Radiation induced base excision repair (BER): A mechanistic mathematical approach

DNA Repair 22 (2014) 89–103

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Radiation induced base excision repair (BER): A mechanistic mathematical approach Shirin Rahmanian a , Reza Taleei b , Hooshang Nikjoo a,∗ a b

Radiation Biophysics Group, Department of Oncology-Pathology, Karolinska Institutet, Box 260 P9-02, Stockholm 17176, Sweden Radiation Physics, MD Anderson Cancer Center, 1515 Holcombe Blvd., Unit 94, Houston, TX 77030-4409, USA

a r t i c l e

i n f o

Article history: Received 2 April 2014 Received in revised form 17 July 2014 Accepted 18 July 2014 Keywords: BER SSB Repair kinetics Damage complexity Mathematical model Mechanistic model

a b s t r a c t This paper presents a mechanistic model of base excision repair (BER) pathway for the repair of singlestand breaks (SSBs) and oxidized base lesions produced by ionizing radiation (IR). The model is based on law of mass action kinetics to translate the biochemical processes involved, step-by-step, in the BER pathway to translate into mathematical equations. The BER is divided into two subpathways, short-patch repair (SPR) and long-patch repair (LPR). SPR involves in replacement of single nucleotide via Pol ␤ and ligation of the ends via XRCC1 and Ligase III, while LPR involves in replacement of multiple nucleotides via PCNA, Pol ␦/␧ and FEN 1, and ligation via Ligase I. A hallmark of IR is the production of closely spaced lesions within a turn of DNA helix (named complex lesions), which have been attributed to a slower repair process. The model presented considers fast and slow component of BER kinetics by assigning SPR for simple lesions and LPR for complex lesions. In the absence of in vivo reaction rate constants for the BER proteins, we have deduced a set of rate constants based on different published experimental measurements including accumulation kinetics obtained from UVA irradiation, overall SSB repair kinetic experiments, and overall BER kinetics from live-cell imaging experiments. The model was further used to calculate the repair kinetics of complex base lesions via the LPR subpathway and compared to foci kinetic experiments for cells irradiated with ␥ rays, Si, and Fe ions. The model calculation show good agreement with experimental measurements for both overall repair and repair of complex lesions. Furthermore, using the model we explored different mechanisms responsible for inhibition of repair when higher LET and HZE particles are used and concluded that increasing the damage complexity can inhibit initiation of LPR after the AP site removal step in BER. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Exposure to ionizing radiation (IR) produces a broad spectrum of damage in the DNA of mammalian cells, including single strand breaks (SSBs), double strand breaks (DSBs), and base damages (BDs). In response to such DNA insult, cells have developed various repair and signalling pathways to protect and maintain genomic stability. A comprehensive and quantitative understanding of the mechanisms involved in repair of these lesions is imperative for targeted cancer therapy and radiation risk estimation. While DSBs are considered to be the most lethal consequence of ionizing radiation, base damages and single strand breaks have also been linked to deleterious effects including mutagenesis and higher incidence of various pathologies including cancer, neurological disorders and ageing [1–4]. The main pathway responsible

∗ Corresponding author. Tel.: +46 8 517 724 90. E-mail address: [email protected] (H. Nikjoo). http://dx.doi.org/10.1016/j.dnarep.2014.07.011 1568-7864/© 2014 Elsevier B.V. All rights reserved.

for repairing base damages and single strand breaks is a highly conserved repair pathway amongst higher eukaryotes and is collectively referred to as the base excision repair (BER) [5,6]. In case of damaged bases, the BER pathways start with recognition of the damaged base by a damage-specific DNA glycosylase [7,8]. The glycosylase removes the base by hydrolyzing the Nglycosidic bond, resulting in creation of an Apurinic/Apyrimidic (AP) site [9]. Subsequently, the AP site can either be cleaved by an AP endonuclease or by the intrinsic AP lyase activity of a bifunctional glycosylase, producing a single strand break [10,11]. For the repair to proceed and ligation to occur, the termini of the single strand need to be processed to the form of 3 OH and 5 phosphate, which can be achieved by different proteins depending on the chemical structure of the termini [12]. After processing of the 3 end of the SSB, the repair continues either with replacement of one nucleotide, referred to as short-patch repair, or with replacement of several nucleotides, referred to as long-patch repair [13,14]. The shortpatch repair involves synthesizing a single nucleotide with DNA Polymerase ␤ (Pol ␤) and ligation of the nick by XRCC1 and Ligase

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III (Lig III) proteins [15]. In the long-patch repair subpathway several (2–13) nucleotides are replaced and synthesized by the actions of several proteins including RFC, Polymerase ␦/␧, and proliferating cell nuclear antigen (PCNA)[14,16]. The long-patch repair is completed by cleaving the resulting 5 flap structure by endonuclease FEN1 and sealing of the nick by Ligase I [17]. As single stranded DNA is also an intermediate of the BER pathway, the single strand break repair (SSBR) is also executed via the BER proteins. However, the repair kinetics of directly induced SSBs will be different as there is no base to excise and proteins such as Poly (ADP-ribose) polymerases (PARP) are required to sense the damage and recruit the BER proteins to site of damage [18,19]. Depending on the type of base damage different glycosylases are used to excise the base, each with a different excision kinetic [7,20]. While there are many different types of base damages including oxidation, deamination, alkylation and direct AP sites, the most common type of base damage, especially induced by ionizing radiation, is oxidative damage [21]. Guanine, due to its lowest oxidation potential amongst the four bases, is the primary target of oxidative damage [22]. The most stable product from oxidation of guanine is 7, 8-dihydro-8-oxoguanine commonly referred to as 8-oxoguanine (or 8oxoG) and is often used as biomarker of oxidative damage [23,24]. 8oxoG is highly mutagenic as it can pair with adenine, and thus if not repaired can result in G:C to T:A transversion mutations [24]. In mammalian cells the most common glycosylase for repair of 8oxoG is the bifunctional glycosylase OGG1 (hOGG1in humans), which recognizes and excises 8oxoG paired with cytosine. The wealth of biochemical experimental data available on BER proteins and 8oxoG lesions creates a great opportunity to build quantitative mathematical models to simulate consequence of DNA damage from exposure to oxidizing agents such as IR. Based on Michaelis–Menton enzyme kinetics Sokhansanj et al. have made the first quantitative model of BER [25,26]. While their model is a powerful tool for predicting outcome of oxidative damage, there remains unclear some fundamental quantitative details regarding the repair process of base damages and single strand breaks produced by ionizing radiation. One of the limitations of the model in Sokhansanj et al. publications [25–27] is that the experiments used for obtaining the kinetic parameters and validating the model are based on in vitro experiments using purified proteins and DNA substrates in specific chemical conditions, which cannot predict the actual time scale of BER protein accumulation in living cells, and describe the localization of the proteins at the damage site. Such limitation is evident in the lack of measurement consistency from different experimental settings and the need to make different adjustments and assumptions of the parameters to correct for discrepancies between the model and experiments. Furthermore, while single strands arise as intermediates of BER pathway, they can also arise directly from exposure to IR. The published BER model [25,26] does not differentiate between the two processes and do not provide the time scale that matches the repair of these lesions in irradiated cells [18,28]. Another important issue that needs to be considered for radiation-induced lesions (which have not been addressed in previous BER models) is that how the cells repair closely spaced BDs and SSBs. As opposed to chemical agents such as hydrogen peroxide, the hallmark of ionizing radiation is the production of multiple lesions within 2–3 helical turns of the DNA [29–33]. These clustered base lesions that do not form a DSB are also repaired via BER [21,34,35]. However, the spatial distribution of these lesions within 10–20 bps affects their repair capacity and consequently their potential lethality [36–38]. The aim of the present study is to build a mechanistic model of SSB repair and hOGG1 initiated BER pathways for the repair of IR induced lesions. In the mechanistic model presented in this

paper, the long-patch repair pathway is proposed to be involved in repair of complex lesions and the short-patch repair for simple non-clustered lesions. The overall repair of hOGG1 dependent lesions was compared with live cell imaging experiments. The kinetic parameters of the models were validated by comparing the recruitment kinetics calculated from the model with measurements obtained from in vivo imaging experiments. Furthermore, in order to gain insight into how complex lesions are repaired, we use our model to test mechanism of repair for such lesions and compared our results to foci kinetic experiments. 2. Materials and methods To model the enzymatic reactions involved in the repair process of single strand breaks and oxidized base lesions each step of the biochemical process have been translated to a differential equation based on law of mass action kinetics. The notations Yi , Vi and Ki are used to represent the repair complex, repair rate, and repair rate constant, respectively for the ith step of the repair process. After obtaining the rate constants, the system of differential equations were solved numerically to calculate the repair kinetics of single strands and oxidized base lesions. In order to simplify the mathematical solution, the equations were normalized using a scaling method based on the assumption that the total concentration of a given protein in the repair complex is conserved [39] (see Appendix A for the scaled equations). 2.1. Single strand break repair model Fig. 1 represents a mechanistic model of SSB repair pathway. As described in Eq. (1) the rate of SSB induction linearly increases as a function of dose rate dD/dt, with the SSB induction-rate per unit dose constant ␣SSB , and decreases with the initiation of repair via SSB recognition upon PARP 1 recruitment (Eq. (2)). Several studies have suggested that PARP1 is involved in recognizing single stranded ends and mediates recruitment of other repair proteins, while at the same time protect the ends from further damage [12,18]. dY1 dD = ˛ssb − V1 dt dt

(1)

V1 = K1 [PARP1]Y1

(2)

After recognition of the single strand break and PARP1 activation, the repair continues either via the short-patch repair or the long-patch repair subpathway. Eqs. (3)–(5) explain the initiation of short or long-patch repair. For short-patch repair to initiate (Eq. (4)), the SSB termini need to be in the form of 3 -OH and 5 -phosphopate. Depending on the chemical nature of the ends proteins such as DNA polymerase ␤ (Pol ␤), APE1, or polynucleotide 3 phosphatase (PNKP) are recruited to process the ends into compatible form for ligation and extension [19,40]. Short-patch repair continues with Pol ␤ synthesizing a single nucleotide and ligation of the nicks by Ligase III and XRCC1 as shown in Eqs. (6)–(11). dY2 = V1 − V2 − V6 dt

(3)

V2 = K2 [Polˇ, PNKP, APE1]Y2

(4)

V6 = K6 [Polˇ,

Polı , PCNA, RFC]Y2 ε

(5)

dY3 = V2 − V3 dt

(6)

V3 = K3 [Polˇ polymerase]Y3

(7)

dY4 = V3 − V4 dt

(8)

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Fig. 1. Schematic model of the SSB repair pathway. Yi and Ki represent the repair complex and the rate constant for each stage of repair, respectively. After recognition of the SSB via PARP1 (stage 2) the repair either proceeds through short-patch repair for simple SSBs (stages 3–6) or through long-patch repair for complex SSBs (stages 7–10).

V4 = K4 [XRCC1, Lig III]Y4

(9)

dY5 = V4 − V5 dt

(10)

V5 = K5 Y5

(11)

In case of complex breaks, the repair may proceed through the long-patch repair, described by Eqs. (12)–(17). In the long-patch repair subpathway, 2–13 nucleotides 3 to the gap are removed via actions of RFC, polymerase ␦/␧ and PCNA. This step may be accompanied by initial gap filling attempt by Pol ␤ [41,42]. This displacement results in a 5 single strand flap, which is cut by the flap endonuclease FEN1. The long patch-repair is completed with sealing of the nick by Ligase I.

2.2. hOGG1 dependent base excision repair model Fig. 2 represents the mechanistic model of hOGG1 dependent BER. As described in Eqs. (18)–(19), the rate of base damage induction linearly increase as a function of dose rate (with base damage induction-rate per unit dose constant ˛BER ) and decreases with the excision of the oxidized guanine via hOGG1. dY1 dD = ˛BER − V1 dt dt

(18)

V1 = K1 [hOGG1]Y1

(19)

In Eqs. (20)–(21) we describe the lyase activity of hOGG1 in removing the AP site. As hOGG1 is a bifunctional glycosylase, it also has a lyase activity which cleaves the DNA phosphodiester backbone 3 to the abasic site via a ␤-elimination reaction resulting in a 3 2,3-didehydro-2,3-dideoxy-ribose (3 ddR5p) and 5 phosphate termini [43,44].

dY7 = V6 − V7 dt

(12)

V7 = K7 [FEN 1]Y7

(13)

dY8 = V7 − V8 dt

dY2 = V1 − V2 dt

(14)

V2 = K2 [hOGG1 lyase, APE1]Y2

V8 = K8 [Lig I]Y8

(15)

dY9 = V8 − V9 dt

(16)

V9 = K9 Y9

(17)

(20) (21) 3 ddR5p

As shown in Eqs. (22)–(23), the moiety is removed by the 3 phosphodiesterase activity of AP endonuclease 1 (APE 1), generating a 3 OH terminus that is suitable for ligation [12]. Since in vitro experiments indicate that the lyase activity of hOGG1 is very weak [45,46], several experiments suggest that APE1 stimulates the activity of hOGG1 and increase its turnover [46–48]. It

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Fig. 2. Schematic model of the hOGG1 dependent BER pathway. Yi and Ki represent the repair complex and the rate constant for each stage of repair, respectively. The repair process begins with recognition and excision of the oxidized guanine via hOGG1 (stage 2) and continues to produce a SSB by removal of the AP site and processing of the ends (stages 3–4). Depending on complexity of damage, the repair either proceeds through short-patch repair (stages 5–7) or long-patch repair (stages 8–11).

has been suggested that such stimulation with APE1 is a result of APE1 making hOGG1 only function as a glycosylase and blocks its lyase activity. However, the majority of studies suggest that hOGG1 produces mainly ␤-elimination product, which is not achieved if it functions as a monofunctional glycosylase [44,49,50]. Therefore, in the model the hOGG1 was described as only bifunctional, while APE1 was included in this step to show that it cooperates with hOGG1 to aid the lyase step. Alternatively, in case that hOGG1 does act as a monofunctional glycosylase with excess presence of APE1, the ␤-elimination and APE1 termini removal step can be considered as an extra step for the APE1 to remove the AP site, which would produce the same result.

The resulting SSB generated from these reactions (Eqs. (20)–(23)) can be repaired by either short-patch (or long-patch repair as shown in Eqs. (24)–(26)). Since the substrate being repaired (see Fig. 2 step 4) is identical to a single strand break (see Fig. 1 step 2), the remaining steps are equivalent to the repair of single strand break as described in the previous section. Therefore, Eqs. (27)–(30) represent the short-patch repair, which is equivalent to Eqs. (8)–(11), and Eqs. (31)–(36) represent the long-patch repair with steps equivalent to the ones described by Eqs. (12)–(17). dY4 = V3 − V4 − V7 dt V4 = K4 [Polˇ]Y4



dY3 = V2 − V3 dt

(22)

V7 = K7 Polˇ,

V3 = K3 [APE1]Y3

(23)

dY5 = V4 − V5 dt

(24)



Polı , PCNA, RFC Y4 ε

(25) (26)

(27)

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V5 = K5 [XRCC1, Lig III]Y5

(28)

dY6 = V5 − V6 dt

(29)

V6 = K6 Y6

(30)

dY8 = V7 − V8 dt

(31)

V8 = K8 [FEN 1]Y8

(32)

dY9 = V8 − V9 dt

(33)

V9 = K9 [Lig I]Y9

(34)

dY10 = V9 − V10 dt

(35)

V10 = K10 Y10

(36)

2.3. Derivation of rate constants In the first approximation step, the Michaelis–Menton parameters for base excision repair proteins [8,25,26,51–56] were used to get an initial estimate for the rate constants in the model. These experiments provide in vitro rate constants for individual protein interactions and their affinity for their substrates. While the models in this paper require different rate constants to represent the entire repair process in living cells, the published available Michaelis–Menton rate parameters provide a starting point to estimate the time scale of protein actions with respect to one another. In the second stage, the accumulation kinetics of BER proteins from in vivo imaging experiments [28] were used to obtain the correct parameters for different steps. These experiments show how fast proteins such as hOGG1, Pol ␤, Ligase III and PCNA accumulate at site of damage. The process for rate estimation involves carefully examining the effects of changing each rate constant on the complex kinetics. Sum of the scaled complexes (y1 –y9 for SSBs and y1 –y10 for BDs as shown in Appendix A) equals to unrepaired lesions at each time point. The number of SSBs remaining over time (normalized to percentage remaining) were compared to three sets of experimental data [57–59], and the number of 8oxoG base lesions were compared to two different experimental studies [28,60]. As the repair of single strands and base lesions have overlapping proteins, the same rate constants were used for the common steps, allowing for the use of one model to derive the common rate constants for the other. That is, for the common steps, each rate constant must assure that the overall repair kinetics of both SSBs and BDs agrees with experimental results, while at the same time ensuring the accumulation behaviours of individual proteins (if the data is available for that protein) is also consistent with the experiments. 3. Results The numerically solved solution of differential equations in the model provides the repair kinetics of base and single strand lesions. While both SSB and base lesions use the BER pathway, the repair kinetics of SSBs and hOGG1 will be different as the initial steps are dissimilar. 3.1. Overall SSB repair kinetics Three sets of different experimental data from published papers were used to validate the SSB repair model solution. The overall single strand break rejoining for human fibroblast cells [57] and Chinese Hamster Ovaries cell lines (CHO-K1 cells) [58] were measured using alkaline elution analysis. The CHO-K1 cell lines and the human fibroblasts were irradiated with 5.8 Gy and 5.0 Gy X-rays, respectively. The 42WT cells are a cell line from mouse

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Table 1 Rate constants for SSB model. Rate constants (h−1 ) k1 = 300 k2 = 100 k3 = 200 k4 = 10 K5 = 100 k6 = 25 k7 = 100 k8 = 100 K9 = 1

Table 2 Rate constants for hOGG1 mediated BER model. Rate constants (h− ) k1 = 200 k2 = 100 k3 = 40 k4 = 20 k5 = 10 K6 = 100 k7 = 25 k8 = 100 k9 = 100 K10 = 1

fibroblasts [59]. The damage for 42WT experiment was induced synthetically by plasmid transformation of oligonuclides containing Furans, which are used as abasic site analogues. The repair then was monitored using an in vitro DNA cleavage assay using autoradiography [59]. Fig. 3 shows the solution of the SSB repair mathematical model (solid line) in comparison with the experimental data (symbols). Table 1 shows the rate constants used to solve the differential equations. As can be seen from Fig. 3, the model agrees well with the experimental result within the margin of error of 5%. Both the model solution and experimental measurements indicate that half time of SSB repair is about 8 ± 2 min and that 90% of lesions are repaired in about 30 min. It can also be seen that the radiation induced damages have slightly slower repair kinetics than the synthetically induced lesions.

3.2. Overall hOGG1 mediated BER The overall hOGG1 mediated BER kinetics was verified using two set of experimental data. In the first experiment [28] Hela cells were irradiated with UVA laser to create oxidized lesions. The repair of base lesions was monitored with antibodies against 8oxoG lesions. The second experimental data used to validate the BER mathematical model is the live-cell foci microscopy experiment from Asaithamby et al. [60]. In the latter experiment, human fibrosarcoma HT1080 cells were irradiated with 1 Gy ␥ rays and the repair of base lesions were monitored by hOGG1 foci count using stained antibodies. The results of those two experiments [28,58] were extracted and normalized to percentage repair. Fig. 4 shows the comparison of the model solution with the experimental data, and Table 2 presents the corresponding rate constants used to solve the differential equations. As can be observed both from the model solution and experimental measurements, the half-time of oxidized lesions is about 20 min and 90% of lesions are repaired in 2 h. The calculated repair kinetics of the oxidized Guanine from the model is in reasonable agreement with the two experimental measurements.

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Fig. 3. Comparison of the SSBR model calculation (solid blue line) with experimental data (symbols). The experimental data were normalized to percentage of SSBs unrejoined as a function of time and represent SSB repair kinetics for CHO-K1 cells irradiated with 5.8 Gy X-rays [58], human fibroblast cells irradiated with 5 Gy X-rays [57] and 42WT cells with synthetically incorporated Furans [59].

3.3. Accumulation kinetics of individual BER repair proteins In an in vivo study of oxidative damage repair, Lan et al. [28] used 365-nm UVA irradiation to produce different lesions in focused area of the cell (1 ␮m diameter) and monitored accumulation of different BER and SSB repair proteins (SSBR) by tagging the proteins with GFP (Green Fluorescent Protein) and measuring the fluorescent intensity at different time points. Accumulation kinetics of four different proteins in the BER pathway using fluorescent-labelled proteins at the damage site was used to verify the kinetic parameters for the BER and SSBR models. To verify the parameters used

in the model, the accumulation kinetics of OGG1, Pol ␤, Lig III, and PCNA were calculated from the model and compared to the accumulation kinetics obtained from experimental measurements. Fig. 5 shows the initial accumulation of hOGG1 calculated from the BER model in comparison with recruitment from the experimental florescent measurement. The initial accumulation of hOGG1 was calculated by adding Y2 and Y3 in the hOGG1 BER model (representing the bifunctional activity of hOGG1 as shown in Fig. 2) and normalizing to the maximum. As illustrated in Fig. 5, the experimental measurement shows that hOGG1 reaches its maximum recruitment at around 30 s and the accumulated hOGG1 rapidly

Fig. 4. Comparison of the hOGG1 BER model calculation (solid blue line) with experimental data (symbols). The experimental data were normalized to percentage of lesions remaining as a function of time and represent hOGG1 dependent BER kinetics for Hela cells irradiated with UVA laser [28] and HT1080 cells irradiated with 1 Gy ␥ rays [60].

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Fig. 5. Comparison of model calculations (solid line) with experimental data (symbols) for accumulation kinetics of hOGG1. The experimental data (green circular symbols) represent the accumulation kinetics of the GFP-tagged OGG1 proteins at site of damage in UVA irradiated Hela cells [28] normalized to maximum fluorescence. The experimental accumulation kinetics is used to verify the rate constants k1 and k2 in the hOGG1 BER model.

decreases afterwards and disappears after 240 s. This is in good agreement with the mathematical calculation, which shows the maximum recruitment around 25 s and disappearance between 240 and 250 s. Fig. 6 shows the initial accumulation of PCNA calculated from the BER model versus PCNA accumulation measured from the florescent microscopy. The initial accumulation of PCNA was calculated by normalizing Y8 (obtained after numerically solving the differential equations) in the BER model (Fig. 2) to its maximum. As can be seen in Fig. 6, the experimental measurement show that recruitment of PCNA is slow in the beginning and reaches its maximum accumulation around 240 s and decreases very slowly afterwards.

The accumulation kinetics of PCNA calculated from the mathematical model (solid line) agrees very well with the experimental measurements and display similar accumulation and disappearance behaviour. Fig. 7 illustrates the initial accumulation of Pol ␤ calculated from the SSBR model in comparison with recruitment from the experimental florescent measurement. The initial accumulation of Pol ␤ was calculated by adding Y3 and Y4 in the SSBR model (representing the activity of Pol ␤ as shown in Fig. 1) and normalizing to the maximum. The fluorescent microscopy measurement shows that Pol ␤ accumulates rapidly and reaches its maximum recruitment after 150 s. As can be seen from Fig. 7, the Pol ␤ recruitment from

Fig. 6. Comparison of model calculations (solid line) with experimental data (symbols) for accumulation kinetics of PCNA. The experimental data (green circular symbols) represent the accumulation kinetics of the GFP-tagged PCNA proteins at site of damage in UVA irradiated Hela cells [28] normalized to maximum fluorescence. The experimental accumulation kinetics is used to verify the rate constants k7 and k8 in the BER model.

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Fig. 7. Comparison of model calculations (solid line) with experimental data (symbols) for accumulation kinetics of Pol ␤. The experimental data (green circular symbols) represent the accumulation kinetics of the GFP-tagged Pol ␤ at site of damage in UVA irradiated Hela cells [28] normalized to maximum fluorescence. The experimental accumulation kinetics is used to verify the rate constants k4 and k5 in the SSBR model.

mathematical calculation shows maximum accumulation around 125 s and shows reasonable agreement with the experimental measurement. Fig. 8 shows the initial accumulation of Lig III calculated from the SSBR model in comparison with recruitment from the experimental florescent measurement. The initial accumulation of Lig III was calculated by normalizing Y5 (obtained after numerically solving the differential equations) in the SSBR model (Fig. 1) to the maximum. As seen in Fig. 8, the experimental accumulation of Lig III is similar to the accumulation of Pol ␤, reaching its maximum intensity around 150 s. The calculation from the model (solid line) also shows reasonable agreement with the experimental measurements. 3.4. Repair of clustered base damages To test the hypothesis that simple base damages are repaired via the short-patch repair, while the clustered lesions are repaired via long-patch repair, the solution of the BER model using only the long-patch repair (by setting k4 , k5 and k6 in Fig. 2 to equal 0) was compared to disappearance kinetics of the overlapping hOGG1 foci (with XRCC1 or 53BP1) in the HT1080 cells irradiated with ␥ rays obtained from the experimental measurements of Asaithamby et al. [60]. As can be seen from Fig. 9 the repair kinetics of clustered base lesions1 induced by ␥ rays (indicated by green circular symbols) matches the calculation from the mathematical model (solid blue line, model A), in which only the long-patch repair subpathway was set to be active. In addition, the model was tested to see what stage of repair is impaired with increasing damage complexity. As shown in Fig. 9, higher percentage of overlapping hOGG1 foci remain after 24 h when the HT1080 cells were irradiated with Fe ions [60] (indicated by red triangular symbols). After analysis of the parameters used in the model, it was observed that this behaviour in repair of clustered lesions, can be obtained by 20% reduction in the activity of proteins involved

1 Here the term clustered base lesions refers to lesions marked with colocalization of hOGG1 foci with XRCC1 and/or 53BP1 foci as defined by Asaithabmy et al. [60]. This definition is only used in this paper for comparison with the experimental data and the shortcoming of such definition is explained in the Section 4.

in initiation of LPR after the AP site incision (K7 in Fig. 2 and Eq. (26)). The calculated model result of this parameter reduction is shown as the solid purple line in Fig. 9 (hOGG1 model B). The hOGG1 disappearance kinetics for Si (LET of 44 keV/␮m) data (black symbols) was not compared with the model prediction since they show similarity with the ␥-photons data (LET = 0.2 keV/␮m), which is inconsistent with biophysical expectation and interpretation. Fig. 9 illustrates that half-time of repair for complex base lesions induced by low LET particles (solid blue line) is about 65–70 min and about 130 min for complex base lesions produced by very high LET Fe ions (purple solid line). The repair for both reaches saturation after 5 h, with 20–24% lesions still remaining for ␥ rays and 45% of complex lesions still remaining for iron ions.

4. Discussion In this study the repair kinetics of single strand breaks and oxidized base lesion repaired by OGG1 was quantified using biochemical kinetic modelling. The approach here is similar to the one used previously to model the repair of DSBs by different repair pathways [61–64]. The base excision repair pathway is one of the most extensively studied repair pathways, with most of the important repair proteins well identified. However, the in vivo mechanism of repair in response to radiation damage is not yet well understood. The biphasic nature of IR induced DSB repair have been subject of extensive discussion in the past three decades. However, not much attention has been paid to the biphasic repair of SSBs and base lesions. As can be observed from Figs. 2 and 3, similar to DSBs repair kinetics, the repair of these lesions also consists of a fast and a slow component. Several experiments using synthetic or enzymatically-induced lesions have been used to study the repair of closely spaced base damages and SSBs [34,35,65–68,68–70]. These studies suggest that depending on the relative position of the lesions to one another, the long-patch repair would be needed for bi-stranded base lesions to replace several nucleotides and can take a longer time. These studies have led us to hypothesize that complex base damages

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Fig. 8. Comparison of model calculations (solid line) with experimental data (symbols) for accumulation kinetics of Lig III. The experimental data (green circular symbols) represent the accumulation kinetics of the GFP-tagged Lig III at site of damage in UVA irradiated Hela cells [28] normalized to maximum fluorescence. The experimental accumulation kinetics is used to verify the rate constants k3 and k4 in the SSBR model.

and single strands lead to the biphasic nature of the curves by using the slow long-patch repair pathway. An important issue that needs to be addressed with regards to complex SSBs and BDs is the repair of these lesions when they are in close proximity to a DSB. Due to experimental limitations, the repair of such lesions has not been studied in context of DSBs. In our definition of complex SSBs and BDs, we include those lesions that are within

10–20 bps of DSBs as well. In our model, the repair of complex SSBs and BDs involving DSBs are also repaired via the long-patch repair subpathway. We base our hypothesis from two experimental observations. The first observation is from the experiments of Lan et al. [28]. The authors report at a low energy pulse they observe most of the BER proteins. However, they only observe PCNA (which is required for long-patch repair) at the highest energy

Fig. 9. Comparison of model calculations (solid lines) with experimental data (symbols) for repair of complex base lesions. The experimental repair kinetics represent disappearance kinetics of overlapping hOGG1 foci (overlapped with XRCC1 or 53BP1) in HT1080 cells irradiate with 1 Gy ␥ rays (circular green symbols) and 1 Gy iron ions (red triangular symbols) extracted from experimental measurements of Asaithamby et al. [60] and normalized to percentage lesions remaining. hOGG1 model A (solid blue line) shows the model calculation using only the long-patch repair for predicting the repair of complex base lesions induced by ␥ rays. hOGG1 model B (solid purple line) the model calculation with 20% reduction in the K4 rate constant in the hOGG1 BER model explaining the reduction in repair of clustered base lesions produced by Fe ions. The experimental Si data in the same publication [60] have not been compared with the model prediction. The Si data with an LET of 44 keV/␮m shows similarity with the ␥-photons data (LET = 0.2 keV/␮m) and are inconsistent with biophysical expectation and interpretation.

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pulse. At that same pulse, they also observe ␥H2AX as indicative of DSBs, which was not observed at the lower energy pulse. Such evidence, indirectly suggests that long-patch repair is only utilized when there are more damages (thus higher probability of them being clustered), as wells as when there are DSBs present. The second observation is from the Asaithamby et al. [60] foci kinetic experiment. Analysis of that experiment show that the hOGG1 foci overlapping 53BP1 foci (representing DSBs) have much slower disappearance kinetics. While this observation does not suggest that the long-patch repair is responsible for repairing these overlapped regions, it does suggest that a slower mechanism is taking place to repair the bases in these regions. Using these two observations, we used our model to test the hypothesis, and observed that using only the long-patch subpathway we observe the slow disappearance of the hOGG1 foci overlapped with 53BP1 foci as shown in Fig. 9. In addition to testing the hypothesis of long-patch repair involvement in repair of complex base damages, our repair model has allowed us to test how increasing the complexity affects BER. Analysis of Asaithamby et al. experimental results show that irradiation with higher LET ions such as iron ions leads to inhibition of repair in the overlapping regions as 45% of those foci still remain after 24 h (Fig. 9). By testing the different parameters in our model, we have observed that a 20% reduction of protein activity after AP incision removal can lead to such inhibition in repair. A possible explanation for this result is that the BER pathway might not be capable of repairing severe complex base damages caused by very high LET particles, such as more than 3 tandem lesions in close proximity. Another possible explanation is that cells actively inhibit the repair of multiple bi-stranded base lesions in close proximity to prevent further DSB formation. While the foci experiment of Asaithamby et al. [60] has led us to draw some conclusion about repair of complex breaks, there are still some biological questions that cannot be addressed from comparison to such data. While the percentage of colocalized foci in that experiment increases with higher LET, the absolute number of overlapped foci do not represent the actual number of complex breaks as these overlapped regions are limited to a precision corresponding to the wavelength of the beam used for visualization (which in terms of DNA scale corresponds to several kilo base pairs). For this reason, it is not possible to test how juxtaposition and number of base damages and single-strand breaks within two helical turns of DNA affect repair kinetics. Another limitation in using foci kinetic experiments is that 53BP1 is a signalling protein in the DSB repair pathway and does not necessarily correspond to the number of DSBs. The time required for 53BP1 foci to reach its maximum number is about 30 min. By this time majority of hOGG1 and XRRC1 foci have disappeared as they are initial responders to BDs and SSBs. Therefore, such discrepancy in kinetics of foci appearance to mark DNA damage make it impossible to correctly estimate the initial number of complex damages with current visualization techniques (even if the assumption that all colocalized foci represent complex damage was correct). By taking into account such shortcomings in the experimental techniques, the comparisons made in Fig. 9 should only be considered as more of a qualitative benchmarking of the model. In order to test the model with a more accurate quantitative data for initial number of damage and their complexity we need Monte Carlo Track Structure simulations to simulate the initial DNA damage by single and multiple radiation tracks for different LET particles. Subjecting the simulated data to the repair model will allow us to test how complexity of base damages affect repair and can further explain how the reduction in repair as seen in Fig. 9 is achieved. While we have stated that use of Fe ions leads to further inhibition of repair by a 20% reduction in the K7 rate constant in Fig. 2, we need to explore what type of complexity (i.e. presence of multiple base lesions or presence of DSB in proximity) leads to

such inhibition and also test the involvement of different repair pathways in that stage that can lead to such result. 4.1. Test of sequential repair of BD simulated by Monte Carlo track structure While the model is based on the assumption that complex lesions are repaired via the long-patch repair in a slow manner, numerous in vitro experiments have concluded that both bi-stranded and tandem lesions can be repaired efficiently via short-patch-repair depending on the juxtaposition of the lesions to each other [21,34,35,37,65–67,71–75]. Several of these studies conclude that if one of the bases generates an AP site is 3 to the unrepaired oxoguanine within either 1, 3 to 5 base pairs, then the ligation would be retarded and most likely proceed through longpatch repair. However, if the AP site is in the 5 of the oxoguanine lesion, the repair can proceed sequentially via short-patch repair. As there are several numerous examples that discuss such different scenarios, we wanted to use the solution of our model and the initial spectrum of damage obtained by Monte Carlo Track Structure simulations to show a practical application of the model to test such scenario. As explored in the aforementioned studies, the base excision repair of complex lesions can be a very complicated process. For mathematical modelling purposes and computational simulations, including all the possible scenarios that can happen for the complex lesion repair creates unnecessary mathematical complexity that makes it not feasible for Monte Carlo simulations. Therefore, to show how instead of using a complicated mathematical model entailing all different events that can happen for repair of clustered lesions, we use a sampling approach and MCTS simulation to present an application of our model using a simplified repair scheme adapted from Lomax et al. [66] and Budworth et al. [73]. In this work we simulated 500 independent tracks of 1.5 keV electrons to test the repair of base damages produced by photons, and 89 independent tracks of 950 MeV/u iron ions. The initial spectrum of base and single strands were scored, which are within single base-pair accuracy as produced by direct and indirect action of the ionizing radiation on atomistic model of DNA. Using the modified scheme, the scored base and single-strand breaks were subjected to the BER model. The inverse sampling method, described in publication [63], was used to sample the protein activity at each stage of repair for both short-patch repair and long patch repair. This sampling method permits us to have the time of repair for each single lesions created. For two lesions within 3 bps of each other (we use three because different experiments report from 1 to 5 bps [21,34,35,37,65–67,71–75]) we subject the lesions to repair scheme as follows. Since there is no preference for the BER process to start with either of the lesions [21,66,73], we assume that 50% of AP sites are generated in the 5 direction and the other 50% in the 3 direction. For the tandem lesions with AP site generated in the 5 position the repair time was calculated from the sampling of shortpatch repair twice and added together to represent the sequential repair. For the other 50% of the lesion, that is if the AP site is 3 to the base lesion and including tandem lesion that have 3 or more base pairs within 10 bps proximity, the lesions were repaired by sequential long patch repair. Similarly for bi-stranded lesion, 50% were subjected to sequential repair by short-patch repair, while the other 50% (again representing the juxtaposition of lesions as either 3 or 5 ) were repaired with long patch repair with the reduced AP incision rate followed by short patch repair [66]. Figs. 10 and 11 show the BER kinetics calculated in the manner described for 500 tacks of 1.5 keV electrons and 89 tracks of iron ions, respectively. The repair kinetics were normalized to initial number of BDs and the percentage remaining were calculated for each 10 min intervals.

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99

Fig. 10. BER repair kinetic calculated for 500 tracks of 1.5 keV electrons. Inverse transform sampling method of protein repair kinetics is used. The unrepaired lesions were calculated for each 10 min time interval and normalized to initial spectrum of BDs.

Many other scenarios can be tested using this technique and compared to each other, which is beyond the scope of the present paper. In future we will use further MCTS simulations to investigate different scenarios and assign hierarchy of repair when multiple types of damages are involved. As the overall of our work is to produce a comprehensive model of DNA repair, we will consider the DSBs generated from these lesions [35,76] and combine our DSB

repair model with the BER model for repair of all radiation induced lesions. 4.2. Is the long patch repair involved in removal of single lesions? In this study we have assumed that non-complex lesions are repaired via the short-patch repair. While long-patch repair can

Fig. 11. BER repair kinetic calculated for 89 tracks of 950 MeV/u iron ions. Inverse transform sampling method of protein repair kinetics is used. The unrepaired lesions were calculated for each 10 min time interval and normalized to initial spectrum of BDs.

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also be involved in repair of single lesion, the published data on the involvement of LPR in hOGG1-mediated repair is inconclusive. We need to distinguish between enzymatic studies and those carried out in biologic cell. Enzymatic studies are subject to variation of concentration of the enzymes in the design of the experiment. Some studies show that about 70–80% of hOGG1 lesions are repaired via short-patch repair [49,77]. Thus, while it is true that 20–30% of these single lesions are repaired via long patch repair in the in vitro reconstruction of hOGG1 pathway, it is not clearly evident why these lesions are repaired via LPR and can depend on the concentration of the long patch repair enzymes in the assay. In the quantitative model calculated by Sokhansanj et al. [25], which describes the repair of single hOGG1 lesions based on the natural concentration of the enzymes in the cell, only up to 2.3% of the hOGG1 lesions are repaired via the long-patch repair. Additionally, Fortini et al. [44] have demonstrated that most hOGG1 lesions are repaired via the short-patch repair and that the lesions repaired via the long-patch repair are the lesions that usually take more than 2 h. Based on this evidence we have assumed that single lesions are efficiently removed by SPR, unless there are some deficiencies due to the nature of gap or enzymatic activities that would lead to LPR activation. For simplicity, in the first instance, we assumed that the single lesions are repaired normally and the only difficulty is due to complexity of damage, which can lead to LPR and consequently slower repair. 4.3. Statistical validation and stability of the BER model solution Various tests were performed including steady-state analysis, moiety conversion, local parameter sensitivity analysis and global sensitivity using the system biology toolbox for Matlab [78]. The data are shown as supporting material. 4.4. Do the common steps between repair of SSB and oxoguanine have the same rate constants? In our models, we made the assumption that the rate constants for the common steps between the repair of SSB and 8oxoG, after incision of 8oxoG by Ape1 are the same (i.e. K3 in SSB model in Fig. 1 and K4 in hOGG1 model in Fig. 2). The fact that SSB repair involves PARP binding, while the 8oxoG is dependent on APE1, might affect the subsequent recruitment of BER proteins. While these differences can lead to different rate constants for the remaining steps, at this stage we cannot test without having new in vivo experimental data that can distinguish the SSBs arising from base lesions from those lesions produced by direct interaction of radiation track. As the functional activity of the proteins in the remaining steps are essentially the same, we assume that the difference in the initial PARP binding and possible competition of APE1 and PARP do not lead to a significant change in the rate constants and are within the margin of error, and only consider the involvement of PARP for the SSB repair in the initial stage.

experimental data can be used to predict the overall repair kinetics of these lesions in cells irradiated with radiations of different quality. It should be noted that while a smaller number of parameters could be used in a mathematical model to predict the repair curves for SSBs and BER, such model would not be mechanistic. There are two classes of mathematical models, namely phenomenological and mechanistic models [80]. In phenomenological models, since curve-fitting is the main issue, the model with smallest number of parameters that fits the data well is the best choice. For mechanistic models, the number of parameters and curve-fitting is not an issue. The issue is about the mechanisms involved in the processes under test. The repair model proposed in this paper, with 9 parameters for SSB repair pathways, and 10 parameters for hOGG1 dependent BER pathways, are not over-parameterization. These parameters reflect the number of repair processes required to modify single strand break or base damage, step-by-step, and can explain very accurately the detailed mechanisms of protein repair actions at the site, depending on the type of damage being simple or complex. The mechanistic repair models proposed for the repair of SSB and BER have been compared with the available experimental data (Figs. 3 and 4) and accumulation kinetics to verify rate constants (Figs. 5–8). The proposed rate constants have to be verified experimentally. Moreover, model calculations have been compared with experimental data for the repair of complex base lesions (Fig. 9). The data for complex base lesions were deduced from experimental data. In the absence of direct experimental data, a more meaningful test would be by comparing simulated data of initial DNA damage by single and multiple radiation tracks and then subjecting them to repair, similar to tests for kinetics of simple and complex DSBs repair published recently [60]. Lastly, the model predictions have not been compared with experimental data for Si (as has been done for Fe ion in Fig. 9). The experimental data in Asaithamby et al. [60] publication for ␥photons, Si and Fe ions have LET values 0.2, 44 and 157 keV/␮m, respectively. However, the yields of lesions remaining for Si ions show similar trends as that of ␥-photons (Fig. 9). This is inconsistent with biophysical expectations. Track structure of Si ions with an LET of 44 keV/␮m produces a lot more ionizations than ␥-photons per unit length. This dictates a lot more production of complex DNA lesions. This subject is being explored in our future publication. In conclusion, some remarks on limitations of models in general, and specific to the proposed model of BER in this paper are noteworthy. As such all theoretical models are limited by the range of their applicability. The model of BER proposed in this paper has limitation too, since it is based on certain assumptions and parameters that define the range of its application. A major limitation is benchmarking due to the scarcity of experimental data of repair proteins reaction rate constants. Therefore, experimental measurements are needed to validate each individual step. In this paper, we have been able to limit the variability of our parameters by using accumulation data for four different protein activities used in the model in addition to the overall repair. Further experimental measurements are needed to benchmark the remaining parameters.

5. Conclusions The current technology for radiation biology experiments imposes limitations that prevent a complete understanding of radiation action. The reason for this is that experimental techniques cannot resolve spectrum of DNA damage induced by a single track of radiation at single base-pair resolution [33,64,79]. Mechanistic mathematical models for radiation action are powerful tools to enhance understanding of the biological processes that are initiated with DNA damage. In this paper we presented a mechanistic model BER. The model predicts the in vivo rate constants for the proteins involved in the repair of SSBs and 8oxoG base lesions, and in the absence of direct

6. Summary • The paper presents a mechanistic model of BER. • In vivo accumulation kinetics of BER proteins were used to verify rate constants. • The long patch repair subpathway is proposed for the repair of complex base lesions. • The calculated repair of complex base lesions agrees with foci kinetic experiments. • We propose that increasing complexity of damage inhibits repair after AP site removal.

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• The model provides insight into understanding the repair of radiation damage than the classical qualitative/phenomenological description of repair of ionizing radiation damage. • The model provides new insight in understanding of the repair of clustered lesions. • The model is potentially useful for further understanding how some radiation modifying factors might affect the efficacy of radiation therapy. • The model suggests need for new in vivo experiment to distinguish between the SSB induced by base lesions and those directly produced by radiation track. Conflict of interest The authors declare that there are no conflicts of interest. Acknowledgements The work of Radiation Biophysics Group (RBG) is partially supported by the Swedish Radiation Safety Authority (SSM) and Karolinska Institutet.

dy8 = v7 − v8 dt dy9 = v8 − v9 dt where,

v1 = k1 (1 − C2 )y1 v2 = k2 (1 − C3 )y2 v3 = k3 (1 − C4 )y3 v4 = k4 (1 − C5 )y4 v5 = K5 y5 v6 = k6 (1 − C7 )y2 v7 = k7 (1 − C8 )y7

Appendix A.

v8 = k8 (1 − C9 )y8 In order to solve the system of differential equations the parameters and variables for the SSBR and hOGG1 dependent BER were scaled with a scaling factor Ci equal to 3000 which is large enough to assure that the sum of total concentration of repair complexes (Yi ) and proteins (Ei ) remain constant over time. The scaled equations for the SSBR and BER are shown in the following subsections, with the uppercase letters representing non-scaled parameters/variables and the lowercase representing the scaled parameters/variables. A.1. Scaled equations for the single strand break repair model Ci = [Ei ] +

9 

Yj = cte

v9 = K9 y9 A.2. Scaled equations for the hOGG1 BER model Ci = [Ei ] +

Yi Ci

yi =

9 ci =

Y j=i j

Ci

Yi Ci

ki = Ci Ki

10 ci =

ki = Ci Ki

Yj = cte

j=1

j=1

yi =

10 

Y j=i j

Ci

dy1 ˛BER dD = − v1 C1 dv dt dy2 = v1 − v2 dt

dy1 ˛ dD = ssb − v1 C1 dt dt

dy3 = v2 − v3 dt

dy2 = v1 − v2 − v6 dt

dy4 = v3 − v4 − v7 dt

dy3 = v2 − v3 dt

dy5 = v4 − v5 dt

dy4 = v3 − v4 dt

dy6 = v5 − v6 dt

dy5 = v4 − v5 dt

dy8 = v7 − v8 dt

dy7 = v6 − v7 dt

dy9 = v8 − v9 dt

101

102

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dy10 = v9 − v10 dt where,

v1 = k1 (1 − C2 )y1 v2 = k2 (1 − C3 )y2 v3 = k3 (1 − C4 )y3 v4 = k4 (1 − C5 )y4 v5 = k5 (1 − C6 )y5 v6 = K6 y6 v7 = k7 (1 − C8 )y3 v8 = k8 (1 − C9 )y8 v9 = k9 (1 − C10 )y9 v10 = K10 y10 Appendix B. Supplementary data Supplementary material related to this article can be found, in the online version, at http://dx.doi.org/10.1016/j.dnarep. 2014.07.011. References [1] S.S. Wallace, D.L. Murphy, J.B. Sweasy, Base excision repair and cancer, Cancer Lett. 327 (2012) 73–89, http://dx.doi.org/10.1016/j.canlet.2011.12.038. [2] S. Maynard, S.H. Schurman, C. Harboe, N.C. de Souza-Pinto, V.A. Bohr, Base excision repair of oxidative DNA damage and association with cancer and aging, Carcinogenesis 30 (2009) 2–10, http://dx.doi.org/10.1093/carcin/bgn250. [3] B. Karahalil, V.A. Bohr, D.M. Wilson 3rd, Impact of DNA polymorphisms in key DNA base excision repair proteins on cancer risk, Hum. Exp. Toxicol. 31 (2012) 981–1005, http://dx.doi.org/10.1177/0960327112444476. [4] K.W. Caldecott, Single-strand break repair and genetic disease, Nat. Rev. Genet. 9 (2008) 619–631, http://dx.doi.org/10.1038/nrg2380. [5] S.S. Wallace, DNA damages processed by base excision repair: biological consequences, Int. J. Radiat. Biol. 66 (1994) 579–589. [6] J. Baute, A. Depicker, Base excision repair and its role in maintaining genome stability, Crit. Rev. Biochem. Mol. Biol. 43 (2008) 239–276, http://dx.doi.org/10.1080/10409230802309905. [7] J.T. Stivers, Y.L. Jiang, A mechanistic perspective on the chemistry of DNA repair glycosylases, Chem. Rev. 103 (2003) 2729–2759, http://dx.doi.org/10.1021/cr010219b. [8] M. Dizdaroglu, Base-excision repair of oxidative DNA damby DNA glycosylases, Mutat. Res. 591 (2005) 45–59, age http://dx.doi.org/10.1016/j.mrfmmm.2005.01.033. [9] G.L. Dianov, K.M. Sleeth, I.I. Dianova, S.L. Allinson, Repair of abasic sites in DNA, Mutat. Res. 531 (2003) 157–163. [10] B. Demple, L. Harrison, D.M. Wilson 3rd, R.A. Bennett, T. Takagi, A.G. Ascione, Regulation of eukaryotic abasic endonucleases and their role in genetic stability, Environ. Health Perspect. 105 (Suppl. 4) (1997) 931–934. [11] M. Sossou, C. Flohr-Beckhaus, I. Schulz, F. Daboussi, B. Epe, J.P. Radicella, APE1 overexpression in XRCC1-deficient cells complements the defective repair of oxidative single strand breaks but increases genomic instability, Nucleic Acids Res. 33 (2005) 298–306, http://dx.doi.org/10.1093/nar/gki173. [12] P. Fortini, E. Dogliotti, Base damage and single-strand break repair: mechanisms and functional significance of short- and longpatch repair subpathways, DNA Repair (Amst.) 6 (2007) 398–409, http://dx.doi.org/10.1016/j.dnarep.2006.10.008. [13] D. Svilar, E.M. Goellner, K.H. Almeida, R.W. Sobol, Base excision repair and lesion-dependent subpathways for repair of oxidative DNA damage, Antioxid. Redox Signal. 14 (2011) 2491–2507, http://dx.doi.org/10.1089/ars.2010.3466. [14] P. Fortini, B. Pascucci, E. Parlanti, R.W. Sobol, S.H. Wilson, E. Dogliotti, Different DNA polymerases are involved in the short- and long-patch base excision repair in mammalian cells, Biochemistry 37 (1998) 3575–3580, http://dx.doi.org/10.1021/bi972999h.

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