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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Modeling Clustered DNA Damage by Ionizing Radiation Using Multinomial Damage Probabilities and Energy Imparted Spectra

Simple and complex clustered DNA damage represent the critical initial damage caused by radiation. In this paper, a multinomial probability model of clustered damage is developed with probabilities dependent on the energy imparted to DNA and surrounding water molecules. The model consists of four probabilities: (A) direct damage of sugar-phosphate moieties leading to SSB, (B) OH− radical formation with subsequent SSB and BD formation, (C) direct damage to DNA bases, and (D) energy imparted to histone proteins and other molecules in a volume not leading to SSB or BD. These probabilities are augmented by introducing probabilities for the relative location of SSB using a ≤10 bp criteria for a double-strand break (DSB) and for the possible success of a radical attack that leads to SSB or BD. Model predictions for electrons, 4He, and 12C ions are compared to the experimental data and show good agreement. Thus, the developed model allows an accurate and rapid computational method to predict simple and complex clustered DNA damage as a function of radiation quality and to explore the resulting challenges to DNA repair.

Biochemistry & Molecular Biology↗
DOE OSTI2024

A goldilocks computational protocol for inhibitor discovery targeting DNA damage responses including replication-repair functions

While many researchers can design knockdown and knockout methodologies to remove a gene product, this is mainly untrue for new chemical inhibitor designs that empower multifunctional DNA Damage Response (DDR) networks. Here, we present a robust Goldilocks (GL) computational discovery protocol to efficiently innovate inhibitor tools and preclinical drug candidates for cellular and structural biologists without requiring extensive virtual screen (VS) and chemical synthesis expertise. By computationally targeting DDR replication and repair proteins, we exemplify the identification of DDR target sites and compounds to probe cancer biology. Our GL pipeline integrates experimental and predicted structures to efficiently discover leads, allowing early-structure and early-testing (ESET) experiments by many laboratories. By employing an efficient VS protocol to examine protein-protein interfaces (PPIs) and allosteric interactions, we identify ligand binding sites beyond active sites, leveraging in silico advances for molecular docking and modeling to screen PPIs and multiple targets. A diverse 3,174 compound ESET library combines Diamond Light Source DSI-poised, Protein Data Bank fragments, and FDA-approved drugs to span relevant chemotypes and facilitate downstream hit evaluation efficiency for academic laboratories. Two VS per library and multiple ranked ligand binding poses enable target testing for several DDR targets. This GL library and protocol can thus strategically probe multiple DDR network targets and identify readily available compounds for early structural and activity testing to overcome bottlenecks that can limit timely breakthrough drug discoveries. By testing accessible compounds to dissect multi-functional DDRs and suggesting inhibitor mechanisms from initial docking, the GL approach may enable more groups to help accelerate discovery, suggest new sites and compounds for challenging targets including emerging biothreats and advance cancer biology for future precision medicine clinical trials.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Integrating chromosome conformation and DNA repair in a computational framework to assess cell radiosensitivity

Objective. The arrangement of chromosomes in the cell nucleus has implications for cell radiosensitivity. The development of new tools to utilize Hi-C chromosome conformation data in nanoscale radiation track structure simulations allows for in silico investigation of this phenomenon. We have developed a framework employing Hi-C-based cell nucleus models in Monte Carlo radiation simulations, in conjunction with mechanistic models of DNA repair, to predict not only the initial radiation-induced DNA damage, but also the repair outcomes resulting from this damage, allowing us to investigate the role chromosome conformation plays in the biological outcome of radiation exposure. Approach. In this study, we used this framework to generate cell nucleus models based on Hi-C data from fibroblast and lymphoblastoid cells and explore the effects of cell type-specific chromosome structure on radiation response. The models were used to simulate external beam irradiation including DNA damage and subsequent DNA repair. The kinetics of the simulated DNA repair were compared with previous results. Main results. We found that the fibroblast models resulted in a higher rate of inter-chromosome misrepair than the lymphoblastoid model, despite having similar amounts of initial DNA damage and total misrepairs for each irradiation scenario. Significance. This framework represents a step forward in radiobiological modeling and simulation allowing for more realistic investigation of radiosensitivity in different types of cells.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Transient histone deacetylase inhibition reveals cell type invariant and specific effects of chromatin decondensation on irradiation response

Radiation therapy plays a prominent role in breast cancer treatment, but the high doses of radiation damage both healthy and cancerous cells. Therefore, additional research is needed into combination therapies that could preferentially radiosensitize cancer cells compared to surrounding healthy tissue without causing deleterious side effects. Histone deacetylase inhibitor drugs (HDACis) have been tested as radiosensitizers in both basic research and clinical trials, but the long exposure time typically used in these treatments and the lack of matched healthy cell controls often leave aspects of their mechanism of action unclear. Here, we show that transient (2 h) trichostatin A (TSA) treatment of cancerous and non-tumorigenic breast epithelial cell lines increases immediate DNA damage and decreases long term cell viability in both cell types at high radiation doses. Transient TSA treatment also causes an increase in DNA damage signals after 5 Gy X-rays in other cancer and healthy cell types: A375 melanoma cells and BJ5-ta fibroblasts. This suggests that chromatin decompaction acts to increase cellular vulnerability to initial DNA damage from high doses of radiation in a cell type independent manner that does not rely on changes to DNA repair pathways caused by longer TSA treatment. However, responses to lower doses of radiation and long term survival are more cell type specific: only MCF7 cells experience an effect of TSA on DNA damage after 1 Gy X-ray radiation while MCF10a cells experience somewhat more evident cell viability effects of combined TSA and radiation treatment long term.

Li, Heng [Biochemistry & Cellular and Molecular Bi↗
DOE OSTI2024

Genome integrity sensing by the broad-spectrum Hachiman antiphage defense complex

Hachiman is a broad-spectrum antiphage defense system of unknown function. We show here that Hachiman is a heterodimeric nuclease-helicase complex, HamAB. HamA, previously a protein of unknown function, is the effector nuclease. HamB is the sensor helicase. HamB constrains HamA activity during surveillance of intact double-stranded DNA (dsDNA). When the HamAB complex detects DNA damage, HamB helicase activity activates HamA, unleashing nuclease activity. Hachiman activation degrades all DNA in the cell, creating "phantom" cells devoid of both phage and host DNA. We demonstrate Hachiman activation in the absence of phage by treatment with DNA-damaging agents, suggesting that Hachiman responds to aberrant DNA states. Phylogenetic similarities between the Hachiman helicase and enzymes from eukaryotes and archaea suggest deep functional symmetries with other important helicases across domains of life.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Dosimetric and biological impact of activity extravasation of radiopharmaceuticals in PET imaging

The increasing use of nuclear medicine and PET imaging has intensified scrutiny of radiotracer extravasation. To our knowledge, this topic is understudied but holds great potential for enhancing our understanding of extravasation in clinical PET imaging. This work aims to (1) quantify the absorbed doses from radiotracer extravasation in PET imaging, both locally at the site of extravasation and with the extravasation location as a source of exposure to bodily organs and (2) assess the biological ramifications within the injection site at the cellular level. A radiation dosimetry simulation was performed using a whole-body 4D Extended Cardiac-Torso (XCAT) phantom embedded in the GATE Monte Carlo platform. A 10-mCi dose of 18 F-FDG was chosen to simulate a typical clinical PET scan scenario, with 10% of the activity extravasated in the antecubital fossa of the right arm of the phantom. The extravasation volume was modeled as a 5.5 mL rectangle in the hypodermal layer of skin. Absorbed dose contributions were calculated for the first two half-lives, assuming biological clearance thereafter. Dose calculations were performed as absorbed doses at the organ and skin levels. Energy deposition was simulated both at the local extravasation site and in multiple organs of interest and converted to absorbed doses based on their respective masses. Each simulation was repeated ten times to estimate Monte Carlo uncertainties. Biological impacts on cells within the extravasated volume were evaluated by randomizing cells and exposing them to a uniform radiation source of 18 F and 68 Ga. Particle types, their energies, and direction cosines were recorded in phase space files using a separate Geant4 simulation to characterize their entry into the nucleus of the cellular volume. Subsequently, the phase space files were imported into the TOPAS-nBio simulation to assess the extent of DNA damage, including double-strand breaks (DSBs) and single-strand breaks (SSBs). Organ-level dosimetric estimations are presented for 18 F and 68 Ga radionuclides in various organs of interest. With 10% extravasation, the hypodermal layer of the skin received the highest absorbed dose of 1.32 ± 0.01 Gy for 18 F and 0.99 ± 0.01 Gy for 68 Ga. The epidermal and dermal layers received absorbed doses of 0.07 ± 0.01 Gy and 0.13 ± 0.01 Gy for 18 F, and 0.14 ± 0.01 Gy and 0.29 ± 0.01 Gy for 68 Ga, respectively. In the extravasated volume, 18 F caused an average absorbed dose per nucleus of 0.17 ± 0.01 Gy, estimated to result in 10.58 ± 0.50 DSBs and 268.11 ± 12.43 SSBs per nucleus. For 68 Ga, the absorbed dose per nucleus was 0.11 ± 0.01 Gy, leading to an estimated 6.49 ± 0.34 DSBs and 161.24 ± 8.12 SSBs per nucleus. Absorbed doses in other organs were on the order of micro-gray (µGy). The likelihood of epidermal erythema resulting from extravasation during PET imaging is low, as the simulated absorbed doses to the epidermis remain below the thresholds that trigger such effects. Moreover, the organ-level absorbed doses were found to be clinically insignificant across various simulated organs. The minimal DNA damage at the extravasation site suggests that long-term harm, such as radiation-induced carcinogenesis, is highly unlikely.

DNA strand breaks↗
DOE OSTI2025

Characterizing and controlling CRISPR repair outcomes in nondividing human cells

Genome editing is poised to revolutionize treatment of genetic diseases, but poor understanding and control of DNA repair outcomes hinders its therapeutic potential. DNA repair is especially understudied in nondividing cells like neurons, limiting the efficiency and precision of genome editing in many clinically relevant tissues. Here, we address this barrier by using induced pluripotent stem cells (iPSCs) and iPSC-derived neurons to examine how postmitotic human neurons repair Cas9-induced DNA damage. CRISPR editing outcomes differ dramatically in neurons compared to genetically identical dividing cells: neurons take longer to fully resolve this damage, and upregulate non-canonical DNA repair factors in the process. Manipulating this response with chemical or genetic perturbations allows us to direct DNA repair toward desired editing outcomes in nondividing human neurons, cardiomyocytes, and primary T cells. By studying DNA repair in clinically relevant cells, we reveal unforeseen challenges and opportunities for precise therapeutic editing.

Ramadoss, Gokul N. [Gladstone Institutes, San Fran↗
DOE OSTI2026

PARP1-HPF1 structure and dynamics on nicked DNA suggest a mechanism for acute and localized ADP-ribosylation

PARP1 detection of DNA strand breaks allosterically leads to PARP1 synthesis of poly(ADP-ribose) modifications that signal DNA damage. HPF1 engages activated PARP1 to control modification site selection. Understanding of the mechanism of DNA break detection and catalytic activation is incomplete, due largely to limited structural information for full-length PARP1. Here, single-particle cryo-EM provides views of the full complement of PARP1 domains engaging a DNA single-strand break in the presence of HPF1 and a fragment of binding partner Timeless. Cryo-EM, single-molecule DNA dynamics, and small-angle X-ray scattering analysis indicate that PARP1 remains dynamic even when the multi-domain structure is organized on a DNA break, with the minimal catalytic region displaying high mobility relative to domains engaging damage. We propose that the organization of PARP1 domains on a DNA break releases a tethered, constitutively active catalytic region to modify molecules in a radius surrounding the DNA break site.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Stable hypermutators revealed by the genomic landscape of genes involved in genome stability among yeast species

Mutator phenotypes are short-lived due to the rapid accumulation of deleterious mutations. Yet, recent observations reveal that certain fungi can undergo prolonged accelerated evolution after losing genes involved in DNA repair. Here, we surveyed 1,154 yeast genomes representing nearly all known yeast species of the subphylum Saccharomycotina (phylum Ascomycota) to examine the relationship between reduced gene repertoires broadly associated with genome stability functions (e.g., DNA repair, cell cycle) and elevated evolutionary rates. We identified three distantly related lineages—encompassing 12% of species—that had both the most streamlined sets of genes involved in genome stability (specifically DNA repair) and the highest evolutionary rates in the entire subphylum. Two of these “faster-evolving lineages” (FELs)—a subclade within the order Pichiales and the Wickerhamiella/Starmerella (W/S) clade (order Dipodascales)—are described here for the first time, while the third corresponds to a previously documented Hanseniaspora FEL. Examination of genome stability gene repertoires revealed a set of genes predominantly absent in these three FELs, suggesting a potential role in the observed acceleration of evolutionary rates. In the W/S clade, genomic signatures are consistent with a substantial mutational burden, including pronounced A|T bias and endogenous DNA damage. Interestingly, we found that the W/S clade also contains DNA repair genes possibly acquired through horizontal gene transfer, including a photolyase of bacterial origin. These findings highlight how hypermutators can persist across macroevolutionary timescales, potentially linked to the loss of genes related with genome stability, with horizontal gene transfer as a possible avenue for partial functional compensation.

DNA repair↗
DOE OSTI2024

Base excision repair and double strand break repair cooperate to modulate the formation of unrepaired double strand breaks in mouse brain

Abstract We lack the fundamental information needed to understand how DNA damage in the brain is generated and how it is controlled over a lifetime in the absence of replication check points. To address these questions, here, we integrate cell-type and region-specific features of DNA repair activity in the normal brain. The brain has the same repair proteins as other tissues, but normal, canonical repair activity is unequal and is characterized by high base excision repair (BER) and low double strand break repair (DSBR). The natural imbalance creates conditions where single strand breaks (SSBs) can convert to double strand breaks (DSBs) and reversibly switch between states in response to oxidation both in vivo and in vitro. Our data suggest that, in a normal background of repair, SSBs and DSBs are in an equilibrium which is pushed or pulled by metabolic state. Interconversion of SSB to DSBs provides a physiological check point, which would allow the formation of unrepaired DSBs for productive functions, but would also restrict them from exceeding tolerable limits.

Science & Technology - Other Topics↗
DOE OSTI2025

Molecular model of TFIIH recruitment to the transcription-coupled repair machinery

Transcription-coupled repair (TCR) is a vital nucleotide excision repair sub-pathway that removes DNA lesions from actively transcribed DNA strands. Binding of CSB to lesion-stalled RNA Polymerase II (Pol II) initiates TCR by triggering the recruitment of downstream repair factors. Yet it remains unknown how transcription factor IIH (TFIIH) is recruited to the intact TCR complex. Combining existing structural data with AlphaFold predictions, we build an integrative model of the initial TFIIH-bound TCR complex. We show how TFIIH can be first recruited in an open repair-inhibited conformation, which requires subsequent CAK module removal and conformational closure to process damaged DNA. In our model, CSB, CSA, UVSSA, elongation factor 1 (ELOF1), and specific Pol II and UVSSA-bound ubiquitin moieties come together to provide interaction interfaces needed for TFIIH recruitment. STK19 acts as a linchpin of the assembly, orienting the incoming TFIIH and bridging Pol II to core TCR factors and DNA. Molecular simulations of the TCR-associated CRL4CSA ubiquitin ligase complex unveil the interplay of segmental DDB1 flexibility, continuous Cullin4A flexibility, and the key role of ELOF1 for Pol II ubiquitination that enables TCR. Collectively, these findings elucidate the coordinated assembly of repair proteins in early TCR.

Paul, Tanmoy↗
DOE OSTI2026

Synthesis and Characterization of Radio-Halogenated Talazoparib Analogues for Imaging and Radioligand Therapy

Abstract Talazoparib (TZ) is a potent poly(ADP-ribose) polymerase 1/2 (PARP1/2) inhibitor that uniquely traps PARP complexes at sites of single-strand DNA damage thereby offering opportunities for targeted radioligand therapy. Radiolabeled halogenated TZ derivatives were synthesized using boronic ester precursors to enable incorporation of diagnostic and therapeutic radionuclides: 18F for PET imaging, 77Br for Auger electron radiotherapy, and 211At for targeted alpha radiotherapy. Copper-mediated radio-halogenation afforded racemic 18F-TZ, 77Br-TZ, and 211At-TZ in sufficient radiochemical yields (4.3 ± 2.6%, n = 33; 29.0 ± 12.0%, n = 4; 3.6 ± 3.8%, n = 9, respectively), ∼99% radiochemical purity and proven stability under formulation conditions. Molecular dynamics simulations of halo-TZ derivatives predicted an inverse relationship between halogen size and PARP1 binding affinity. Indeed, cell uptake of radio-halogenated TZ analogues indicated selective uptake in a panel of cell types that correlated with PARP1 levels but was inversely related to the atomic radii of the halogen series. Despite modest specific activity and specific uptake, 77Br-TZ showed significant cytotoxicity. Further investigation of 18F-TZ with 77Br-TZ as a radiotheranostic pair will be facilitated by the synthetic schemes herein.

Muzzioli, Riccardo [The University of Texas MD And↗
DOE OSTI2024

Mechanistic basis of atypical TERT promoter mutations

Non-coding mutations in the TERT promoter (TERTp), typically at one of two bases -124 and -146 bp upstream of the start codon, are among the most prevalent driver mutations in human cancer. Several additional recurrent TERTp mutations have been reported but their functions and origins remain largely unexplained. Here, we show that atypical TERTp mutations arise secondary to canonical TERTp mutations in a two-step process. Canonical TERTp mutations create de novo binding sites for ETS family transcription factors that induce favourable conditions for DNA damage formation by UV light, thus creating a hotspot effect but only after a first mutational hit. In agreement, atypical TERTp mutations co-occur with canonical driver mutations in large cancer cohorts and arise subclonally specifically on the TERTp driver mutant chromosome homolog of melanoma cells treated with UV light in vitro. Our study gives an in-depth view of TERTp mutations in cancer and provides a mechanistic explanation for atypical TERTp mutations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Revealing ultrafast proton-transfer-mediated autoionization as a source of low-energy electrons in hydrogen-bonded systems

Ionizing radiation can trigger ultrafast proton transfer, a central mechanism in many chemical and biological functions, that in turn can enable or suppress electron relaxation processes and consequently cause abrupt changes in the reaction pathway. This study combines theory and experiment to probe ultrafast relaxation and dissociation in water dimers following inner- and outer-valence photoionization. By tracking electron and nuclear motion simultaneously, we reveal competing fragmentation pathways that produce low-energy electrons, which are key agents in radiation-induced chemistry, including DNA damage. While low-energy electrons are known to arise via intermolecular Coulombic decay, here we identify a faster relaxation mechanism gated by proton transfer following inner-valence ionization, which we call proton-transfer-mediated autoionization. Occurring within 10 femtoseconds, this process alters fragmentation outcomes, yielding either D 3 O + + OD + or D 2 O + + D 2 O + , depending on the interplay of proton migration and hydrogen back-transfer. Our findings underscore the intricate coupling between electronic and nuclear dynamics in hydrogen-bonded systems and establish proton-transfer-mediated autoionization as a significant pathway for low-energy electron generation.

Atomic and molecular interactions with photons↗
DOE OSTI2025

Sulfide stress tolerance as a controller of methane production in temperate wetlands

Abstract Wetlands are a major source of methane emissions and contribute to the observed increase in atmospheric methane over the last 20 years. Methane production in wetlands is the final step of carbon decomposition performed by anaerobic archaea. Although hydrogen/carbon dioxide and acetate are the substrates most often attributed to methanogenesis, other substrates—such as methylated compounds—may additionally play important roles in driving methane production in wetland systems. Here we conducted mesocosm experiments combined with genome-resolved metatranscriptomics to investigate the impact of diverse methanogenic substrate amendment on methanogenesis in two high methane-emitting wetlands with distinct geochemistry, termed P7 and P8. Methanol amendment resulted in high methane production at both sites, whereas acetate and formate amendment only stimulated methanogenesis in P7 mesocosms, where aqueous sulfide concentrations were lower. In P7 sediments, formate amendment fueled acetogenic microbes that produced acetate, which was subsequently utilized by acetoclastic methanogens. In contrast to expression profiles in P7 mesocosms, active methylotrophic methanogen genomes from P8 showed increased expression of genes related to membrane remodeling and DNA damage repair, indicative of stress tolerance mechanisms to counter sulfide toxicity. Methylotrophic methanogenesis generates higher free energy yields than acetoclastic methanogenesis, which likely enables allocation of more energy toward stress responses. These findings contribute to the growing body of literature highlighting methylotrophic methanogenesis as an important methane production pathway in wetlands. By using less competitive substrates like methanol that provide greater energy yields, methylotrophic methanogens may invest in physiological strategies that provide competitive advantages across a range of environmental stresses.

Environmental Sciences & Ecology↗
DOE OSTI2024

DNA double-strand break movement in heterochromatin depends on the histone acetyltransferase dGcn5

Abstract Cells employ diverse strategies to repair double-strand breaks (DSBs), a dangerous form of DNA damage that threatens genome integrity. Eukaryotic nuclei consist of different chromatin environments, each displaying distinct molecular and biophysical properties that can significantly influence the DSB-repair process. DSBs arising in the compact and silenced heterochromatin domains have been found to move to the heterochromatin periphery in mouse and Drosophila to prevent aberrant recombination events. However, it is poorly understood how chromatin components, such as histone post-translational modifications, contribute to these DSB movements within heterochromatin. Using irradiation as well as locus-specific DSB induction in Drosophila tissues and cultured cells, we find enrichment of histone H3 lysine 9 acetylation (H3K9ac) at DSBs in heterochromatin but not euchromatin. We find this increase is mediated by the histone acetyltransferase dGcn5, which rapidly localizes to heterochromatic DSBs. Moreover, we demonstrate that in the absence of dGcn5, heterochromatic DSBs display impaired recruitment of the SUMO E3 ligase Nse2/Qjt and fail to relocate to the heterochromatin periphery to complete repair. In summary, our results reveal a previously unidentified role for dGcn5 and H3K9ac in heterochromatic DSB repair and underscore the importance of differential chromatin responses at heterochromatic and euchromatic DSBs to promote safe repair.

Biochemistry & Molecular Biology↗
DOE OSTI2026

Photonuclear cross sections for the 197 Au ⁢(𝛾, 𝑝⁢𝑛)⁢ 195⁢𝑚 Pt reaction near threshold

Platinum radioisotopes are of growing interest for targeted cancer therapy and diagnostic imaging because their decay delivers highly localized radiation doses in tissue, herewith enabling precise DNA damage through Auger-electron emission. Developing production technologies that provide platinum isotopes with high specific activity is essential in radioisotope therapy. Photonuclear reactions on stable nuclei offer a viable accelerator-based route for isotope production when supported by reliable cross-section data. We report photonuclear cross-section measurements for the 197 Au(γ, pn) 195m Pt reaction at incident γ-ray energies of 27, 29, and 31 MeV using the activation method. The measurements were performed by irradiating a stack of concentric-ring gold targets with a quasi-monoenergetic γ-ray beam provided by the High Intensity Gamma-ray Source (HI γS). The induced 195m Pt activity was quantified using off-line γ-ray spectroscopy. These data provide the first experimental constraints on the 197 Au(γ, pn) 195m Pt cross section in the near-threshold region. Furthermore, the comparison of the measured excitation function to PHITS and TALYS calculations indicates that the reaction becomes measurable only near 30 MeV and that substantially higher bremsstrahlung end-point energies are required for practically meaningful production.

190 ≤ A ≤ 219↗
DOE OSTI2024

Evaluating the risk of data loss due to particle radiation damage in a DNA data storage system

DNA data storage is a potential alternative to magnetic tape for archival storage purposes, promising substantial gains in information density. Critical to the success of DNA as a storage media is an understanding of the role of environmental factors on the longevity of the stored information. In this paper, we evaluate the effect of exposure to ionizing particle radiation, a cause of data loss in traditional magnetic media, on the longevity of data in DNA data storage pools. We develop a mass action kinetics model to estimate the rate of damage accumulation in DNA strands due to neutron interactions with both nucleotides and residual water molecules, then utilize the model to evaluate the effect several design parameters of a typical DNA data storage scheme have on expected data longevity. Finally, we experimentally validate our model by exposing dried DNA samples to different levels of neutron irradiation and analyzing the resulting error profile. Our results show that particle radiation is not a significant contributor to data loss in DNA data storage pools under typical storage conditions.

97 MATHEMATICS AND COMPUTING↗