BACKGROUND
dna damage is of profound biomedical interest, as this type of lesions largely contributes to cancerogenesis  <cit> .
dna damage is induced by environmental factors, like ionizing radiation  <cit> , but also by intrinsic agents, like metabolically generated reactive oxygen species  <cit> .
damaged dna becomes bound by so-called sensor proteins, like replication protein a  or a complex composed of meiotic recombination  <dig>  - radiation  <dig>  - nijmegen breakage syndrome  <dig>  .
they trigger a complex network of signal transduction pathways designated as ddr  <cit> .
the ddr causes temporal cell cycle arrest, if the level of dna damage is low, so the cell can repair it  <cit> .
in response to severe dna damage, cells undergo apoptosis to avoid transformation into tumour cells  <cit> .
alternatively, the cells enter permanent cell cycle arrest, called senescence  <cit> .
in presence of dna damage, the tumour suppressor p <dig> plays a key role in the decision between survival and death of the cell.
activated p <dig> either induces cell cycle arrest or apoptosis, mainly by activation of distinct target genes  <cit> .
as shown in biochemical and network modelling studies, p <dig> levels oscillate in response to dna damage caused by ionizing radiation.
the p53-dependent expression of wild-type p53-induced phosphatase  <dig>  and murine double minute  <dig>  mediates the oscillations  <cit> .
whereas wip <dig> is essential for the generation of oscillations, mdm <dig> mediates their fine tuning  <cit> .
the duration of the oscillations was proposed to determine, whether p <dig> acts pro-apoptotic or not  <cit> .
however, apoptosis can be counteracted by activation of nf-κb, the main anti-apoptotic transcription factor in the ddr.
posttranslational modifications of nf-κb essential modulator  exert an important role in the signal transduction that links dna damage in the nucleus with activation of nf-κb in the cytoplasm  <cit> .
whether dsbs trigger stable oscillations of nf-κb on the level of single cells has not been shown.
ssbs and dsbs are the most lethal types of dna damage  <cit> .
they can be triggered by ionizing radiation or topoisomerase inhibitors, as therapeutically applied to eliminate tumour cells.
usually, higher proliferation rates of tumour cells render them more susceptible to dna damage induced apoptosis than normal cells  <cit> .
the efficiency of dna damaging therapies can be potentiated by blocking cell survival pathways in tumour cells   <cit> .
a strategy to sensitize tumours to dna damaging agents is adjuvant abolishment of cycle arrest, resulting in necrosis or apoptosis-like cell death by mitotic catastrophy  <cit> .
other important sensitization targets are components that contribute to nf-κb activation, which otherwise often impedes efficient elimination of cancer cells  <cit> .
however, most tumour cells have a defective ddr  <cit> .
such molecular defects due to mutations within tumours can be exploited to selectively sensitize tumours to therapy.
inhibitions that result in cell death only in combination with a molecular defect in targeted tumour cells would predominantly eliminate the tumour.
corresponding proteins are thus ideal drug targets  <cit> .
based on a network modelling approach following this strategy, inhibition targets that sensitize p53-deficient tumours to dna damaging treatment were found  <cit> .
despite the high clinical relevance of the ddr, the interplay of the signal transduction involved herein is poorly understood, particularly due to high complexity.
therefore, systems biology approaches are of high value to gain deeper insights.
quantitative modelling requires both, detailed knowledge of kinetic parameters and high computational power.
therefore, such approaches are suitable to model rather small signal transduction modules.
qualitative models provide a better basis for the representation and analysis of large-scale signal transduction networks.
particularly discrete logical modelling is a powerful tool to address important issues, such as detection of network-wide functional interdependencies, identification of intervention targets and predictions on the network dynamics  <cit> .
for instance, a literature-based boolean model has been used to identify cellular myelocytomatosis oncogene  as a putative therapeutic target to treat breast cancer  <cit> .
we previously identified putative therapeutic targets in signal transduction pathways induced by the pathogen helicobacter pylori <cit> .
with a boolean model of the ddr, we predicted candidate targets to abolish nf-κb activation, while leaving apoptotic pathways unaffected.
the latter targets might be suitable to sensitize carcinomas to dsbs-inducing therapeutics by promoting apoptosis  <cit> .
a literature-based boolean model of t cell large granular lymphocyte  leukemia has been used to identify potential therapeutic targets and to investigate the dynamics of the signal transduction underlying this disease  <cit> .
signal transduction emanating from the death receptor has been studied with a discrete logical model.
after inactivating certain proteins, the fraction of pathways that lead to a particular cell fate  has been determined in dynamical analyses  <cit> .
here, we present a comprehensive discrete logical model of the response to ssbs and dsbs based on published experimental data.
our dynamical analysis provided new insights into the regulation of p <dig> and nf-κb in the ddr.
we identified candidate target molecules to sensitize tumour cells to dna damaging therapeutics.
by failure mode analysis, we predicted mutations that might contribute to the formation of carcinomas and validated our model with data from published studies.
RESULTS
logical model of the ddr
based on quality-controlled literature data, we built a discrete logical model of the response to ssbs and dsbs in human epithelial cells.
the model encompasses  <dig> regulatory components, connected by  <dig> interactions.
it is represented by a logical interaction hypergraph , and a list of logical functions describing the interactions .
the numbers assigned to interactions in figure  <dig> correspond to the numbers of the logical functions.
the network shows the typical structure of signal transduction networks: the input layer is given by stimuli, which damage the dna, from where signals are being transmitted to and processed in the intermediate layer, finally reaching the output layer .
we chose ‘onset of apoptosis’ instead of ‘apoptosis’ as an output, as this output corresponds to the beginning of apoptotic processes, but not to completion of apoptosis, ie.
cell death.
the activity levels of most regulatory components  are represented by boolean state variables, i.e.
they can only attain the values ‘0’  or ‘1’ .
ternary  variables were only assigned to phosphorylated ataxia telangiectasia mutated , phosphorylated inhibitor of kappa b kinase  and inhibitor of kappa b α .
in that way, we took account for the fact that each of those components differs in its functions, depending on whether its activity is low  or high .
specifically, a low activity of atm  is required for inactivation of the atm phosphatase protein phosphatase  <dig> a   <cit>  .
once pp2a is inactivated, dsbs can induce high activity of atm , which is now able to phosphorylate further substrates  <cit>  .
similarly, the ikk complex has a low basal activity , which is sufficient for partial degradation of iκbα , leading to activation of proto-oncogene c-rel  in absence of induced dna damage  <cit>  .
upon induction of dna damage, the ikk complex attains high activity , which enables more degradation of iκbα , enabling the activation of the nf-κb dimers p50-p65-p and p50-p <dig>  <cit>  .
for some structural analyses, we took account for the limited knowledge of time-dependent signal transmission by assigning each interaction to one of three time scale values.
interactions composing the signal transduction pathways leading to activation/inactivation of components that are directly linked to the components “cell cycle arrest” or “onset of apoptosis” were assigned to time scale value  <dig>  as long as literature data did not indicate a distinct delay.
examples of components that are directly linked to “cell cycle arrest” or “onset of apoptosis” are the transcription factors.
time scale value  <dig> was assigned to interactions that also lead to cell cycle arrest, apoptosis, or anti-apoptosis, but were shown to occur distinctively later than interactions of time scale value  <dig>  for example, p53-induced protein with a death domain  binds to nemo , and later, pidd binds to rip1-associated ich-1/ced- <dig> homologous protein with a death domain    <cit> .
time scale value  <dig> was also assigned to interactions linked directly to the regulatory components “cell cycle arrest” or “onset of apoptosis”.
activation of proteins that initiate switching off parts of the ddr was assigned time scale value  <dig>  this was based on the assumption that these events occur during the latest phase of the ddr.
for instance, wip <dig> interrupts signal transduction pathways by dephosphorylating atm and other proteins  <cit>  .
accordingly, induction of wip <dig> expression  <cit>   has been assigned to time scale value  <dig>  detailed information on assignments of time scale values are given in additional file 1: table s <dig>  for most analyses, we simulated the ddr at time scale value  <dig>  i.e., at a time before feedback inhibition comes into play.
our study focused on inhibitions and molecular defects interfering with cell cycle arrest, apoptosis, or anti-apoptosis.
as follows from the considerations above, only time scale value  <dig> pertains to maximum activity of all components promoting cell cycle arrest, apoptosis, or anti-apoptosis.
hence, for this time scale value, the sensitivity of the simulation results to changes in time scales of interactions should be minimal.
for dynamical analyses, we took account for the knowledge of time-dependent signal transmission by defining three priority classes .
validation of the predictive quality of the model
in order to validate the predictive quality of our model, we evaluated simulations on the basis of published studies on epithelial cells .
we inactivated certain proteins in the model and then calculated the logical steady state of the model at time scale value ‘2’, i.e.
prior to onset of negative feedback inhibition.
cells can be sensitized to dna damaging therapy by events that promote cell death  <cit> .
blockage of cell cycle arrest can cause mitotic catastrophy, a form of cell death  <cit> , whereas blocking of the anti-apoptotic transcription factor nf-κb promotes apoptosis  <cit> .
inactivation of atm blocked all pro-survival pathways  in the response to dsbs.
this is confirmed by studies in which atm inhibition sensitizes cells to agents causing dsbs  <cit> .
ataxia telangiectasia and rad3-related protein  inactivation blocked two pathways leading to cell cycle arrest  in response to ssbs in our model.
this is in agreement with the reported potentiation of ssbs-induced cell death by atr inactivation in carcinoma cells  <cit> .
in our simulation of the response to ssbs, loss of checkpoint kinase  <dig>  blocked one of two pathways promoting cell division cycle  <dig> a  degradation.
degradation of cdc25a leads to cell cycle arrest.
additionally blocked was one pathway leading to activation of p <dig>  a pro-apoptotic and cell cycle arresting protein.
thus, loss of chk <dig> suppressed pathways leading to cell cycle arrest and apoptosis.
hence, our results do not indicate, whether chk <dig> inhibition sensitizes cells to ssbs inducers.
chk <dig> inhibition was demonstrated to increase the cytotoxicity to topoisomerase i  inhibitors by diminishing cell cycle arrest in carcinoma cells with functional p <dig>  <cit> .
as previously proposed, a partial suppression of p <dig> activation diminishes predominantly its apoptotic function and to a lesser extent its cell cycle arresting function  <cit> .
this effect might contribute to the sensitization by chk <dig> inhibition, but is not captured by the model.
in response to ionizing radiation, absence of chk <dig> in our model blocked cell cycle arresting phosphorylation of cdc25c, and one of two pathways leading to degradation of cdc25a.
on the other hand, activation of the pro-apoptotic effectors promyelocytic leukemia   and phosphorylated adenovirus e <dig> gene promoter region binding factor  <dig> , and one p <dig> activating pathway are blocked.
hence, the numbers of both, cell cycle arresting and apoptotic pathways were reduced.
the simulation did not indicate, whether chk <dig> inhibition confers sensitization or protection from cell death caused by ionizing radiation.
in most studies, chk <dig> inhibition diminished cell death caused by ionizing radiation  <cit> .
correspondingly, chk <dig> knockdown protects mia paca- <dig> carcinoma cells against ionizing radiation  <cit> .
when simulating the response to camptothecin  in the model, inhibition of tgf-β activated kinase  <dig>  abolished two cell cycle arresting pathways .
hence, the model indicates a sensitizing effect of tak <dig> knockdown, which was demonstrated in carcinoma cell lines treated with camptothecin  <cit> .
moreover, putative therapeutic targets for the sensitization of tumours with dysfunctional p <dig> have been proposed .
we compared the response to the topoisomerase ii  inhibitor doxorubicin in absence of p <dig> only with the response in absence of p <dig> and atm.
in the absence of only p <dig>  four cell survival pathways were still active, i.e.
activation of anti-apoptotic nf-κb, cell cycle arrest induced by c-myc downregulation, cyclin-dependent kinase  <dig>  inhibition, and phosphorylation of cdc25c.
when p <dig> and atm were absent, no cell survival pathway was activated by doxorubicin in the model.
accordingly, the atm inhibitor ku- <dig> sensitizes p53-deficient human carcinoma cells to doxorubicin.
moreover, p53-deficient breast and lung tumours showed higher sensitivity to genotoxic chemotherapy when atm is inactive as well  <cit> .
in the p53-deficient model, topi inhibitors still induced cell cycle arrest.
additional loss of chk <dig> abolished one of the pathways leading to degradation of cdc25a, a phosphatase necessary for cell cycle progression.
apoptotic pathways in p53-deficient cells were not suppressed by inactivation of chk <dig>  hence, our model indicated that p53-deficient cells might be sensitized to ssbs inducers by inhibition of chk <dig>  indeed, the aforementioned sensitization to topi inhibitors by chk <dig> inhibition was reported to be more pronounced when p <dig> is dysfunctional  <cit> .
accordingly, preclinical studies support the combination of chk <dig> inhibitors with ssbs inducers particularly for treatment of p53-deficient tumours  <cit> .
in the model, inactivation of chk <dig> in absence of p <dig> reduced the number of cell cycle arresting and pro-apoptotic pathways.
the sensitivity of tumours with dysfunctional p <dig> to dsb-causing agents was reported to be potentiated by inactivation of chk <dig>  <cit> .
in contrast, another study showed no pronounced potentiation of cell death by chk <dig> inhibition in carcinoma cells with a loss of function mutation in p <dig>  <cit> .
as suggested by our simulations, whether chk <dig> inhibition potentiates cell death caused by dsbs might depend on the genetic background, providing a possible explanation for the conflicting experimental data.
in summary, our simulations recapitulated most published studies on the sensitivity of carcinoma cells to dna damaging agents after inactivation of a certain protein.
these results support the suitability of the model for the generation of predictions.
network-wide interdependencies
network-wide causal relationships between all pairs of regulatory components are displayed in the dependency matrix .
two components have a causal relationship, if a sequence of adjacent components, a pathway, links them.
as the large fraction of yellow matrix elements in figure  <dig> illustrates, in most causal relationships between two components i and ji is an ambivalent factor for j. in other words, i has an activating as well as an inhibiting influence on another component j. usually, the activating influence becomes operational at another time scale than the inhibiting influence.
atm for instance phosphorylates, i.e.
has an activating influence on chk <dig>  <cit>  .
however, atm phosphorylates p <dig> as well  <cit>  , leading to expression of wip <dig> later   <cit>  .
wip <dig> in turn deactivates chk <dig> by means of dephosphorylation  <cit>  .
therefore, the activation of chk <dig> by atm is counteracted by the atm-dependent deactivation of chk <dig> by wip <dig>  thus, atm is an ambivalent factor for chk <dig>  as the yellow matrix element in figure  <dig> indicates.
as the high frequency of coincidences of activating and inhibiting relationships indicates, most pathways become inactivated in a later phase of the ddr.
moreover, these coincidences suggest an important role of crosstalk in the ddr.
dynamics of the ddr
feed-forward loops  and feedback loops  can play decisive roles in the processing of the signals, which are being transmitted in signal transduction networks.
moreover, they may profoundly influence the dynamics  of a signal transduction network  <cit> .
for these reasons, we identified ffls .
they appear in two groups, those with ‘and gates’ and those with ‘or gates’.
for example, ‘and gated’ is the activation of sumoylated and phosphorylated ikkϵ  by ikkϵ-p and pml-p , as ikkϵ-s-p activation requires both proteins, i.e.
ikkϵ-p and pml-p. ‘or gated’ is for instance the activation of p53-p by either atm-p or chk2-p , as either atm-p or chk2-p phosphorylates p <dig>
coherent ffls of type  <dig> with ‘and gates’ may delay the transmission of activating signals  <cit> .
such ffls in the model are shown in figure 3a-e. coherent ffls of type  <dig> can have the same function  <cit> ; they are shown in figure 3s-Ä.
as also reported by mangan and alon  <cit> , transmission of the fade away of signals  in a pathway could be delayed by coherent type  <dig> ffls with ‘or gate’ , by coherent type  <dig> ffls with ‘and’ gate , as well as by the coherent type  <dig> ffls .
incoherent type  <dig> ffls with ‘and gate’ may accelerate the transmission of ‘off’ signals  <cit> .
we found only one example .
in summary, all but one  ffls identified may delay either ‘on’ or ‘off’ signals, thereby transmitting only long-term signals.
moreover, we found that most of these ffls include either p <dig>  or its regulators.
taken together, short-term signals arising from noise rather than from dna damage might be filtered out.
the same regards signals arising from minor damage of dna, which becomes rapidly repaired.
only long-term signals from more severe dna damage would be transmitted to and activate p <dig>  such a careful regulation seems reasonable in light of the well-known key role of p <dig> in determining cell fate  after dna damage.
indeed, such a regulation of the actelyation of p <dig> involving so far unknown ffls has been proposed  <cit> ; our results provide evidence for a regulation of p <dig> phosphorylation by only long term signals and provide candidate ffls for that mechanism.
as we found moreover, the ffl in figure 3a might delay ‘on’ signals transmitted to ikkϵ-s-p. similarly, the ffls in figure 3z and Ä could delay ‘on’ signal transmission to the ikk complex.
in both cases, short-term signals could be filtered out.
ikkϵ-s-p and the ikk complex mediate activation of nf-κb.
similarly to the mentioned control of p <dig>  such a careful regulation of nf-κb seems reasonable in light of its mayor role in counteracting apoptosis.
next, we identified fls that are functional in the logical model .
all of them are negative.
the presence of a negative fl is necessary for stable oscillations  <cit> .
again, most fls  contain p <dig>  whereas the fl in figure 3g contains the nf-κb dimer p50-p <dig>  in the latter fl, nf-κb drives the expression of its own inhibitor iκbα.
this fl was shown to cause oscillatory behaviour of nf-κb in a multitude of cells and treatment conditions  <cit> .
also the fls in figure 3a-c have been studied previously with ordinary differential equation or stochastic models as well as experimentally in cells exposed to ionizing radiation  <cit> .
in a logical approach, effects of varied  degradation rates of mdm <dig>   transcriptional activities of p <dig>  and  dna damage levels on the dynamic behaviour of the mdm2-p <dig> circuit has been studied.
it has been shown that variations in parameter values  can lead to only four different scenarios of dynamical behaviour of the network  <cit> .
recently, the feedback-controlled oscillations of p <dig> were proposed to impact the ultimate cell fate decision  <cit> .
as our results suggest, the negative fls in figure 3d-f might cause oscillations of p <dig> levels in vivo as well.
in order to study the terminal fate  of the network, we reduced it to a model with conserved attractors.
previously, a method has been proposed to reduce boolean models to their functional interactions.
however, this method is only applicable to models of intermediate dimension   <cit> .
therefore, we used a different network reduction technique, which is applicable to large-scale models .
the reduced model contains only the regulatory components dsbs early, dsbs late, rpa-atr-atrip-p, atm-p, p53-p and nf-κb  .
we calculated the state transition graph of the reduced model by using an asynchronous updating schedule with three priority classes.
the state transitions that were assigned to priority classes  <dig>   <dig>  and  <dig> coincide with the interactions of time scale values  <dig>   <dig>  and  <dig>  respectively.
hence, state transitions involving activations of rpa-atr-atrip-p, atm-p, p53-p or nuclear nf-κb were assigned to priority class 1; priority class  <dig> embraces the subsequent state transitions leading to activation of ‘dsbs late’ by ‘dsbs early’.
state transitions coinciding with the initiation of the inactivation of signal transduction pathways, i.e., the downregulation of rpa-atr-atrip-p, atm-p, p53-p and nf-κb, constitute priority class  <dig>
we emphasize that the attractors of the model variants correspond to the fate of the ddr before the cell either completes dna repair or dies.
in response to dsbs, the model  finally enters a complex cyclic attractor .
this suggests the cellular network might transit through an intertwined cycle of states before completion of either dna repair or apoptosis.
negative feedbacks are necessary for cyclic attractors  <cit> .
we thus aimed to elucidate in more detail the roles of the identified feedbacks  in generating the cyclic attractor.
for this purpose, we calculated state transition graphs for model variants with interrupted feedbacks.
models with constitutively active nf-κb  or deficiency of p53-p  still enter cyclic attractors .
similarly, the model variant with deficiency of nf-κb enters a cyclic attractor as well .
in contrast, the model variant with both p53-deficiency and constitutively active nf-κb  enters a logical steady state .
even constitutive activation of only p53-p is sufficient to direct the network into a logical steady state .
the network reduction we applied can lead to loss of trajectories in the stg.
therefore, not every trajectory in the stg of the full model might have a counterpart in the stg of the reduced model  <cit> .
consequently, the reduced model variant’s attractors we identified might be different from those of the full model variants .
therefore, we checked for each of the five reduced model variant’s attractors , whether it is equivalent to the attractor of the corresponding full model variant.
in general, any attractor is either a logical steady state or a cyclic  attractor  <cit> .
whereas we were able to identify the logical steady states of the full model variants, their state spaces are too big to identify cyclic attractors.
therefore, if a full model variant has no logical steady state, we inferred the presence of a cyclic attractor.
the identified logical steady states are independent of the updating scheme applied  <cit> , and therefore, insensitive to changes in the priority classes.
as our aim now was only to check for the type of attractor , there was no need to specify priority classes.
as we found, neither the wildtype full model, nor its variant with constitutively active nf-κb or deficiency of p53-p enter a logical steady state .
hence, these full model variants should enter cyclic attractors; the results are in agreement with the identified cyclic attractors of the corresponding reduced model variants .
the full model variants with both p53-deficiency and constitutively active nf-κb  as well as the full model variant with constitutively activative p53-p  enter logical steady states.
again, the results agree with the results from the analyses of the reduced model counterparts .
in addition, none of the full model variants contains a functional positive fl ; thus, this necessary condition for bi- or multistability  <cit>  is not fulfilled.
therefore, each full model variant possesses only a single attractor.
again, our results coincide with the finding that each reduced model variant possesses only a single attractor.
we conclude that all attractors of the reduced model variants correspond to those of the full model variants.
both, the results gained from the analyses of the attractors and the identified functional fls independently suggest an essential role of p <dig> and nf-κb in the generation of cyclic attractors of the ddr.
this and the prevalence of p <dig>  and nf-κb in the ffls support the importance of these proteins in governing the dynamics of the ddr.
candidate target proteins for sensitization of carcinomas to therapies
to identify putative targets for sensitization of carcinomas to therapy, we simulated treatments with agents causing ssbs  or only dsbs .
p <dig>  homeo-domain interacting protein kinase  <dig> , atm or chk <dig> are frequently mutated and inactive in carcinoma cells  <cit> , therefore, we simulated treatment with inhibitors of topi or topii in the absence of these proteins.
in order to simulate the behaviour of the network before the onset of feedback inhibition, we chose the time scale value ‘2’ of the model.
we calculated minimal intervention sets of targets, whose inhibition might sensitize tumours by fulfilling three intervention goals:  blocking cell cycle arrest,  blocking activation of anti-apoptotic nf-κb, and  keeping at least one pathway activating ‘onset of apoptosis’ intact.
in presence of  severe dna damage inhibitors that fill out goal  would eliminate tumour cells by mitotic catastrophy, and inhibitors fulfilling goals  and  would potentiate apoptosis.
we identified  <dig> sets of molecular targets that could sensitize tumour cells to therapies inducing ssbs or dsbs , and protein sets containing putatively less suitable targets .
atm deficiency in the model already fulfils the intervention goals in presence of dsbs.
hence, we found no sensitization target for such conditions.
this result agrees with most studies, showing that atm inhibition sensitizes cells to therapeutics causing dsbs  <cit> .
accordingly, cells isolated from ataxia telangiectasia  patients show enhanced radiosensitivity  <cit> .
for certain sets, inhibitions of the target proteins might specifically sensitize tumour cells with the indicated mutation, but allow normal cells to survive by entering cell cycle arrest .
* sets of targets whose inhibition might specifically sensitize tumor cells with the indicated mutation, but allow normal cells to survive by entering cell cycle arrest.
some predicted target sets include atr or chk <dig>  which beside their contributions to the ddr are essential for proliferation.
nevertheless, partial and transient inhibition of atr or chk <dig> during dna damage diminishes cell cycle arrest rather than proliferation  <cit> .
additionally, some protein target sets that sensitize chk2-deficient tumours include p <dig>  although p <dig> can promote apoptosis, it mediates predominantly cell cycle arrest in chk2-deficient tumours, resulting in tumour cell survival  <cit> .
correspondingly, p <dig> inhibition might sensitize certain tumours to therapeutic treatment  <cit> .
hence, inhibition of p <dig> in chk2-deficient cells seems reasonable.
taken together, we predict putative protein target sets that might sensitize tumours carrying certain mutations to therapeutic interventions.
our candidate target sets in table  <dig> include all published sensitization targets in tables  <dig> and  <dig>  however, with the exception of atm, inhibiting the published sensitization targets in tables  <dig> and  <dig>  blocks only part of the cell survival pathways of the model in tumours containing certain mutations.
in contrast, our proposed target sets  might block all cell survival pathways of the model in tumours containing certain mutations.
hence, our candidate targets might sensitize tumours to dna damaging therapeutics with higher efficiency.
simulation of genetic disorders
next, we aimed to enlighten the ddr in genetic diseases.
for this purpose we inactivated in our model the protein whose defect causes a given disease.
then, we simulated the response to ssbs and dsbs simultaneously at time scale value ‘2’, and evaluated our in silico results based on published data.
for investigations of the feedback control of the ddr, we simulated at time scale value ‘3’ .
the disease ataxia telangiectasia  has been associated with defects in the activation of p <dig>  g1/s, intra-s, and g2/s cell cycle checkpoints, genomic instability, enhanced radiosensitivity and increased incidence of lymphoid tumours  <cit> .
in our simulation, loss of atm blocked p <dig> activation and p <dig> expression, resulting in abolished cell cycle arrest by these proteins.
additionally, the cell cycle promoting protein c-myc became expressed, and abolished another cell cycle arrest pathway.
cell cycle checkpoint defects are known to contribute to genomic instability, which promotes tumorigenesis  <cit> , and increased cell death by mitotic catastrophy  <cit> .
the abolished activation of nf-κb in the model might further promote apoptosis, although p53-dependent apoptosis was blocked as well.
moreover, in absence of atm we identified in our model the loss of many signalling pathways involved in the regulation of p <dig> and nf-κb target genes.
ataxia telagiectasia-like-disorder  is also associated with defective induction of cell cycle arrest, genomic instability, and enhanced radiosensitivity  <cit> .
as mre <dig> in the model is a subunit of the mrn complex, which solely activates atm, the blocked pathways are the same as in the ataxia telangiectasia simulation.
the same is true for nijmegen breakage syndrome , as in the model also nbs <dig> is only a mrn complex subunit.
nijmegen breakage syndrome has moreover been reported to diminish dna repair  <cit> .
however, dna damage induced cell cycle arrest promotes dna repair  <cit> .
hence, the abolishment of cell cycle arrest by p <dig> phosphorylation, p <dig> expression, and c-myc downregulation in the simulation might contribute to lost repair capabilities.
moreover, breast cancer  <dig>  early onset  is essential for homologous recombination repair of dsbs  <cit> .
atm-dependent phosphorylation of brca <dig> is averted by loss of nbs <dig> in the model, possibly further contributing to dna repair deficiencies.
also rad <dig> in the model is a subunit of the mrn complex, which solely activates atm.
hence, the pathways blocked in nijmegen breakage syndrome-like disorder   <cit>  are identical to those in the ataxia telangiectasia simulation.
a reduction of the atr level causes atr-seckel syndrome.
hence, atr-dependent phosphorylations of chk <dig> and p <dig> are diminished, whereas atm-dependent responses to ionizing radiation remain intact.
there is no pronounced radiosensitivity, and no enhanced incidence of cancer  <cit> .
in line with this report, atr inactivation in the model did not affect atm-dependent signalling induced by ionizing radiation.
instead, atr-deficiency abolished cell cycle arrest mediated by p <dig> expression and c-myc downregulation in the model.
however, these cell cycle arresting pathways could still be active in presence of an atr level as low as in atr-seckel syndrome cells.
molecular defects putatively contributing to carcinogenesis
ddr defects that diminish apoptosis and cell cycle arrest are well known to contribute to carcinogenesis by promoting uncontrolled proliferation  <cit> .
we aimed to identify putatively relevant malfunctions in the ddr in epithelial cells.
for this purpose, we simulated the response to both ssbs and dsbs simultaneously.
again, we chose the time scale value ‘2’ of the model.
by calculating minimal intervention sets, we identified protein defects .
from our search, we excluded activations and inactivations that according to literature data might counteract uncontrolled proliferation .
by doing so, we accounted for protein functions being relevant to carcinogenesis, but are not captured by the model.
each row gives an alternative combination of relevant defects .
here,  <cit>  means inactive;  <cit> : constitutive active at level ‘1’;  <cit> : constitutively active at level ‘2’.
among the results are inactivities of the known or suspected tumour suppressors atm, the mrn complex subunit nbs <dig>  fragile histidin triad gene , p <dig>  brca <dig>  as well as chk <dig>  and activities of the known oncogene mdm <dig>  <cit> .
in  <dig> combinations, the nf-κb dimer p50-p <dig> was found to be constitutively active, as frequently observed in tumours  <cit> .
carcinogenesis might also be promoted by constitutive active iκbα or the ikk complex .
alternatively, constitutive active iκbα or the ikk complex may promote carcinogenesis in combination with other molecules .
to our knowledge, most of the putative carcinogenic mutations we found have not been implicated in tumorigenesis previously.
this gap of knowledge could be explained by ‘low penetrance genes’ assumed to confer cancer susceptibility or resistance  <cit> .
these were proposed to act in combination in a dosage-dependent manner to incrementally determine cancer predisposition.
a major obstacle to their identification is the vast number of possible combinations of mutations to be tackled experimentally  <cit> .
however, our results may provide a valuable preselection for follow-up experiments.
it is important to note that the identified mutations might cause cell death by mitotic catastrophy only in response to severe dna damage, as it is induced in cancer therapies.
in contrast, in response to low levels of dna damage, which is compatible with cell survival, the defects might promote tumorigenesis by enabling uncontrolled proliferation.
such limited dna damage is caused permanently by cellular insults, like reactive oxygen species generated in metabolic processes  <cit> .
CONCLUSIONS
we presented a comprehensive logical model of the ddr including the dynamics of p <dig> and nf-κb regulation in human epithelial tumours.
the large scale of the model and the implementation of posttranslational protein modifications allowed us to account for extensive crosstalk among signal transduction pathways.
our analyses enlightened the dynamics of the ddr and functional consequences of defects underlying cancerogenesis, but also hereditary genetic diseases.
we identified candidate target proteins suitable for sensitization of epithelial tumours with different mutations to chemo- and radiotherapy, thus, our predicted target proteins provide a basis for follow up studies to demonstrate their therapeutic usefulness.
overall, the results reflect an approach to facilitate a holistic view on the ddr in health and disease.
an important aim of further work is the inclusion of more quantitative data into the model.
this would allow to recapitulate observations that lower levels of dna damage predominantly induce temporary cell cycle arrest and dna repair, whereas higher levels of dna damage mainly cause apoptosis.

 dna damage is of profound biomedical interest, as this type of lesions largely contributes to cancerogenesis. dna damage is induced by environmental factors, like ionizing radiation, but also by intrinsic agents, like metabolically generated reactive oxygen species. damaged dna becomes bound by so-called sensor proteins, like replication protein a or a complex composed of meiotic recombination - radiation - nijmegen breakage syndrome. they trigger a complex network of signal transduction pathways designated as ddr. the ddr causes temporal cell cycle arrest, if the level of dna damage is low, so the cell can repair it. in response to severe dna damage, cells undergo apoptosis to avoid transformation into tumour cells. alternatively, the cells enter permanent cell cycle arrest, called senescence. in presence of dna damage, the tumour suppressor p plays a key role in the decision between survival and death of the cell. activated p either induces cell cycle arrest or apoptosis, mainly by activation of distinct target genes. as shown in biochemical and network modelling studies, p levels oscillate in response to dna damage caused by ionizing radiation. the p53-dependent expression of wild-type p53-induced phosphatase and murine double minute mediates the oscillations. whereas wip is essential for the generation of oscillations, mdm mediates their fine tuning. the duration of the oscillations was proposed to determine, whether p acts pro-apoptotic or not. however, apoptosis can be counteracted by activation of nf-κb, the main anti-apoptotic transcription factor in the ddr. posttranslational modifications of nf-κb essential modulator exert an important role in the signal transduction that links dna damage in the nucleus with activation of nf-κb in the cytoplasm. whether dsbs trigger stable oscillations of nf-κb on the level of single cells has not been shown. ssbs and dsbs are the most lethal types of dna damage. they can be triggered by ionizing radiation or topoisomerase inhibitors, as therapeutically applied to eliminate tumour cells. usually, higher proliferation rates of tumour cells render them more susceptible to dna damage induced apoptosis than normal cells. the efficiency of dna damaging therapies can be potentiated by blocking cell survival pathways in tumour cells. a strategy to sensitize tumours to dna damaging agents is adjuvant abolishment of cycle arrest, resulting in necrosis or apoptosis-like cell death by mitotic catastrophy. other important sensitization targets are components that contribute to nf-κb activation, which otherwise often impedes efficient elimination of cancer cells. however, most tumour cells have a defective ddr. such molecular defects due to mutations within tumours can be exploited to selectively sensitize tumours to therapy. inhibitions that result in cell death only in combination with a molecular defect in targeted tumour cells would predominantly eliminate the tumour. corresponding proteins are thus ideal drug targets. based on a network modelling approach following this strategy, inhibition targets that sensitize p53-deficient tumours to dna damaging treatment were found. despite the high clinical relevance of the ddr, the interplay of the signal transduction involved herein is poorly understood, particularly due to high complexity. therefore, systems biology approaches are of high value to gain deeper insights. quantitative modelling requires both, detailed knowledge of kinetic parameters and high computational power. therefore, such approaches are suitable to model rather small signal transduction modules. qualitative models provide a better basis for the representation and analysis of large-scale signal transduction networks. particularly discrete logical modelling is a powerful tool to address important issues, such as detection of network-wide functional interdependencies, identification of intervention targets and predictions on the network dynamics. for instance, a literature-based boolean model has been used to identify cellular myelocytomatosis oncogene as a putative therapeutic target to treat breast cancer. we previously identified putative therapeutic targets in signal transduction pathways induced by the pathogen helicobacter pylori. with a boolean model of the ddr, we predicted candidate targets to abolish nf-κb activation, while leaving apoptotic pathways unaffected. the latter targets might be suitable to sensitize carcinomas to dsbs-inducing therapeutics by promoting apoptosis. a literature-based boolean model of t cell large granular lymphocyte leukemia has been used to identify potential therapeutic targets and to investigate the dynamics of the signal transduction underlying this disease. signal transduction emanating from the death receptor has been studied with a discrete logical model. after inactivating certain proteins, the fraction of pathways that lead to a particular cell fate has been determined in dynamical analyses. here, we present a comprehensive discrete logical model of the response to ssbs and dsbs based on published experimental data. our dynamical analysis provided new insights into the regulation of p and nf-κb in the ddr. we identified candidate target molecules to sensitize tumour cells to dna damaging therapeutics. by failure mode analysis, we predicted mutations that might contribute to the formation of carcinomas and validated our model with data from published studies.  logical model of the ddr based on quality-controlled literature data, we built a discrete logical model of the response to ssbs and dsbs in human epithelial cells. the model encompasses regulatory components, connected by interactions. it is represented by a logical interaction hypergraph, and a list of logical functions describing the interactions. the numbers assigned to interactions in figure correspond to the numbers of the logical functions. the network shows the typical structure of signal transduction networks: the input layer is given by stimuli, which damage the dna, from where signals are being transmitted to and processed in the intermediate layer, finally reaching the output layer. we chose ‘onset of apoptosis’ instead of ‘apoptosis’ as an output, as this output corresponds to the beginning of apoptotic processes, but not to completion of apoptosis, ie. cell death. the activity levels of most regulatory components are represented by boolean state variables, i.e. they can only attain the values ‘0’ or ‘1’. ternary variables were only assigned to phosphorylated ataxia telangiectasia mutated, phosphorylated inhibitor of kappa b kinase and inhibitor of kappa b α. in that way, we took account for the fact that each of those components differs in its functions, depending on whether its activity is low or high. specifically, a low activity of atm is required for inactivation of the atm phosphatase protein phosphatase a. once pp2a is inactivated, dsbs can induce high activity of atm, which is now able to phosphorylate further substrates. similarly, the ikk complex has a low basal activity, which is sufficient for partial degradation of iκbα, leading to activation of proto-oncogene c-rel in absence of induced dna damage. upon induction of dna damage, the ikk complex attains high activity, which enables more degradation of iκbα, enabling the activation of the nf-κb dimers p50-p65-p and p50-p. for some structural analyses, we took account for the limited knowledge of time-dependent signal transmission by assigning each interaction to one of three time scale values. interactions composing the signal transduction pathways leading to activation/inactivation of components that are directly linked to the components “cell cycle arrest” or “onset of apoptosis” were assigned to time scale value as long as literature data did not indicate a distinct delay. examples of components that are directly linked to “cell cycle arrest” or “onset of apoptosis” are the transcription factors. time scale value was assigned to interactions that also lead to cell cycle arrest, apoptosis, or anti-apoptosis, but were shown to occur distinctively later than interactions of time scale value for example, p53-induced protein with a death domain binds to nemo, and later, pidd binds to rip1-associated ich-1/ced- homologous protein with a death domain. time scale value was also assigned to interactions linked directly to the regulatory components “cell cycle arrest” or “onset of apoptosis”. activation of proteins that initiate switching off parts of the ddr was assigned time scale value this was based on the assumption that these events occur during the latest phase of the ddr. for instance, wip interrupts signal transduction pathways by dephosphorylating atm and other proteins. accordingly, induction of wip expression has been assigned to time scale value detailed information on assignments of time scale values are given in additional file 1: table s for most analyses, we simulated the ddr at time scale value i.e., at a time before feedback inhibition comes into play. our study focused on inhibitions and molecular defects interfering with cell cycle arrest, apoptosis, or anti-apoptosis. as follows from the considerations above, only time scale value pertains to maximum activity of all components promoting cell cycle arrest, apoptosis, or anti-apoptosis. hence, for this time scale value, the sensitivity of the simulation results to changes in time scales of interactions should be minimal. for dynamical analyses, we took account for the knowledge of time-dependent signal transmission by defining three priority classes. validation of the predictive quality of the model in order to validate the predictive quality of our model, we evaluated simulations on the basis of published studies on epithelial cells. we inactivated certain proteins in the model and then calculated the logical steady state of the model at time scale value ‘2’, i.e. prior to onset of negative feedback inhibition. cells can be sensitized to dna damaging therapy by events that promote cell death. blockage of cell cycle arrest can cause mitotic catastrophy, a form of cell death, whereas blocking of the anti-apoptotic transcription factor nf-κb promotes apoptosis. inactivation of atm blocked all pro-survival pathways in the response to dsbs. this is confirmed by studies in which atm inhibition sensitizes cells to agents causing dsbs. ataxia telangiectasia and rad3-related protein inactivation blocked two pathways leading to cell cycle arrest in response to ssbs in our model. this is in agreement with the reported potentiation of ssbs-induced cell death by atr inactivation in carcinoma cells. in our simulation of the response to ssbs, loss of checkpoint kinase blocked one of two pathways promoting cell division cycle a degradation. degradation of cdc25a leads to cell cycle arrest. additionally blocked was one pathway leading to activation of p a pro-apoptotic and cell cycle arresting protein. thus, loss of chk suppressed pathways leading to cell cycle arrest and apoptosis. hence, our results do not indicate, whether chk inhibition sensitizes cells to ssbs inducers. chk inhibition was demonstrated to increase the cytotoxicity to topoisomerase i inhibitors by diminishing cell cycle arrest in carcinoma cells with functional p. as previously proposed, a partial suppression of p activation diminishes predominantly its apoptotic function and to a lesser extent its cell cycle arresting function. this effect might contribute to the sensitization by chk inhibition, but is not captured by the model. in response to ionizing radiation, absence of chk in our model blocked cell cycle arresting phosphorylation of cdc25c, and one of two pathways leading to degradation of cdc25a. on the other hand, activation of the pro-apoptotic effectors promyelocytic leukemia and phosphorylated adenovirus e gene promoter region binding factor, and one p activating pathway are blocked. hence, the numbers of both, cell cycle arresting and apoptotic pathways were reduced. the simulation did not indicate, whether chk inhibition confers sensitization or protection from cell death caused by ionizing radiation. in most studies, chk inhibition diminished cell death caused by ionizing radiation. correspondingly, chk knockdown protects mia paca- carcinoma cells against ionizing radiation. when simulating the response to camptothecin in the model, inhibition of tgf-β activated kinase abolished two cell cycle arresting pathways. hence, the model indicates a sensitizing effect of tak knockdown, which was demonstrated in carcinoma cell lines treated with camptothecin. moreover, putative therapeutic targets for the sensitization of tumours with dysfunctional p have been proposed. we compared the response to the topoisomerase ii inhibitor doxorubicin in absence of p only with the response in absence of p and atm. in the absence of only p four cell survival pathways were still active, i.e. activation of anti-apoptotic nf-κb, cell cycle arrest induced by c-myc downregulation, cyclin-dependent kinase inhibition, and phosphorylation of cdc25c. when p and atm were absent, no cell survival pathway was activated by doxorubicin in the model. accordingly, the atm inhibitor ku- sensitizes p53-deficient human carcinoma cells to doxorubicin. moreover, p53-deficient breast and lung tumours showed higher sensitivity to genotoxic chemotherapy when atm is inactive as well. in the p53-deficient model, topi inhibitors still induced cell cycle arrest. additional loss of chk abolished one of the pathways leading to degradation of cdc25a, a phosphatase necessary for cell cycle progression. apoptotic pathways in p53-deficient cells were not suppressed by inactivation of chk hence, our model indicated that p53-deficient cells might be sensitized to ssbs inducers by inhibition of chk indeed, the aforementioned sensitization to topi inhibitors by chk inhibition was reported to be more pronounced when p is dysfunctional. accordingly, preclinical studies support the combination of chk inhibitors with ssbs inducers particularly for treatment of p53-deficient tumours. in the model, inactivation of chk in absence of p reduced the number of cell cycle arresting and pro-apoptotic pathways. the sensitivity of tumours with dysfunctional p to dsb-causing agents was reported to be potentiated by inactivation of chk. in contrast, another study showed no pronounced potentiation of cell death by chk inhibition in carcinoma cells with a loss of function mutation in p. as suggested by our simulations, whether chk inhibition potentiates cell death caused by dsbs might depend on the genetic background, providing a possible explanation for the conflicting experimental data. in summary, our simulations recapitulated most published studies on the sensitivity of carcinoma cells to dna damaging agents after inactivation of a certain protein. these results support the suitability of the model for the generation of predictions. network-wide interdependencies network-wide causal relationships between all pairs of regulatory components are displayed in the dependency matrix. two components have a causal relationship, if a sequence of adjacent components, a pathway, links them. as the large fraction of yellow matrix elements in figure illustrates, in most causal relationships between two components i and ji is an ambivalent factor for j. in other words, i has an activating as well as an inhibiting influence on another component j. usually, the activating influence becomes operational at another time scale than the inhibiting influence. atm for instance phosphorylates, i.e. has an activating influence on chk. however, atm phosphorylates p as well, leading to expression of wip later. wip in turn deactivates chk by means of dephosphorylation. therefore, the activation of chk by atm is counteracted by the atm-dependent deactivation of chk by wip thus, atm is an ambivalent factor for chk as the yellow matrix element in figure indicates. as the high frequency of coincidences of activating and inhibiting relationships indicates, most pathways become inactivated in a later phase of the ddr. moreover, these coincidences suggest an important role of crosstalk in the ddr. dynamics of the ddr feed-forward loops and feedback loops can play decisive roles in the processing of the signals, which are being transmitted in signal transduction networks. moreover, they may profoundly influence the dynamics of a signal transduction network. for these reasons, we identified ffls. they appear in two groups, those with ‘and gates’ and those with ‘or gates’. for example, ‘and gated’ is the activation of sumoylated and phosphorylated ikkϵ by ikkϵ-p and pml-p, as ikkϵ-s-p activation requires both proteins, i.e. ikkϵ-p and pml-p. ‘or gated’ is for instance the activation of p53-p by either atm-p or chk2-p, as either atm-p or chk2-p phosphorylates p coherent ffls of type with ‘and gates’ may delay the transmission of activating signals. such ffls in the model are shown in figure 3a-e. coherent ffls of type can have the same function; they are shown in figure 3s-Ä. as also reported by mangan and alon, transmission of the fade away of signals in a pathway could be delayed by coherent type ffls with ‘or gate’, by coherent type ffls with ‘and’ gate, as well as by the coherent type ffls. incoherent type ffls with ‘and gate’ may accelerate the transmission of ‘off’ signals. we found only one example. in summary, all but one ffls identified may delay either ‘on’ or ‘off’ signals, thereby transmitting only long-term signals. moreover, we found that most of these ffls include either p or its regulators. taken together, short-term signals arising from noise rather than from dna damage might be filtered out. the same regards signals arising from minor damage of dna, which becomes rapidly repaired. only long-term signals from more severe dna damage would be transmitted to and activate p such a careful regulation seems reasonable in light of the well-known key role of p in determining cell fate after dna damage. indeed, such a regulation of the actelyation of p involving so far unknown ffls has been proposed; our results provide evidence for a regulation of p phosphorylation by only long term signals and provide candidate ffls for that mechanism. as we found moreover, the ffl in figure 3a might delay ‘on’ signals transmitted to ikkϵ-s-p. similarly, the ffls in figure 3z and Ä could delay ‘on’ signal transmission to the ikk complex. in both cases, short-term signals could be filtered out. ikkϵ-s-p and the ikk complex mediate activation of nf-κb. similarly to the mentioned control of p such a careful regulation of nf-κb seems reasonable in light of its mayor role in counteracting apoptosis. next, we identified fls that are functional in the logical model. all of them are negative. the presence of a negative fl is necessary for stable oscillations. again, most fls contain p whereas the fl in figure 3g contains the nf-κb dimer p50-p in the latter fl, nf-κb drives the expression of its own inhibitor iκbα. this fl was shown to cause oscillatory behaviour of nf-κb in a multitude of cells and treatment conditions. also the fls in figure 3a-c have been studied previously with ordinary differential equation or stochastic models as well as experimentally in cells exposed to ionizing radiation. in a logical approach, effects of varied degradation rates of mdm transcriptional activities of p and dna damage levels on the dynamic behaviour of the mdm2-p circuit has been studied. it has been shown that variations in parameter values can lead to only four different scenarios of dynamical behaviour of the network. recently, the feedback-controlled oscillations of p were proposed to impact the ultimate cell fate decision. as our results suggest, the negative fls in figure 3d-f might cause oscillations of p levels in vivo as well. in order to study the terminal fate of the network, we reduced it to a model with conserved attractors. previously, a method has been proposed to reduce boolean models to their functional interactions. however, this method is only applicable to models of intermediate dimension. therefore, we used a different network reduction technique, which is applicable to large-scale models. the reduced model contains only the regulatory components dsbs early, dsbs late, rpa-atr-atrip-p, atm-p, p53-p and nf-κb. we calculated the state transition graph of the reduced model by using an asynchronous updating schedule with three priority classes. the state transitions that were assigned to priority classes and coincide with the interactions of time scale values and respectively. hence, state transitions involving activations of rpa-atr-atrip-p, atm-p, p53-p or nuclear nf-κb were assigned to priority class 1; priority class embraces the subsequent state transitions leading to activation of ‘dsbs late’ by ‘dsbs early’. state transitions coinciding with the initiation of the inactivation of signal transduction pathways, i.e., the downregulation of rpa-atr-atrip-p, atm-p, p53-p and nf-κb, constitute priority class we emphasize that the attractors of the model variants correspond to the fate of the ddr before the cell either completes dna repair or dies. in response to dsbs, the model finally enters a complex cyclic attractor. this suggests the cellular network might transit through an intertwined cycle of states before completion of either dna repair or apoptosis. negative feedbacks are necessary for cyclic attractors. we thus aimed to elucidate in more detail the roles of the identified feedbacks in generating the cyclic attractor. for this purpose, we calculated state transition graphs for model variants with interrupted feedbacks. models with constitutively active nf-κb or deficiency of p53-p still enter cyclic attractors. similarly, the model variant with deficiency of nf-κb enters a cyclic attractor as well. in contrast, the model variant with both p53-deficiency and constitutively active nf-κb enters a logical steady state. even constitutive activation of only p53-p is sufficient to direct the network into a logical steady state. the network reduction we applied can lead to loss of trajectories in the stg. therefore, not every trajectory in the stg of the full model might have a counterpart in the stg of the reduced model. consequently, the reduced model variant’s attractors we identified might be different from those of the full model variants. therefore, we checked for each of the five reduced model variant’s attractors, whether it is equivalent to the attractor of the corresponding full model variant. in general, any attractor is either a logical steady state or a cyclic attractor. whereas we were able to identify the logical steady states of the full model variants, their state spaces are too big to identify cyclic attractors. therefore, if a full model variant has no logical steady state, we inferred the presence of a cyclic attractor. the identified logical steady states are independent of the updating scheme applied, and therefore, insensitive to changes in the priority classes. as our aim now was only to check for the type of attractor, there was no need to specify priority classes. as we found, neither the wildtype full model, nor its variant with constitutively active nf-κb or deficiency of p53-p enter a logical steady state. hence, these full model variants should enter cyclic attractors; the results are in agreement with the identified cyclic attractors of the corresponding reduced model variants. the full model variants with both p53-deficiency and constitutively active nf-κb as well as the full model variant with constitutively activative p53-p enter logical steady states. again, the results agree with the results from the analyses of the reduced model counterparts. in addition, none of the full model variants contains a functional positive fl; thus, this necessary condition for bi- or multistability is not fulfilled. therefore, each full model variant possesses only a single attractor. again, our results coincide with the finding that each reduced model variant possesses only a single attractor. we conclude that all attractors of the reduced model variants correspond to those of the full model variants. both, the results gained from the analyses of the attractors and the identified functional fls independently suggest an essential role of p and nf-κb in the generation of cyclic attractors of the ddr. this and the prevalence of p and nf-κb in the ffls support the importance of these proteins in governing the dynamics of the ddr. candidate target proteins for sensitization of carcinomas to therapies to identify putative targets for sensitization of carcinomas to therapy, we simulated treatments with agents causing ssbs or only dsbs. p homeo-domain interacting protein kinase, atm or chk are frequently mutated and inactive in carcinoma cells, therefore, we simulated treatment with inhibitors of topi or topii in the absence of these proteins. in order to simulate the behaviour of the network before the onset of feedback inhibition, we chose the time scale value ‘2’ of the model. we calculated minimal intervention sets of targets, whose inhibition might sensitize tumours by fulfilling three intervention goals: blocking cell cycle arrest, blocking activation of anti-apoptotic nf-κb, and keeping at least one pathway activating ‘onset of apoptosis’ intact. in presence of severe dna damage inhibitors that fill out goal would eliminate tumour cells by mitotic catastrophy, and inhibitors fulfilling goals and would potentiate apoptosis. we identified sets of molecular targets that could sensitize tumour cells to therapies inducing ssbs or dsbs, and protein sets containing putatively less suitable targets. atm deficiency in the model already fulfils the intervention goals in presence of dsbs. hence, we found no sensitization target for such conditions. this result agrees with most studies, showing that atm inhibition sensitizes cells to therapeutics causing dsbs. accordingly, cells isolated from ataxia telangiectasia patients show enhanced radiosensitivity. for certain sets, inhibitions of the target proteins might specifically sensitize tumour cells with the indicated mutation, but allow normal cells to survive by entering cell cycle arrest. * sets of targets whose inhibition might specifically sensitize tumor cells with the indicated mutation, but allow normal cells to survive by entering cell cycle arrest. some predicted target sets include atr or chk which beside their contributions to the ddr are essential for proliferation. nevertheless, partial and transient inhibition of atr or chk during dna damage diminishes cell cycle arrest rather than proliferation. additionally, some protein target sets that sensitize chk2-deficient tumours include p although p can promote apoptosis, it mediates predominantly cell cycle arrest in chk2-deficient tumours, resulting in tumour cell survival. correspondingly, p inhibition might sensitize certain tumours to therapeutic treatment. hence, inhibition of p in chk2-deficient cells seems reasonable. taken together, we predict putative protein target sets that might sensitize tumours carrying certain mutations to therapeutic interventions. our candidate target sets in table include all published sensitization targets in tables  and however, with the exception of atm, inhibiting the published sensitization targets in tables  and blocks only part of the cell survival pathways of the model in tumours containing certain mutations. in contrast, our proposed target sets might block all cell survival pathways of the model in tumours containing certain mutations. hence, our candidate targets might sensitize tumours to dna damaging therapeutics with higher efficiency. simulation of genetic disorders next, we aimed to enlighten the ddr in genetic diseases. for this purpose we inactivated in our model the protein whose defect causes a given disease. then, we simulated the response to ssbs and dsbs simultaneously at time scale value ‘2’, and evaluated our in silico results based on published data. for investigations of the feedback control of the ddr, we simulated at time scale value ‘3’. the disease ataxia telangiectasia has been associated with defects in the activation of p g1/s, intra-s, and g2/s cell cycle checkpoints, genomic instability, enhanced radiosensitivity and increased incidence of lymphoid tumours. in our simulation, loss of atm blocked p activation and p expression, resulting in abolished cell cycle arrest by these proteins. additionally, the cell cycle promoting protein c-myc became expressed, and abolished another cell cycle arrest pathway. cell cycle checkpoint defects are known to contribute to genomic instability, which promotes tumorigenesis, and increased cell death by mitotic catastrophy. the abolished activation of nf-κb in the model might further promote apoptosis, although p53-dependent apoptosis was blocked as well. moreover, in absence of atm we identified in our model the loss of many signalling pathways involved in the regulation of p and nf-κb target genes. ataxia telagiectasia-like-disorder is also associated with defective induction of cell cycle arrest, genomic instability, and enhanced radiosensitivity. as mre in the model is a subunit of the mrn complex, which solely activates atm, the blocked pathways are the same as in the ataxia telangiectasia simulation. the same is true for nijmegen breakage syndrome, as in the model also nbs is only a mrn complex subunit. nijmegen breakage syndrome has moreover been reported to diminish dna repair. however, dna damage induced cell cycle arrest promotes dna repair. hence, the abolishment of cell cycle arrest by p phosphorylation, p expression, and c-myc downregulation in the simulation might contribute to lost repair capabilities. moreover, breast cancer early onset is essential for homologous recombination repair of dsbs. atm-dependent phosphorylation of brca is averted by loss of nbs in the model, possibly further contributing to dna repair deficiencies. also rad in the model is a subunit of the mrn complex, which solely activates atm. hence, the pathways blocked in nijmegen breakage syndrome-like disorder are identical to those in the ataxia telangiectasia simulation. a reduction of the atr level causes atr-seckel syndrome. hence, atr-dependent phosphorylations of chk and p are diminished, whereas atm-dependent responses to ionizing radiation remain intact. there is no pronounced radiosensitivity, and no enhanced incidence of cancer. in line with this report, atr inactivation in the model did not affect atm-dependent signalling induced by ionizing radiation. instead, atr-deficiency abolished cell cycle arrest mediated by p expression and c-myc downregulation in the model. however, these cell cycle arresting pathways could still be active in presence of an atr level as low as in atr-seckel syndrome cells. molecular defects putatively contributing to carcinogenesis ddr defects that diminish apoptosis and cell cycle arrest are well known to contribute to carcinogenesis by promoting uncontrolled proliferation. we aimed to identify putatively relevant malfunctions in the ddr in epithelial cells. for this purpose, we simulated the response to both ssbs and dsbs simultaneously. again, we chose the time scale value ‘2’ of the model. by calculating minimal intervention sets, we identified protein defects. from our search, we excluded activations and inactivations that according to literature data might counteract uncontrolled proliferation. by doing so, we accounted for protein functions being relevant to carcinogenesis, but are not captured by the model. each row gives an alternative combination of relevant defects. here, means inactive;: constitutive active at level ‘1’;: constitutively active at level ‘2’. among the results are inactivities of the known or suspected tumour suppressors atm, the mrn complex subunit nbs fragile histidin triad gene, p brca as well as chk and activities of the known oncogene mdm. in combinations, the nf-κb dimer p50-p was found to be constitutively active, as frequently observed in tumours. carcinogenesis might also be promoted by constitutive active iκbα or the ikk complex. alternatively, constitutive active iκbα or the ikk complex may promote carcinogenesis in combination with other molecules. to our knowledge, most of the putative carcinogenic mutations we found have not been implicated in tumorigenesis previously. this gap of knowledge could be explained by ‘low penetrance genes’ assumed to confer cancer susceptibility or resistance. these were proposed to act in combination in a dosage-dependent manner to incrementally determine cancer predisposition. a major obstacle to their identification is the vast number of possible combinations of mutations to be tackled experimentally. however, our results may provide a valuable preselection for follow-up experiments. it is important to note that the identified mutations might cause cell death by mitotic catastrophy only in response to severe dna damage, as it is induced in cancer therapies. in contrast, in response to low levels of dna damage, which is compatible with cell survival, the defects might promote tumorigenesis by enabling uncontrolled proliferation. such limited dna damage is caused permanently by cellular insults, like reactive oxygen species generated in metabolic processes.  we presented a comprehensive logical model of the ddr including the dynamics of p and nf-κb regulation in human epithelial tumours. the large scale of the model and the implementation of posttranslational protein modifications allowed us to account for extensive crosstalk among signal transduction pathways. our analyses enlightened the dynamics of the ddr and functional consequences of defects underlying cancerogenesis, but also hereditary genetic diseases. we identified candidate target proteins suitable for sensitization of epithelial tumours with different mutations to chemo- and radiotherapy, thus, our predicted target proteins provide a basis for follow up studies to demonstrate their therapeutic usefulness. overall, the results reflect an approach to facilitate a holistic view on the ddr in health and disease. an important aim of further work is the inclusion of more quantitative data into the model. this would allow to recapitulate observations that lower levels of dna damage predominantly induce temporary cell cycle arrest and dna repair, whereas higher levels of dna damage mainly cause apoptosis. 
the genome is continuously attacked by a variety of agents that cause dna damage. recognition of dna lesions activates the cellular dna damage response, which comprises a network of signal transduction pathways to maintain genome integrity. in response to severe dna damage, cells undergo apoptosis to avoid transformation into tumour cells, or alternatively, the cells enter permanent cell cycle arrest, called senescence. for therapeutic purposes dna damage signalling processes are induced to induce apoptosis in tumour cells. our comprehensive discrete logical model provided new insights into the dynamics of the ddr in human epithelial tumours. however, the efficiency of radio- and chemotherapy is strongly hampered by cell survival pathways in tumour cells. further, we enlightened the ddr in different genetic diseases, and by failure mode analysis we defined molecular defects putatively contributing to carcinogenesis. most tumour cells have defects in pathways leading to dna repair or apoptosis. in this study logical modelling was performed to facilitate understanding of the complexity of the signal transduction networks in the ddr and to provide cancer treatment options. topoisomerase inhibitorssignal transductioncell cycle arrestapoptosiscancerlogical model despite the high clinical relevance, the interplay of the ddr pathways is poorly understood. simulating therapeutic intervention by agents causing dna single-strand breaks or dna double-strand breaks we identified candidate target proteins for sensitization of carcinomas to therapeutic intervention. by logic modelling we identified candidate target proteins that could be suitable for radio- and chemotherapy, and contributes to the design of more effective therapies. in addition, apoptosis could be counteracted by nuclear factor kappa b, the main anti-apoptotic transcription factor in the ddr.
 the genome is continuously attacked by a variety of agents that cause dna damage. recognition of dna lesions activates the cellular dna damage response, which comprises a network of signal transduction pathways to maintain genome integrity. in response to severe dna damage, cells undergo apoptosis to avoid transformation into tumour cells, or alternatively, the cells enter permanent cell cycle arrest, called senescence. most tumour cells have defects in pathways leading to dna repair or apoptosis. in addition, apoptosis could be counteracted by nuclear factor kappa b, the main anti-apoptotic transcription factor in the ddr. despite the high clinical relevance, the interplay of the ddr pathways is poorly understood. for therapeutic purposes dna damage signalling processes are induced to induce apoptosis in tumour cells. however, the efficiency of radio- and chemotherapy is strongly hampered by cell survival pathways in tumour cells. in this study logical modelling was performed to facilitate understanding of the complexity of the signal transduction networks in the ddr and to provide cancer treatment options.  our comprehensive discrete logical model provided new insights into the dynamics of the ddr in human epithelial tumours. we identified new mechanisms by which the cell regulates the dynamics of the activation of the tumour suppressor p and nf-κb. simulating therapeutic intervention by agents causing dna single-strand breaks or dna double-strand breaks we identified candidate target proteins for sensitization of carcinomas to therapeutic intervention. further, we enlightened the ddr in different genetic diseases, and by failure mode analysis we defined molecular defects putatively contributing to carcinogenesis.  by logic modelling we identified candidate target proteins that could be suitable for radio- and chemotherapy, and contributes to the design of more effective therapies. topoisomerase inhibitorssignal transductioncell cycle arrestapoptosiscancerlogical model 