Modeling non-homologous end joining

Kinetics model of DNA double-strand break repair in eukaryotes

This manuscript outlines the kinetics of two main repair pathways of DNA double-strand break (DSB) in eukaryotes: non-homologous end joining (NHEJ) and homologous recombination repair (HRR). In this review, we discuss the precise study of recruitment kinetics of repair proteins based on the latest technologies in the past two decades. Then we simulate the theoretical description of the DNA repair process by mathematical models. In our study, the consecutive reactions chain (CRC) model and continuous-time random walk (CTRW) model have been unified by us, so that we can obtain the function of the number of intermediates with time in the same framework of equations, overcome the incompatibility between the two models. On this basis, we propose a data fitting workflow using these both models. Finally, we give an overview of different real-time quantitative methods and the new mechanism complexity that can be found from the corresponding dynamic models.

Mathematical Model of ATM Activation and Chromatin Relaxation by Ionizing Radiation

We propose a comprehensive mathematical model to study the dynamics of ionizing radiation induced Ataxia-telangiectasia mutated (ATM) activation that consists of ATM activation through dual mechanisms: the initiative activation pathway triggered by the DNA damage-induced local chromatin relaxation and the primary activation pathway consisting of a self-activation loop by interplay with chromatin relaxation. The model is expressed as a series of biochemical reactions, governed by a system of differential equations and analyzed by dynamical systems techniques. Radiation induced double strand breaks (DSBs) cause rapid local chromatin relaxation, which is independent of ATM but initiates ATM activation at damage sites. Key to the model description is how chromatin relaxation follows when active ATM phosphorylates KAP-1, which subsequently spreads throughout the chromatin and induces global chromatin relaxation. Additionally, the model describes how oxidative stress activation of ATM triggers a self-activation loop in which PP2A and ATF2 are released so that ATM can undergo autophosphorylation and acetylation for full activation in relaxed chromatin. In contrast, oxidative stress alone can partially activate ATM because phosphorylated ATM remains as a dimer. The model leads to predictions on ATM mediated responses to DSBs, oxidative stress, or both that can be tested by experiments.

A Stochastic Model of DNA Double-Strand Breaks Repair Throughout the Cell Cycle

Cell cycle phase is a decisive factor in determining the repair pathway of DNA double-strand breaks (DSBs) by non-homologous end joining (NHEJ) or homologous recombination (HR). Recent experimental studies revealed that 53BP1 and BRCA1 are the key mediators of the DNA damage response (DDR) with antagonizing roles in choosing the appropriate DSB repair pathway in G1, S, and G2 phases. Here, we present a stochastic model of biochemical kinetics involved in detecting and repairing DNA DSBs induced by ionizing radiation during the cell cycle progression. A three-dimensional stochastic process is defined to monitor the cell cycle phase and DSBs repair at times after irradiation. To estimate the model parameters, a Metropolis Monte Carlo method is applied to perform maximum likelihood estimation utilizing the kinetics of γ-H2AX and RAD51 foci formation in G1, S, and G2 phases. The recruitment of DSB repair proteins is verified by comparing our model predictions with the corresponding experimental data on human cells after exposure to X and γ-radiation. Furthermore, the interaction between 53BP1 and BRCA1 is simulated for G1 and S/G2 phases determining the competition between NHEJ and HR pathways in repairing induced DSBs throughout the cell cycle. In accordance with recent biological data, the numerical results demonstrate that the maximum proportion of HR occurs in S phase cells and the high level of NHEJ takes place in G1 and G2 phases. Moreover, the stochastic realizations of the total yield of simple and complex DSBs ligation are compared for G1 and S/G2 damaged cells. Finally, the proposed stochastic model is validated when DSBs induced by different particle radiation such as iron, silicon, oxygen, proton, and carbon.

Modeling the interplay between DNA-PK, Artemis, and ATM in non-homologous end-joining repair in G1 phase of the cell cycle

Modeling a biological process equips us with more comprehensive insight into the process and a more advantageous experimental design. Non-homologous end joining (NHEJ) is a major double-strand break (DSB) repair pathway that occurs throughout the cell cycle. The objective of the current work is to model the fast and slow phases of NHEJ in G1 phase of the cell cycle following exposure to ionizing radiation (IR). The fast phase contains the major components of NHEJ; Ku70/80 complex, DNA-dependent protein kinase catalytic subunit (DNA-PKcs), and XLF/XRCC4/ligase IV complex (XXL). The slow phase in G1 phase of the cell cycle is associated with more complex lesions and involves ATM and Artemis proteins in addition to the major components. Parameters are mainly obtained from experimental data. The model is successful in predicting the kinetics of DSB foci in 13 normal, ATM-deficient, and Artemis-deficient mammalian fibroblast cell lines in G1 phase of the cell cycle after exposure to low doses of IR. The involvement of ATM provides the model with the potency to be connected to different signaling pathways. Ku70/80 concentration and DNA-binding rate as well as XXL concentration and enzymatic activity are introduced as the best targets for affecting NHEJ DSB repair process. On the basis of the current model, decreasing concentration and DNA binding rate of DNA-PKcs is more effective than inhibiting its activity towards the Artemis protein.

The effect of stochasticity on repair of DNA double strand breaks throughout non-homologous end joining pathway

DNA double strand breaks (DSBs) are the most lethal lesions of DNA induced by ionizing radiation, industrial chemicals and a wide variety of drugs used in chemotherapy. In the context of DNA damage response system modelling, uncertainty may arise in several ways such as number of induced DSBs, kinetic rates and measurement error in observable quantities. Therefore, using the stochastic approaches is imperative to gain further insight into the dynamic behaviour of DSBs repair process. In this article, a continuous-time Markov chain (CTMC) model of the non-homologous end joining (NHEJ) mechanism is formulated according to the DSB complexity. Additionally, a Metropolis Monte Carlo method is used to perform maximum likelihood estimation of the kinetic rate constants. Here, the effects of fluctuating kinetic rates and DSBs induction rate of the NHEJ mechanism are investigated. The stochastic realizations of the total yield of simple and complex DSBs ligation are simulated to compare their asymptotic dynamics. Furthermore, it has been proved that the total yield of DSBs has a normal distribution for sufficiently large number of DSBs. In order to estimate the expected duration of repairing DSBs, the probability distribution of DSBs lifetime is calculated based on the CTMC NHEJ model. Moreover, the variability of total yield of DSBs during constant low-dose radiation is evaluated in the presented model. The findings indicate that in stochastic NHEJ model, when there is no new DSBs induction through the repair process, all DSBs are eventually repaired. However, when DSBs are induced by constant low-dose radiation, a number of DSBs remains un-repaired.

A New Standard DNA Damage (SDD) Data Format

Our understanding of radiation-induced cellular damage has greatly improved over the past few decades. Despite this progress, there are still many obstacles to fully understand how radiation interacts with biologically relevant cellular components, such as DNA, to cause observable end points such as cell killing. Damage in DNA is identified as a major route of cell killing. One hurdle when modeling biological effects is the difficulty in directly comparing results generated by members of different research groups. Multiple Monte Carlo codes have been developed to simulate damage induction at the DNA scale, while at the same time various groups have developed models that describe DNA repair processes with varying levels of detail. These repair models are intrinsically linked to the damage model employed in their development, making it difficult to disentangle systematic effects in either part of the modeling chain. These modeling chains typically consist of track-structure Monte Carlo simulations of the physical interactions creating direct damages to DNA, followed by simulations of the production and initial reactions of chemical species causing so-called "indirect" damages. After the induction of DNA damage, DNA repair models combine the simulated damage patterns with biological models to determine the biological consequences of the damage. To date, the effect of the environment, such as molecular oxygen (normoxic vs. hypoxic), has been poorly considered. We propose a new standard DNA damage (SDD) data format to unify the interface between the simulation of damage induction in DNA and the biological modeling of DNA repair processes, and introduce the effect of the environment (molecular oxygen or other compounds) as a flexible parameter. Such a standard greatly facilitates inter-model comparisons, providing an ideal environment to tease out model assumptions and identify persistent, underlying mechanisms. Through inter-model comparisons, this unified standard has the potential to greatly advance our understanding of the underlying mechanisms of radiation-induced DNA damage and the resulting observable biological effects when radiation parameters and/or environmental conditions change.

Computational analysis of androgen receptor dependent radiosensitivity in prostate cancer

In this study, we quantitatively analyze the mechanism by which androgen deprivation therapy (ADT) is enhancing radiosensitivity in prostate cancer (PCa) patients. It has been shown in laboratory experiments, as well as in patient data in the literature, that the androgen receptor (AR) reduces the effectiveness of ionizing radiation treatment by enhancing the non-homologous end joining (NHEJ) repair of radiation damage. The suppression of AR by ADT suppresses the activity of NHEJ that leads to radiosensitivity in PCa patients. In this paper, we have studied this positive interaction between AR and NHEJ using mathematical models of the NHEJ that we have developed using both the experimental and clinical data for PCa. Our results show that the biological observation of suppression of AR by ADT leading to down-regulation of the first NHEJ protein Ku and NHEJ is a plausible biological mechanism that explains both the experimental and clinical observations in the literature. The presented analysis is the first step in quantitatively analyzing possible treatment scenarios to find the optimal treatment strategies for PCa using the combination treatment with ADT, NHEJ inhibitors, and IR.

An Intrinsically Disordered APLF Links Ku, DNA-PKcs, and XRCC4-DNA Ligase IV in an Extended Flexible Non-homologous End Joining Complex

DNA double-strand break (DSB) repair by non-homologous end joining (NHEJ) in human cells is initiated by Ku heterodimer binding to a DSB, followed by recruitment of core NHEJ factors including DNA-dependent protein kinase catalytic subunit (DNA-PKcs), XRCC4-like factor (XLF), and XRCC4 (X4)-DNA ligase IV (L4). Ku also interacts with accessory factors such as aprataxin and polynucleotide kinase/phosphatase-like factor (APLF). Yet, how these factors interact to tether, process, and ligate DSB ends while allowing regulation and chromatin interactions remains enigmatic. Here, small angle X-ray scattering (SAXS) and mutational analyses show APLF is largely an intrinsically disordered protein that binds Ku, Ku/DNA-PKcs (DNA-PK), and X4L4 within an extended flexible NHEJ core complex. X4L4 assembles with Ku heterodimers linked to DNA-PKcs via flexible Ku80 C-terminal regions (Ku80CTR) in a complex stabilized through APLF interactions with Ku, DNA-PK, and X4L4. Collective results unveil the solution architecture of the six-protein complex and suggest cooperative assembly of an extended flexible NHEJ core complex that supports APLF accessibility while possibly providing flexible attachment of the core complex to chromatin. The resulting dynamic tethering furthermore, provides geometric access of L4 catalytic domains to the DNA ends during ligation and of DNA-PKcs for targeted phosphorylation of other NHEJ proteins as well as trans-phosphorylation of DNA-PKcs on the opposing DSB without disrupting the core ligation complex. Overall the results shed light on evolutionary conservation of Ku, X4, and L4 activities, while explaining the observation that Ku80CTR and DNA-PKcs only occur in a subset of higher eukaryotes.

Genome-based, mechanism-driven computational modeling of risks of ionizing radiation: The next frontier in genetic risk estimation?

Research activity in the field of estimation of genetic risks of ionizing radiation to human populations started in the late 1940s and now appears to be passing through a plateau phase. This paper provides a background to the concepts, findings and methods of risk estimation that guided the field through the period of its growth to the beginning of the 21st century. It draws attention to several key facts: (a) thus far, genetic risk estimates have been made indirectly using mutation data collected in mouse radiation studies; (b) important uncertainties and unsolved problems remain, one notable example being that we still do not know the sensitivity of human female germ cells to radiation-induced mutations; and (c) the concept that dominated the field thus far, namely, that radiation exposures to germ cells can result in single gene diseases in the descendants of those exposed has been replaced by the concept that radiation exposure can cause DNA deletions, often involving more than one gene. Genetic risk estimation now encompasses work devoted to studies on DNA deletions induced in human germ cells, their expected frequencies, and phenotypes and associated clinical consequences in the progeny. We argue that the time is ripe to embark on a human genome-based, mechanism-driven, computational modeling of genetic risks of ionizing radiation, and we present a provisional framework for catalyzing research in the field in the 21st century.

Modeling damage complexity-dependent non-homologous end-joining repair pathway

Non-homologous end joining (NHEJ) is the dominant DNA double strand break (DSB) repair pathway and involves several repair proteins such as Ku, DNA-PKcs, and XRCC4. It has been experimentally shown that the choice of NHEJ proteins is determined by the complexity of DSB. In this paper, we built a mathematical model, based on published data, to study how NHEJ depends on the damage complexity. Under an appropriate set of parameters obtained by minimization technique, we can simulate the kinetics of foci track formation in fluorescently tagged mammalian cells, Ku80-EGFP and DNA-PKcs-YFP for simple and complex DSB repair, respectively, in good agreement with the published experimental data, supporting the notion that simple DSB undergo fast repair in a Ku-dependent, DNA-PKcs-independent manner, while complex DSB repair requires additional DNA-PKcs for end processing, resulting in its slow repair, additionally resulting in slower release rate of Ku and the joining rate of complex DNA ends. Based on the numerous experimental descriptions, we investigated several models to describe the kinetics for complex DSB repair. An important prediction of our model is that the rejoining of complex DSBs is through a process of synapsis formation, similar to a second order reaction between ends, rather than first order break filling/joining. The synapsis formation (SF) model allows for diffusion of ends before the synapsis formation, which is precluded in the first order model by the rapid coupling of ends. Therefore, the SF model also predicts the higher number of chromosomal aberrations observed with high linear energy transfer (LET) radiation due to the higher proportion of complex DSBs compared to low LET radiation, and an increased probability of misrejoin following diffusion before the synapsis is formed, while the first order model does not provide a mechanism for the increased effectiveness in chromosomal aberrations observed.

Deducing Underlying Mechanisms from Protein Recruitment Data

By using fluorescent labelling techniques, the distribution and dynamics of proteins can be measured within living cells, allowing to study in vivo the response of cells to a triggering event, such as DNA damage. In order to evaluate the reaction rate constants and to identify the proteins and reactions that are essential for the investigated process, mechanistic models are used, which often contain many proteins and associated parameters and are therefore underdetermined by the data. In order to establish criteria for assessing the significance of a model, we present here a systematic investigation of the information that can be reliably deduced from protein recruitment data, assuming that the complete set of reactions that affect the data of the considered protein species is not known. To this purpose, we study in detail models where one or two proteins that influence each other are recruited to a substrate. We show that in many cases the kind of interaction between the proteins can be deduced by analyzing the shape of the recruitment curves of one protein. Furthermore, we discuss in general in which cases it is possible to discriminate between different models and in which cases it is impossible based on the data. Finally, we argue that if different models fit experimental data equally well, conducting experiments with different protein concentrations would allow discrimination between the alternative models in many cases.

DNA and cellular effects of charged particles

Development of new radiotherapy strategies based on the use of hadrons, as well as reduction of uncertainties associated with radiation health risk during long-term space flights, requires increasing knowledge of the mechanisms underlying the biological effects of charged particles. It is well known that charged particles are more effective in damaging biological systems than photons. This capability has been related to the production of spatially correlated and/or clustered DNA damage, in particular two or more double-strand breaks (DSB) in close proximity or DSB associated with other lesions within a localized DNA region. These kinds of complex damages are rarely induced by photons. They are difficult to repair accurately and are therefore expected to produce severe consequences at the cellular level. This paper provides a review of radiation-induced cellular effects and will discuss the dependence of cell death and mutation induction on the linear energy transfer of various light and heavy ions. This paper will show the inadequacy of a single physical parameter for describing radiation quality, underlining the importance of the characteristics of the track structure at the submicrometer level to determine the biological effects. This paper will give a description of the physical properties of the track structure that can explain the differences in the spatial distributions of DNA damage, in particular DSB, induced by radiation of different qualities. In addition, this paper will show how a combined experimental and theoretical approach based on Monte Carlo simulations can be useful for providing information on the damage distribution at the nanoscale level. It will also emphasize the importance, especially for DNA damage evaluation at low doses, of the more recent functional approaches based on the use of fluorescent antibodies against proteins involved in the cellular processing of DNA damage. Advantages and limitations of the different experimental techniques will be discussed with particular emphasis on the still unsolved problem of the clustered DNA damage resolution. Development of biophysical models aimed to describe the kinetics of the DNA repair process is underway, and it is expected to support the experimental investigation of the mechanisms underlying the cellular radiation response.

A stochastic model of DNA fragments rejoining

When cells are exposed to ionizing radiation, DNA damages in the form of single strand breaks (SSBs), double strand breaks (DSBs), base damage or their combinations are frequent events. It is known that the complexity and severity of DNA damage depends on the quality of radiation, and the microscopic dose deposited in small segments of DNA, which is often related to the linear transfer energy (LET) of the radiation. Experimental studies have suggested that under the same dose, high LET radiation induces more small DNA fragments than low-LET radiation, which affects Ku efficiently binding with DNA end and might be a main reason for high-LET radiation induced RBE [1] since DNA DSB is a major cause for radiation-induced cell death. In this work, we proposed a mathematical model of DNA fragments rejoining according to non-homologous end joining (NHEJ) mechanism. By conducting Gillespie's stochastic simulation, we found several factors that impact the efficiency of DNA fragments rejoining. Our results demonstrated that aberrant DNA damage repair can result predominantly from the occurrence of a spatial distribution of DSBs leading to short DNA fragments. Because of the low efficiency that short DNA fragments recruit repair protein and release the protein residue after fragments rejoining, Ku-dependent NHEJ is significantly interfered with short fragments. Overall, our work suggests that inhibiting the Ku-dependent NHEJ may significantly contribute to the increased efficiency for cell death and mutation observed for high LET radiation.

Spatial and temporal organization of multi-protein assemblies: achieving sensitive control in information-rich cell-regulatory systems

The regulation of cellular processes in living organisms requires signalling systems that have a high signal-to-noise ratio. This is usually achieved by transient, multi-protein complexes that assemble cooperatively. Even in the crowded environment of the cell, such assemblies are unlikely to form by chance, thereby providing a sensitive regulation of cellular processes. Furthermore, selectivity and sensitivity may be achieved by the requirement for concerted folding and binding of previously unfolded components. We illustrate these features by focusing on two essential signalling pathways of eukaryotic cells: first, the monitoring and repair of DNA damage by non-homologous end joining, and second, the mitotic spindle assembly checkpoint, which detects and corrects defective attachments of chromosomes to the kinetochore. We show that multi-protein assemblies moderate the full range of functional complexity and diversity in the two signalling systems. Deciphering the nature of the interactions is central to understanding the mechanisms that control the flow of information in cell signalling and regulation.