ATM and ATR activation through crosstalk between DNA damage response pathways

Abstract

Cells losing the ability to self-regulate in response to damage is a hallmark of cancer. When a cell encounters damage, regulatory pathways estimate the severity of damage and promote repair, cell cycle arrest, or apoptosis. This decision-making process would be remarkable if it were based on the total amount of damage in the cell, but because damage detection pathways vary in the rate and intensity with which they promote pro-apoptotic factors, the cell’s real challenge is to reconcile dissimilar signals. Crosstalk between repair pathways, crosstalk between pro-apoptotic signaling kinases, and signals induced by damage byproducts complicate the process further. The cell’s response to γ and UV radiation neatly illustrates this concept. While these forms of radiation produce lesions associated with two different pro-apoptotic signaling kinases, ATM and ATR, recent experiments show that ATM and ATR react to both forms of radiation. To simulate the pro-apoptotic signal induced by γ and UV radiation, we construct a mathematical model that includes three modes of crosstalk between ATM and ATR signaling pathways: positive feedback between ATM/ATR and repair proteins, ATM and ATR mutual upregulation, and changes in lesion topology induced by replication stress or repair. We calibrate the model to agree with 21 experimental claims about ATM and ATR crosstalk. We alter the model by adding or removing specific processes, then examine the effects of each process on ATM/ATR crosstalk by recording which claims the altered model violates. Not only is this the first mathematical model of ATM/ATR crosstalk, it provides a strong argument for treating pro-apoptotic signaling as a holistic effort rather than attributing it to a single dominant kinase.

1. Introduction

All cells receive damage from a wide variety of stressors, each of which contributes to the cell’s ultimate fate. Repair pathways communicate with damage aggregators, and these aggregators choose whether to promote repair, cell cycle arrest, or apoptosis in response (Adimoolam and Ford, 2003; Bartek et al., 2004; Harper and Elledge, 2007). Without this regulation, the cell can develop tumor-like characteristics such as increased mutation rates and the ability to survive in low-nutrient, low-oxygen, or overcrowded environments (Harper and Elledge, 2007).

The damage aggregators’ roles would be challenging enough if the signals they received represented the total amount of damage in the cell; however, this is not often the case (Harper and Elledge, 2007). Because some signaling pathways only respond to lesions after they undergo preprocessing by the cell, while others activate within minutes after the damage appears, cellular damage induces signals that vary in delay and magnitude (van den Bosch et al., 2003; Adamowicz, 2018; Dupré et al., 2006; Lavin et al., 2015; Auclair et al., 2009; Bartek et al., 2004; Buisson et al., 2015; Cliby et al., 2002). The aggregator must base cell fate decisions on inferences from these signals. Gamma and UV radiation neatly illustrate this concept: both agents cause DNA damage and promote apoptosis, but UV photoproducts weakly activate pro-apoptotic proteins through their repair intermediates while γ radiation produces a strong pro-apoptotic response immediately after its induction (Kurz et al., 2004; Thorn et al., 2011; Iliakis et al., 2004; Jackson, 2002; Ünsal-Kaçmaz et al., 2002; Auclair et al., 2009; Vrouwe et al., 2011; Pabla et al., 2008). Understanding how the cell distinguishes between lethal and non-lethal signals in these two cases is the first step in understanding its decision-making process.

Gamma and UV radiation both produce lesions that bind to PIKK-family kinases: ataxia telangiectasia mutated (ATM) binds to the double-strand DNA breaks induced by γ radiation, and ataxia telangiectasia mutated and Rad3-related (ATR) responds to repair intermediates of UV photoproducts (van den Bosch et al., 2003; Adamowicz, 2018; Dupré et al., 2006; Lavin et al., 2015; Auclair et al., 2009; Bartek et al., 2004; Buisson et al., 2015; Cliby et al., 2002). ATM and ATR are respectively considered to be the dominant pro-apoptotic kinases associated with γ and UV radiation (Kurz et al., 2004; Thorn et al., 2011; Iliakis et al., 2004; Jackson, 2002; Ünsal-Kaçmaz et al., 2002; Auclair et al., 2009; Vrouwe et al., 2011; Pabla et al., 2008). However, recent research shows that γ and UV radiation activate both kinases, suggesting that although the cell’s apoptotic decision-making process requires the dominant kinase, it is responding to a pro-apoptotic signal produced by multiple kinases (Jazayeri et al., 2006; Stiff et al., 2006; Gamper et al., 2013; Ray et al., 2013). Several mathematical models explore the apoptotic decision-making response to γ or UV radiation based on the dominant kinase activity, but none have attempted to characterize post-radiation signaling as a joint effort between ATM and ATR (Batchelor et al., 2008; Eliaš et al., 2014; Li et al., 2011; Loewer et al., 2013; Ma et al., 2005; Zhang et al., 2014).

Ataxia-telangiectasia mutated (ATM) and ataxia-telangiectasia mutated and Rad3 related (ATR) are two DNA-damage-sensing proteins in the phosphoinositide 3-kinase (PI3K) family (Bakkenist and Kastan, 2003; Lee and Paull, 2005; Ward et al., 2004; Zou and Elledge, 2003). They activate proteins responsible for making decisions on cell cycle arrest or apoptosis (Reinhardt et al., 2007). They also promote histone unwinding by phosphorylating H2AX: once phosphorylated, the histone allows damaged DNA to unwind so that repair proteins have easier access to the lesion (Lavin et al., 2015; Gannon et al., 2012; Kodama et al., 2010; Reinhardt et al., 2007). They have a multitude of other substrates, including damage response proteins such as p53 and Mdm2, and DSB signaling proteins such as Mre11, Rad50, Nbs1, MDC1, 53BP1, and BRCA1 (Lavin et al., 2015; Gannon et al., 2012; Kodama et al., 2010; Reinhardt et al., 2007).

While ATM and ATR are similar in structure and function, they are activated by different types of DNA damage. ATM becomes active when it binds to the ends of a double-stranded DNA break (DSB) or when it encounters catalysts in the large mass around a DSB, called a focus (van den Bosch et al., 2003; Adamowicz, 2018; Dupré et al., 2006; Lavin et al., 2015; Ma et al., 2005; Zhang et al., 2009). ATM is classically associated with DSB-causing agents such as γ radiation and doxorubicin (Kurz et al., 2004; Thorn et al., 2011; Iliakis et al., 2004; Jackson, 2002). Along with DSBs, γ radiation also induces smaller lesions, such as single-stranded DNA breaks and abasic sites, and clusters of lesions called multiply damaged sites (MDS) (Ward, 1988, 1994).

ATR is activated by single-stranded DNA (ssDNA) bound to replication protein A (RPA) (Ward et al., 2004; Zou and Elledge, 2003; Shechter et al., 2004; Awasthi et al., 2015). That is, rather than binding directly to lesions, ATR interacts with the strands of RPA-bound ssDNA created as repair intermediates or through cellular misprocessing (Buisson et al., 2015; Zou and Elledge, 2003). The cell can create RPA-bound ssDNA during all stages of the cell cycle, but ATR reacts more strongly to ssDNA created during replication stress, so it is primarily active during S and G2 phases (Liu et al., 2009). ATR is classically associated with lesions that are excised during repair, such as those produced by UV radiation and cisplatin (Ünsal-Kaçmaz et al., 2002; Auclair et al., 2009; Vrouwe et al., 2011; Pabla et al., 2008).

Although ATM and ATR appear to compartmentalize two different classes of damage, researchers have discovered situations where ATM acts downstream of ATR, ATR acts downstream of ATM, and knocking down one of these kinases drastically changes the activity of the other (Hannan et al., 2002; Jazayeri et al., 2006; Cuadrado et al., 2006; Stiff et al., 2006; Ray et al., 2013). Hannan et al. (2002) reported that cells with defective ATM (A-T cells) were slower in repairing UV damage, and showed higher concentrations of ATM targets 4 hours after UV induction than wild-type cells (Hannan et al., 2002). This suggests that ATM plays a nontrivial role in UV damage signaling despite being unable to bind to photoproducts or their cellular processing intermediates. This result was further confirmed by Stiff et al. (2006), who also found that silencing ATR suppresses the ATM response to UV radiation and hydroxyurea (Stiff et al., 2006). Earlier, Jazayeri et al. (2006) showed that ATR was activated during replication as part of the cell’s response to γ radiation and that ATR activation after γ irradiation required ATR (Jazayeri et al., 2006; Cuadrado et al., 2006). Jazayeri et al. also found that A-T cells had significantly lower concentrations of RPA-bound ssDNA after γ radiation exposure and identified this as the mechanism responsible for upregulating ATR. Hence, ATM and ATR operate both upstream and downstream of each other in their kinase cascades (Tomimatsu et al., 2009; Cimprich and Cortez, 2008).

Since ATM and ATR recognize similar amino acid motifs and ATM phosphorylates itself, ATR can recognize and activate the autophosphorylation motif on ATM (Matsuoka et al., 2007). ATR does not have this motif, but although ATM likely does not phosphorylate ATR, it can phosphorylate mutual substrates, such as TopBP1, that promote ATR activation (Matsuoka et al., 2007; Yoo et al., 2007; Burrows and Elledge, 2008). Sharing a substrate motif also allows ATM and ATR to promote repair pathways that are classically associated with either kinase. Both kinases phosphorylate H2AX to Ser139H2AX/γH2AX, unwinding the lesion from the chromatin structure to make it accessible to regulatory proteins (van den Bosch et al., 2003; Adamowicz, 2018).

This model considers three different mechanisms of crosstalk between ATM and ATR. Kinase cascades are the first and most direct mechanism: ATR can phosphorylate ATM, and ATM activates TopBP1, one of the cofactors required for ATM activation. Chromatin unwinding is another: both kinases promote histone modifications that unwind and stabilize damaged sections of DNA, so the involvement of one kinase makes the damaged region more accessible to the other. And lastly, cellular processing can change the structure of a lesion: DSB repair often involves creating RPA-bound ssDNA, and RPA-bound ssDNA can break to form DSBs. By identifying the lesions γ radiation and UV damage cause, how these lesions are processed by the cell, and how they interact with ATR and ATM, we simultaneously model these three forms of crosstalk.

We introduce a model of ATM and ATR response to γ and UV radiation that incorporates several known or hypothesized modes of crosstalk between the kinases and repair pathways. These include the effects of ATM and ATR on lesion repair, mutual upregulation between ATM and ATR, and changes in kinase binding affinity that occur when the cell alters the structure of a lesion (Matsuoka et al., 2007; Yoo et al., 2007; Burrows and Elledge, 2008; van den Bosch et al., 2003; Adamowicz, 2018). The model also accounts for changes in ATR activity during S phase and the effects of replication on damage response. From the experimental works we collected, we identified 24 distinct claims about ATM and ATR activation in response to γ or UV radiation. We calibrate the model to agree with 21 of these claims, where the final three suggest potential extensions. To explore how each mode of crosstalk affects ATM and ATR signaling, we identify seven key processes and build alternate versions of the model that changes one of these processes. If the alternate model violates one of the original 21 claims, we discuss the implications of this change. Our simulated knockout experiments provide insight on the kinetic effects of different crosstalk mechanisms, and our dose response curves suggest non-dominant kinase activity might be a crucial component of the cell’s response to UV radiation. We intend for this model to be a first step towards studying pro-apoptotic signaling dynamics as a combined effort between multiple damage response pathways.

2. Methods

We introduce a mathematical model of ATM and ATR response to γ and UV radiation, where ATM and ATR are the two dominant regulatory kinases that promote apoptosis in response to these forms of radiation. We estimate the total pro-apoptotic signal received by the cell as the combined activity of ATM and ATR.

Figure 1 outlines structural changes of the lesions represented in the model. The first column in Figure 1 shows the four types of DNA lesion we consider in this model: simple DSBs, complex DSBs, multiply damaged sites, and UV photoproducts. Additional classes in Figure 1 show changes in lesion structure as they undergo repair or induce replication stress, naming the repair process and key proteins responsible for each change. The processes in Figure 1 are lesion-specific, but interactions between lesions and regulatory proteins, including ATM and ATR, all follow the same generic structure.

Fig. 1.

The possible fate of each lesion class in the model. GAMMA RADIATION: Gamma radiation creates simple and complex double-strand breaks (DSBs, C-DSBs) and clusters of damaged bases (multiply damaged sites, MDS). Non-homologous end joining (NHEJ) can repair DSBs. If end-resection enzymes outcompete NHEJ factors, DSBs undergo end resection and move to the end-resected DSB class (ER). DSBs in this class can be repaired by alternate end joining (a-EJ) or single-strand annealing (SSA). Regulatory proteins such as BRCA2 and Rad51 may induce further end-resection, which moves the DSB into the extensive-end-resected class (EER) where it can be repaired by homologous recombination (HR). UV RADIATION: UV radiation creates photoproducts, which may appear on either transcribed (P_T) or non-transcribed (P_N) DNA. Once a photoproduct is detected (P_D), it undergoes nucleotide excision repair (NER). REPLICATION STRESS: If the replication machinery encounters an existing lesion, it creates a stalled fork F. A stalled fork may be repaired by translesion synthesis (TLS), break-induced repair (BIR), or homologous recombination (HR). These processes use TLS polymerases to pair bulky lesions with complementary bases, leaving the original lesion intact. The 4.10.4 label is used in a later section. Black arrows denote lesion creation, progression, or detection; red arrows represent lesion repair.

2.1. Generic lesion class behavior

Once induced, a lesion can change state in five ways: it can bind to ATM, bind to ATR, change lesion classes through processing (e.g., through end resection), undergo repair, or, if the cell is in S phase, stall a replication fork. Because every lesion in the model evolves in the same basic manner, we outline these structural patterns in a system that represents generic lesion behavior. Let L be the number of unbound generic lesions. The initial condition $L_0=D{L}_0^{*}$ represents the number of lesions L induced by D units of γ radiation where $L_0^{*}$ is the estimated number of lesions in class L induced by 1 unit of radiation. We measure γ radiation in Gy and UV radiation in J/m². For clarity, we color-code the terms in these equations according to which of the five processes they represent (Table 1).

Table 1.

Color-coding for state variable equations.

Figure 2 shows the evolution of a generic lesion class, including active ATM and ATR classes. In the equations below, the function s(L) represents transitions between L and all other lesion classes, where L is the set of all lesion classes. Generic lesions undergo repair at a constant rate k_r.

Fig. 2.

Diagram of state variable changes in the generic lesion system. Red arrows represent repair processes; black arrows represent replication fork stress. The red dashed arrows are optional interactions for when replication fork repair leaves the original lesion intact. Lesion classes with green backgrounds only change during S phase, and lesion classes with orange backgrounds change during all phases of the cell cycle. Purple and blue arrows represent ATM and ATR binding, respectively, and ATM and ATR classes are color-coded in the same manner. A split blue-and-purple arrow indicates that a lesion can interact with either ATR or ATM, but not necessarily both, to enter the kinase-bound class. The parenthetical numbers appear in a later section.

Lesions bound to active ATM or ATR undergo modifications, such as histone unwinding, that make them more accessible to regulatory proteins. We separate lesions that have interacted with at least one ATM or ATR molecule into a kinase-bound class (L_A). For kinase-bound lesions, we assume ATM or ATR induces chromatin unwinding on a faster timescale than DNA repair. Because unwinding makes these lesions more accessible to nucleic proteins than unbound lesions, we assume all protein interactions—including end resection, repair, and, notably, ATR/ATM recruitment—happen faster. We represent chromatin restructuring by a constant scaling factor, r_A > 1, such that regulatory proteins interact with kinase-bound lesions r_A times faster than they do with unbound lesions. We assume this rate is independent of the number of kinases bound to the lesion: as long as the lesion has interacted with at least one kinase, it is permanently altered, even if all kinases dissociate afterward. Two functions, f (ATM, L) and g(ATR, L), govern ATM and ATR binding, respectively.

While L_A and L_AR compartmentalize lesions that have interacted with ATM or ATR at least once, ATM_p,L and ATR_p,L, the phosphorylated kinase classes, represent the total number of bound kinases across all lesions of type L. Kinases deactivate either spontaneously, at a basal dephosphorylation rate k_dATR or k_dATM, or when the lesion they are bound to undergoes repair.

During S phase, we assume replication machinery encounters lesions at an average rate ρ. If we induce damage in the middle of S phase, only lesions on unreplicated DNA can cause replication stress. We therefore introduce two additional kinase-unbound and -bound lesion classes, L_R and L_AR, with associated kinase classes ATM_p,LR and ATR_p,LR. These lesions do not cause replication stress but otherwise behave identically to their unreplicated counterparts. When the cell is not in S phase, ρ = 0. Figure 2 separates the evolution of unreplicated lesion classes, which also represent lesion behavior outside of S phase, from the replication stress subsystem.

Replication forks stall when they separate a lesion from its complementary strand. The RPA-bound ssDNA in these stalled forks directly interacts with ATR, which may then activate ATM. Stalled forks undergo repair at rate k_L and break endogenously, forming DSBs, at rate k_PL. The process that repairs the stalled fork may not repair the original lesion; if this is the case, it returns the lesion to its original class. Fork-associated ATR behaves the same way it does when bound to L; fork-associated ATM binds to ATR at a rate k_aaf (ATM). Even if the original lesion is still present, all ATM and ATR proteins dissociate from the stalled fork upon repair. We let F_L be the number of replication forks stalled at lesions of type L, F_LA be the number of ATR-bound replication forks of this type, and $AT{M}_{p,F_L}$ and $AT{R}_{p,F_L}$ be the number of ATM or ATR proteins bound to these forks.

Lastly, let ATM_tot be the total number of ATM molecules in the cell, which we assume is constant, and let ATM_p be the number of phosphorylated ATM molecules at time t. The difference between these quantities is the number of free ATM molecules at time t. Free ATR is the difference between analogous quantities ATR_tot and ATR_p. The system that governs the kinase-bound classes, replication stress classes, and associated kinase classes of a generic lesion is as follows:

2.2. State variable classes and exceptions

We consider four types of lesion: double-stranded DNA breaks (DSBs), multiply damaged sites (MDS), UV photoproducts, and stalled replication forks. We separate DSBs into four classes with decreasing repair speeds: simple DSBs (L_DSB), complex DSBs (L_CDSB), end-resected DSBs (L_ER), and extensively end-resected DSBs (L_EER). Both simple and complex DSBs can undergo processing to move to the end-resected class, and end-resected DSBs can undergo further processing to enter the L_EER class. There are two classes of photoproduct: detected (L_PD) and undetected (L_P), where only undetected photoproducts can stall replication forks. Like in the generic case, each class of lesion has an associated ATM-or-ATR-bound state (L_DSBA, LCDSBA, LERA, LEERA, LPA, LPDA).

While a model built according to these rules would need twelve state variables for each type of lesion, some classes can be removed without significantly changing the model’s behavior. Allowing DSBs to stall replication forks did not significantly impact the model’s behavior, so we omit DSB classes relating to replication stress (e.g., L_DSBR, L_DSBAR, F_DSB and F_DSBA). Replication forks stalled by photoproducts did significantly impact ATM and ATR activation, so we do include an unreplicated photoproduct class (L_PR) and stalled fork classes (F_P, F_PA), where F_PA is the ATM-or-ATR-bound class. One experiment accounts for replication fork stalling due to γ-radiation-induced lesions besides DSBs, requiring four lesion classes for MDS (L_MDS, L_MDSR, F_MDS, F_MDSA). We assume the repair machinery blocks detected photoproducts from causing replication stress, and therefore do not distinguish between detected photoproducts. Moreover, ssDNA can break to form DSBs at a low rate. Figure 3 shows selected state transitions.

Fig. 3.

The evolution of lesion classes. Gamma radiation induces simple DSBs (DSBs), complex DSBs (CDSBs), and multiply damaged sites (MDSs). Once created, these lesions may bind to ATM or ATR, be repaired, or be processed by the cell to create secondary lesions: end-resected DSBs (ER) or extensively end-resected DSBs (ERR). Arrows in purple or blue denote interactions with ATM or ATR, respectively. Of the UV-induced lesions, L_P represents undetected photoproducts, L_PD represents detected photoproducts, and F_P represents forks stalled on photoproducts. Arrows in purple or blue denote interactions with ATM or ATR, respectively; red arrows represent repair processes. Classes marked in green are only nonzero during S phase. The parenthetical numbers appear in a later section.

The model includes four classes of DSB-bound ATM (ATM_p,DSB, ATM_p,CDSB, ATM_p,ER, ATM_p,EER), which follow the same rules of state transfer and repair as their break-class counterparts. Since ATM and ATR recognize similar amino acid motifs and ATM phosphorylates itself, ATR can recognize and activate the autophosphorylation motif on ATM (Matsuoka et al., 2007). An additional two classes account for ATR-bound ATM at lesions with RPA-bound ssDNA: ATM_p,P for photoproducts and ATM_p,F for stalled replication forks. We assume TLS removes all RPA-bound ssDNA from the damaged site, which deactivates all fork-associated ATR and ATM, and assume the total amount of ATM in the cell (ATM_tot) is held constant on this timescale.

This model accounts for ATR bound to six classes of ssDNA, including the single-stranded overhangs of DSBs (ATR_p,DSB, ATR_p,CDSB, ATR_p,ER, ATR_p,EER, ATR_p,P, ATR_p,F). They follow the same rules of state transfer and repair as their break-class counterparts. To account for ATM upregulation of ATR through TopBP1, we identify the terms representing ATR binding to kinase-bound DSBs and multiply them by a factor k_top > 1. ATR is most active during S phase and controls S/G2 damage checkpoints. We assume this increase in ATR activity is controlled by cell-cycle-specific regulators. Here, we treat ATR cell-cycle-specificity as a piecewise property, where XPA is a constant that scales ATR binding rates and is set to different values for S and G1 phases.

2.3. Cell cycle progression

This model supports two parts of the cell cycle: G1 phase and S phase. To model progression through S phase, we record the number of base pairs that have yet to be replicated (G) and the amount of free Pol δ.

Let G_tot = 3.3×10⁹ be the total length of the human genome and let G(t) be the amount of unreplicated DNA remaining in the cell during S phase. We set G(0)= 0 to simulate G1 phase, G(0) = G_max to start S phase. We consider S phase to have ended when G(t) < 1; that is, when less than one base pair remains to be replicated. For experimental claims involving G2 phase, we consider G2 phase to have started when S phase has ended.

We assume origins of replication are distributed uniformly across the genome, so that when G(t) unreplicated base pairs remain, the ratio between free origins of replication at time t and total origins of replication in the genome is approximately $\frac{G(t)}{G_{tot}}$. Free Pol δ binds with high affinity to these origins of replication during S phase. If ATR is active, it suppresses the rate at which origins of replication fire (Shechter et al., 2004).

The amount of unreplicated DNA, G(t), can change in two ways: it can be successfully replicated or become the site of a stalled fork at rate ρ. In this model, r is the replication fork speed in bp/m, such that rF_a is the net speed of replication by all active forks. While r is held constant, ρ varies with lesion density.

Table 2 outlines cell-specific function and parameter changes, where the variables assume their S-phase-specific values when G(t) ≥ 1 and their G1-specific values when G(t) < 1.

Table 2.

Cell-cycle-specific parameters.

Variable	S phase (G(t) ≥ 1)	G1 phase (G(t) < 1)
ρ(t)	$\frac{r{F}_a(t)}{G(t)}$	0
MRNs	2	1
XPAs	10	1

2.4. Initial conditions

The state variables used in this system can be split into five categories: active ATM, active ATR, lesions that have been processed by the cell, lesions that have yet to be processed, and cell cycle control variables. We expose the cell to radiation at t = 0. In an undamaged cell, all variables in the first three categories start at zero.

To estimate the number of lesions produced by radiation exposure, we use measurements from the existing literature. Meldrum et al. (2003) state that 4500 photoproducts are produced per J/m² of UV radiation the cell receives (Meldrum et al., 2003). For γ radiation, we use Ward’s 1988 meta-study, which finds that each Gy of γ radiation produces four complex DSBs, 36 simple DSBs, and 400 MDS per cell (Ward, 1988). Both papers model the dose-response relationship as linear for lower levels of damage, noting that both forms of radiation reach a threshold above which complex combinations of lesions start to appear at a higher frequency. Our model is not capable of simulating lesion interactions beyond this threshold; its results should only be considered relevant for radiation exposure under 50 J/m² UV or 100 Gy of γ radiation.

Lesions induced during S phase can cause replication stress only if the DNA they appear on has not already been replicated. Let s represent the proportion of the genome that has been replicated by t = 0 and let G_tot refer to the total length of the uniformly distributed throughout the genome, we expect radiation to induce approx-genome, approximately 3.3×10⁹ bp in humans (Weinberg, 2013). If L lesions are uniformly distributed throughout the genome, we expect radiation to induce approximately (1−s)L lesions on unreplicated DNA.

Radiation given to a cell during S phase can damage not only the cell’s original genome but the newly replicated DNA as well. A cell irradiated during S phase would then have more total lesions than an irradiated non-replicating cell, but the lesion density would be the same. An actively replicating cell has roughly (1+s)G_tot base pairs, and if the lesion density estimates above originate from dormant cells, we expect radiation to induce L(1+s) lesions. Lastly, we estimate the total number of lesions by multiplying the above lesion densities by the magnitude of induced damage, D_IR Gy for γ radiation and D_UV J/m² for UV. We provide the initial conditions of all state variables in Table 3.

Table 3.

State variables used in the ATM/ATR crosstalk model. Here, s is the proportion of the genome that has been replicated at t = 0, D_IR is the amount of γ radiation in Gy the cell receives at t = 0, D_UV is the amount of UV radiation in Gy the cell receives at t = 0, and G_tot is the total number of base pairs in the human genome.

Variable	Description	Initial value
G	Number of unreplicated base pairs in genome	Gtot(1 − s)
Polδf	Free Polδ available for replication	0
LDSB	Simple double-strand breaks (DSBs)	36DIR(1 + s)
LDSBA	ATM- or ATR-bound simple DSBs	0
LCDSB	Complex DSBs	4DIR(1 + s)
LCDSBA	ATM- or ATR-bound complex DSBs	0
LER	MRN end-resected DSBs	0
LERA	ATM- or ATR-bound MRN end-resected DSBs	0
LERR	Extensively end-resected DSBs	0
LERRA	ATM- or ATR-bound extensively end-resected DSBs	0
LMDS	Multiply damaged sites (MDS) on unreplicated DNA	400DIR(1 − s)
LMDSR	MDS on replicated DNA	400DIR(2s)
LP	Undetected photoproducts on unreplicated DNA	4500DIR(1 − s)
LPR	Undetected photoproducts on replicated DNA	4500DIR(2s)
LPD	Detected photoproducts	0
LPDA	ATR-bound photoproducts	0
FMDS	MDS-stalled replication forks	0
FMDSA	ATR-bound MDS-stalled replication forks	0
FP	Photoproduct-stalled replication forks	0
FPA	ATR-bound photoproduct-stalled replication forks	0
ATMp,DSB	Active ATM bound to simple DSBs	0
ATMp,CDSB	Active ATM bound to complex DSBs	0
ATMp,ER	Active ATM bound to MRN end-resected DSBs	0
ATMp,ERR	Active ATM bound to extensively end-resected DSBs	0
ATMp,P	Active ATM bound to photoproduct-bound ATR	0
ATMp,F	Active ATM bound to stalled-replication-fork-bound ATR	0
ATRp,DSB	Active ATR bound to simple DSBs	0
ATRp,CDSB	Active ATR bound to complex DSBs	0
ATRp,ER	Active ATR bound to MRN end-resected DSBs	0
ATRp,ERR	Active ATR bound to extensively end-resected DSBs	0
ATRp,P	Active ATR bound to photoproducts	0
ATRp,F	Active ATR bound to stalled replication forks	0

2.5. Full model

We list the names of each state variable in Table 3 and the evolution of all 29 state variables below. See Supplemental Materials for a detailed construction of this model. We used MATLAB to numerically solve this system and perform the virtual experiments. The code used in this paper is available on GitHub at https://github.com/lfedak/atmandatr.

where

$$F_a=\mathrm{Pol}{\delta }_{tot}-\mathrm{Pol}{\delta }_f$$

$$f(\text{ATM},\mathbf{L})=\frac{k_{ATM}\text{ATM}}{D},$$

$$\begin{gathered} D=j_{ATM}+L_{DSB}+L_{DSBA}+L_{CDSB}+L_{CDSBA}+L_{ER}+L_{ERA}+L_{EER}, \\ +L_{EERA}+{\text{ATR}}_{p,P}+{\text{ATR}}_{p,F}, \end{gathered}$$

$$\begin{gathered} {\mathrm{ATM}}_p(t)={\mathrm{ATM}}_{p,DSB}(t)+{\mathrm{ATM}}_{p,\mathit{CDSB}}(t)+{\mathrm{ATM}}_{p,ER}(t)+{\mathrm{ATM}}_{p,EER}(t)+{\mathrm{ATM}}_{p,P}(t) \\ +{\mathrm{ATM}}_{p,F}(t), \end{gathered}$$

$$\mathrm{ATM}(t)={\mathrm{ATM}}_{tot}-{\mathrm{ATM}}_p(t),$$

$$g(\text{ATR},\mathbf{L})=\frac{k_{ATR}\text{XPA}\cdot \text{ATR}}{E},$$

$$\begin{gathered} E=j_{ATR}+F_P+F_{PA}+L_{PD}+L_{PDA}+L_{DSB}+L_{DSBA}+L_{CDSB}, \\ +L_{CDSBA}+L_{ER}+L_{ERA}+L_{EER}+L_{EERA}, \end{gathered}$$

$$\begin{gathered} {\mathrm{ATR}}_p(t)={\mathrm{ATR}}_{p,DSB}(t)+{\mathrm{ATR}}_{p,CDSB}(t)+{\mathrm{ATR}}_{p,ER}(t)+{\mathrm{ATR}}_{p,EER}(t)+{\mathrm{ATR}}_{p,P}(t) \\ +{\mathrm{ATR}}_{p,F}(t), \end{gathered}$$

$$\mathrm{ATR}(t)={\text{ATR}}_{tot}-{\mathrm{ATR}}_p(t).$$

2.6. Calibration and validation

Table 4 lists descriptions and values of all non-cell-specific parameters used in the model. These parameters are not strict, and we report a range of suggested parameter values in Table S8 of the Supplemental Information.

Table 4.

Parameters in ATM/ATR crosstalk model. If we have not provided a source, the parameter value represents an order-of-magnitude estimate.

Parameter	Value	Units	Description	Source
rA	6	None	Histone unwinding factor	(Reynolds et al., 2012)
kNHEJ	$\frac{\ln 2}{20r_A}$	min−1	NHEJ repair rate	(DiBiase et al., 2000)
kD	1.5 × 10−3	prot·min−1	CPD detection rate
kSNHEJ	$\frac{\ln 2}{300r_A}$	min−1	NHEJ with preprocessing
kPL	1×10−8	min−1	ssDNA breakage rate
kMRN	$\frac{\ln 2}{200r_A}$	min−1	MRN complex binding rate
MRNs	2	None	MRN upregulation in S phase
kBRCA	$\frac{\ln 2}{60r_A}$	min−1	Rad51 binding rate
kSSA	$\frac{\ln 2}{200r_A}$	min−1	Rate of SSA
kHR	$\frac{\ln 2}{600r_A}$	min−1	HR rate	(DiBiase et al., 2000)
kNER	$\frac{\ln 2}{20r_A}$	min−1	NER rate	(Ray et al., 2013)
kATM	0.5	prot·min−1	Maximal ATM activation rate
jATM	4000	prot	ATM half-maximal activation parameter
XPAs	10	None	ATR upregulation in S phase
kATR	0.03	prot·min−1	Maximal ATR activation rate
jATR	4 × 104	prot	ATR half-maximal activation parameter
kdATM	0.005	min−1	ATM basal deactivation rate
kdATR	0.005	min−1	ATR basal deactivation rate
r	3000	bp/m	Maximal DNA replication rate
kpd	0.1	min−1	Polδ binding rate to DNA
kd pd	0.005	min−1	Basal Polδ dissociation rate
kd pda	1 × 10−5	(prot·min)−1	Polδ inhibition by ATR
kTLS	$\frac{\ln 2}{100r_A}$	min−1	TLS repair rate
kaa	0.008	None	Rate of ATM activation by ATR
ktop	4	None	ATR binding to ATM-bound DSBs
Polδtot	3.3 ×103	prot	Total Polδ proteins in cell
Gtot	3.3 × 109	bp	number of base pairs in human genome	(Weinberg, 2013)
ATMtot	5000	prot	Total ATM proteins in cell	(Ho et al, 2018; Wang et al., 2019)
ATRtot	1000	prot	Total ATR proteins in cell	(Ho et al., 2018; Wang et al., 2019)

2.7. Experimental conditions

We add or remove several key interactions to assess how they change the system’s qualitative behavior. The following subsections describe which components change to model these cases. For a thorough description of which equations and parameters change in each case, consult the Supporting Information.

2.7.1. ATM kinase activity does not activate ATR

In the full model, both ATM and ATR promote ATR binding by locally activating TopBP1. We allow ATR to upregulate itself through TopBP1, but not ATM, by splitting each DSB class into three categories: the existing kinase-unbound and ATM- or ATR-bound categories, and an additional category for breaks bound to ATR. The ATM classes do not change. We label the interactions related to this experimental condition as (1) in Fig. 3.

2.7.2. ATR kinase activity does not activate ATM

ATR directly binds to and activates ATM k_aa times as fast as DSBs activate ATM. We set k_aa = 0 to remove this interaction.

2.7.3. ATM and ATR do not phosphorylate H2AX

We assume histones are phosphorylated quickly after either kinase binds, and all subsequent protein interactions with the damaged site are r_A times faster. To remove the effects of histone phosphorylation, we set r_A = 1. We label the interactions affected by this change as (3) in Fig. 2.

2.7.4. Replication stress on MDS activates ATR

Gamma radiation induces many non-DSB lesions, some of which can cause replication stress during S phase. To account for post-γ-radiation replication fork stalling, we use MDS as a representative class of persistent non-DSB lesions. We partition unprocessed MDS into non-replicated and replicated DNA classes (L_MDS, L_MDSR), where only lesions in L_MDS can cause replication stress; and include forks stalled on MDS in ATR-unbound and -bound states (F_s,MDS, F_s,MDSA). In particular, if TLS repairs all replication forks at the same rate, we do not need separate classes for ATR bound to forks stalled on photoproducts and MDS. All four new classes break to form DSBs, where DSBs created by endemic breakage of stalled replication forks move into the end-resected class.

This case adds one new parameter: k_MR, the repair rate of MDS, which we set to $\frac{\ln 2}{200}{\min }^{-1}$. We label the class of lesions added to accommodate this experimental condition as (4) in Fig. 1.

2.7.5. ssDNA breaks to form DSBs

The parameter k_pL controls the rate at which ssDNA endemically breaks to form DSBs. We set k_pL << 1 for ssDNA breakage.

2.7.6. ATM dissociates from end-resected DSBs

Based on the hypothesis set by Shiotani and Zhou that ATM dissociates from DSBs upon end resection, we remove ATM_p,_ER and ATM_p,_EER the end-resected-DSB-bound ATM classes (Shiotani and Zou, 2009). In addition, neither end-resected DSB class can move to the kinase-bound class by interacting with ATM. We label the ATM classes affected by this experimental condition as (6) in Fig. 3.

2.7.7. ATR dissociates from extensively-end-resected DSBs

Rad51 displaces RPA on ssDNA to initiate extensive end resection. To account for the possibility that RPA does not re-bind to the ssDNA after being outcompeted, we remove ATR_p,EER, the extensively-end-resected ATR class, prevent extensively end-resected DSBs from binding to ATR. We label the ATR class affected by this experimental condition as (7) in Fig. 3.

3. Results

The ATM and ATR signaling dynamics predicted by the base model are consistent with 21 experimental observations laid out in Section 2.6. To test how modes of crosstalk influence ATM and ATR signaling, we add or remove seven activation mechanisms as outlined in Section 2.7. Table 6 indicates whether the altered model is consistent with those same experimental observations. When inconsistencies arise, we briefly discuss what they imply about damage response signaling. Lastly, we introduce the cell to radiation at different times to the cell cycle relative to the start of S phase and record the change in ATM and ATR response.

Table 6.

Changes in the qualitative model validation with or without key processes. Some rows are missing because all eight models satisfied the claims they represent. Column 1: the original model. Column 2: Model without ATM kinase activation of ATR. Column 3: Model with k_aa = 0, removing ATR kinase activation of ATM. Column 4: Model with r_A = 1, removing increase in binding rates to kinase-bound lesions. Column 5: Model with replication fork stalling on γ-radiation-induced lesions. Column 6: Model with k_PL = 1 × 10⁻⁷, adding the possibility that ssDNA can endogenously break to form DSBs. Column 7: Model with ATM_p,ER and ATM_p,EER removed to represent the hypothesis that ATM dissociates from end-resected DSBs (Shiotani and Zou, 2009). Column 8: Model with ATR_p,EER removed to represent the possibility that RPA cannot re-bind to Rad51-bound ssDNA after being displaced.

		1	2	3	4	5	6	7	8
Source	Claim	Full	ATM ↛ ATR	ATR ↛ ATM	No γH2AX	MDS → ATR	ssDNA breakage	ER ↛ ATM	EER ↛ ATR
(Reynolds et al. 2012)	Inhibiting ATM slows complex DSB repair
(Stiff et al. 2006)	ATM responds downstream of ATR to UV damage
(Bakkenist and Kastan 2003)	ATM can robustly respond to as little as 0.4 Gy within 15 min
(Bakkenist and Kastan 2003)	Active ATM is not detectable 1 hour after 10 J/m2 UV exposure, but is after 5 h
(Jazayeri et al. 2006)	Both ATM and ATR localize to DSBs within 10 min
(Tomimatsu et al. 2009)	ATR can localize to DSBs in ATM-deficient cells
(Kousholt et al. 2012)	ATR is activated before DSBs undergo extensive resection
(Kousholt et al. 2012)	Robust post-γ-radiation ATR response requires end resection
(Gamper et al. 2013)	ATR can be activated by γ radiation in G1 phase
(Gamper et al. 2013)	ATR focus formation around DSBs depends on ATR kinase activity
(Myers and Cortez, 2006)	ATM- or Mre11-deficient cells form fewer ATR foci after γ radiation
(Mladenov et al. 2019a)	Inhibiting ATM affects end resection rates during G2 phase

3.1. Wild-type model dynamics

Figure 4 shows the time evolution of both active kinases in response to γ or UV radiation administered at the start of S phase. Although the time course is unrealistic for an actively replicating cell, we show how the signal would evolve over 96 hours if downstream regulatory pathways did not suppress ATM or ATR activation. This simulated cell has 5000 ATM molecules and 1000 ATR molecules, reflecting the result in Wang et al. that most human organs have more ATM than ATR (Wang et al., 2019).

Fig. 4.

Representative behavior of both kinases for 48 hours after exposure to (A) 10 Gy γ radiation or (B) 10 J/m² UV at the beginning of S phase. In B, the initial number of photoproducts induced by 10 J/m² UV radiation is 45,000.

After γ irradiation, almost every ATM and ATR molecule in the cell becomes active within an hour of exposure. Active ATR declines two hours after irradiation as simple DSBs are repaired, and continues to decline over the course of three days as fewer persistent breaks remain. ATM remains active even when only a few complex DSBs remain in the cell. This reflects observations that only one or two DSBs can effectively activate ATM, although stochastic effects may dominate in a system with few lesions.

ATR responds within minutes of the start of S phase in a UV-irradiated cell and persists at a high-activity level that remains constant over 96 hours. ATM rises slowly, reaching a maximum almost a day after exposure. Although 1 J/m² UV radiation produces thousands of photoproducts and 1 Gy γ radiation produces only four complex DSBs, the combined response of ATM and ATR to UV damage is lower.

Because the claims this model addresses are qualitative, its results in both the wild-type and experimental cases do not rely on specific parameter values. In Table S8 of the Supplemental Material, we suggest parameter ranges and record when altering a parameter violates any of these claims. Parameter values affected only two of the claims listed in Table 6: the second claim, which was only affected by parameters already reported in the experimental conditions; and the fourth claim about ATM activation timing in response to UV damage, which was sensitive and quantitative.

3.2. ATM and ATR mutual upregulation drives early kinase dynamics

ATM interacts with DSBs and is canonically associated with γ radiation signaling, while ATR interacts with RPA-bound ssDNA and is canonically associated with UV radiation and replication stress signaling. Each kinase can respond to its non-canonical form of damage through one of three mechanisms: ATR operates downstream of ATM and vice versa, ATM and ATR modify the lesion to encourage interactions with regulatory proteins, and the lesion itself can undergo structural changes that interact with its non-canonical kinase. We individually removed each of these mechanisms to assess how they affect secondary kinase behavior.

ATM activates TopBP1, a mediator required for ATR binding. Column 2 of Table 6 describes the qualitative behavior of a model where ATM does not activate ATR through a kinase cascade. Although removing this interaction lowered the amount of active ATR following γ irradiation, the only claim this model violated was that fewer ATR foci develop in ATM-deficient cells.

Active ATR directly phosphorylates ATM. If we remove this interaction, as shown in Column 3 of Table 6, not only does ATM no longer depend on ATR to be activated after UV damage, it cannot act quickly enough to match experimental observations. Single-strand DNA breakage also activates ATM after UV damage but was not strong enough to restore ATM activity during the first five hours after irradiation.

In the third form of mutual upregulation, ATM and ATR can cause the lesion to undergo conformational changes, such as histone unwinding, that promote interaction with both kinases. As shown in Column 4 of Table 6, when we remove this interaction, the resulting model fails almost every claim. It even violated observations unrelated to crosstalk: ATM did not pass the detectability threshold in response to 10 Gy γ radiation. Despite the kinases responding weakly, their kinetic properties such as initial activation speed, time to maximal activation, and signal duration were similar to those of the original model.

3.3. Changes to lesion structure do not initiate secondary kinase activation

Gamma radiation induces RPA-bound ssDNA in one of three ways: RPA can bind to the 1–10 bp ssDNA tails on unprocessed DSBs, DSBs can undergo end resection to lengthen these ssDNA tails, and replication forks can stall on any radiation-induced lesion. The full model includes the first two processes. When we allow replication forks to stall on γ-radiation-induced lesions (Table 6, Column 5), replication stress drives ATR activation during S phase. This conflicts with experiments showing that active ATR primarily localizes to DSBs in all stages of the cell cycle. In particular, Kousholt et al. identify DSB end resection as the mechanism that prolongs ATR signaling after five hours, but replication fork stalling dominates ATR activation so thoroughly that suppressing end resection does not affect the S-phase signal (Kousholt et al., 2012).

DSBs can form after UV damage when ssDNA breaks. Adding a low rate of ssDNA breakage did not cause the model to violate any claims (Table 6, Column 6). If the ssDNA breakage rate is too high, ATM can activate independently of ATR after UV exposure. We found that k_pL = 1 × 10⁻⁷ is a reasonable estimate for which all claims hold. Hence, aside from DSB end resection, changes in lesion structure due to cellular processing do not initially activate secondary kinases; however, it is still possible for them to influence long-term signaling behavior.

3.4. Interactions with end-resected DSBs lengthen kinase signals

As DSBs undergo end resection, they gain longer ssDNA tails and lose the short ends that initially attract ATM. In a model where end-resected DSBs were incapable of activating ATM (Table 6, Column 7), the cell cannot respond to low levels of ionizing radiation. Moreover, while ATM and ATR could both respond proficiently to 10 Gy γ radiation, both kinases decay to undetectable levels within 8 hours. This is at odds with experiments in which, with its negative regulator Wip1 silenced, ATM produces a strong signal 10 hours after exposure to 10 Gy γ radiation (Batchelor et al., 2011).

Rad51 drives extensive end-resection by outcompeting RPA on ssDNA. If RPA cannot re-bind to ssDNA after being outcompeted, extensively-end-resected DSBs would not be able to upregulate ATR. When we prevent this DSB class from activating ATR (Table 6, Column 8), the post-γ-radiation ATR signal is transient, lasting for only five hours. This model also predicts a stronger ATR response in end-resection-deficient cells, when removing end resection should instead attenuate long-term ATR activation.

3.5. The cell cycle influences ATM and ATR activation

To understand how the cell cycle affects ATM and ATR activity, we modeled their response to damage induced at different times relative to the start of S phase. Figure 5 shows the cell-cycle-specific activity of a cell with a 16-hour G1 phase and a 6-hour S phase in damage-free conditions. We induced damage during G1 phase or S phase at times separated by 1 hour relative to the start of S phase.

Fig. 5.

Effects of the cell cycle on damage response. Each line represents a cell damaged at a different time relative to the start of S phase, which we model as lasting 6 hours in a healthy cell. Colored lines represent cells damaged during S phase. Black lines represent cells damaged between 1 and 16 hours before the start of S phase, where signals progress monotonically. These diagrams show (A) DSB repair, (B) photoproduct repair, (C) ATM activity after γ irradiation, (D) ATR activity after γ irradiation, (E) ATM activity after UV irradiation, (F) ATR activity after UV irradiation.

Since photoproducts on stalled replication forks require an additional step to repair, the cell cycle affects photoproduct repair rates (Fig. 5B) but not DSB repair rates (Fig. 5A). This agrees with experimental observations. Radiation creates more lesions during S phase because it can react with the extra DNA synthesized during replication.

ATM is robustly activated by γ radiation in both G1 and S phase (Fig. 5C). ATR responds most strongly to γ radiation induced during S phase (Fig. 5D). If the cell is irradiated during G1 phase, ATR responds weakly to γ radiation until the start of S phase, when it increases sharply relative to the amount of remaining DSBs. This scenario would not happen in a real cell, since targets of active ATM would arrest the cell cycle in G1 phase until no breaks remain.

If we expose the cell to UV in G1 phase, or close to the start of S phase, ATR quickly reaches a maximum and equilibrates within 5 hours to a high level (Fig. 5E). ATM does not achieve the same maximum if the cell is damaged during S phase, but converges to a similar high-activity equilibrium, albeit at a reduced rate that lowers as the cell is damaged later in S phase. UV damage activates ATM most efficiently when it is administered close to the start of S phase (Fig. 5F). If we damage the cell in the middle of S phase, ATM operates downstream of a reduced amount of ATR, and if we damage the cell early in G1 phase, it has more time to repair photoproducts before they induce replication stress, lowering the number of stalled forks that endemically break. We do not model metaphase, and understand G2 phase to be the state of the model after it completes replication.

3.6. Endemic breakage enhances post-UV kinase signal variation

Figure 6 shows how the area under the active ATM or ATR curve varies with radiation dose over 24 hours. Increasing the γ radiation dose raises the level of both active ATM and active ATR with diminishing results (Fig. 6A). In a cell with ten times less ATR (Fig. 6C), the change in active ATM remains the same.

Fig. 6.

Dose response curves for ATM and ATR. (A) Response to varying doses of γ radiation; ATM_tot = 5000, ATR_tot = 1000. (B) Response to UV radiation; ATM_tot = 5000, ATR_tot = 1000. (C) Response to γ radiation; ATM_tot = 5000, ATR_tot = 100. (D) Response to UV radiation; ATM_tot = 5000, ATR_tot = 100.

The cell is sensitive enough to UV damage that mutual targets of ATM and ATR show graded responses to UV damage in the range of 2–10 J/m² (Batchelor et al., 2011). We therefore expect total kinase activity to vary over this range. As shown in Fig. 6B, in a cell with the same total amounts of ATM and ATR given in Table 4, UV damage activates ATR quickly and efficiently even at low levels of exposure. Both ATM and ATR increase over the given UV dose range. For a cell with ten times less ATR (Fig. 6D), ATR is not sensitive to changes in UV dose; it becomes maximally active even at low doses of UV radiation. Instead, active ATM levels are what cause the net signal to vary. This happens because more ssDNA breaks to form DSBs as the number of photoproducts in the cell increases.

4. Discussion

We introduce the first mathematical model of ATM and ATR co-activation, one that satisfies 21 claims from various experimental sources. This model includes three modes of ATM/ATR crosstalk: mutual upregulation of ATM and ATR, enhanced protein recruitment to lesions bound by ATM or ATR, and changes in lesion structure caused by cellular processing.

Altering these modes of crosstalk provides insight into how each mode affects ATM and ATR signaling. While mutual upregulation drives the activation of both kinases in the early stages of damage response, changes in lesion structure due to cellular processing are what prolong kinase activation in response to both γ and UV radiation.

The model also has cell-cycle-specific functionality for damage induced in S or G1 phase. Replication stress, preferential activation of ATR during S phase, and replication slowing by ATR all change the model’s predicted kinase activity during S phase. But while ATR is indispensable for promoting apoptosis in response to replication stress, if nearly all ATR molecules become active shortly after replication stress appears, secondary kinases such as ATM are what cause the combined pro-apoptotic signal to vary with damage intensity.

Overall, this model successfully resolves qualitative experimental claims about ATM and ATR crosstalk that have been collected over the past 17 years.

4.1. Kinase dynamics

The three ATR and ATM crosstalk mechanisms operate on different timescales. Immediately after radiation exposure, ATM and ATR kinase activity drive their activation. Structural changes to the lesions prolong the combined kinase signal: in the model, double-stranded break end resection sustains ATM and ATR hours after γ irradiation, and ssDNA breakage activates ATM for days after exposure to UV light.

Although the model requires end-resected DSBs to drive kinase activation, experimentalists have shown that the long ssDNA tails on end-resected DSBs cannot bind to ATM. To reconcile these results, we suggest that ATM may bind to the breaks before end-resection and then drives its own activation through autophosphorylation; that is, without directly binding to the break. This supports a model in which DSB foci may not necessarily be held together by chemical bonds, but could also form as a cloud of active proteins around the original lesion.

Thousands of UV photoproducts do not constitute a lethal amount of damage, but a cell can apoptose in response to only a few sustained double-strand breaks. We do not yet understand how kinase signaling distinguishes between small amounts of lethal damage and large amounts of non-lethal damage. In this model, γ radiation activates almost all ATM and ATR molecules in the cell within minutes, and the signal it produces can be sustained by a single double-strand break. UV damage effectively activates ATR and produces an ATM signal that reaches a maximum hours after irradiation.

The effect on UV-induced single-strand DNA breakage on ATM activation also has fascinating implications. A recent proteomics study suggests that ATM is much more abundant in human cells than ATR. In two organs, the heart and esophagus, the researchers detected no ATR. We considered whether cells with low ATR levels could distinguish between high and low doses of UV. In these cells, UV radiation produces an abundance of non-lethal photoproducts that cause high ATR activity regardless of the extent of damage. Because ATR is so thoroughly activated by even small numbers of photoproducts, it seems incapable of distinguishing between small and large doses of UV damage. Instead, larger doses of UV damage cause repair processes to create more single-strand DNA. This increases the number of single-strand DNA regions that break endemically and activate ATM. In cells with naturally low levels of ATR, we therefore expect ATM, not ATR, to produce a signal that varies with the strength of UV doses.

Since we consider the cell’s UV response to be wholly dependent on ATR, it is not at all expected that ATM would be the protein responsible for distinguishing between lethal and non-lethal amounts of UV damage. This prediction can be tested by exposing ATM-knockout cells to varying doses of UV damage: if these cells showed similar proportions of cell cycle arrest and apoptosis across all dose strengths, it would be in agreement with the model.

4.2. Potential improvements

Spatial properties affect several model components. Chromatin unwinding, DSB focus geometry, and diffusion of regulatory proteins away from the break can only be addressed indirectly in a non-spatial model. In particular, DSB foci may attract more regulatory proteins as they grow, but our model treats increased interaction rates like a switch, which turns on fully when the break has interacted with at least one PIKK-family kinase. Modeling either the three-dimensional focus size or the number of regulatory molecules in the focus would be more realistic, and would also be more mathematically challenging to construct. Lastly, because prolonged signals in response to γ radiation require few complex DSBs, stochastic interactions become more important in the late stage of the cell’s ionizing radiation response.

The experimental papers we use to validate the model represent different cell lines, methodology, and time scales. Often, instead of recording changes in active ATR over time, authors infer ATR activation from its downstream effects, such as Chk1 activation or the prevalence of G2 arrest. This led in some cases to different papers presenting seemingly contradictory claims about ATR activity. Because we base our parameter estimates on data sets across a range of cell types, they do not attempt to quantitatively predict cellular behavior.

Downstream regulatory pathways cause ATM to oscillate in response to γ radiation, and can also cause cell-cycle arrest. In a future work, we will present a continuation of this model that incorporates ATM auto-suppression as part of p53 autoregulatory function.

Table 5.

Comparison of the model results to experimental crosstalk claims.

Source	Claim	Matched by Model?	Notes
(Ray et al. 2013)	Knocking down ATM or ATR does not affect the rate of CPD repair	Yes	Used Fig. 6 for calibration
(DiBiase et al. 2000)	DSB repair is biphasic	Yes	Used Fig. 3 for calibration
(Reynolds etal. 2012)	Inhibiting ATM slows complex DSB repair by a factor of 3.5	Yes
(Jazayeri et al. 2006)	Both ATM and ATR localize to DSBs within 10 min	Yes
(Jazayeri et al. 2006)	Downstream ATR targets are only activated by γ radiation in S/G2 phase	Yes	ATR targets are outside the scope of the model; threshold = 400 proteins
(Bakkenist and Kastan 2003)	ATM can robustly respond to as little as 0.4 Gy within 15 min	Yes
(Bakkenist and Kastan 2003)	Active ATM is not detectable 1 hour after 10 J/m2 UV exposure, but is after 5 h	Yes	Non-detectable = fewer than 100 proteins
(Kousholt et al. 2012)	ATR is activated before DSBs undergo extensive resection	Yes
(Gamper et al. 2013)	ATR can be activated by γ radiation in G1 phase	Yes
(Ward et al. 2004)	ATR does not respond to UV damage in G1 phase	Yes	Threshold = 100 proteins
(Stiff et al. 2006)	ATM works downstream of ATR in response to UV damage	Yes
(Tomimatsu et al. 2009)	ATR can localize to DSBs in ATM-deficient cells	Yes
(Myers and Cortez 2006)	ATM- or Mrel 1-deficient cells form fewer ATR foci	Yes
(Kousholt et al. 2012)	Knocking out end resection does not change the initial ATR response to γ radiation	Yes
(Kousholt et al. 2012)	Robust post-γ-radiation ATR response requires end resection	Yes	ATR targets are beyond the scope of the model; threshold = 400 proteins
(Gamper et al. 2013)	ATR focus formation around DSBs depends on ATR kinase activity	Yes
(Ray et al. 2016)	Fewer post-UV ATM/ATR foci form in G1 phase in NER-deficient cells	Yes
(Ray et al. 2016)	NER deficiency does not affect post-UV ATM/ATR activation in S phase	Yes
(Mladenov et al. 2019a)	Inhibiting ATR does not affect post-γ ATM activation during G2 phase	Yes
(Mladenov et al. 2019a)	Inhibiting ATM affects end resection rates during G2 phase	Yes
(Mladenov et al. 2019b)	ATR does not control end resection rates during S phase	Yes
(Mladenov et al. 2019a)	Inhibiting ATR affects end resection rates during G2 phase	No	We do not include downstream effects of ATR on end resection
(Batchelor et al. 2011, 2008)	Wip1 downregulation causes ATM to oscillate in response to γ radiation	No	We do not include downstream feedback loops
(Vrouwe et al. 2011)	NER-deficient cells arrest in G1 phase after UV damage	No	We do not model ssDNA formation in repair-deficient cells