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Recently, we have shown that C6-ceramides efficiently suppress viral replication by trapping the virus in lysosomes. Here, we use antiviral assays to evaluate a synthetic ceramide derivative α-NH2-ω-N3-C6-ceramide (AKS461) and to confirm the biological activity of C6-ceramides inhibiting SARS-CoV-2. Click-labeling with a fluorophore demonstrated that AKS461 accumulates in lysosomes. Previously, it has been shown that suppression of SARS-CoV-2 replication can be cell-type specific. Thus, AKS461 inhibited SARS-CoV-2 replication in Huh-7, Vero, and Calu-3 cells up to 2.5 orders of magnitude. The results were confirmed by CoronaFISH, indicating that AKS461 acts comparable to the unmodified C6-ceramide. Thus, AKS461 serves as a tool to study ceramide-associated cellular and viral pathways, such as SARS-CoV-2 infections, and it helped to identify lysosomes as the central organelle of C6-ceramides to inhibit viral replication.
Infected wounds pose a major mortality risk in animals. Injuries are common in the ant Megaponera analis, which raids pugnacious prey. Here we show that M. analis can determine when wounds are infected and treat them accordingly. By applying a variety of antimicrobial compounds and proteins secreted from the metapleural gland to infected wounds, workers reduce the mortality of infected individuals by 90%. Chemical analyses showed that wound infection is associated with specific changes in the cuticular hydrocarbon profile, thereby likely allowing nestmates to diagnose the infection state of injured individuals and apply the appropriate antimicrobial treatment. This study demonstrates that M. analis ant societies use antimicrobial compounds produced in the metapleural glands to treat infected wounds and reduce nestmate mortality.
Seasonal plasticity in insects is often triggered by temperature and photoperiod changes. When climatic conditions become sub-optimal, insects might undergo reproductive diapause, a form of seasonal plasticity delaying the development of reproductive organs and activities. During the reproductive diapause, the cuticular hydrocarbon (CHC) profile, which covers the insect body surface, might also change to protect insects from desiccation and cold temperature. However, CHCs are often important cues and signals for mate recognition and changes in CHC composition might affect mate recognition. In the present study, we investigated the CHC profile composition and the mating success of Drosophila suzukii in 1- and 5-day-old males and females of summer and winter morphs. CHC compositions differed with age and morphs. However, no significant differences were found between the sexes of the same age and morph. The results of the behavioral assays show that summer morph pairs start to mate earlier in their life, have a shorter mating duration, and have more offspring compared to winter morph pairs. We hypothesize that CHC profiles of winter morphs are adapted to survive winter conditions, potentially at the cost of reduced mate recognition cues.
T cell exhaustion is a hallmark of cancer and persistent infections, marked by inhibitory receptor upregulation, diminished cytokine secretion, and impaired cytolytic activity. Terminally exhausted T cells are steadily replenished by a precursor population (Tpex), but the metabolic principles governing Tpex maintenance and the regulatory circuits that control their exhaustion remain incompletely understood. Using a combination of gene-deficient mice, single-cell transcriptomics, and metabolomic analyses, we show that mitochondrial insufficiency is a cell-intrinsic trigger that initiates the functional exhaustion of T cells. At the molecular level, we find that mitochondrial dysfunction causes redox stress, which inhibits the proteasomal degradation of hypoxia-inducible factor 1α (HIF-1α) and promotes the transcriptional and metabolic reprogramming of Tpex cells into terminally exhausted T cells. Our findings also bear clinical significance, as metabolic engineering of chimeric antigen receptor (CAR) T cells is a promising strategy to enhance the stemness and functionality of Tpex cells for cancer immunotherapy.
Machine learning techniques are excellent to analyze expression data from single cells. These techniques impact all fields ranging from cell annotation and clustering to signature identification. The presented framework evaluates gene selection sets how far they optimally separate defined phenotypes or cell groups. This innovation overcomes the present limitation to objectively and correctly identify a small gene set of high information content regarding separating phenotypes for which corresponding code scripts are provided. The small but meaningful subset of the original genes (or feature space) facilitates human interpretability of the differences of the phenotypes including those found by machine learning results and may even turn correlations between genes and phenotypes into a causal explanation. For the feature selection task, the principal feature analysis is utilized which reduces redundant information while selecting genes that carry the information for separating the phenotypes. In this context, the presented framework shows explainability of unsupervised learning as it reveals cell-type specific signatures. Apart from a Seurat preprocessing tool and the PFA script, the pipeline uses mutual information to balance accuracy and size of the gene set if desired. A validation part to evaluate the gene selection for their information content regarding the separation of the phenotypes is provided as well, binary and multiclass classification of 3 or 4 groups are studied. Results from different single-cell data are presented. In each, only about ten out of more than 30000 genes are identified as carrying the relevant information. The code is provided in a GitHub repository at https://github.com/AC-PHD/Seurat_PFA_pipeline.
In the fast-evolving landscape of biomedical research, the emergence of big data has presented researchers with extraordinary opportunities to explore biological complexities. In biomedical research, big data imply also a big responsibility. This is not only due to genomics data being sensitive information but also due to genomics data being shared and re-analysed among the scientific community. This saves valuable resources and can even help to find new insights in silico. To fully use these opportunities, detailed and correct metadata are imperative. This includes not only the availability of metadata but also their correctness. Metadata integrity serves as a fundamental determinant of research credibility, supporting the reliability and reproducibility of data-driven findings. Ensuring metadata availability, curation, and accuracy are therefore essential for bioinformatic research. Not only must metadata be readily available, but they must also be meticulously curated and ideally error-free. Motivated by an accidental discovery of a critical metadata error in patient data published in two high-impact journals, we aim to raise awareness for the need of correct, complete, and curated metadata. We describe how the metadata error was found, addressed, and present examples for metadata-related challenges in omics research, along with supporting measures, including tools for checking metadata and software to facilitate various steps from data analysis to published research.
Highlights
• Data awareness and data integrity underpins the trustworthiness of results and subsequent further analysis.
• Big data and bioinformatics enable efficient resource use by repurposing publicly available RNA-Sequencing data.
• Manual checks of data quality and integrity are insufficient due to the overwhelming volume and rapidly growing data.
• Automation and artificial intelligence provide cost-effective and efficient solutions for data integrity and quality checks.
• FAIR data management, various software solutions and analysis tools assist metadata maintenance.
Infection research largely relies on classical cell culture or mouse models. Despite having delivered invaluable insights into host-pathogen interactions, both have limitations in translating mechanistic principles to human pathologies. Alternatives can be derived from modern Tissue Engineering approaches, allowing the reconstruction of functional tissue models in vitro. Here, we combined a biological extracellular matrix with primary tissue-derived enteroids to establish an in vitro model of the human small intestinal epithelium exhibiting in vivo-like characteristics. Using the foodborne pathogen Salmonella enterica serovar Typhimurium, we demonstrated the applicability of our model to enteric infection research in the human context. Infection assays coupled to spatio-temporal readouts recapitulated the established key steps of epithelial infection by this pathogen in our model. Besides, we detected the upregulation of olfactomedin 4 in infected cells, a hitherto unrecognized aspect of the host response to Salmonella infection. Together, this primary human small intestinal tissue model fills the gap between simplistic cell culture and animal models of infection, and shall prove valuable in uncovering human-specific features of host-pathogen interplay.
CRISPR/Cas9 gene editing has revolutionised loss-of-function experiments in Leishmania, the causative agent of leishmaniasis. As Leishmania lack a functional non-homologous DNA end joining pathway however, obtaining null mutants typically requires additional donor DNA, selection of drug resistance-associated edits or time-consuming isolation of clones. Genome-wide loss-of-function screens across different conditions and across multiple Leishmania species are therefore unfeasible at present. Here, we report a CRISPR/Cas9 cytosine base editor (CBE) toolbox that overcomes these limitations. We employed CBEs in Leishmania to introduce STOP codons by converting cytosine into thymine and created http://www.leishbaseedit.net/ for CBE primer design in kinetoplastids. Through reporter assays and by targeting single- and multi-copy genes in L. mexicana, L. major, L. donovani, and L. infantum, we demonstrate how this tool can efficiently generate functional null mutants by expressing just one single-guide RNA, reaching up to 100% editing rate in non-clonal populations. We then generated a Leishmania-optimised CBE and successfully targeted an essential gene in a plasmid library delivered loss-of-function screen in L. mexicana. Since our method does not require DNA double-strand breaks, homologous recombination, donor DNA, or isolation of clones, we believe that this enables for the first time functional genetic screens in Leishmania via delivery of plasmid libraries.
Alpine bumble bees are the most important pollinators in temperate mountain ecosystems. Although they are used to encounter small-scale successions of very different climates in the mountains, many species respond sensitively to climatic changes, reflected in spatial range shifts and declining populations worldwide. Cuticular hydrocarbons (CHCs) mediate climate adaptation in some insects. However, whether they predict the elevational niche of bumble bees or their responses to climatic changes remains poorly understood. Here, we used three different approaches to study the role of bumble bees’ CHCs in the context of climate adaptation: using a 1,300 m elevational gradient, we first investigated whether the overall composition of CHCs, and two potentially climate-associated chemical traits (proportion of saturated components, mean chain length) on the cuticle of six bumble bee species were linked to the species’ elevational niches. We then analyzed intraspecific variation in CHCs of Bombus pascuorum along the elevational gradient and tested whether these traits respond to temperature. Finally, we used a field translocation experiment to test whether CHCs of Bombus lucorum workers change, when translocated from the foothill of a cool and wet mountain region to (a) higher elevations, and (b) a warm and dry region. Overall, the six species showed distinctive, species-specific CHC profiles. We found inter- and intraspecific variation in the composition of CHCs and in chemical traits along the elevational gradient, but no link to the elevational distribution of species and individuals. According to our expectations, bumble bees translocated to a warm and dry region tended to express longer CHC chains than bumble bees translocated to cool and wet foothills, which could reflect an acclimatization to regional climate. However, chain lengths did not further decrease systematically along the elevational gradient, suggesting that other factors than temperature also shape chain lengths in CHC profiles. We conclude that in alpine bumble bees, CHC profiles and traits respond at best secondarily to the climate conditions tested in this study. While the functional role of species-specific CHC profiles in bumble bees remains elusive, limited plasticity in this trait could restrict species’ ability to adapt to climatic changes.
Xiphophorus fish exhibit a clear phenotypic polymorphism in puberty onset and reproductive strategies of males. In X. nigrensis and X. multilineatus, puberty onset is genetically determined and linked to a melanocortin 4 receptor (Mc4r) polymorphism of wild-type and mutant alleles on the sex chromosomes. We hypothesized that Mc4r mutant alleles act on wild-type alleles by a dominant negative effect through receptor dimerization, leading to differential intracellular signaling and effector gene activation. Depending on signaling strength, the onset of puberty either occurs early or is delayed. Here, we show by Förster Resonance Energy Transfer (FRET) that wild-type Xiphophorus Mc4r monomers can form homodimers, but also heterodimers with mutant receptors resulting in compromised signaling which explains the reduced Mc4r signaling in large males. Thus, hetero- vs. homo- dimerization seems to be the key molecular mechanism for the polymorphism in puberty onset and body size in male fish.
Fungal infections are a major global health burden where Candida albicans is among the most common fungal pathogen in humans and is a common cause of invasive candidiasis. Fungal phenotypes, such as those related to morphology, proliferation and virulence are mainly driven by gene expression, which is primarily regulated by kinase signaling cascades. Serine-arginine (SR) protein kinases are highly conserved among eukaryotes and are involved in major transcriptional processes in human and S. cerevisiae. Candida albicans harbors two SR protein kinases, while Sky2 is important for metabolic adaptation, Sky1 has similar functions as in S. cerevisiae. To investigate the role of these SR kinases for the regulation of transcriptional responses in C. albicans, we performed RNA sequencing of sky1Δ and sky2Δ and integrated a comprehensive phosphoproteome dataset of these mutants. Using a Systems Biology approach, we study transcriptional regulation in the context of kinase signaling networks. Transcriptomic enrichment analysis indicates that pathways involved in the regulation of gene expression are downregulated and mitochondrial processes are upregulated in sky1Δ. In sky2Δ, primarily metabolic processes are affected, especially for arginine, and we observed that arginine-induced hyphae formation is impaired in sky2Δ. In addition, our analysis identifies several transcription factors as potential drivers of the transcriptional response. Among these, a core set is shared between both kinase knockouts, but it appears to regulate different subsets of target genes. To elucidate these diverse regulatory patterns, we created network modules by integrating the data of site-specific protein phosphorylation and gene expression with kinase-substrate predictions and protein-protein interactions. These integrated signaling modules reveal shared parts but also highlight specific patterns characteristic for each kinase. Interestingly, the modules contain many proteins involved in fungal morphogenesis and stress response. Accordingly, experimental phenotyping shows a higher resistance to Hygromycin B for sky1Δ. Thus, our study demonstrates that a combination of computational approaches with integration of experimental data can offer a new systems biological perspective on the complex network of signaling and transcription. With that, the investigation of the interface between signaling and transcriptional regulation in C. albicans provides a deeper insight into how cellular mechanisms can shape the phenotype.
Highlights
• The integrated stress response leads to a general ATF4-dependent activation of NRF2
• ATF4 causes a CHAC1-dependent GSH depletion, resulting in NRF2 stabilization
• An elevation of NRF2 transcript levels fosters this effect
• NRF2 supports the ISR/ATF4 pathway by improving cystine and antioxidant supply
Summary
The redox regulator NRF2 becomes activated upon oxidative and electrophilic stress and orchestrates a response program associated with redox regulation, metabolism, tumor therapy resistance, and immune suppression. Here, we describe an unrecognized link between the integrated stress response (ISR) and NRF2 mediated by the ISR effector ATF4. The ISR is commonly activated after starvation or ER stress and plays a central role in tissue homeostasis and cancer plasticity. ATF4 increases NRF2 transcription and induces the glutathione-degrading enzyme CHAC1, which we now show to be critically important for maintaining NRF2 activation. In-depth analyses reveal that NRF2 supports ATF4-induced cells by increasing cystine uptake via the glutamate-cystine antiporter xCT. In addition, NRF2 upregulates genes mediating thioredoxin usage and regeneration, thus balancing the glutathione decrease. In conclusion, we demonstrate that the NRF2 response serves as second layer of the ISR, an observation highly relevant for the understanding of cellular resilience in health and disease.
To fire action-potential-like electrical signals, the vacuole membrane requires the two-pore channel TPC1, formerly called SV channel. The TPC1/SV channel functions as a depolarization-stimulated, non-selective cation channel that is inhibited by luminal Ca\(^{2+}\). In our search for species-dependent functional TPC1 channel variants with different luminal Ca\(^{2+}\) sensitivity, we found in total three acidic residues present in Ca\(^{2+}\) sensor sites 2 and 3 of the Ca\(^{2+}\)-sensitive AtTPC1 channel from Arabidopsis thaliana that were neutral in its Vicia faba ortholog and also in those of many other Fabaceae. When expressed in the Arabidopsis AtTPC1-loss-of-function background, wild-type VfTPC1 was hypersensitive to vacuole depolarization and only weakly sensitive to blocking luminal Ca\(^{2+}\). When AtTPC1 was mutated for these VfTPC1-homologous polymorphic residues, two neutral substitutions in Ca\(^{2+}\) sensor site 3 alone were already sufficient for the Arabidopsis At-VfTPC1 channel mutant to gain VfTPC1-like voltage and luminal Ca\(^{2+}\) sensitivity that together rendered vacuoles hyperexcitable. Thus, natural TPC1 channel variants exist in plant families which may fine-tune vacuole excitability and adapt it to environmental settings of the particular ecological niche.
Interleukin-4 (IL-4) plays a key role in atopic diseases. It coordinates T-helper cell differentiation to subtype 2, thereby directing defense toward humoral immunity. Together with Interleukin-13, IL-4 further induces immunoglobulin class switch to IgE. Antibodies of this type activate mast cells and basophilic and eosinophilic granulocytes, which release pro-inflammatory mediators accounting for the typical symptoms of atopic diseases. IL-4 and IL-13 are thus major targets for pharmaceutical intervention strategies to treat atopic diseases. Besides neutralizing antibodies against IL-4, IL-13, or its receptors, IL-4 antagonists can present valuable alternatives. Pitrakinra, an Escherichia coli-derived IL-4 antagonist, has been evaluated in clinical trials for asthma treatment in the past; however, deficits such as short serum lifetime and potential immunogenicity among others stopped further development. To overcome such deficits, PEGylation of therapeutically important proteins has been used to increase the lifetime and proteolytic stability. As an alternative, glycoengineering is an emerging strategy used to improve pharmacokinetics of protein therapeutics. In this study, we have established different strategies to attach glycan moieties to defined positions in IL-4. Different chemical attachment strategies employing thiol chemistry were used to attach a glucose molecule at amino acid position 121, thereby converting IL-4 into a highly effective antagonist. To enhance the proteolytic stability of this IL-4 antagonist, additional glycan structures were introduced by glycoengineering utilizing eucaryotic expression. IL-4 antagonists with a combination of chemical and biosynthetic glycoengineering could be useful as therapeutic alternatives to IL-4 neutralizing antibodies already used to treat atopic diseases.
Recent studies link increased ozone (O\(_3\)) and carbon dioxide (CO\(_2\)) levels to alteration of plant performance and plant-herbivore interactions, but their interactive effects on plant-pollinator interactions are little understood. Extra floral nectaries (EFNs) are essential organs used by some plants for stimulating defense against herbivory and for the attraction of insect pollinators, e.g., bees. The factors driving the interactions between bees and plants regarding the visitation of bees to EFNs are poorly understood, especially in the face of global change driven by greenhouse gases. Here, we experimentally tested whether elevated levels of O\(_3\) and CO\(_2\) individually and interactively alter the emission of Volatile Organic Compound (VOC) profiles in the field bean plant (Vicia faba, L., Fabaceae), EFN nectar production and EFN visitation by the European orchard bee (Osmia cornuta, Latreille, Megachilidae). Our results showed that O\(_3\) alone had significant negative effects on the blends of VOCs emitted while the treatment with elevated CO\(_2\) alone did not differ from the control. Furthermore, as with O\(_3\) alone, the mixture of O\(_3\) and CO\(_2\) also had a significant difference in the VOCs’ profile. O\(_3\) exposure was also linked to reduced nectar volume and had a negative impact on EFN visitation by bees. Increased CO\(_2\) level, on the other hand, had a positive impact on bee visits. Our results add to the knowledge of the interactive effects of O\(_3\) and CO\(_2\) on plant volatiles emitted by Vicia faba and bee responses. As greenhouse gas levels continue to rise globally, it is important to take these findings into consideration to better prepare for changes in plant-insect interactions.
Natural DNA storage allows cellular differentiation, evolution, the growth of our children and controls all our ecosystems. Here, we discuss the fundamental aspects of DNA storage and recent advances in this field, with special emphasis on natural processes and solutions that can be exploited. We point out new ways of efficient DNA and nucleotide storage that are inspired by nature. Within a few years DNA-based information storage may become an attractive and natural complementation to current electronic data storage systems. We discuss rapid and directed access (e.g. DNA elements such as promotors, enhancers), regulatory signals and modulation (e.g. lncRNA) as well as integrated high-density storage and processing modules (e.g. chromosomal territories). There is pragmatic DNA storage for use in biotechnology and human genetics. We examine DNA storage as an approach for synthetic biology (e.g. light-controlled nucleotide processing enzymes). The natural polymers of DNA and RNA offer much for direct storage operations (read-in, read-out, access control). The inbuilt parallelism (many molecules at many places working at the same time) is important for fast processing of information. Using biology concepts from chromosomal storage, nucleic acid processing as well as polymer material sciences such as electronical effects in enzymes, graphene, nanocellulose up to DNA macramé , DNA wires and DNA-based aptamer field effect transistors will open up new applications gradually replacing classical information storage methods in ever more areas over time (decades).
The increasing loss of pollinators over the last decades has become more and more evident. Intensive use of plant protection products is one key factor contributing to this decline. Especially the mixture of different plant protection products can pose an increased risk for pollinators as synergistic effects may occur. In this study we investigated the effect of the fungicide Cantus® Gold (boscalid/dimoxystrobin), the neonicotinoid insecticide Mospilan® (acetamiprid) and their mixture on honeybees. Since both plant protection products are frequently applied sequentially to the same plants (e.g. oilseed rape), their combination is a realistic scenario for honeybees. We investigated the mortality, the sucrose responsiveness and the differential olfactory learning performance of honeybees under controlled conditions in the laboratory to reduce environmental noise. Intact sucrose responsiveness and learning performance are of pivotal importance for the survival of individual honeybees as well as for the functioning of the entire colony. Treatment with two sublethal and field relevant concentrations of each plant protection product did not lead to any significant effects on these behaviors but affected the mortality rate. However, our study cannot exclude possible negative sublethal effects of these substances in higher concentrations. In addition, the honeybee seems to be quite robust when it comes to effects of plant protection products, while wild bees might be more sensitive.
Highlights
• Mix of SBI fungicides and neonicotinoids can lead to synergistic effects for bees.
• Combination of non-SBI fungicide and neonicotinoid in field-realistic doses tested.
• Synergistic effect on mortality of honeybees.
• No effects on sucrose responsiveness and learning performance of honeybees.
• Synergistic effects by other pesticide mixtures or on wild bees cannot be excluded.
Modern lifestyle is often at odds with endogenously driven rhythmicity, which can lead to circadian disruption and metabolic syndrome. One signature for circadian disruption is a reduced or altered metabolite cycling in the circulating tissue reflecting the current metabolic status. Drosophila is a well-established model in chronobiology, but day-time dependent variations of transport metabolites in the fly circulation are poorly characterized. Here, we sampled fly hemolymph throughout the day and analyzed diacylglycerols (DGs), phosphoethanolamines (PEs) and phosphocholines (PCs) using LC-MS. In wild-type flies kept on sugar-only medium under a light-dark cycle, all transport lipid species showed a synchronized bimodal oscillation pattern with maxima at the beginning and end of the light phase which were impaired in period01 clock mutants. In wild-type flies under constant dark conditions, the oscillation became monophasic with a maximum in the middle of the subjective day. In strong support of clock-driven oscillations, levels of the targeted lipids peaked once in the middle of the light phase under time-restricted feeding independent of the time of food intake. When wild-type flies were reared on full standard medium, the rhythmic alterations of hemolymph lipid levels were greatly attenuated. Our data suggest that the circadian clock aligns daily oscillations of DGs, PEs, and PCs in the hemolymph to the anabolic siesta phase, with a strong influence of light on phase and modality.
Introduction
Pro-thrombotic events are one of the prevalent causes of intensive care unit (ICU) admissions among COVID-19 patients, although the signaling events in the stimulated platelets are still unclear.
Methods
We conducted a comparative analysis of platelet transcriptome data from healthy donors, ICU, and non-ICU COVID-19 patients to elucidate these mechanisms. To surpass previous analyses, we constructed models of involved networks and control cascades by integrating a global human signaling network with transcriptome data. We investigated the control of platelet hyperactivation and the specific proteins involved.
Results
Our study revealed that control of the platelet network in ICU patients is significantly higher than in non-ICU patients. Non-ICU patients require control over fewer proteins for managing platelet hyperactivity compared to ICU patients. Identification of indispensable proteins highlighted key subnetworks, that are targetable for system control in COVID-19-related platelet hyperactivity. We scrutinized FDA-approved drugs targeting indispensable proteins and identified fostamatinib as a potent candidate for preventing thrombosis in COVID-19 patients.
Discussion
Our findings shed light on how SARS-CoV-2 efficiently affects host platelets by targeting indispensable and critical proteins involved in the control of platelet activity. We evaluated several drugs for specific control of platelet hyperactivity in ICU patients suffering from platelet hyperactivation. The focus of our approach is repurposing existing drugs for optimal control over the signaling network responsible for platelet hyperactivity in COVID-19 patients. Our study offers specific pharmacological recommendations, with drug prioritization tailored to the distinct network states observed in each patient condition. Interactive networks and detailed results can be accessed at https://fostamatinib.bioinfo-wuerz.eu/.
The narrow escape theory (NET) predicts the escape time distribution of Brownian particles confined to a domain with reflecting borders except for one small window. Applications include molecular activation events in cell biology and biophysics. Specifically, the mean first passage time τ can be analytically calculated from the size of the domain, the escape window, and the diffusion coefficient of the particles. In this study, we systematically tested the NET in a disc by variation of the escape opening. Our model system consisted of micro-patterned lipid bilayers. For the measurement of τ, we imaged diffusing fluorescently-labeled lipids using single-molecule fluorescence microscopy. We overcame the lifetime limitation of fluorescent probes by re-scaling the measured time with the fraction of escaped particles. Experiments were complemented by matching stochastic numerical simulations. To conclude, we confirmed the NET prediction in vitro and in silico for the disc geometry in the limit of small escape openings, and we provide a straightforward solution to determine τ from incomplete experimental traces.