Self-similarity and vanishing diffusion in fluvial landscapes.

Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems.

Exome-wide association study to identify rare variants influencing COVID-19 outcomes: Results from the Host Genetics Initiative.

Host genetics is a key determinant of COVID-19 outcomes. Previously, the COVID-19 Host Genetics Initiative genome-wide association study used common variants to identify multiple loci associated with COVID-19 outcomes. However, variants with the largest impact on COVID-19 outcomes are expected to be rare in the population. Hence, studying rare variants may provide additional insights into disease susceptibility and pathogenesis, thereby informing therapeutics development. Here, we combined whole-exome and whole-genome sequencing from 21 cohorts across 12 countries and performed rare variant exome-wide burden analyses for COVID-19 outcomes. In an analysis of 5,085 severe disease cases and 571,737 controls, we observed that carrying a rare deleterious variant in the SARS-CoV-2 sensor toll-like receptor TLR7 (on chromosome X) was associated with a 5.3-fold increase in severe disease (95% CI: 2.75-10.05, p = 5.41x10-7). This association was consistent across sexes. These results further support TLR7 as a genetic determinant of severe disease and suggest that larger studies on rare variants influencing COVID-19 outcomes could provide additional insights.

Mendelian pathway analysis of laboratory traits reveals distinct roles for ciliary subcompartments in common disease pathogenesis.

Rare monogenic disorders of the primary cilium, termed ciliopathies, are characterized by extreme presentations of otherwise common diseases, such as diabetes, hepatic fibrosis, and kidney failure. However, despite a recent revolution in our understanding of the cilium's role in rare disease pathogenesis, the organelle's contribution to common disease remains largely unknown. Hypothesizing that common genetic variants within Mendelian ciliopathy genes might contribute to common complex diseases pathogenesis, we performed association studies of 16,874 common genetic variants across 122 ciliary genes with 12 quantitative laboratory traits characteristic of ciliopathy syndromes in 452,593 individuals in the UK Biobank. We incorporated tissue-specific gene expression analysis, expression quantitative trait loci, and Mendelian disease phenotype information into our analysis and replicated our findings in meta-analysis. 101 statistically significant associations were identified across 42 of the 122 examined ciliary genes (including eight novel replicating associations). These ciliary genes were widely expressed in tissues relevant to the phenotypes being studied, and eQTL analysis revealed strong evidence for correlation between ciliary gene expression levels and laboratory traits. Perhaps most interestingly, our analysis identified different ciliary subcompartments as being specifically associated with distinct sets of phenotypes. Taken together, our data demonstrate the utility of a Mendelian pathway-based approach to genomic association studies, challenge the widely held belief that the cilium is an organelle important mainly in development and in rare syndromic disease pathogenesis, and provide a framework for the continued integration of common and rare disease genetics to provide insight into the pathophysiology of human diseases of immense public health burden.

Unraveling a history of overlap: A phenotypic comparison of RBCK1-related disease and glycogen storage disease type IV.

RBCK1-related disease is a rare, multisystemic disorder for which our current understanding of the natural history is limited. A number of individuals initially carried clinical diagnoses of glycogen storage disease IV (GSD IV), but were later found to harbor RBCK1 pathogenic variants, demonstrating challenges of correctly diagnosing RBCK1-related disease. This study carried out a phenotypic comparison between RBCK1-related disease and GSD IV to identify features that clinically differentiate these diagnoses. Literature review and retrospective chart review identified 25 individuals with RBCK1-related disease and 36 with the neuromuscular subtype of GSD IV. Clinical features were evaluated to assess for statistically significant differences between the conditions. At a system level, any cardiac, autoinflammation, immunodeficiency, growth, or dermatologic involvement were suggestive of RBCK1, whereas any respiratory involvement suggested GSD IV. Several features warrant further exploration as predictors of RBCK1, such as generalized weakness, heart transplant, and recurrent infections, among others. Distinguishing RBCK1-related disease will facilitate correct diagnoses and pave the way for accurately identifying affected individuals, as well as for developing management recommendations, treatment, and an enhanced understanding of the natural history. This knowledge may also inform which individuals thought to have GSD IV should undergo reevaluation for RBCK1.

Microcystic lymphatic malformations in Turner syndrome are due to somatic mosaicism of PIK3CA.

Turner syndrome (45,X) is caused by a complete or partial absence of a single X chromosome. Vascular malformations occur due to abnormal development of blood and/or lymphatic vessels. They arise from either somatic or germline pathogenic variants in the genes regulating growth and apoptosis of vascular channels. Aortic abnormalities are a common, known vascular anomaly of Turner syndrome. However, previous studies have described other vascular malformations as a rare feature of Turner syndrome and suggested that vascular abnormalities in individuals with Turner syndrome may be more generalized. In this study, we describe two individuals with co-occurrence of Turner syndrome and vascular malformations with a lymphatic component. In these individuals, genetic testing of the lesional tissue revealed a somatic pathogenic variant in PIK3CA-a known and common cause of lymphatic malformations. Based on this finding, we conclude that the vascular malformations presented here and likely those previously in the literature are not a rare part of the clinical spectrum of Turner syndrome, but rather a separate clinical entity that may or may not co-occur in individuals with Turner syndrome.

Unmasking the challenges of Kabuki syndrome in adulthood: A case series.

Kabuki syndrome is a recognizable Mendelian disorder characterized by the clinical constellation of childhood hypotonia, developmental delay or intellectual impairment, and characteristic dysmorphism resulting from monoallelic pathogenic variants in KMT2D or KDM6A. In the medical literature, most reported patients are children, and data is lacking on the natural history of the condition across the lifespan, with little known about adult-specific presentations and symptoms. Here, we report the results of a retrospective chart review of eight adult patients with Kabuki syndrome, seven of whom are molecularly confirmed. We use their trajectories to highlight the diagnostic challenges unique to an adult population, expand on neurodevelopmental/psychiatric phenotypes across the lifespan, and describe adult-onset medical complications, including a potential cancer risk and unusual and striking premature/accelerated aging phenotype.

Comparison of Transthoracic Contrast Echocardiography with High-Resolution Chest CT after Embolization of Pulmonary Arteriovenous Malformation.

PURPOSE: To compare postembolotherapy follow-up graded transthoracic contrast echocardiography (TTCE) and high-resolution computed tomography (CT) of the chest and to evaluate the use of graded TTCE in the early postembolic period. MATERIALS AND METHODS: Thirty-five patients (6 men and 29 women; mean age, 56 years; range, 27-78 years) presenting for postembolotherapy follow-up between 2017 and 2021 with concurrent high-resolution CT and graded TTCE were analyzed retrospectively. Untreated pulmonary arteriovenous malformations (PAVMs) with a feeding artery of ≥2 mm were considered treatable. RESULTS: Ninety-four percent of patients (33 of 35) did not have treatable PAVMs on high-resolution CT. TTCE was negative for shunts (Grade 0) in 34% of patients (n = 12). Of patients with a TTCE positive for shunts (23 of 35, 66%), 83% had a Grade 1 shunt, 13% had a Grade 2 shunt, and 4% had a Grade 3 shunt. No patient with a Grade 0 or 1 shunt had a treatable PAVM on high-resolution CT. Of the 2 patients with PAVMs requiring treatment, one had a Grade 2 shunt and one had a Grade 3 shunt. TTCE grade was significantly associated with the presence of a treatable PAVM on high-resolution CT (P < .01). CONCLUSIONS: Graded TTCE predicts the need for repeat embolotherapy and does so reliably in the early postembolotherapy period. This suggests that graded TTCE can be utilized in the postembolotherapy period for surveillance, which has the potential to lead to a decrease in cumulative radiation in this patient population.

A network of nuclear envelope membrane proteins linking centromeres to microtubules.

In the fission yeast S. pombe, nuclei are actively positioned at the cell center by microtubules. Here, we show that cytoplasmic microtubules are mechanically coupled to the nuclear heterochromatin through proteins embedded in the nuclear envelope. This includes an integral outer nuclear membrane protein of the KASH family (Kms2) and two integral inner nuclear membrane proteins, the SUN-domain protein Sad1 and the previously uncharacterized protein Ima1. Ima1 specifically binds to heterochromatic regions and promotes the tethering of centromeric DNA to the SUN-KASH complex. In the absence of Ima1, or in cells harboring mutations in the centromeric Ndc80 complex, inefficient coupling of centromeric heterochromatin to Sad1 leads to striking defects in the ability of the nucleus to tolerate microtubule-dependent forces, leading to changes in nuclear shape, loss of spindle pole body components from the nuclear envelope, and partial dissociation of SUN-KASH complexes. This work highlights a framework for communication between cytoplasmic microtubules and chromatin.

Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment.

A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon-anomalous dissipation-is sometimes called the 'zeroth law of turbulence' as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions [Formula: see text] exhibit persistent power-law scaling in the inertial range, namely [Formula: see text] for exponents [Formula: see text] over an ever increasing (with Reynolds) range of scales. This behaviour indicates that the velocity field retains some fractional differentiability uniformly in the Reynolds number. The Kolmogorov 1941 theory of turbulence predicts that [Formula: see text] for all [Formula: see text] and Onsager's 1949 theory establishes the requirement that [Formula: see text] for [Formula: see text] for consistency with the zeroth law. Empirically, [Formula: see text] and [Formula: see text], suggesting that turbulent Navier-Stokes solutions approximate dissipative weak solutions of the Euler equations possessing (nearly) the minimal degree of singularity required to sustain anomalous dissipation. In this note, we adopt an experimentally supported hypothesis on the anti-alignment of velocity increments with their separation vectors and demonstrate that the inertial dissipation provides a regularization mechanism via the Kolmogorov 4/5-law. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries.

We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number [Formula: see text], this estimate interpolates between the Whitehead-Doering bound by [Formula: see text] for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering-Constantin [Formula: see text] bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957-5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

The final demise of Rodriguez lethal acrofacial dysostosis: A case report and review of the literature.

We evaluated a newborn with acrofacial dysostosis in whom a clinical diagnosis of Nager syndrome was entertained. Radiographs revealed hypoplasia of the scapulae and bilateral humeroradial synostosis, with absent ulna on the left and hypoplastic ulna on the right. The finding of bilateral humeroradial synostosis had not been seen in cases of Nager syndrome before and we considered other diagnoses. Humeroradial synostosis has been found in three cases of acrofacial dysostosis Rodriguez type, a syndrome characterized by mandibular hypoplasia, upper and lower extremity phocomelia, and oligodactyly of the upper limbs. More recently, haploinsufficiency of the SF3B4 gene has been identified as the cause of both Nager and Rodriguez syndrome, leading many to believe that Rodriguez syndrome represents a more severe end of a Nager syndrome spectrum. An SF3B4 mutation was found in our patient, prompting a review of the previous known cases of Rodriguez syndrome, which revealed no clustering of SF3B4 mutations, and four cases of Rodriguez syndrome with mutations identical to those in cases of Nager syndrome. Rodriguez syndrome was previously thought of as a lethal acrofacial dysostosis distinct from Nager syndrome. A number of more mild cases, as well as our case, intermediate between the two phenotypes, illustrate that Rodriguez syndrome is a severe manifestation of Nager syndrome, and is not lethal with aggressive medical care.

Inertial-Range Reconnection in Magnetohydrodynamic Turbulence and in the Solar Wind.

In situ spacecraft data on the solar wind show events identified as magnetic reconnection with wide outflows and extended "X lines," 10(3)-10(4) times ion scales. To understand the role of turbulence at these scales, we make a case study of an inertial-range reconnection event in a magnetohydrodynamic simulation. We observe stochastic wandering of field lines in space, breakdown of standard magnetic flux freezing due to Richardson dispersion, and a broadened reconnection zone containing many current sheets. The coarse-grain magnetic geometry is like large-scale reconnection in the solar wind, however, with a hyperbolic flux tube or apparent X line extending over integral length scales.

CEP290 and the primary cilium.

The protein CEP290 has recently emerged as a major player in the biology of the cilium and as a causative protein in a number of human syndromic diseases, most of which are associated with the devastating blinding disease Leber congenital amaurosis. (Coppieters et al., Hum Mutat 31, 2010, 1097-1108) CEP290 is known to be an important component of the primary cilium, localizing to the Y-links of the ciliary transition zone and having a role in the regulation of transport in and out of the ciliary compartment (Craige et al., J Cell Biol 190, 2010, 927-940). While many mutations in CEP290 have been identified in human patients, how these mutations result in the spectrum of human disease attributed to the protein remain unknown. As we begin to learn more about the normal role of CEP290, it is likely that we will begin to shed light on how these mutations result in the various CEP290 disease phenotypes. Here we discuss many of these diverse aspects of CEP290 biology and pathology in an attempt to link what we know about the molecular mechanisms of CEP290 function with what we know about CEP290-associated disease.

Universal Exome Sequencing in Critically Ill Adults: A Diagnostic Yield of 25% and Race-Based Disparities in Access to Genetic Testing.

Numerous studies have underscored the diagnostic and therapeutic potential of exome or genome sequencing in critically ill pediatric populations. However, an equivalent investigation in critically ill adults remains conspicuously absent. We retrospectively analyzed whole exome sequencing (WES) data available through the PennMedicine Biobank (PMBB) from all 365 young adult patients, aged 18-40 years, with intensive care unit (ICU) admissions at the University of Pennsylvania Health System who met inclusion criteria for our study. For each participant, two Medical Genetics and Internal Medicine-trained clinicians reviewed WES reports and patient charts for variant classification, result interpretation, and identification of genetic diagnoses related to their critical illness. Of the 365 individuals in our study, 90 (24.7%) were found to have clearly diagnostic results on WES; an additional 40 (11.0%) had a suspicious variant of uncertain significance (VUS) identified; and an additional 16 (4.4%) had a medically actionable incidental finding. The diagnostic rate of exome sequencing did not decrease with increasing patient age. Affected genes were primarily involved in cardiac function (18.8%), vascular health (16.7%), cancer (16.7%), and pulmonary disease (11.5%). Only half of all diagnostic findings were known and documented in the patient chart at the time of ICU admission. Significant disparities emerged in subgroup analysis by EHR-reported race, with genetic diagnoses known/documented for 63.5% of White patients at the time of ICU admission but only for 28.6% of Black or Hispanic patients. There was a trend towards patients with undocumented genetic diagnoses having a 66% increased mortality rate, making these race-based disparities in genetic diagnosis even more concerning. Altogether, universal exome sequencing in ICU-admitted adult patients was found to yield a new definitive diagnosis in 11.2% of patients. Of these diagnoses, 76.6% conferred specific care-altering medical management recommendations. Our study suggests that the diagnostic utility of exome sequencing in critically ill young adults is similar to that observed in neonatal and pediatric populations and is age-independent. The high diagnostic rate and striking race-based disparities we find in genetic diagnoses argue for broad and universal approaches to genetic testing for critically ill adults. The widespread implementation of comprehensive genetic sequencing in the adult population promises to enhance medical care for all individuals and holds the potential to rectify disparities in genetic testing referrals, ultimately promoting more equitable healthcare delivery.

Sex-Specific Effect of MTSS1 Downregulation on Dilated Cardiomyopathy.

MTSS1 (metastasis suppressor 1) is an I-BAR protein that regulates cytoskeleton dynamics through interactions with actin, Rac, and actin-associated proteins. In a prior study, we identified genetic variants in a cardiac-specific enhancer upstream of MTSS1 that reduce human left ventricular (LV) MTSS1 expression and associate with protection against dilated cardiomyopathy (DCM). We sought to probe these effects further using population genomics and in vivo murine models. We crossed Mtss1-/- mice with a transgenic (Tg) murine model of human DCM caused by the D230N pathogenic mutation in Tpm1 (tropomyosin 1). In females, Tg/Mtss1+/- mice had significantly increased LV ejection fraction and reduced LV volumes relative to their Tg/Mtss1+/+ counterparts, signifying partial rescue of DCM due to Mtss1 haploinsufficiency. No differences were observed in males. To study effects in humans, we fine-mapped the MTSS1 locus with 82 cardiac magnetic resonance (CMR) traits in 22,381 UK Biobank participants. MTSS1 enhancer variants showed interaction with biological sex in their associations with several CMR traits. After stratification by biological sex, associations with CMR traits and colocalization with MTSS1 expression in the Genotype-Tissue Expression (GTEx) Project were observed principally in women and were substantially weaker in men. These findings suggest sex dimorphism in the effects of MTSS1-lowering alleles, and parallel the increased LV ejection fraction and reduced LV volumes observed female Tg/Mtss1+/- mice. Together, our findings at the MTSS1 locus suggest a genetic basis for sex dimorphism in cardiac remodeling and motivate sex-specific study of common variants associated with cardiac traits and disease.

Progesterone for Neurodevelopment in Fetuses With Congenital Heart Defects: A Randomized Clinical Trial.

Importance: Neurodevelopmental outcomes for children with congenital heart defects (CHD) have improved minimally over the past 20 years. Objectives: To assess the feasibility and tolerability of maternal progesterone therapy as well as the magnitude of the effect on neurodevelopment for fetuses with CHD. Design, Setting, and Participants: This double-blinded individually randomized parallel-group clinical trial of vaginal natural progesterone therapy vs placebo in participants carrying fetuses with CHD was conducted between July 2014 and November 2021 at a quaternary care children's hospital. Participants included maternal-fetal dyads where the fetus had CHD identified before 28 weeks' gestational age and was likely to need surgery with cardiopulmonary bypass in the neonatal period. Exclusion criteria included a major genetic or extracardiac anomaly other than 22q11 deletion syndrome and known contraindication to progesterone. Statistical analysis was performed June 2022 to April 2024. Intervention: Participants were 1:1 block-randomized to vaginal progesterone or placebo by diagnosis: hypoplastic left heart syndrome (HLHS), transposition of the great arteries (TGA), and other CHD diagnoses. Treatment was administered twice daily between 28 and up to 39 weeks' gestational age. Main Outcomes and Measures: The primary outcome was the motor score of the Bayley Scales of Infant and Toddler Development-III; secondary outcomes included language and cognitive scales. Exploratory prespecified subgroups included cardiac diagnosis, fetal sex, genetic profile, and maternal fetal environment. Results: The 102 enrolled fetuses primarily had HLHS (n = 52 [50.9%]) and TGA (n = 38 [37.3%]), were more frequently male (n = 67 [65.7%]), and without genetic anomalies (n = 61 [59.8%]). The mean motor score differed by 2.5 units (90% CI, -1.9 to 6.9 units; P = .34) for progesterone compared with placebo, a value not statistically different from 0. Exploratory subgroup analyses suggested treatment heterogeneity for the motor score for cardiac diagnosis (P for interaction = .03) and fetal sex (P for interaction = .04), but not genetic profile (P for interaction = .16) or maternal-fetal environment (P for interaction = .70). Conclusions and Relevance: In this randomized clinical trial of maternal progesterone therapy, the overall effect was not statistically different from 0. Subgroup analyses suggest heterogeneity of the response to progesterone among CHD diagnosis and fetal sex. Trial Registration: ClinicalTrials.gov Identifier: NCT02133573.

Inference of Causal Relationships Between Genetic Risk Factors for Cardiometabolic Phenotypes and Female-Specific Health Conditions.

Background Cardiometabolic diseases are highly comorbid, but their relationship with female-specific or overwhelmingly female-predominant health conditions (breast cancer, endometriosis, pregnancy complications) is understudied. This study aimed to estimate the cross-trait genetic overlap and influence of genetic burden of cardiometabolic traits on health conditions unique to women. Methods and Results Using electronic health record data from 71 008 ancestrally diverse women, we examined relationships between 23 obstetrical/gynecological conditions and 4 cardiometabolic phenotypes (body mass index, coronary artery disease, type 2 diabetes, and hypertension) by performing 4 analyses: (1) cross-trait genetic correlation analyses to compare genetic architecture, (2) polygenic risk score-based association tests to characterize shared genetic effects on disease risk, (3) Mendelian randomization for significant associations to assess cross-trait causal relationships, and (4) chronology analyses to visualize the timeline of events unique to groups of women with high and low genetic burden for cardiometabolic traits and highlight the disease prevalence in risk groups by age. We observed 27 significant associations between cardiometabolic polygenic scores and obstetrical/gynecological conditions (body mass index and endometrial cancer, body mass index and polycystic ovarian syndrome, type 2 diabetes and gestational diabetes, type 2 diabetes and polycystic ovarian syndrome). Mendelian randomization analysis provided additional evidence of independent causal effects. We also identified an inverse association between coronary artery disease and breast cancer. High cardiometabolic polygenic scores were associated with early development of polycystic ovarian syndrome and gestational hypertension. Conclusions We conclude that polygenic susceptibility to cardiometabolic traits is associated with elevated risk of certain female-specific health conditions.

Phenotypes of undiagnosed adults with actionable OTC and GLA variants.

Inherited metabolic disorders (IMDs) are variably expressive, complicating identification of affected individuals. A genotype-first approach can identify individuals at risk for morbidity and mortality from undiagnosed IMDs and can lead to protocols that improve clinical detection, counseling, and management. Using data from 57,340 participants in two hospital biobanks, we assessed the frequency and phenotypes of individuals with pathogenic/likely pathogenic variants (PLPVs) in two IMD genes: GLA, associated with Fabry disease, and OTC, associated with ornithine transcarbamylase deficiency. Approximately 1 in 19,100 participants harbored an undiagnosed PLPV in GLA or OTC. We identified three individuals (2 male, 1 female) with PLPVs in GLA, all of whom were undiagnosed, and three individuals (3 female) with PLPVs in OTC, two of whom were undiagnosed. All three individuals with PLPVs in GLA (100%) had symptoms suggestive of mild Fabry disease, and one individual (14.2%) had an ischemic stroke at age 33, likely indicating the presence of classic disease. No individuals with PLPVs in OTC had documented hyperammonemia despite exposure to catabolic states, but all (100%) had chronic symptoms suggestive of attenuated disease, including mood disorders and migraines. Our findings suggest that GLA and OTC variants identified via a genotype-first approach are of high penetrance and that population screening of these genes can be used to facilitate stepwise phenotyping and appropriate care.

A genotype-first approach identifies high incidence of NF1 pathogenic variants with distinct disease associations.

Loss of function variants in the NF1 gene cause neurofibromatosis type 1 (NF1), a genetic disorder characterized by complete penetrance, prevalence of 1 in 3,000, characteristic physical exam findings, and a substantially increased risk for malignancy. However, our understanding of the disorder is entirely based on patients ascertained through phenotype-first approaches. Leveraging a genotype-first approach in two large patient cohorts, we demonstrate unexpectedly high prevalence (1 in 450-750) of NF1 pathogenic variants. Half were identified in individuals lacking clinical features of NF1, with many appearing to have post-zygotic mosaicism for the identified variant. Incidentally discovered variants were not associated with classic NF1 features but were associated with an increased incidence of malignancy compared to a control population. Our findings suggest that NF1 pathogenic variants are substantially more common than previously thought, often characterized by somatic mosaicism and reduced penetrance, and are important contributors to cancer risk in the general population.

The statistical geometry of material loops in turbulence.

Material elements - which are lines, surfaces, or volumes behaving as passive, non-diffusive markers - provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate implications for mixing in the oceans or the atmosphere, as well as the emergence of self-sustained dynamos in astrophysical settings. Here, we uncover robust statistical properties of an ensemble of material loops in a turbulent environment. Our approach combines high-resolution direct numerical simulations of Navier-Stokes turbulence, stochastic models, and dynamical systems techniques to reveal predictable, universal features of these complex objects. We show that the loop curvature statistics become stationary through a dynamical formation process of high-curvature folds, leading to distributions with power-law tails whose exponents are determined by the large-deviations statistics of finite-time Lyapunov exponents of the flow. This prediction applies to advected material lines in a broad range of chaotic flows. To complement this dynamical picture, we confirm our theory in the analytically tractable Kraichnan model with an exact Fokker-Planck approach.