well-known lesions that can be labeled by a fluorophore with a nucleophile (e.g., aminooxy group). In contrast, oxidative nucleobases such as 8-oxoguanine and thymine glycol do not selectively and covalently bind with known fluorescent dyes. The other is its potential to visualize a cluster in the genomic DNA extracted from cells and eventually in a cell using single-molecule microscopy. Here, we analyzed clusters produced by ionizing radiation in the solid state by the steady-state homo-FRET method to demonstrate its usefulness, especially in estimating clusters with chemically identical lesions.

Construction of a theoretical relationship between base separation and fluorescence anisotropy

Equations 17 can convert the value of fluorescence anisotropy to a distance between two lesions by base separation. The relationship between base separation and anisotropy, which was obtained using several DNA oligomers with two APs in opposing strands and a given base separation, is fairly consistent with the theoretical result [30]. The dotted and dashed lines in Fig. 1a plot the theoretical fluorescence anisotropy as a function of base separation for APs at opposing strands and for those at one strand, respectively. The anisotropy is converted to the FRET efficiency when N is equal to 2 using Eq. 4 (Fig. 1b). The wavy lines are due to the double helical structure of B-type DNA. However, the reliability of the simulated curves should degrade as the anisotropy decreases [30, 38] due to the assumption that the fluorescent probes are “perpendicularly fixed” on the side of a DNA cylinder. Considering the real radiation damage production in DNA, we assume that the production probability of two close lesions on a strand is identical to that on opposing strands. The solid lines in Fig. 1a and b, which are the average anisotropy and FRET efficiency, respectively, of the two lesions on one strand and on two strands, indicate the relationships between the “observed” anisotropy/FRET efficiency and the “apparent” base separation under the above assumption.

Dose-response curves for carbon, helium ion beams, and 60Co γ-rays

Figure 2 shows the averaged AP density (λAP: average number of APs per base pair) as a function of absorbed dose. The radiation chemical yields of AP are similar to each other under the same irradiation condition. In the solid state, radiation barely produces an AP (i.e., a site with an electrophilic aldehyde/ketone) in dry DNA since a high dose is needed for detection. This suggests that an abundance of oxygen or water is essential for its production. In the labeling reaction of AF488 to AP, the reaction became saturated until 24 h at 35 °C in the Tris buffer (data not shown). Although the labeling efficiency was not determined, the good linearity shown in Fig. 2 implies that the reactivity of a fluorescence dye is almost not affected by the damage clustering.

Fig. 2
figure 2

AP density (λAP) of irradiated DNA as a function of absorbed dose for 60Co γ-rays (●), 2.0 MeV/u 4He2+ (▲), 0.52 MeV/u 4He2+ (■), and 0.37 MeV/u 12C5+ (♦) beams

Estimation of AP localization for carbon, helium, and 60Co γ-rays in the solid state by means of the homo-FRET method based on fluorescence anisotropy measurements

Figure 3a shows the observed fluorescence anisotropy of the irradiated DNA tested as a function of the AP averaged density in comparison with that of the heat-treated DNA with randomly distributed APs as a standard. The observed fluorescence anisotropy, robs, generally decreases with (i) increasing AP density (λAP) and (ii) increasing LET. The decrease with (i) would result in a “sequentially produced” cluster due to overlapping two or more radiation tracks, whereas that with (ii) would be caused by increasing close AP–AP pairs accompanied by increasing a local dose of a radiation track [39, 40]. In addition, it is interesting that the degree of localization for 60Co γ-rays is unexpectedly higher than that for a random distribution (bold line), implying that a low-energy electron likely induces a cluster [4, 5]. Another possible reason for the difference would be due to the difference in the chemical structure of the damaged site such as an AP. By the heat incubation, DNA is known to be depurinated by hydrolysis to produce the typical AP, having an aldehyde moiety at C1′ of the sugar [41]. On the other hand, irradiation to the “dry” DNA sample would produce a variety of electrophilic carbonyl groups reactive to an aminooxyl fluorescent dye used as well as the typical AP.

Fig. 3
figure 3

Fluorescence anisotropy (a), FRET efficiency (b), and apparent distance between APs (c) of 60Co γ-rays (●), 2.0 MeV/u 4He2+ (▲), 0.52 MeV/u 4He2+ (■), and 12C5+ beams (♦), as a function of AP density (λAP). The open circles in panel a indicate the data for the DNA incubated in the citrate buffer (pH 4.7) at 70 °C for the given periods (heat-treated DNA) as previously reported [30], as a model DNA with almost randomly distributed APs. The error bars are the standard deviations of at least three measurements of each sample. The dotted three lines are fitted to the points by eye. The solid lines are described based on a random distribution [30]

The anisotropy can be converted into the FRET efficiency (Fig. 3b) and apparent base separation, iap (Fig. 3c), using Eqs. 27. The y-intercept of each curve can elucidate the cluster formation produced by a single radiation track. However, obtaining data near the y-intercept is difficult due to the very small amount of AP labeled with the fluorophore (i.e., λAP ~ 0). Fortunately, the central regions of each radiation track for He (~ 70, ~ 150 keV/μm) and C (~ 760 keV/μm) do not overlap significantly at the lowest doses (20, 20, 10 kGy, respectively) according to the theoretical studies on microdosimetry (data not shown) [39, 40]. The apparent base separation, iap, corresponding to each lowest dose is 21.1, 19.4, and 18.7 bp, respectively. Hence, the value of the apparent base separation at the lowest doses fairly reflects the degree of damage localization produced in a single radiation track. This tendency —the degree of DNA damage clustering increases with increasing LET—is consistent with the previous reports [e.g., 18–24, 39, 40, 42].

The homo-FRET method is better suited than the hetero-FRET in terms of the detection sensitivity. Hetero-FRET cannot detect cluster lesions labeled only with donors or acceptors. In addition, a small donor (e.g., a coumarin-based fluorophore), which is necessary for complete labeling, typically has a low absorption coefficient and quantum yield. This leads to a low detection sensitivity of an emission from an acceptor. In this study, the cluster detection sensitivity by the hetero-FRET (donor: AF350, acceptor: AF488) for 0.37 MeV/u carbon ion particles [29] is actually much lower than that by the homo-FRET. Moreover, the homo-FRET is simpler and more feasible than the hetero-FRET. The fluorescence intensity of a non-FRET DNA sample digested by DNA digestion enzymes is essential to calculate both the AP density and the FRET efficiency in the steady-state mode of the hetero-FRET, whereas the homo-FRET method does not require pretreatment. This simplicity leads to fewer experimental errors using the homo-FRET.

Our approach can compare ionizing radiations by the parameters of “apparent” base separation between APs (iap). However, several issues must also be considered. Firstly, two extremely close APs may not both be labeled with the fluorophores due to a steric hindrance. Secondly, a lot of AP–AP distances not only are within the FRET limit (< ~ 40 bp) but also are more than ~ 40 bp. That is, there are non-negligible “isolated” APs not related to FRET.

For simplicity, our estimation of iap assumes that each photo-excited fluorophore on a lesion can transfer energy only to one of the two adjacent fluorophores. In other words, each lesion is regarded as a member of n = 2 “cluster” with any i value (0 ≤ i ≤ 2686) (Fig. 3b–c). However, the energy can be transferred to both. In this case, Eobs is given by

$$ {E}_{\mathrm{obs}}=<{E}_{n=3}>\approx \sum \limits_{i,j=0}^{2686}\left({E}_{ij}{p}_{ij}\right)\kern2.25em \left(\sum \limits_{i,j=0}^{2686}{p}_{ij}=1\right), $$
(11)

where Eij is the individual FRET efficiency among the three fluorophores on DNA strands triggered by a photo-excitation at its center fluorophore (i, j: the distances among the three) (Fig. 4). Here, an “isolated lesion” can be defined as a lesion where both i and j are more than ~ 40 base pairs in which FRET hardly occurs. <En = 3> is approximated as <EN = 2> in Eq. 8 when n ≥ 3 cluster with a small i, j is rarely produced [28]. Thus, the existence of isolated lesions, which may not be negligible at a low dose, would underestimate the extent of clusters. Indeed, the iap values estimated for 2.0 MeV/u He, 0.52 MeV/u He, and 0.37 MeV/u C seem to be large compared to the expectation due to isolated lesions [42]. Considering “N” in Eq. 3 as a parameter, it may play an important role in obtaining a more effective iap value that only reflects clusters. Eq. 3′ indicates that N and E are almost inversely proportional. However, it is impossible to individually determine their values by the steady-state homo-FRET method.

Fig. 4
figure 4

A schematic representation of homo-FRET considered in three-membered fluorescent dye-labeled lesions on ds DNA. A photo-excited dye practically can transfer its energy only to the nearest neighbor two dyes on a DNA molecule. The other dyes far from a photo-excited one hardly involve in FRET, so that the homo-FRET method practically can detect maximum of three-membered cluster. In fact, it is unlikely that a lot of APs exist within several nanometers in the irradiated DNA sample due to the chemical instability of APs. When three-membered cluster is negligibly produced (i.e., i and/or j > ~ 40 bp), each lesion is regarded as a member of n = 2 “cluster” with any distance between the two (i or j)

Thirdly, this study focuses only on aldehyde/ketone moieties mainly at APs as representative DNA lesions. However, ionizing radiation can produce a hundred kinds of lesions that incorporate APs [43]. If lesions other than such electrophilic carbonyls are covalently labeled with a fluorescent dye, a variety of information will be obtained about the quality of the clusters at a low dose.

The ultimate goal of our study is to understand the repair process of complex DNA damage by visualizing the damage itself and its subsequent biological processing. This study provides clear evidence for the existence of clusters by the photo-physicochemical method. However, the development of a labeling method to a damaged genomic DNA in a cell and a technique to detect a slight FRET signal from a cluster is necessary to discover its biological processing. Some high-resolution imaging techniques such as the fluorescence anisotropy imaging microscopy (FAIM) [44, 45] will enable us to observe the repair process of a cluster.

In conclusion, the steady-state homo-FRET can detect the localization of a cluster produced by a radiation track, which can be denoted as an index of apparent base separation, “iap.” In fact, “iap” decreases as LET increases. This method should be applicable to other DNA damaging agents beside ionizing radiation. However, the index likely underestimates the extent of a cluster because non-negligible amounts of isolated lesions increase the magnitude of the “averaged” i value. In the future, it is necessary to improve the technique to only reflect the clusters.