This was followed by pumice fall, and finally the emplacement of up to 40 m-thick ignimbrite that completely buried the site. However, unlike the seemingly similar AD 79 Vesuvius eruption that buried Pompeii by hot pyroclastic density currents, the presence of fallen but uncharred tree trunks, branches, and intact leaves in the basal pyroclastic deposits at Ipolytarnóc as well as rock paleomagnetic properties indicate a low-temperature pyroclastic event, that superbly preserved the coastal habitat, including unique fossil tracks.During Earth’s history, geosphere-biosphere interactions were often determined by momentary, catastrophic changes such as large explosive volcanic eruptions. The Miocene ignimbrite flare-up in the Pannonian Basin, which is located along a complex convergent plate boundary between Europe and Africa, provides a superb example of this interaction. In North Hungary, the famous Ipolytarnóc Fossil Site, often referred to as “ancient Pompeii”, records a snapshot of rich Early Miocene life buried under thick ignimbrite cover. Here, we use a multi-technique approach to constrain the successive phases of a catastrophic silicic eruption (VEI ≥ 7) dated at 17.2 Ma. An event-scale reconstruction shows that the initial PDC phase was phreatomagmatic, affecting ≥ 1500 km These large-magnitude eruptions are often associated with grabens hosting caldera clusters . The Pannonian Basin , representing a complex convergent plate tectonic setting that belongs to the Mediterranean region, experienced repetitive explosive silicic eruptions in Miocene times8. Producing large-volume ignimbrites and other pyroclastic sequences, these eruptions, which occurred in the Paratethys with an archipelago and rich subtropical vegetation on land9, certainly impacted the ecosystem. However, due to intense neotectonic movements and related erosion that resulted in a poor preservation of pyroclastic rocks, very little information is available on the contemporary habitats that were commonly buried by thick pyroclastic deposits.Catastrophic explosive silicic eruptions may affect the landscape in tens of thousands of km10, which has been considered an “ancient Pompeii”11 as it was disrupted and buried by an ignimbrite eruption c. 17–17.5 Ma13. Although it has been known since 183614 and holds an European Diploma for Protected Areas15, the specific eruption that affected the area has not been identified and characterized. In general, despite recent progress to date major eruptive units in the Pannonian Basin17, a detailed event stratigraphy of the ignimbrites that occur over large areas has not yet been reconstructed. To fill these gaps, herein we present new findings of the initiation of ignimbrite flare-up in the Pannonian Basin between 18 and 17 Ma. In particular, we focus on how a highly explosive, high-intensity, large-volume, multi-phase eruption impacted the peculiar habitat of Ipolytarnóc, by reconstructing the volcanic succession in time and space through field volcanology, pumice geochemistry, pyroclast texture characterization via BSE imaging, and Ar–Ar and U–Pb dating.A rare example of contemporary life is the famous Ipolytarnóc Fossil Site9. Subduction- and/or collision-related volcanism occurred along the Carpathian arc from the Mid-Miocene to the Late Quaternary20, whereas the basin itself was an area of intense explosive silicic volcanism throughout the Miocene (c. 20–12 Ma21). Basin subsidence, neotectonic faulting, block uplift, and related intense erosion22 resulted in the disintegration and removal of most pyroclastic rocks. The stratigraphy has been traditionally divided into Lower, Middle and Upper Tuff Formations23, that occur in scattered locations 28. The deposition of this sandstone marks the minimum age of the earliest arrival of Proboscidea (ancestors of today elephants) in Central Europe13. Paleogeographically, the sandstone facies characteristics  indicate a terrestrial habitat (“Rhinoland”)—likely a fluvial environment of braided rivers—interfingered with tide pools of a shallow epicontinental sea setting (“Crocodilia”)28. The spectacular tracks were preserved within oscillating, repetitive fluvial sequences of cm-thick footprint-bearing sandstone layers28.Seventy km northwest of Eger, at Ipolytarnóc, sedimentary deposits of the Central Paratethys are represented by marine ‘schlier’ (silty or sandy marl) and sandstone from the Eggenburgian/Ottnangian stages . The sandstone reveals a diverse fossil fauna of shark teeth, molluscs, foraminifers, and coralsPinuxylon tarnocziense , a relative to sugar pines, was found bridging two sides of a ravine29. Following the initial discovery, detailed analysis of the sandstone and the tuff revealed a number of tree trunks, branches, and more than 15,000 leaves. In all, seven conifers, four deciduous and one palm species were identified31, which indicated a multi-layer subtropical forest31. This habitat was hit by a large-scale volcanic eruption that knocked over and transported the tree logs a short distance, and eventually buried and preserved the track site with up to 40 m of tuff.The track site was discovered in the early nineteenth century where an exposed petrified giant tree trunk of 2 (75–78 wt%) and high-K2O (> 4 wt%) rhyolitic glass17, and a mineral assemblage of quartz, plagioclase and biotite similar to many other pyroclastic deposits in the Pannonian Basin. Recently, detailed field-based volcanology studies of ca. 150 outcrops in North Hungary has facilitated an improved pyroclastic stratigraphy basin-wide33, including a robust correlation of the Lower Rhyolite Tuff.In order to reconstruct the catastrophic volcanic event, we performed a detailed analysis of the volcanic deposit that buried Ipolytarnóc: its units, stratigraphic relations, and precise age. It belongs to the Lower Rhyolite Tuff , which is characterized by high-SiONear the Wind Quarry, at Eger Northeast outskirts, we have found a complex outcrop in the deep cut of Homok Street exposing pyroclastic deposits Fig. . Its basUlmus genus and the Cyclocarya cyclocarpa species have been identified; both of them also occur in the Ipolytarnóc and the nearby Lipovany (Slovakia) flora30. The basal units in turn are draped by a 42 cm-thick coarse tuff  with pumice clasts up to 1 cm, passing upward to a few m-thick fine-grained lapilli tuff . Charred, mm- to cm-sized organic material (plant remains) are evenly distributed in its matrix. The same ignimbrite with ca. 20 m thickness and reverse grading of pumices is found at an abandoned quarry 0.3 km eastward (‘Eger Bányakert’), and in the lower yard of a double-level quarry 0.8 km southward  overlain by a fines-rich accretionary lapilli-bearing tuff (Unit B). Unit A contains sporadic but intact leaf fossils, of which the 34 revealed the same—although poorly preserved—basal succession as above  shows a generally broader range of vesicularity than the coarse-grained sample (Unit C). However, the fine-grained Unit A sample also contains poorly vesicular clasts, represented by small-sized ash plates and ash flakes. These finds are interpreted in the Discussion.To understand the development of successive phases of the Eger-Ipolytarnóc eruption in light of the main fragmentation processes, vesicularity (glass/void ratio of the pyroclasts) of selected tuff units (Units A and C) was determined via quantitative image analysis of BSE pictures  and laser ablation inductively coupled mass spectrometry (LA-ICP-MS) techniques  with hundreds of km3 tephra volume41 and, typically, caldera formation42, had disrupting impact on the local ecosystem and even the global climate43. While subsequent to these young eruptions the massive tephra cover has buried the paleotopography, at ancient settings the millions of years of erosion can bring buried habitats to the surface. This is the case, for example, with the Permian Chemnitz petrified forest in Germany44, the Cretaceous Jihol biota in Liaoning Province, China45, or the Miocene Ashfall Fossil Beds, Nebraska, USA46. Our study on Ipolytarnóc adds a poorly preserved but still reconstructible large Early Miocene explosive silicic eruption that preserves an important paleohabitat to the global picture.Several of the well-known Late Pleistocene high-end VEI = 7 or VEI = 8 large-magnitude eruptions 47. As presented above, the Wind Ignimbrite sanidine has been precisely dated here at 18.06 ± 0.02 Ma, and this can be taken as the eruption age. However, as the subsequent Eger-Ipolytarnóc Ignimbrite does not contain sanidine, it was dated using plagioclase.As for the precise dating of these first two eruptions of the Northern Pannonian Basin, both the 40Ar–39Ar dating, the Eger-Ipolytarnóc eruption yields more scattered data and a less constrained isochron age of 17.17 ± 0.18 Ma  steps of 17, show a significant scatter and even the younger values are consistently ca. 0.2 My older than the 40Ar–39Ar ages  for the revised Fish Canyon Tuff age51, or the Ar–Ar biotite age (17.28 ± 0.06 Ma) of Šarinová et al.36 .Notably, within 2σ uncertainty, the 6 52 and are close to the high-end VEI = 7 Late Bronze Age Minoan eruption of Santorini 53 and the 7700 ka Mt. Mazama (Crater Lake) eruption in Oregon, USA 54.Based on the large areal distribution of the Eger-Ipolytarnóc Ignimbrite Fig. , it affe6 Fig. , defines6 Fig. , define 55. However, since Unit A contains abundant very fine juvenile glass shards, its fragmentation was more effective than Unit C. The broad range of vesicularity in Unit A indicates an additional effect during fragmentation that is beyond vesicle bursting. We suggest that ‘wet’ fragmentation due to already vesiculated magma and external water interaction in the conduit at a specific ratio of the two components56 was responsible for producing this fine-grained, laminated layer, that we interpret as being deposited from a subcritical pyroclastic density current (PDC), namely a highly energetic, dilute phreatomagmatic surge59. The wet character of this phase became even more enhanced during the deposition of Unit B considering the abundance of accretionary lapilli. Units A and B are collectively interpreted as a “couplet” in which the phreatomagmatic PDC (surge) was associated with a co-PDC ash fall60. As no abundant lithics were found in the basal units, we suggest that shallow water was the main source of external water supply.Analysis of the pyroclastic sequence of this large-magnitude explosive eruption shows that its first two phases were a double event. As BSE imaging reveals Fig. , vesicleHighly vesicular pumice clasts in Unit C Fig.  are infeFinally, Unit D corresponds to a typical pumiceous pyroclastic flow emplacing a large-volume ignimbrite. During this phase, limited access to water should have re-appeared, as indicated by (a) the total absence of welding in the deposit 61. At Ipolytarnóc, the presence of uncharred plant remains indicates a maximum temperature of 150 °C63.Effect of water on temperature can also be assessed by analysing paleomagnetic properties. A large number of paleomagnetic measurements are available from the Miocene tuffs of the Salgótarján Basin and the Bükk Foreland Volcanic Area Fig. . Severalite Fig. . This fiAs for paleogeographic implications, the pyroclastic succession was deposited in a terrestrial environment both in Eger and Ipolytarnóc, 70 km apart, which points to a period of marine regression during the Central Paratethys evolution. We argued that Unit A and Unit B which show phreatomagmatic character suggest an accessible water supply, but it must have been confined .2 in less than 10 min52. This implies that, although the first, double eruption event at Ipolytarnóc deposited only thin layers, it was a highly energetic PDC which hit the paleoenvironment catastrophically.To understand the scenario of the natural catastrophe at Ipolytarnóc, let us recall the onset of the eruption, when the area—as shown above—was characterized by a peculiar habitat of a fluvial environment interfingered with shallow-marine tide pools. Based on the richness of fossil tracks, this environment was populated by a wide variety of animals. In order to get an idea what a momentary event it may have been, the Taupō AD 232 eruption, similar in magnitude, can serve as an extreme analogy: its pyroclastic flows were inferred to have had a velocity of 150 m/s and, with a similar radius (80 km runout distance) to the Eger-Ipolytarnóc Ignimbrite . It is also different from the Taupō AD 232 eruption, where charred tree trunks indicate 270–400 °C67. At Ipolytarnóc, in agreement with the inferred low temperature of the first phreatomagmatic phases, logs remained uncharred, there are plenty of leafs, whereas animal bones or remains killed by hot gas are neither expected nor found—contrary to, for instance, the above-mentioned Ashfall Fossil Beds, which reveals a mass-death assemblage of a diverse fauna under 3-m-thick ultra-distal ash-fall deposit1.However, based on the analysis of the successive pyroclastic layers, the two initial phases were ‘wet’ phreatomagmatic events. This means that, in contrast to previous views, the Eger-Ipolytarnóc eruption was not similar to ‘Pompeii’—i.e., the AD 79 Plinian eruption of Somma-Vesuvius—where the lethal events for living organisms were 200–500 °C hot PDCsIn summary, the successive events of the Eger-Ipolytarnóc eruption Fig.  indicateSupplementary Information 1A.Supplementary Information 1B.Supplementary Information 1C.Supplementary Information 2A.Supplementary Information 2B.Supplementary Information 3A.Supplementary Information 3B.Supplementary Information 4A.Supplementary Information 4B.Supplementary Information 4C.Supplementary Information 4D.Supplementary Information 5.Supplementary Information Summary.


Thirty-six participants were examined, 18 with VP (52.6 ± 18.1 years) and 18 age-matched with normal vestibulocochlear testing (NP 50.3 ± 16.5 years). This study investigated whether (i) NA, (ii) DTI changes, or (iii) ELH occur in VP, and (iv) to what extent said parameters relate. Methods included vestibulocochlear testing and MRI data analyses for neurovascular compression (NVC) and NA verification, DTI and ELS quantification. As a result, (i) NA increased NVC specificity. (ii) DTI structural integrity was reduced on the side affected by VP (p < 0.05). (iii) 61.1% VP showed mild ELH and higher asymmetry indices than NP (p > 0.05). (iv) “Disease duration” and “total number of attacks” correlated with the decreased structural integrity of the affected nerve in DTI (p < 0.001). NVC distance within the nerve’s root-entry zone correlated with nerve function , nerve integrity loss , and ELS volume  in VP. In conclusion, this study is the first to link eighth cranial nerve function, microstructure, and ELS changes in VP to clinical features and increased vulnerability of NVC in the root-entry zone. Combined MRI with NVC or NA verification, DTI and ELS quantification increased the diagnostic accuracy at group-level but did not suffice to diagnose VP on a single-subject level due to individual variability and lack of diagnostic specificity.Combining magnetic resonance imaging (MRI) sequences that permit the determination of vestibular nerve angulation , structural nerve integrity via diffusion tensor imaging (DTI), and exclusion of endolymphatic hydrops (ELH) via delayed gadolinium-enhanced MRI of the inner ear ( Vestibular paroxysmia (VP) is a rare cause of short episodic vertigo with or without auditory and vegetative symptoms . The assClinical and neurophysiological parameters vary in VP. Patients can exhibit signs of mild to moderate unilateral nerve failure , 7, exci(i)Can nerve angulation/distortion improve the NVC informative value in VP?(ii)Are there measurable structural differences in the affected eighth cranial nerve in VP?(iii)Does ELH play a role in VP?(iv)To what extent are clinical, diagnostic, and MRI VP parameters related?The question was whether an MR imaging approach tailored to VP could improve the overall predictive diagnostic value in VP. Therefore, the combination of three sequences permits the determination of vestibular nerve angulation, structural nerve integrity via diffusion tensor imaging (DTI), and non-invasive quantification of the endolymphatic space (ELS) by delayed gadolinium-enhanced MRI of the inner ear (iMRI) were used. Nerve angulation/distortion (NA) was proposed to be a more specific imaging feature than NVC . In addiAll data were acquired at the Interdisciplinary German Center for Vertigo and Balance Disorders (DSGZ) and the Neurology Department of the Munich University Hospital (LMU) between 2018 and 2020. Institutional Review Board approval was obtained before the initiation of the study (no. 641-15). Furthermore, all participants provided informed oral and written consent in accordance with the Declaration of Helsinki before inclusion in the study.n = 4), epilepsy (n = 3), optic neuritis (n = 2), polyneuropathy (n = 2), headache (n = 2), idiopathic facial nerve palsy (n = 1), viral meningitis (n = 1), subdural hematoma (n = 1), spinal inflammatory lesion (n = 1), and decompensated esophoria (n = 1). The laterality quotient for right-handedness was assessed with the ten-item inventory of the Edinburgh test , video-oculography (VOG) during caloric and head impulse testing (HIT), as well as ocular and cervical vestibular evoked myogenic potentials (o/cVEMPs), and pure tone audiometry (PTA).A tilt of the SVV is a sensitive sign of an acute graviceptive vestibular tone imbalance. SVV was assessed with the subject sitting upright in front of a half-spherical dome with the head fixed on a chin rest . A mean C) was calculated based on the slow-phase velocity of the caloric nystagmus:The impairment of the vestibulo-ocular reflex (VOR) in higher frequencies was measured by HIT  using hiO/CV) of VEMP amplitudes and latencies were analyzed to avoid bias by examiners  = (lll) Successive differences tensor map approach: The 100 generated 1% subsegments were transformed into statistical summary parameters (SSP) to reduce the statistical testing and extract relevant features. SSP assessing the “overall” effects of VP vs. NP included the “mean”, “median”, “standard deviation”, and “interquartile range” across all 100 generated 1% steps, i.e., treating each part of the nerve similarly to every other part, as though each segment were a random manifestation of one overall effect. Furthermore, the deviations along the nerve were assessed via statistics of successive differences of first (1st) and second (2nd) order. Successive differences of 1st order are the differences between every two adjacent values of the 100 generated 1% steps divided by the first value to get a percentage. The 2nd order is the repetition of the process using the generated 99 differences of the 1st order step. The statistical parameters then calculated were the mean of the squared differences (MSSD) and the mean of the absolute differences (MASD). Note that the squared differences allow a more substantial weighting of large deviations even if few, while the absolute differences do not weigh the larger deviations more strongly than many small ones. Therefore, the mean squared successive differences , and the mean absolute successive differences  were calculated as a measure of the relative influence of larger deviations. Due to the use of successive differences, SSPs treat local parts of effectively 2 (1st order) and 4 (2nd order) segments of the nerve as though they are realizations of a random process related to successive local deteriorations of the nerve. Differential entropy ; ordinal or scalar values are presented as (mean ± standard deviation).p < 0.05 and p < 0.001, corrected for multiple comparisons.One-way analysis of variance (ANOVA) for multiple comparisons, which was post-hoc Bonferroni-corrected for multiple testing, was used for scalar  and ordinal  values. Group differences were assessed between all VP vs. NP and definite VP vs. NP. Linear agreement between parameter pairs was calculated for each method separately using the two-sided Spearman’s correlation coefficient. Results were reported at a significance level of p < 0.001.DTI continuous data types were assessed for differences in “central tendency “ and “dispersion”  between groups (VP vs. NP). The group differences were assessed using the non-parametric Wilcoxon rank-sum test for differences in medians between the groups and via the Brown–Forsythe test for group differences in variance of the two groups via the median absolute deviation. The collections named above  were aggregated into single variables using principal component analysis (PCA) and choosing only the most significant principal component score as the representation of the collection for group difference assessment. The group differences were assessed by the non-parametric Wilcoxon rank-sum test for differences in “medians” between the groups and via the Brown–Forsythe test for group differences in variance of the two groups via the “median absolute deviation”. The correlation of the “collections’’ to disease parameters, such as “disease duration”, “number of attacks”, “average duration of attacks”, and “number of attacks in the three months prior to examination”, was assessed via projection to latent space PLS analog to previous work , 48, 56.p < 0.001.Correlations between clinical and diagnostic features, NVC distances [mm], structural DTI quantifications, and ELS volumes were assessed with a PLS approach . Results were reported at correlation coefficient > 0.5 for all measures and significant in 1000 permutation tests, i.e., Eighteen VP patients , one left-handed (LH)] and 18 age-matched NP  were included in the study. VP patients could be further divided into ten definite  and eight probable VP patients . A detailed description of the VP groups’ symptomatology with accompanying complaints and signs, duration of attacks and disorder, and therapeutic success are given in Table Eleven patients were treated with carbamazepine , 3 patients were treated with lacosamide  and 2 patients received oxcarbazepine . Two patients received a combination of lacosamide  with either carbamazepine (200 mg/d) or oxcarbazepine (900 mg/dl).In 8/18 VP patients , the neurophysiological testing pattern was unremarkable. 7/18 VP patients  showed a clear pattern of unilateral reduction of audiovestibular function. The remaining 3/18 VP patients  revealed complex neurophysiological patterns representing decreased as well as increased eighth cranial nerve function, that is, a combination of nerve lesion (= hypofunction) and nerve irrigation (= hyperexcitability) within the same side. Beyond that, no significant group differences or correlations with clinical parameters were found. A detailed description of the clinical and neurophysiological results is given in Table In 15/18 VP patients  and 10/18 NP (55.6%), a NVC between the eighth cranial nerve and a blood vessel was detected. The contacts were documented between the nerve and the anterior inferior cerebellar artery , the posterior inferior cerebellar artery , the superior cerebellar artery , and the vertebral artery . In another patient, the NVC was between a vein and the nerve. The VP mean distance between the PE and the NVC was 6.1 ± 2.8 mm , the mean VP diameter of the compressing vessels was 0.7 ± 0.1 mm . The NP mean distance between PE and NVC was 6.6 ± 4.3 mm (range 1.3–14.2 mm), between NVC and IAC 9.7 ± 1.3 mm (range 7.8–11.9 mm), and the mean NP diameter 0.8 ± 0.3 mm (range 0.5–1.3 mm). NA at the contact site was seen in 8/15 NVC . In comparison, NA was only seen in 2/10 NVC (20%) in NP.In 6/18 VP patients , the neurophysiological testing pattern and course of the nerve were unremarkable. Clinical side and NVC were found to correspond in 3/18 VP , contradictory in 3/18 VP , or inconclusive in 6/18 VP . A detailed description of the NVC results can be seen in Table p < 0.05, corrected for multiple testing). The aggregated data for the ipsilateral and the difference between the ipsilateral vs. contralateral side and the average (mean) are shown in Fig. Average (l) and localized (ll) tensor map approaches showed no significant differences or correlations. However, within the successive difference map approach (lll), the most significant group differences (VP vs. NP) were found for the 1st order successive difference aggregated data collections . This means that in the overall effect along the whole nerve (between PE and IAC), VP showed a higher difference between the ipsilateral and contralateral nerve than NP, where both sides were similar. This supports the theory that there is a measurable structural difference in the affected nerve compared to the non-affected nerve in VP. An overview can be seen in Table p < 0.001 (no failures in 1000 permutation tests) with an r-squared of 0.596. The scatter plot of the ranked “disease duration” data and ranks of the 1st order successive difference PLS scores with an overlayed trendline can be viewed in Fig. PLS correlations between the disease parameters “disease duration” and “total number of attacks” and the 1st order of successive differences were significant at 3, range 4.7–17.9 mm3; dVP: 3, range 5.2–17.9 mm3; pVP:3, range 4.7–15.4 mm3). In comparison, 5/18 NP (27.8%) showed a mild ELH with an altogether lower mean semiquantitative and volumetric ELS quantification . VP and NP differed significantly regarding the extent of the asymmetry index of the inner ear and vestibulum volume . Definite VP and NP, on the other hand, differed significantly regarding the extent of the asymmetry index of the vestibulum volume and difference in volume between ipsi- and contralateral side . No correlations were found between electrophysiological data or degree of ELH and disease duration or number of attacks. A detailed description of the ELS results can be seen in Table Following a 3-point ordinal scale , semi-quClinical side and ELS quantification lateralization were inconclusive in 13/18 VP , and found to correspond in 3/18 VP . In 2/18 VP patients , the neurophysiological testing pattern and ELS were unremarkable. NVC side and ELS quantification lateralization were inconclusive in 12/18 VP , contradictory in 3/18 VP , found to correspond in 2/18 VP , or normal in 1/18 .p < 0.001), structural nerve integrity, i.e., DTI SSPs , and inner ear ELS . Scatter plots with trendlines are shown in Fig. The distance between PE and NVC (PE-to-NVC [mm]) correlated with audiovestibular function, i.e., neurophysiological testing ; 3. DTI showed structural differences in the affected vestibular nerve in VP at group-level (p < 0.05), (aim ii); 4. Endolymphatic space (ELS) asymmetry index was mildly but significantly increased at group-level (p < 0.05), (aim iii); 5. “Disease duration” and “total number of attacks” correlated positively with DTI, i.e., with structural nerve integrity , (aim iv); 6. Distance between PE (point of entry/exit for afferent/efferent fibers out of/into the brainstem) and NVC (“PE-to-NVC”) correlated positively with audiovestibular function  and negatively with structural nerve integrity , or volume of the inner ear ELS , (aim iv). At the group level, there were significant differences between VP participants and NP. In sum, the predictive value of MRI is increased. However, on a single-subject level, the methodology’s specificity is insufficient to diagnose VP.The current study focused on a detailed characterization of structures affecting the cisternal part of the eighth cranial nerve to increase the diagnostic value of MRI in patients with vestibular paroxysmia (VP) using an MR imaging approach tailored to VP. The high-resolution MRI sequences were used to determine neurovascular compression (NVC) and nerve angulation/distortion (NA), structural nerve integrity via diffusion tensor imaging (DTI), and in-vivo non-invasive verification of endolymphatic hydrops (ELH). The findings were the following: 1. Previously established evidence on the typical clinical and heterogenous diagnostic picture could be confirmed. 2. Nerve angulation (NA) increases NVC diagnostic specificity in VP In the following, we discuss these findings compared to previously published VP studies and the significance of dedicated VP MRI to quantify ELS and vestibular nerve structural integrity, its clinical implications, and recommendations for future studies and methodical limitations.VP pathophysiology seems to be best explained by a “dual”, i.e., combined peripheral and central pathology . While NThis study’s clinical and diagnostic results mirror the clinical picture of this vestibular NVC syndrome. The current VP cohort was characterized by the typical monomorphic clinical syndrome –4 and acp < 0.05; Fig. p < 0.001; Fig. NVC syndromes entail a local peripheral nerve compression. It, therefore, seems reasonable to assume a DTI structural correlation in the affected nerve of VP patients. The current study found measurable DTI structural differences in the median difference between the affected and non-affected side of the first order successive difference data of the eighth cranial nerve in VP at group level , a disease with similar underlying pathophysiology . The resFollowing the 4-point ordinal scale, semi-quantitative classification of the ELS for the vestibulum and cochlea , 76, volp < 0.001). The nerve compression might then lead to a disturbance in the inner ear fluid homeostasis, either directly or via a central pathology inducing hyperexcitability within the cranial nerve nuclei or reduced inhibitory projection to the cranial nerve nuclei.With respect to the current study, VP seems to be another vestibular disorder that can entail mild ELH. Although nonspecific, this finding may be one of several parameters that help diagnose the affected side  and nerve structural integrity (p < 0.001), and the larger inner ear ELS (p < 0.001) were. The intracisternal part of the eighth nerve starts covered by central myelin , then 6–15 mm as measured from the PE [The nearer the NVC was to the PE, the poorer audiovestibular function ”), holds potential. This study’s sequence acquisition parameters represent a compromise between novel technical possibilities, resolution, and reasonable scan time while enabling a wide range of clinical applications. Novel MR neurography imaging techniques might prove helpful for the investigation of the structural integrity of the vestibular nerve, such as high-resolution isotropic [The improvement of the MR sequences, especially DTI  could only be done in patients with other  pathologies that did not affect the peripheral or central vestibulocochlear systems. First, given the variation in symptomatology, a higher number of VP participants would be desirable. If possible, 20 participants per clinical pattern should be included. Second, influences of the NP’s underlying neurological pathologies on the ELS appeared unlikely . Significant differences were reached at group level . However, moderate specificity of MR NVC and NA evidence, DTI quantification, or ELH verification means they do not suffice to diagnose VP on a single-subject level.This study is the first to link eighth cranial nerve function, microstructure, and endolymphatic space changes in VP patients to clinical features and neurovascular compression in the root-entry zone (correlation coefficient > 0.5,


Using systems biology approaches, we then determined, at multiple levels of analysis, how these EASR genes could be related to PD pathology. A key result was the identification of functional connections between EASR genes and previously identified PD-related genes by employing the proteins’ interactions networks and 9 brain region-specific co-expression networks. In each brain region, co-expression modules of EASR genes were enriched for gene sets whose expression are altered by SARS-CoV-2 infection, leading to the hypothesis that EASR co-expression genes may explain the observed links between COVID-19 and PD. An examination of the expression pattern of EASR genes in different non-neurological healthy brain regions revealed that regions with lower mean expression of the upregulated EASR genes, such as substantia nigra, are more vulnerable to αSN aggregates and lose their neurological functions during PD progression. Gene Set Enrichment Analysis of healthy and PD samples from substantia nigra revealed that a specific co-expression network, “TNF-α signaling via NF-κB”, is an upregulated pathway associated with the PD phenotype. Inhibitors of the “TNF-α signaling via NF-κB” pathway may, therefore, decrease the activity level of this pathway and thereby provide therapeutic benefits for PD patients. We virtually screened FDA-approved drugs against these upregulated genes  using docking-based drug discovery and identified several promising drugs. Altogether, our study provides a better understanding of αSN toxicity mechanisms in PD and identifies potential therapeutic targets and small molecules for treatment of PD.Despite extensive research, the molecular mechanisms underlying the toxicity of αSN in Parkinson’s disease (PD) pathology are still poorly understood. To address this, we used a microarray dataset to identify genes that are induced and differentially expressed after exposure to toxic αSN aggregates, which we call  Its prevalence has grown dramatically worldwide . The mosIt has been proposed that intercellular transmission of αSN to neighboring cells and across brain regions follows a spatiotemporal pattern, which begins from the brainstem and later spreads to more rostral sites of the brain . AlthougFurthermore, the spatiotemporal pattern of αSN spread correlates with changes in gene expression in particular regions of the brain . Accordiexogenous αSN response (EASR) genes using a microarray dataset collected using SH-SY5Y cells that were treated with αSN aggregates. We then applied system biology approaches to find associations of EASR genes with PD-related genes.Characterizing the distinct expression patterns in different parts of the brain helps to identify the factors contributing to cell vulnerability to αSN aggregates. Here, we identified what we call To this end, we developed and analyzed two different network models. First, we obtained PD-related genes and concentrated on the protein-protein interaction network (PPI) between these genes and the EASR genes to study the functional connections between PD and αSN response at the protein level. Then, we collected expression data of healthy brains from different data sources and, at the expression level, studied their transcriptomes and compared the expression patterns of EASR genes between the distinct brain regions. Subsequently, we developed the second network model by constructing the co-expression network of EASR genes for each studied brain region and examined pathways that were enriched in these networks. We also studied the co-expression network of two brain regions, the substantia nigra and amygdala, between PD and control phenotypes, and characterized the enhanced activity of the “TNF-α signaling via the NF-κB” pathway as a significant pathway in substantia nigra-mediated αSN neurotoxicity during PD. Identifying this critical pathway could lead to the development of effective treatment for PD patients. Furthermore, our studies yielded important insights into the molecular mechanisms underlying αSN toxicity and PD progression. Finally, we applied docking-based virtual screening to identify approved drugs that could potentially be repurposed for PD treatment.GSE120569 dataset to detect transcriptional changes induced by exogenous αSN. This dataset released expression data of SH-SY5Y cells, which were exposed to the special aggregate of αSN that produced during fibrillation condition  was used to download the GTEx expression data.To investigate the patterns of EASR gene expression in different parts of the brain, we used expression data from the Genotype-Tissue Expression (GTEx) project that collected samples from 54 non-diseased tissue sites across nearly 1,000 individuals. After preprocessing, we selected samples that related to 9 different brain regions, including the amygdala (by 68 samples), anterior cingulate cortex (by 83 samples), caudate (by 109 samples), cerebellum (by 118 samples), frontal cortex (by 95 samples), hippocampus (by 84 samples), hypothalamus (by 82 samples), putamen (by 79 samples), and substantia nigra (by 57 samples). The UCSC Xena Browser (http://www.braineac.org) datasets include microarray expression data of healthy  brain samples, which is available through accession code. The UKBEC data cover 4 of the 9 brain regions of interest in our study, including the frontal cortex, hippocampus, putamen, and substantia nigra. These datasets were used as validation sets.The UK Brain Expression Consortium (UKBEC)  to obtain cell type gene expression markers.Eventually, we also used PanglaoDB (https://www.disgenet.org/home/), which contains 1,134,942 gene-disease associations (https://inetmodels.com/). The node limit and the edge pruning parameter  were taken as 25 and 2, respectively.All network illustrations and analyses were performed using Cytoscape version 3.7.2 . The metciations . Subsequciations , so thatciations . FinallyTo process PD RNA-seq data, we applied the commonly used RNA-seq pipeline . First, we used Trimmomatic to obtain clean data (clean reads) by trimming the paired-end raw reads and removing the read containing adapter, poly-N, and low-quality bases .p-value < 0.05 and |fold change| > 1.5 were considered as a final DEGs.Then, the cleaned data were mapped to the indexed reference genome by applying Hisat2. HTSeq was then applied to count the reads mapped to each gene . Moreovep-value < 0.05 to identify statistically significant pathways and GO functions. To examine pathway enrichment between control and PD conditions, Gene Set Enrichment Analysis (GSEA) was performed using the Broad Institute’s Molecular Signatures Database  and GSEA software (v4.1.0)  analyses, including Molecular Function (MF), Biological Process (BP), and Cellular Component (CC) enrichment analyses using the enrichR and clusterProfiler R packages . We used(v4.1.0) , 2015. I(v4.1.0)  and usin(v4.1.0) .http://bioconductor.org/ packages. Gene-gene expression-based correlation was performed using the https://CRAN.R-project.org/package=Hmisc/ Hmisc and Corrplot R packages https://CRAN.R-project.org/package=corrplot/ to calculate Spearman’s correlation and to perform visualization, respectively. We applied Corrplot with hierarchical clustering and set the significance level  to 0.01. In addition, we used the Complexheatmap package https://jokergoo.github.io/ComplexHeatmap-reference/ to visualize all heatmaps. We also employed ggplot2 to apply analysis of variance (ANOVA) and Student’s t-test to assess and visualize the statistical difference in multi and two groups, respectively. A p-value < 0.05 was considered a significant level.All statistical analyses were performed with R version 4.0.3 and the Bioconductor https://chemoinfo.ipmc.cnrs.fr/MOLDB/index.php). The structures were then optimized using Open Babel in PyRx. Subsequently, proteins structures were downloaded from (https://www.rcsb.org/). Afterward, using AutoDockTools , the structures were prepared for the molecular docking study, and nonessential chains, water, and ligand molecules, if present, were eliminated. The final structures were converted into PDBQT format. Docking simulations for all ligands in the prepared library and the selected proteins  was performed by AutoDock Vina 1.1.2 in the PyRx software. Visual illustration of the drug-protein interactions were generated with Discovery Studio visualizer 19.1.0.219 .We performed docking-based virtual screening to find new inhibitors that could target the pathways and proteins that were identified in our analyses. To this end, molecular structures of drugs that were approved by the FDA prior to 2021 with molecular weight ≤2000 g/mol were downloaded from e-Drug3D  in response to exposure to exogenous αSN aggregate species, we used GSE120569 datasets , and only a few nodes have high number of degrees (59 nodes with degree >200), suggesting that the PD-EASR network is a scale-free and very robust network . AdditioGO:0070997) and response to oxidative stress (GO:0006979) were the most significant GO: BP of the PD-EASR network  the expression pattern of EASR genes in the brain regions, and 2) identified co-expression modules and networks that are involved in each region, and also 3) determined co-expression network-related pathways which could contribute to αSN vulnerability. We also studied the putative roles of αSN-related genes and brain region co-expression networks in PD.https://gtexportal.org/home/) was utilized to examine the expression pattern of the EASR genes in 9 brain regions, including the amygdala, anterior cingulate cortex, caudate, cerebellum, frontal cortex, hippocampus, hypothalamus, putamen, and substantia nigra .Firstly, we examined the expression level of these genes in different brain regions. GTEx data  correlations with each other, their correlation coefficients were weak to moderate  between |0.1| and |0.4|)  , suggestIn addition to the region-specific expression of EASR genes, we extracted and analyzed co-expressed networks for all 9 regions of the brain and examined their functional annotation. We reconstructed networks by top 25 co-expression genes using the Inetmodels (considering positive and negative correlations) for each region. The constructed networks had 654–808 nodes and 9,007–10889 edges, respectively . We alsoAdditionally, we performed enrichment analysis for all EASR co-expression networks. We found that genes that correlated to EASR genes significantly enriched for “MYC targets V1”, “protein secretion”, “TNF-α signaling via NF-κB”, and “reactive oxygen species pathway” .GO:0006415), “cellular protein complex disassembly”, “translational elongation”, “co-translational protein targeting to the membrane” (GO:0006613), “protein targeting to ER” (GO:0045047), and “establishment of protein localization into the endoplasmic reticulum” (GO:0019083) and viral life cycle , “IL6 JAK STAT3 signaling” (NES = 2.1603885), “allograft rejection” (NES = 1.9858677), “inflammatory response” (NES = 1.8908404), “epithelial-mesenchymal transition” (NES = 1.850037), “angiogenesis” (NES = 1.8474189), “TGFβ signaling” (NES = 1.7642163), “interferon-gamma response” (NES = 1.6653343), “hypoxia” (NES = 1.626201), “complement” (NES = 1.6150334), “P53 pathway” (NES = 1.5878932), “apoptosis” (NES = 1.5682892), “KRAS signaling UP” (NES = 1.56), “IL2 STAT5 signaling” (NES = 1.56), “coagulation” (NES = 1.53), and “interferon alpha response” (NES = 1.4)  conditions. We observed that the EASR co-expression network was significantly (FDR <0.05) enriched and up-regulated in 3 hallmark pathways , includiS = 1.4) . ConsequWe also applied the same analysis for the EASR co-expression network in the amygdala and, interestingly, found no pathway to be significantly enriched in PD phenotype . TherefoDNAJB4, KLF2, KLF4, PPP1R15A, FOS, DUSP1, IER5, and NR4A1, and only NR4A2 were downregulated , only Pseudoephedrine can cross the blood-brain barrier (BBB). Therefore, we conducted virtual screening on FDA-approved drugs to identify new inhibitors for NR4A1 (PDB: 3V3E), DUSP1 (PDB: 6D66), and FOS (PDB: 1S9K) using their available structures. We performed docking simulations and then ranked the drugs according to binding affinity, focusing on the top 50 ranked drugs. Next, the common drugs considered as “TNF-α signaling via NF-κB” pathway inhibitors (https://go.drugbank.com/), 5 drugs  cross BBB and during PD could find use as inhibitors of the “TNF-α signaling via NF-κB” pathway. Docking simulations indicated entrectinib and irinotecan had the lowest negative energy for NR4A1, DUSP1, and FOS  to identify EASR genes. We reasoned that these genes, which are affected by αSN aggregation, might provide insights into molecular mechanisms of αSN toxicity and lead to effective treatments. Therefore, we applied systems biology approaches to characterize EASR genes functions in different brain regions and their association to PD.αSN is one of the principal factors associated with the onset and progression of PD . HoweverGO:0070997). The pathway enrichment analysis suggested that the association between “apoptosis”, “inflammatory response”, and “reactive oxygen species” pathways through the core PD-EASR network leads to loss of neurons in PD.In the first step, we constructed a PD-EASR network by mapping PD-related and EASR genes on the human PPI network. Subsequently, we examined the topological features of the PD-EASR network. This revealed that the PD-EASR network is a scale-free network, which is a common characteristic of biological networks . Also, tBy identifying the functional connection between EASR genes and PD, we next examined the expression of these genes in different brain regions to determine whether EASR genes have region-specific expression patterns. We observed that the mean expression of upregulated and downregulated EASR genes were significantly different across all 9 regions of a healthy brain. Specifically, cerebellum, frontal cortex, anterior cingulate cortex, and substantia nigra, showed the lowest mean expression level of upregulated-EASR genes. Although cerebellum function in PD has not been fully clarified, it has been demonstrated that morphological and functional modifications of the cerebellum are associated with αSN aggregation in patients with synucleinopathies , and itsOn the other hand, caudate and putamen  had the highest expression level of upregulated-EASR genes. The striatum is connected to the substantia nigra through the nigrostriatal pathway, one of the four major dopamine pathways . Howeverin vivo and in vitro studies that show NF-κB to be dysregulated and activated in PD  in the substantia nigra of PD patients. This result is supported by other ed in PD . Furthered in PD . Some sted in PD . Howevervia NF-κB” pathway. However, this association was seen in both the PD-EASR network and region-specific EASR co-expression network in healthy substantia nigra, amygdala, cortex, and putamen. Although the genes that altered in response to exogenous αSN were not directly involved in the “TNF-α signaling via NF-κB” pathway, they could be connected and could affect this pathway through a protein/region-specific co-expression network. Given that the EASR co-expression network in the amygdala has no significant alteration in this signaling pathway, it seems that the region-specific gene expression pattern in substantia nigra leads to higher vulnerability to exogenous αSN in PD.Pathway enrichment studies on EASR genes showed no association between EASR genes and the “TNF-α signaling Identifying and understanding molecular mechanisms behind the toxicity of αSN aggregation could pave the way towards more efficient treatments for PD patients. Hence, drugs that inhibit the TNF-α signaling via the NF-κB pathway, as a key pathway involved in αSN toxicity, could be an effective therapeutic approach for PD. Furthermore, our results represented EASR genes co-expression networks as a molecular mechanism to link PD and COVID-19. It has already been reported that PD patients with COVID-19 present aggravated parkinsonian symptoms, and higher mortality has been reported in patients with advanced PD . NeverthTargeting the αSN neurotoxicity pathway runs counter to most existing treatments that try to restore the dopaminergic system . TherefoAnother point is that this study was based on the SH-SY5Y cells line only. However, our examinations have shown that the EASR genes are not specific markers for dopaminergic, adrenergic or cholinergic neuron phenotypes. Therefore, regardless of the cell model, we could use the EASR genes for subsequent analyses. We reasoned that these genes could provide insights into molecular mechanisms of αSN toxicity and lead to discover new effective treatments. Moreover, in the next step of our study, we used the expression data of healthy brain tissue with various types of cells. Therefore, the effect of cell-specific pathways that are related to each glia or neuron cells has not been evaluated and needs more studies in the future.via NF-κB” pathway during PD could be one of the effects of exogenous αSN through the EASR genes co-expression network. In total, our observations provide a better insight into the pathology of exogenous αSN and may point the way towards future new treatments.In conclusion, we determined functional cross-links between EASR and PD-related genes in PPI and region-specific co-expression networks. Our finding identified genes and pathways that could be involved in toxicity and different vulnerability to exogenous αSN. Furthermore, we highlighted exogenous αSN effects in different brain regions by characterizing interactions between EASR genes and pathways in healthy brain regions. Also, these results suggest that an increase in the “TNF-α signaling


The markers “KukRi_c94792_127” and “wsnp_Ex_c298_580660” showed a significant correlation with grain yield, biomass and grain number and were associated with a significant increase in yield performance at the semiarid site . The ground cover was found associated with grain yield and biomass through the markers “wsnp_Ex_Rep_c67786_66472676” (+11%) and “KukRi_c49927_151” (+10%). One marker “TduRuM_contig25432_1377” on chromosome 5B at 20 cM was consistently correlated with the number of fertile spikes across both environments. Further research should be considered to validate the efficiency of these markers to undertake selection for drought tolerance under various environments and genetic backgrounds.The present research aims to identify the efficient combination of drought-tolerance selection criteria and associated quantitative trait loci. A panel of 197 bread wheat genotypes was evaluated for yield- and drought-tolerance-related traits in two environments (favorable and semiarid) for 2 years (2015–2016). Grain number, biomass, number of fertile spikes per plant and ground cover exhibited a significant correlation with grain yield and constitute potential secondary selection criteria for yield under drought conditions. About 73 significant marker–trait associations were detected along various chromosomal positions. The markers “ Triticum aestivum L.) is one of the most important staple crops in the world. It represents an important source of calories and proteins in most developing countries. Drought remains one of the main stresses threatening wheat production, especially under climate change conditions [Bread wheat  have been an effective and powerful tool in identifying candidate genes and mapping complex quantitative traits for many species. Taking advantage of the available large populations and high throughput sequencing technology, association mapping has gained importance over linkage mapping for the identification and mapping of marker trait associations (MTAs) without the need to develop a bi-parental mapping population ,19,20. TIn the current study, a large panel of 197 diverse bread wheat lines from ICARDA germplasm is phenotyped and sequenced using 15k SNP markers derived from the 90k Illumina iSelect arrays . Our hyp−1  compared to 3.02 t ha−1  for the semi-arid site “Sidi El Aidi”. ANOVA showed highly significant effects of genotypes for all traits at both stations. Similarly, significant genotypes x year interactions were observed, especially at the Sidi El Aidi experimental site.Both locations experienced periods of drought, especially in 2016 season. The humid site “Taoujdate” showed higher average yield with 3.87 t hap < 0.001), and number of fertile spikes per plant (NFSP) for both experimental sites. The ground cover (GC) showed high positive correlation with grain yield at the semi-arid station , while it was very weak  at the optimum conditions. There was no significant correlation observed between days to flowering (DTF) and grain yield (Grain yield expressed significant positive correlation with biomass (BM), grain number (GN)  .Path analysis showed that GN had the highest direct effect on both environments . Under the dry environment, the GC also had a significant direct effect on grain yield (0.31), whereas NFSP and BM act indirectly supporting GN effect. On the other hand, only BM had an important indirect effect through GN at Taoujdate conditions (0.58) .Additionally, GC was also able to explain a great percentage of BM, GN and NFSP variations  at the Sidi El Aidi station as compared to the low variations under Taoujdate conditions .p < 0.001  was detected along various chromosomes for yield- and drought-related traits at  < 0.001 . Most ofBS00067775_51) at the favorable rainfed station “Taoujdate” with significant increase in yield , in addition to the markers “TduRuM_contig14482_1013” and “RAC875_c78248_154”  showed a significant yield increase of 10% (+0.32 t/ha) under drought conditions. Moreover, the lines carrying the G base at the marker “wsnp_Ex_Rep_c67786_66472676”  increased their yield by 11%  at the dry site. All these markers accounted for 5 to 7% of the variance (For grain yield (GY), three highly significant markers were located on chromosomes 4B . The marker “RAC875_c34888_65”  identified at Taoujdate is only 3 cM far located from the marker “TduRuM_contig42479_3800”  at the Sidi El Aidi site. Twelve MTAs were detected for NFSP on chromosomes 5B, 7B, 7D and 2B for Taoujdate at p < 0.001, whereas seven MTAs were associated with the chromosomes 5B and 7B at Sidi El Aidi at p < 0.003. One marker on chromosome 5B at 20 cM (TduRuM_contig25432_1377) was consistent across both the Taoujdate and Sidi El Aidi locations.Regarding yield components, six MTAs were associated with BM on chromosomes 1A, 5D and 3A at the Taoujdate station, while six significant associations were identified at the Sidi El Aidi site on chromosomes 1D, 2B and 2D, at p < 0.001  at the Sidi El Aidi site. The highest number of significant MTAs were detected for GC on the chromosomes 7B, 1D, 5A, 7A for Taoujdate and on the chromosomes 2B, 3A, 6A and 6B for Sidi El Aidi at  < 0.001 .KukRi_c94792_127” was linked to GY, BM and GN on chromosome 2B (153 cM). This marker allowed a yield increase of 7% (+0.22 t/ha) for the genotypes holding the “G” base in comparison with the “A” base. At the same chromosome, the marker “wsnp_Ex_c298_580660” (154 cM) was detected for the same traits and exhibited a significant yield increase of 11%  when holding the T allele , “ExcalibuR_c24593_1217” (T), “wsnp_Ex_Rep_c67786_66472676” (G), “wsnp_Ex_c3145_5812670” (T), “wsnp_Ex_c298_580660” (A) and “KukRi_c49927_151” (T), and enabled a high yield over drought and optimum conditions.The derivative synthetic lines “OPATA/RAYON//KAUZ/3/2 * MILAN/DUCULA” and “PFAU/MILAN” achieved the highest yield performances under stressed and optimum conditions. Their grain yield varied from 4.5 to 4.7 t/ha under drought conditions and from 4.7 to 4.5 t/ha under a favorable environment with a respective genetic gain of 35 and 26%. These lines incorporated five to six of the main identified markers, namely “Breeding for drought tolerance is one of the top priorities in most wheat breeding programs worldwide. A number of important yield-related traits play an important role in drought resistance mechanisms and influence either directly or indirectly grain yield ,34,35. TPhenotypic correlations showed that grain yield is positively correlated with grain number at both sites, Sidi El Aidi (semi-arid) and Taoujdate (favorable rainfed). These results are in agreement with many previous studies that highlighted the importance of grain number as a critical determinant of yield in wheat ,34,35,36In addition, grain yield was positively correlated with biomass and number of fertile spikes per plant under optimum and stressed conditions. These two parameters contributed indirectly through grain number on yield improvement, especially under a drought environment. An important above ground biomass enables an active photosynthesis process and presents a positive correlation with root biomass and length to meet the nutrient requirements of the plant . AdditioOn the other hand, our results show that grain yield expressed a strong positive correlation with ground cover, especially under the dry environment. This physiological trait was able to explain a great part of yield variation through its impact on biomass, grain number and to a lesser extent the number of fertile spikes per plant. Indeed, early development contributes to a rapid coverage of the soil surface, thereby conserving soil moisture and promoting root development. Identifying new sources of germplasm with early vigor and early ground coverage is therefore of outmost importance .p < 0.001) at the Taoujdate and Sidi El Aidi stations. In line with earlier studies [Association mapping yielded a total of 73 significant MTAs . Previous studies have reported drought-resistance genes on the same chromosomes [wsnp_Ex_Rep_c67786_66472676”  and “ExcalibuR_c24593_1217”  detected for Sidi El Aidi had a significant impact on yield improvement . The marker “wsnp_Ex_Rep_c67786_66472676” has been aligned to the scarecrow-like protein 1, a transcriptional regulator mastering growth repressors [ExcalibuR_c24593_1217”, also known by the names “BS00128708” and “IWB24184”, was related to Yr genes and was linked to plant-drought adaptability related traits [Given its polygenic character, grain-yield-related QTLs have been reported on different chromosomal positions ,56,57,58omosomes ,60,61. Momosomes  and Qassomosomes . The marpressors ,64, wherd traits .Ra_c4397_542” to 10% “KukRi_Rep_c109397_59”. On the other hand, seven MTAs were identified for the semi-arid environment on chromosomes 5B and 7B [TduRuM_contig25432_1377” is linked to tauschii probable polyamine transporter At1g31830 [Additionally, twelve MTAs associated with fertile spikes number were identified in the present study on chromosomes 2B, 5B, 7B and 7D ,56,61 atB and 7B ,59,60,61t1g31830 . One comFurthermore, significant MTAs were detected for the remaining drought-related traits namely TKW and GC. The MTAs detected were environment-specific and genetically unstable over environments. This demonstrates the presence of a very strong QTL x environment interaction for yield- and drought-related traits as reported by Edae et al. .Given the polygenic character of drought tolerance expression, pleiotropic effects are particularly useful in the context of crop improvement, as they allow the breeder to select simultaneously for multiple traits ,62. ManyKukRi_c94792_127” and “wsnp_Ex_c298_580660” on chromosome 2B  associated with grain yield, biomass and grain number and showed a significant increase in yield performance at the sem-iarid environment (+7 and +11%) when holding, respectively, the “G” and “A” nucleotides. Furthermore, ground cover was linked to grain yield and biomass on chromosome 3A via the marker “wsnp_Ex_Rep_c67786_66472676”. This marker showed an increase of 0.38 t/ha on yield performance. The marker “KukRi_c49927_151” associated with grain yield and ground cover showed a yield improvement of 0.37 t/ha. Many studies have reported that chromosome 2B and 3A carry productivity and adaptability related genes [In the present study, one QTL harbored two markers “ed genes ,71. Thesed genes .A panel of 197 spring bread wheat genotypes, originating from the ICARDA bread wheat breeding program, was assessed to identify closely associated markers for grain yield and various agro-physiological traits related to drought tolerance. This panel consists of synthetic derived lines, cultivars from the Central and West Asia and North Africa (CWANA) region, and elite lines from ICARDA’s wheat breeding program . This paThe mapping population was evaluated under contrasting field conditions at the Taoujdate and Sidi El Aidi experimental stations of the National Institute of Agricultural Research (INRA-Morocco). The Sidi El Aidi station is located at the semi-arid zone of Morocco (Settat region) (<300 mm), while Taoujdate station belongs to the favorable humid agro-ecological zone (Sais region) (>400 mm).Following an alpha lattice design with two replications, the panel was planted in 6 rows plots of 3 m length and with 0.25 m spacing between rows. The trial was conducted at both experimental stations (Taoujdate and Sidi El Aidi) during two cropping seasons (2015 and 2016). The cropping seasons were dry; however, 2016 was drier than 2015 season. The Taoujdate site received 407 mm in 2015 versus 321 mm during 2016 season. On the other hand, the Sidi El Aidi site accumulated 258 and 135 mm in 2015 and 2016 cropping seasons, respectively. The average temperatures were also higher during 2016 season with 21 °C and 18 °C for Taoujdate and Sidi El Aidi, respectively, as compared to 15 and 14 °C during 2015 season.Agronomic management was performed according to the recommended practices at each location. Chemical treatments against foliar diseases and weeds were performed as needed during the crop cycle. For each trial, days to flowering was recorded for each plot when 50% of the plants in a plot reached the Zadoks’ stage 58 (flowering stage). At harvest, aboveground biomass (BM) was determined by cutting from the ground level the plants in one linear meter from a central row of each plot. From this sample, the number of fertile spikes (NFS) and the number of grains per m² (GN) were counted. Thousand-kernel weight (TKW) was calculated by weighing 1000 grains sample. Grain yield (GY) was recorded from 4.5 m² of the harvested plot and converted to the standard unit at metric ton per hectare (t/ha). Moreover, ground cover was represented by soil cover percentage using digital camera photos and Sigma Scan Pro 5.0 software .GenStat 18  was used to carry out ANOVA and basic statistics for yield- and drought-related traits across environments. Following the mixed-model approach for multiyear alpha-lattice designs, the genotype, year, and genotype x year were considered fixed factors, while the interactions year x replication and year x block were considered random. Additionally, IBM SPSS version 21  was used to perform Pearson’s correlation and regression analysis.The lines were genotyped by a service provider company  using 15K single nucleotide polymorphism (SNP) from the wheat 90 K Illumina iSelect SNP array . The genp-values ≤ 0.001 for each pair of loci were considered significant. The LD decay was slower in the D genome (7 cM) compared to A and B genomes (3 cM)  .p-value of 0.001 were considered as a significant association and the Manhattan plots were generated using GAPIT under R software (The GAPIT program was used to identify the best model and find marker trait associations (MTAs) for each trait. Based on Bayesian Information Content (BIC), the model with the highest value was the simplest one using only the kinship model (MLM+PCA). Best linear unbiased estimations for the genotypic factor and the corresponding marker data were used to perform GWAS analysis. All the detected MTAs at a critical software .ExcalibuR_c24593_1217” (T), “wsnp_Ex_Rep_c67786_66472676” (G), “wsnp_Ex_c298_580660” (A), “KukRi_c49927_151” (T) and “Kukri_c94792_127” (G) were the most important ones showing significant mean yield increase varying from 7 to 11%. Further investigations should be carried out to validate the efficiency of these markers in the selection for drought tolerance under various environments and genetic backgrounds. The top high yielding lines identified from the current study will be considered for potential release targeting the semi-arid lands in Morocco after agronomic validation trials.In light of these results, the grain number and biomass supported by the number of fertile spikes per plant and ground cover have a significant impact on yield improvement under dry conditions and constitute potential secondary selection criteria for drought resistance. The GWAS analysis identified significant associations between markers and target traits at various chromosomal positions, especially on chromosomes 2B and 5B followed by 3A and 5A, respectively. Some linkage groups involved multiple traits of interest reflecting eventual pleiotropic effects, which are of great interest for gene pyramiding. Our results indicated that the genotypes holding the positive allele of the markers “


Fracture phenomenain soft materials span multiple length and timescales. This poses a major challenge in computational modeling andpredictive materials design. To pass quantitatively from molecularto continuum scales, a precise representation of the material responseat the molecular level is vital. Here, we derive the nonlinear elasticresponse and fracture characteristics of individual siloxane moleculesusing molecular dynamics (MD) studies. For short chains, we find deviationsfrom classical scalings for both the effective stiffness and meanchain rupture times. A simple model of a nonuniform chain of Kuhnsegments captures the observed effect and agrees well with MD data.We find that the dominating fracture mechanism depends on the appliedforce scale in a nonmonotonic fashion. This analysis suggests thatcommon polydimethylsiloxane (PDMS) networks fail at cross-linkingpoints. Our results can be readily lumped into coarse-grained models.Although focusing on PDMS as a model system, our study presents ageneral procedure to pass beyond the window of accessible rupturetimes in MD studies employing mean first passage time theory, whichcan be exploited for arbitrary molecular systems. This basic concept also appliesto the failure of soft materials, emerging from the rupture of interatomicbonds. Predicting the fracture journey that follows becomes a questionof failure mechanisms and length scales.elasto-adhesive length. Thislength scale is typically microscopic and represents the region ofnonlinear elastic deformation around a macroscopic crack tip.3 It can be coupled to molecular failure processesat small scale7 as well as energy dissipationat the mesoscale10 and macroscopic effects such as crack blunting.12 In a recent work, scale-free cavity growth at constant driving pressurewas accessed in the mesoscopic region.13 In this picture, no well-defined crack tip exists and correspondingprocess zones for the calculation of fracture energies becomes obsolete.Multiple length scales formthe basis of the classical fracturemechanics picture. In the ideally brittle limit, dissipation and materialfailure occur on the scale of the atomistic separation length. Insoft tough materials, the characteristic length scale in the continuumlimit is the so-called Fracture in soft solids thus displays manifold characteristicsthat are deviating from classical theories. To get further insightinto what governs these deviations, multiple length and time scalesneed to be bridged, which poses a major computational challenge. Here,we address this challenge by providing a detailed description of thenonlinear elastic response of molecular building blocks up to fracture.These building blocks can then provide starting grounds for higherlevel coarse grained models.17 optical tweezers,20 and magnetic tweezers.23 Due to itslarge accessible force range up to ) and high resolution,AFM has been widely adopted.24 Investigationsusing AFM comprise a wide spectrum, ranging from proteins,26 DNA,28 polysaccharides,29 poly(ethylene glycol),30 and poly(methacrylicacid)31 to polydimethylsiloxane (PDMS).32Previous studies on the force–extensionrelation and fractureof individual molecules encompass both experimental and computationalinvestigations. Experimental studies include atomic force microscopy(AFM),34 simulations allow foran on-the-fly computation of electronic structuresbased on quantum mechanics. While bond fracture can be modeled inthis setting, high computational costs limit AIMD studies to ) and ).37 At higher lengthand time scales, steered molecular dynamics (MD) simulations haveemerged as the primary method in studying the force–extensionbehavior of molecules.41 Classical MD methods are amenable of treating system sizes of severalhundreds of nanometers and time scales on the order of nanoseconds.However, atomic interactions are typically modeled via empirical interatomicpotentials, which require a predefined atomic connectivity remainingunchanged throughout simulations, such that fracture of interatomicbonds cannot be described. As an alternative, bond-order-based forcefields were developed to bridge the gap between ab initio and empiricalforce fields. Here, we derive the quasi-static force–extensionand rupture properties of single molecules up to 46 with the help of the LAMMPS software package.47 Unlike classical atomistic bond potentials, ReaxFF allowsfor different atomic bonding states, such that fracture events canbe captured. Simulations thus reduce the gap between length and timescales accessible using ab initio computational methods and experimentalapproaches. We focus on PDMS as a model system as used in previousstudies,13 for which both linear PDMS andcross-linked PDMS are investigated.Using computational methods, ab initiomolecular dynamics (AIMD)22.1n molecules of varying polymerization degree n arecreated. n as anexample. Each PDMS-n molecule is embedded in a simulationbox, which is set up both with and without solvent molecules. Whensolvent molecules are present, periodic boundary conditions are applied.We use hexamethyldisiloxane (HMDSO) molecules as a solvent, as interactionsbetween HMDSO and PDMS do not alter the rupture behavior of PDMS (comparedto interactions with itself).37 In comparison,trace amounts of water were found to lower the maximally attainedrupture stretch.37Priorto failure, the static molecular response is governed by entropicelasticity at extensions well below the unstretched contour lengthand enthalpic elasticity at higher extensions. The exact shape ofthis nonlinear elastic force–extension relation depends onthe specific molecular structure under investigation. To derive thenonlinear elastic response of siloxane molecules, PDMS-43 Withoutsolvent molecules, the number of degrees of freedom is 3na, with na being the numberof atoms in PDMS-n. na scales linearlywith polymerization degree n. For simulations inwhich solvent molecules are present, the overall system size increasesby 3ns degrees of freedom based on ns solvent molecules. There is no upper constrainton ns. Its lower bound is set by the requirementof generating sufficiently large RVE′s for subsequent steeredmolecular dynamics runs, preventing self-interactions. For simulationsof PDMS-27 up to fracture, ns/na ∼ 60 amounts to 60 × 3na degrees of freedom. Here, the multiplicativefactor of 60 stems from the presence of solvent molecules. In allsimulations, a time step of 0.1 fs is applied. Systems are relaxedin an NPT ensemble at ambient conditions . Following relaxation, a constant repulsiveforce F between the two terminal Si atoms is appliedin an NVT ensemble. In this ensemble, volume V isheld constant, such that the equilibrated end-to-end distance is purelybased on the applied force .Results are compared to a displacement controlled setting, in whichboth terminal Si atoms are held constant at fixed end-to-end distance R and the exerted force is recorded. R ≪ L) and enthalpic (R > L) regimes, where the unstretched contourlength L marks the crossover point. For comparisonwith classicalpolymer models, the inset of 21 for an end-to-end chain distance R approaching the unstretched contour length L = 6.4 nm. In contrast, the elastic freely jointed chain model (EFJC)48 captures the nonlinear elastic force–extensionrelation also within the enthalpic regime R > L. The change of slope at large forces is encoded in the F-dependent bond potential of mean force U, as investigated in moredetail in All simulations are performed with the parameterset specificallytrained and optimized for PDMS.F/F0). Within theentropic regime, elasticity is modeled via the Langevin function K as an additional elastic parameter within the enthalpicregime.The force–extension curve at large deformation islinear.As expected from the EFJC model, the force–extension relationof a single polymer chain is given asF0, and T = 1 K is chosen to reduce thermal noise. All other simulations areperformed at T = 300 K. Note that in this study wefocus on the enthalpic regime, in which temperature effects on themechanical response become negligible. Insensitivity of F0 toward both temperature and solvent molecules in theenthalpic regime is tested for short oligomers . We findthat both temperature and solvent molecules do not influence F0 in the enthalpic regime. For small forces F ≪ F0 in the entropiclimit, we have R(F) ≃ F/K̃, with K̃ = 3kBT/(LLk) the elastic Hookean spring constantwithin the entropic regime. For large forces F ≫ F0 in the enthalpic limit, R(F) ≃ F/K, as the Langevin function Lk is obtained from fittingthe EFJC model to the measured force–extension curve at T = 300 K (see L) is shown in Figure S2). Furthersupport giving an independent estimate of Lk from analyzing the Si–Si vector correlationfunction is given in Supporting Information Section S2. Here, Lk = 5.5 ± 0.7 Å is the Kuhn length of the polymer chaincorresponding to the mean end-to-end distance of a Si–O–Si–O–Sitriplet, which in the following is abbreviated as Si–Si–Si.For computational efficiency, solvent molecules areremoved forthe determination of 00 K see 1c. A comn = 2, theresultant slope F0 when plotting force F versus stretch R/L attainsits maximum value F0 = 31.35 nN .Using a fit to simulation results for PDMS-5 to calculate the remainingfree parameters, we find that ki = 40.82 ± 0.01 nN/nm and li = 0.48 ± 0.01 nm of the internal Kuhn segment.As shown by the solid black line in n as well as convergence of F0 to a plateau at large n.For a low polymerization degree of Lk based on tworeasons: First, the entropic part of the force–extension curvesuggests Lk to be identicalwith the extension of a Si–Si–Si triplet. Second, n dependencies of K and L are consistently captured only if the number (n/2) of Si–Si–Si triplets is used in F-dependent characteristics of single covalent atomic bonds.To summarize,the elastic response of PDMS oligomers  is characterized by the Si tripletlength 2.2At the molecularscale, fracture is stochastic. An intuitive question to ask is, “whereand when does a network tend to break?”. Here, we try to quantitativelyanswer this question for PDMS in terms of mean rupture times and preferredfracture modes.n backbone (chain scission) and ruptureat cross-linking sites (cross-link failure), we takeinto account two different structures: PDMS-n asused in the previous section as well as two PDMS-4 molecules linkedvia a cross-linking site −CH2–CH2. Chain scission thus stems from the rupture of Si–O bonds,while cross-link failure results from rupturing Si–C bonds.The accessible window of mean rupture times in MD studies lies inthe range of 10–2–100 ns. Theupper limit is set by computational feasibility, while the lower limitdepends on the molecular vibration frequency of the polymer chainbelow which inertial effects dominate the response.To distinguish between rupture of the PDMS-F) on longer time scales, weuse a statistical extrapolation scheme. Our approach renders a closeanalogy to the calculation of mean first passage times for chemicalprocesses with a single reaction coordinate,49 for the thermal or enforced breakage of discrete one-dimensionalchains,50 Morse chains,51 and biomolecules.52 Its derivationis provided in the Supporting Information. We proceed in the following way: Stationary equilibrium Si–Oand Si–C bond length probability densities p(b) of PDMS-4, PDMS-376, and linked PDMS-4 are measuredat different levels of constant force (cf. p(b), we calculate mean chain rupture times, for which we need to passfrom rupture times of single bonds to those of chains with 2n bonds.To extendbeyond this rupture time window and determine mean bondrupture times τ(orce cf. 2. Using p(b) serve to define an effective potential,withbr is the rupture bond length. For later calculations of meanchain rupture times, we need a functional form of the effective bondpotential U. In the following, using the notation U, we emphasize thatthe potential is a function of bond length b, whileits parameters (in this case b1) dependon F. Numerically solving for U from U needs to satisfy thefollowing properties: It should have the generic form of a double-wellpotential  with minima corresponding to twodifferent equilibrium bond lengths . Here, we denote b1 as theequilibrium bond length corresponding to the first minimum and choose U(b1) = 0 for convenience. Mostimportantly, we observe a nearly F-independent parabolicshape of U″(b) about itssecond minimum at b ≃ b2, i.e., U″(b) = c2 + k2(b – b2)2 . Because U″(b) exhibits a parabolic and F-independentshape and location, the corresponding parameters b2, c2,and k2 can be treated as F-independent constants.This finding forms the basis of rendering our statistical extrapolationscheme feasible because b1(F) remains as the only force-dependent fitting parameter. In addition,we only observe a weak dependence of b1 on F, which forms the basis for an extrapolationto higher force regimes. These observations lead to a functional formof U asTable S1. The resulting radial bond potentials of mean forceare illustratedin b2 = k2 = 0). Note that fitting deviations in Si–Cpotentials are based on restricting b1(F) to be the only force-dependent parameter. Thelargest possible instantaneous Si–O an Si–C bond lengthvalue in stable chain configurations is given in Table S1. As shown in At fixed force, directly measuredsingle bond probability densities ibutions2a,b aregths cf. S7. Here,gths cf. S7. Here,U at hand, we proceed with the calculation of mean chainrupture times, passing from rupture times of single bonds to thoseof chains with 2n bonds. Furthermore, it needs tobe verified that a theory neglecting inertia effects captures theattendant fracture characteristics.With anexpression for 55n. ζ is ana priori unknown friction coefficient, which will be determined laterby matching theoretical rupture times τn(F) with those obtained from MD simulations.Utilizing the Fokker–Planck approach, eq S-2  can be used to explore the rupture timedistribution p of a single bond, which is nearly monoexponential.Neglecting inertia effects,the mean rupture time of a single bondis calculated from the Fokker–Planck equation aspn of a chain with polymerizationdegree n (which thus contains 2n bonds), we assumeindependent bonds. The probability of a chain  rupturing during time interval t after onset of F at time t = 0 ist. The probabilitydistribution for rupture times tr of n-chains (PDMS-n) isthus pn = (d/dtr)Pn = 2nentr/τ(F)–2/τ(F), from which the mean chain rupture time τn(F) follows as τn(F) = τ(F)/2n. We compare these theoretical expressions tothose measured in MD simulations. p4, whichis in agreement with the Fokker–Planck prediction for a singlebond and the assumption of independent bonds in chains of higher polymerizationdegree.In order to pass to the rupture time distribution n(F) at threedifferent constant stretching forces F, for whicheach data point is the average of 10000 independent samples. For large n, τn(F) approaches the expected ∝1/n limit. Deviationsfrom this scaling for short chains are reminiscent of the nonuniformchain of springs effect highlighted in F =6.25 nN are obtained as a0 = −24± 1 and a = 0.108 ± 0.004, while at F = 6.11 nN, a0 = −9.1± 0.4, and a = 0.28 ± 0.01. Single bondmean rupture times depicted in Si–O(F) = limn → ∞2nτn(F) = 2a ns. For Si–C bonds (which are presenttwice in linked PDMS-4), force levels of F = 5.21nN, F = 5.28 nN, and F = 5.35 nNare investigated. This force range in MD already spans 2 decades insingle-bond mean rupture time τ(F). The resultingsingle bond mean rupture time is computed as τSi–C(F) = 2τlinked-PDMS-4(F).n withthe theoretically predicted one, we can furthermore determine ζ. Solid lines in F) resulting from the Fokker–Planck equation .By matching the measured τequation . This soequation 3c. We fin, τnSi–O(F) decreases, while τnSi–C(F) is constant  at different levelsof applied force. Tracking the crossover polymerization degree nc allows to identify two differentfailure regimes: For n < nc, cross-link failure is anticipated, whilechain scission is the preferred failure mode for n > nc. n and F. Again, the crossover polymerization degree nc differentiates a region dominated bycross-link failure (green) from a regime dominated by chain scission(blue).To determine preferred fracture mechanisms, we note that with increasingpolymerization degree 56 myosin and actin,57 or signalingreceptors and their ligands.59 This strengtheningemerges as a “re-entrant” effect of cross-link failurefor polymerization degrees n > 103,whichcan be related to the higher order structure of Si–O bond potentials. Si–O bonds are stable at low forces, at whichthe failure of cross-linking junctions is the dominating fracturemechanism. At intermediate forces, chain scission dominates. At highforces, at which the increasing stiffness of the second minimum inSi–O potentials comes into play, fracture characteristics aredominated by cross-link failure again. With increasing n, the force regime dominated by chain scission grows, which is inkeeping with We observe a strengthening effect in Si–O bonds with increasingforce, which is reminiscent of phenomena observed in systems involvingcatch bonds, e.g., membrane-to-surface adhesion,n. Single molecules in Sylgard184 and DMS-V31 are entirely dominated by cross-link failure. In contrast,individual molecules in Sylgard 186 feature a much higher polymerizationdegree. As such, their fracture behavior strongly depends on the appliedforce, with cross-link failure in the low force regime transitioningto chain scission at F > 2.5 nN.Typical siloxane materials used in the laboratory setting are highlightedin pn. While the dynamics of bondlengths exhibits inertia effects, we find the rupture time distributionto be unaffected by the presence/absence of explicit solvent molecules,as shown in Figure S8. Without solventmolecules, inertia effects are maximal and friction is absent. Thepresence of solvent molecules provides additional noise and stochasticcollisions, such that inertia effects are diminished. The rupturetime distribution is thus also unaffected by the degree of suppressionof inertia effects. Furthermore, we observe a nearly monoexponentialrupture time probability distribution, in which the majority of bondsdoes not break during the first oscillation but at later times. Thisis in stark contrast to the dominance of inertial effects, for whichbonds that are still intact after the first oscillation would neverfail. In theabove, we model rupture time distributions using an inertia-freeFokker–Planck approach. To justify this approach, it remainsto investigate the absence of solvent molecules on rupture time distributions 3n, we find a deviationfrom a classical scaling of effective stiffness K ∝ 1/n, which can be captured with a simplemodel of nonuniform chains of springs, with each spring constitutinga Kuhn segment.This work characterizesthe nonlinear elastic and fracture behaviorof PDMS. The nonlinear elastic response of siloxane oligomers is capturedwell using the EFJC model, within both entropic and enthalpic regimes.At low polymerization degrees n(F) ∝ 1/n) at low polymerization degrees. Similar to the nonlinear elasticpart, a model including the “end effect” on mean chainrupture times agrees well with simulations.Passing to the inelastic behavior of PDMS, wefocus on rupturetimes of both Si–O bonds (present in the backbone of siloxaneoligomers) as well as Si–C bonds (present at cross-linkingsites). When calculating mean chain rupture times of siloxane oligomers,we again observe a deviation from classical scalings (τnc at which thedominating rupture mechanism of the cross-linked network passes fromcross-link failure (rupture of Si–C bonds) to chain scission(rupture of Si–O bonds on PDMS-n). To passto long time scales, we use a statistical extrapolation scheme inorder to understand bond fracture within the network. Surprisingly,we find that the dominating fracture mechanism depends on the appliedforce scale in a nonmonotonous fashion. The nonmonotonic dependenceof nc on F is rooted in nonlinearities in the Si–O bond potential andthe corresponding stiffness dependence on force at the two minima.We find that thelifetime of single Si–O bonds is much longerthan that of a Si–C bond. We define a crossover polymerizationdegree F > 2.5 nN. It furthermore bearsmentioningthat our analysis focuses on the single chain level. Possible inhomogeneitiesin force distribution based on network topology (and the resultantchanges in fracture characteristics) furnish an important point forfuture studies. These could aid in elucidating network propertiespassing from the single chain to the continuum level, focusing onthe influence of polymerization degree and cross-link density.For single molecules in typical siloxane materials used in thelaboratory setting, such as Sylgard 184 and DMS-V31, our analysissuggests breakage exclusively at cross-links. For individual moleculesin Sylgard 186 featuring higher polymerization degrees, however, theattendant failure mode depends on the magnitude of applied force.While cross-link failure dominates at low forces, chain scission isexpected for Our results provide building blocks, which can be readily usedin coarse-grained higher scale models. As an example, network modelsof nonlinear springs could be easily tailored to siloxane systemsby implementing a material model corresponding to the nonlinear elasticresponse derived in this work. In this setting, cross-linking moleculescould be lumped into nodes representing cross-linking sites. Trackingattendant forces upon deformation would then allow for the implementationof fracture criteria corresponding to those derived in this work.Finally, our work provides a generic procedure to pass beyond thewindow of accessible rupture times in MD studies, which can be appliedfor arbitrary molecular systems.