Genomes of the Banyan Tree and Pollinator Wasp Provide Insights into Fig-Wasp Coevolution.

Banyan trees are distinguished by their extraordinary aerial roots. The Ficus genus includes species that have evolved a species-specific mutualism system with wasp pollinators. We sequenced genomes of the Chinese banyan tree, F. microcarpa, and a species lacking aerial roots, F. hispida, and one wasp genome coevolving with F. microcarpa, Eupristina verticillata. Comparative analysis of the two Ficus genomes revealed dynamic karyotype variation associated with adaptive evolution. Copy number expansion of auxin-related genes from duplications and elevated auxin production are associated with aerial root development in F. microcarpa. A male-specific AGAMOUS paralog, FhAG2, was identified as a candidate gene for sex determination in F. hispida. Population genomic analyses of Ficus species revealed genomic signatures of morphological and physiological coadaptation with their pollinators involving terpenoid- and benzenoid-derived compounds. These three genomes offer insights into and genomic resources for investigating the geneses of aerial roots, monoecy and dioecy, and codiversification in a symbiotic system.

IDR-targeting compounds suppress HPV genome replication via disruption of phospho-BRD4 association with DNA damage response factors.

Compounds binding to the bromodomains of bromodomain and extra-terminal (BET) family proteins, particularly BRD4, are promising anticancer agents. Nevertheless, side effects and drug resistance pose significant obstacles in BET-based therapeutics development. Using high-throughput screening of a 200,000-compound library, we identified small molecules targeting a phosphorylated intrinsically disordered region (IDR) of BRD4 that inhibit phospho-BRD4 (pBRD4)-dependent human papillomavirus (HPV) genome replication in HPV-containing keratinocytes. Proteomic profiling identified two DNA damage response factors-53BP1 and BARD1-crucial for differentiation-associated HPV genome amplification. pBRD4-mediated recruitment of 53BP1 and BARD1 to the HPV origin of replication occurs in a spatiotemporal and BRD4 long (BRD4-L) and short (BRD4-S) isoform-specific manner. This recruitment is disrupted by phospho-IDR-targeting compounds with little perturbation of the global transcriptome and BRD4 chromatin landscape. The discovery of these protein-protein interaction inhibitors (PPIi) not only demonstrates the feasibility of developing PPIi against phospho-IDRs but also uncovers antiviral agents targeting an epigenetic regulator essential for virus-host interaction and cancer development.

Surging compound drought-heatwaves underrated in global soils.

Compound drought-heatwaves (CDHWs) accelerate the warming and drying of soils, triggering soil compound drought-heatwaves (SCDHWs) that jeopardize the health of soil ecosystems. Nevertheless, the behavior of these events worldwide and their responses to climatic warming are underexplored. Here, we show a global escalation in the frequency, duration, peak intensity, and severity of SCDHWs, as well as an increase in affected land area, from 1980 to 2023. The increasing trends, which are particularly prominent since the early 2000 s, and projected to persist throughout this century, are dominated by summertime SCDHWs and enhanced by El Niño. Intensive soil warming as well as climatologically lower soil temperatures compared to air temperatures lead to localized hotspots of escalating SCDHW severity in northern high latitudes, while prolonged duration causes such hotspots in northern South America. Transformation of natural ecosystems, particularly forests and wetlands, to cropland as well as forest degradation substantially enhance the strength of SCDHWs. Global SCDHWs consistently exhibit higher frequencies, longer durations, greater severities, and faster growth rates than CDHWs in all aspects from 1980 to 2023. They are undergoing a critical transition, with droughts replacing heatwaves as the primary constraint. We emphasize the significant intensification of SCDHWs in northern high latitudes as well as the prolonged duration of SCDHWs in the Southern Hemisphere, posing an underrated threat to achieving carbon neutrality and food security goals.

FRL and DAAM are required for lateral adhesion of interommatidial cells and patterning of the retinal floor.

Optical insulation of the unit eyes (ommatidia) is an important prerequisite of precise sight with compound eyes. Separation of the ommatidia is ensured by pigment cells that organize into a hexagonal lattice in the Drosophila eye, forming thin walls between the facets. Cell adhesion, mediated by apically and latero-basally located junctional complexes, is crucial for stable attachment of these cells to each other and the basal lamina. Whereas former studies have focused on the formation and remodelling of the cellular connections at the apical region, here, we report a specific alteration of the lateral adhesion of the lattice cells, leaving the apical junctions largely unaffected. We found that DAAM and FRL, two formin-type cytoskeleton regulatory proteins, play redundant roles in lateral adhesion of the interommatidial cells and patterning of the retinal floor. We show that formin-dependent cortical actin assembly is crucial for latero-basal sealing of the ommatidial lattice. We expect that the investigation of these previously unreported eye phenotypes will pave the way toward a better understanding of the three-dimensional aspects of compound eye development.

Looking across the gap: Understanding the evolution of eyes and vision among insects.

The compound eyes of insects exhibit stunning variation in size, structure, and function, which has allowed these animals to use their vision to adapt to a huge range of different environments and lifestyles, and evolve complex behaviors. Much of our knowledge of eye development has been learned from Drosophila, while visual adaptations and behaviors are often more striking and better understood from studies of other insects. However, recent studies in Drosophila and other insects, including bees, beetles, and butterflies, have begun to address this gap by revealing the genetic and developmental bases of differences in eye morphology and key new aspects of compound eye structure and function. Furthermore, technical advances have facilitated the generation of high-resolution connectomic data from different insect species that enhances our understanding of visual information processing, and the impact of changes in these processes on the evolution of vision and behavior. Here, we review these recent breakthroughs and propose that future integrated research from the development to function of visual systems within and among insect species represents a great opportunity to understand the remarkable diversification of insect eyes and vision.

How the technologies behind self-driving cars, social networks, ChatGPT, and DALL-E2 are changing structural biology.

The performance of deep Neural Networks (NNs) in the text (ChatGPT) and image (DALL-E2) domains has attracted worldwide attention. Convolutional NNs (CNNs), Large Language Models (LLMs), Denoising Diffusion Probabilistic Models (DDPMs)/Noise Conditional Score Networks (NCSNs), and Graph NNs (GNNs) have impacted computer vision, language editing and translation, automated conversation, image generation, and social network management. Proteins can be viewed as texts written with the alphabet of amino acids, as images, or as graphs of interacting residues. Each of these perspectives suggests the use of tools from a different area of deep learning for protein structural biology. Here, I review how CNNs, LLMs, DDPMs/NCSNs, and GNNs have led to major advances in protein structure prediction, inverse folding, protein design, and small molecule design. This review is primarily intended as a deep learning primer for practicing experimental structural biologists. However, extensive references to the deep learning literature should also make it relevant to readers who have a background in machine learning, physics or statistics, and an interest in protein structural biology.

Climate change will accelerate the high-end risk of compound drought and heatwave events.

Compound drought and heatwave (CDHW) events have garnered increased attention due to their significant impacts on agriculture, energy, water resources, and ecosystems. We quantify the projected future shifts in CDHW characteristics (such as frequency, duration, and severity) due to continued anthropogenic warming relative to the baseline recent observed period (1982 to 2019). We combine weekly drought and heatwave information for 26 climate divisions across the globe, employing historical and projected model output from eight Coupled Model Intercomparison Project 6 GCMs and three Shared Socioeconomic Pathways. Statistically significant trends are revealed in the CDHW characteristics for both recent observed and model simulated future period (2020 to 2099). East Africa, North Australia, East North America, Central Asia, Central Europe, and Southeastern South America show the greatest increase in frequency through the late 21st century. The Southern Hemisphere displays a greater projected increase in CDHW occurrence, while the Northern Hemisphere displays a greater increase in CDHW severity. Regional warmings play a significant role in CDHW changes in most regions. These findings have implications for minimizing the impacts of extreme events and developing adaptation and mitigation policies to cope with increased risk on water, energy, and food sectors in critical geographical regions.

From soap bubbles to multicellular organisms: Unraveling the role of cell adhesion and physical constraints in tile pattern formation and tissue morphogenesis.

Tile patterns, in which numerous cells are arranged in a regular pattern, are found in a variety of multicellular organisms and play important functional roles. Such regular arrangements of cells are regulated by various cell adhesion molecules. On the other hand, cell shape is also known to be regulated by physical constraints similar to those of soap bubbles. In particular, circumference minimization plays an important role, and cell adhesion negatively affects this process, thereby regulating tissue morphogenesis based on physical properties. Here, we focus on the Drosophila compound eye and the mouse auditory epithelium, and summarize the mechanisms of tile pattern formation by cell adhesion molecules such as cadherins, Irre Cell Recognition Modules (IRMs), and nectins. Phenomena that cannot be explained by physical stability based on cortical tension alone have been reported in the tile pattern formation in the compound eye, suggesting that previously unexplored forces such as cellular concentric expansion force may play an important role. We would like to summarize perspectives for future research on the mechanisms of tissue morphogenesis.

Reactivating Hippo by drug compounds to suppress gastric cancer and enhance chemotherapy sensitivity.

The Hippo signaling pathway plays an essential role in organ size control and tumorigenesis. Loss of Hippo signal and hyper-activation of the downstream oncogenic YAP signaling are commonly observed in various types of cancers. We previously identified STRN3-containing PP2A phosphatase as a negative regulator of MST1/2 kinases (i.e., Hippo) in gastric cancer (GC), opening the possibility of selectively targeting the PP2Aa-STRN3-MST1/2 axis to recover Hippo signaling against cancer. Here, we further discovered 1) disulfiram (DSF), an FDA-approved drug, which can similarly block the binding of STRN3 to PP2A core enzyme and 2) CX-6258 (CX), a chemical inhibitor, that can disrupt the interaction between STRN3 and MST1/2, both allowing reactivation of Hippo activity to inhibit GC. More importantly, we found these two compounds, via an MST1/2 kinase-dependent manner, inhibit DNA repair to sensitize GC towards chemotherapy. In addition, we identified thiram, a structural analog of DSF, can function similarly to inhibit cancer cell proliferation or enhance chemotherapy sensitivity. Interestingly, inclusion of copper ion enhanced such effects of DSF and thiram on GC treatment. Overall, this work demonstrated that pharmacological targeting of the PP2Aa-STRN3-MST1/2 axis by drug compounds can potently recover Hippo signal for tumor treatment.

Effects of phosphorylation on CsTT12 transport function: A comparative phosphoproteomic analysis of flavonoid biosynthesis in tea plants (Camellia sinensis).

Monomeric flavan-3-ols and their oligomeric forms, proanthocyanidins (PAs), are closely related to the bitterness of tea beverages. Monomeric flavan-3-ols are characteristic flavor compounds in tea. Increasing the content of PAs and anthocyanins enhances the resistance of tea plants to pathogen invasion but decreases the quality of tea beverages. MATE family transporters play a critical role in transferring monomeric flavan-3-ols and anthocyanins into vacuoles for storage or subsequent condensation into PAs. Their activities modulate the ratio of monomeric flavan-3-ols to PAs and increase anthocyanin content in tea plants. In this study, it was observed that the gene expression and protein phosphorylation level of the MATE transporter CsTT12, a vacuole-localized flavonoid transporter, were notably upregulated following exogenous sucrose treatment, promoting PA synthesis in tea plants. Further analysis revealed that overexpression of CsTT12 and CsTT12S17D significantly increased the content of anthocyanins and PAs in plants, whereas CsTT12S17A did not. In CsTT12 knockdown plants, PA's accumulation decreased significantly, while monomeric catechin content increased. Moreover, phosphorylation modification enhanced the vacuolar membrane localization of CsTT12, whereas dephosphorylation weakened its vacuolar membrane localization. This study uncovers the crucial role of phosphorylation in flavonoid biosynthesis and provides insights into balancing quality improvements and resistance enhancement.

LKB1 suppresses KSHV reactivation and promotes primary effusion lymphoma progression.

Viruses normally reprogram the host cell metabolic pathways as well as metabolic sensors to facilitate their persistence. The serine-threonine liver kinase B1 (LKB1) is a master upstream kinase of 5'-AMP-activated protein kinase (AMPK) that senses the energy status and therefore regulates the intracellular metabolic homeostasis. Previous studies showed that AMPK restricts Kaposi's sarcoma-associated herpesvirus (KSHV) lytic replication in endothelial cells during primary infection and promotes primary effusion lymphoma (PEL) cell survival. However, the role of LKB1 in KSHV lytic reactivation and KSHV-associated malignancies is unclear. In this study, we found that LKB1 is phosphorylated or activated in KSHV-positive PEL cells. Mechanistically, KSHV-encoded vCyclin mediated LKB1 activation in PEL cells, as vCyclin knockout ablated, while vCyclin overexpression enhanced LKB1 activation. Furthermore, knockdown of LKB1 inactivated AMPK and induced KSHV reactivation, as indicated by the increased expression of viral lytic genes and the increased virions in supernatants. Accordingly, AMPK inhibition by functional knockdown or a pharmacologic inhibitor, Compound C, promoted KSHV reactivation in PEL cells. Furthermore, inhibition of either LKB1 or AMPKα1 efficiently induced cell death by apoptosis of PEL cells both in vitro and in vivo. Together, these results identify LKB1 as a vulnerable target for PEL, which could be potentially exploited for treating other virus-associated diseases.IMPORTANCEKaposi's sarcoma-associated herpesvirus (KSHV) is an oncogenic virus associated with several human cancers, such as primary effusion lymphoma (PEL). Here, we showed that serine-threonine liver kinase B1 (LKB1), upstream of 5' AMP-activated protein kinase (AMPK), is activated by KSHV-encoded vCyclin and maintains KSHV latency in PEL cells. Inhibition of either LKB1 or AMPK enhances KSHV lytic replication from latency, which at least partially accounts for PEL cell death by apoptosis. Compound C, a potent AMPK inhibitor, induced KSHV reactivation and efficiently inhibited PEL progression in vivo. Thus, our work revealed that LKB1 is a potential therapeutic target for KSHV-associated cancers.

Benchmark of embedding-based methods for accurate and transferable prediction of drug response.

Prediction of therapy response has been a major challenge in cancer precision medicine due to the extensive tumor heterogeneity. Recently, several deep learning methods have been developed to predict drug response by utilizing various omics data. Most of them train models by using the drug-response screening data generated from cell lines and then use these models to predict response in cancer patient data. In this study, we focus on and evaluate deep learning methods using transcriptome data for the long-standing question of personalized drug-response prediction. We developed an embedding-based approach for drug-response prediction and benchmarked similar methods for their performance. For all methods, we used pretreatment transcriptome data to train models and then conducted a comprehensive evaluation and comparison of the models using cross-panels, cross-datasets and target genes. We further validated the methods using three independent datasets assessing multiple compounds for their predictive capability of drug response, survival outcome and cell line status. As a result, the methods building on gene embeddings had an overall competitive performance with reduced overfitting when we applied evaluation parameters for model fitting as well as the correlation with clinical outcomes in the validation data. We further developed an ensemble model to combine the results from the three most competitive methods for an overall prediction. Finally, we developed DrVAEN (https://bioinfo.uth.edu/drvaen), a user-friendly and easy-accessible web-server that hosts all these methods for drug-response prediction and model comparison for broad use in cancer research, method evaluation and drug development.

MulinforCPI: enhancing precision of compound-protein interaction prediction through novel perspectives on multi-level information integration.

Forecasting the interaction between compounds and proteins is crucial for discovering new drugs. However, previous sequence-based studies have not utilized three-dimensional (3D) information on compounds and proteins, such as atom coordinates and distance matrices, to predict binding affinity. Furthermore, numerous widely adopted computational techniques have relied on sequences of amino acid characters for protein representations. This approach may constrain the model's ability to capture meaningful biochemical features, impeding a more comprehensive understanding of the underlying proteins. Here, we propose a two-step deep learning strategy named MulinforCPI that incorporates transfer learning techniques with multi-level resolution features to overcome these limitations. Our approach leverages 3D information from both proteins and compounds and acquires a profound understanding of the atomic-level features of proteins. Besides, our research highlights the divide between first-principle and data-driven methods, offering new research prospects for compound-protein interaction tasks. We applied the proposed method to six datasets: Davis, Metz, KIBA, CASF-2016, DUD-E and BindingDB, to evaluate the effectiveness of our approach.

DLTKcat: deep learning-based prediction of temperature-dependent enzyme turnover rates.

The enzyme turnover rate, ${k}_{cat}$, quantifies enzyme kinetics by indicating the maximum efficiency of enzyme catalysis. Despite its importance, ${k}_{cat}$ values remain scarce in databases for most organisms, primarily because of the cost of experimental measurements. To predict ${k}_{cat}$ and account for its strong temperature dependence, DLTKcat was developed in this study and demonstrated superior performance (log10-scale root mean squared error = 0.88, R-squared = 0.66) than previously published models. Through two case studies, DLTKcat showed its ability to predict the effects of protein sequence mutations and temperature changes on ${k}_{cat}$ values. Although its quantitative accuracy is not high enough yet to model the responses of cellular metabolism to temperature changes, DLTKcat has the potential to eventually become a computational tool to describe the temperature dependence of biological systems.

Enhanced compound-protein binding affinity prediction by representing protein multimodal information via a coevolutionary strategy.

Due to the lack of a method to efficiently represent the multimodal information of a protein, including its structure and sequence information, predicting compound-protein binding affinity (CPA) still suffers from low accuracy when applying machine-learning methods. To overcome this limitation, in a novel end-to-end architecture (named FeatNN), we develop a coevolutionary strategy to jointly represent the structure and sequence features of proteins and ultimately optimize the mathematical models for predicting CPA. Furthermore, from the perspective of data-driven approach, we proposed a rational method that can utilize both high- and low-quality databases to optimize the accuracy and generalization ability of FeatNN in CPA prediction tasks. Notably, we visually interpret the feature interaction process between sequence and structure in the rationally designed architecture. As a result, FeatNN considerably outperforms the state-of-the-art (SOTA) baseline in virtual drug evaluation tasks, indicating the feasibility of this approach for practical use. FeatNN provides an outstanding method for higher CPA prediction accuracy and better generalization ability by efficiently representing multimodal information of proteins via a coevolutionary strategy.

Integrated annotation prioritizes metabolites with bioactivity in inflammatory bowel disease.

Microbial biochemistry is central to the pathophysiology of inflammatory bowel diseases (IBD). Improved knowledge of microbial metabolites and their immunomodulatory roles is thus necessary for diagnosis and management. Here, we systematically analyzed the chemical, ecological, and epidemiological properties of ~82k metabolic features in 546 Integrative Human Microbiome Project (iHMP/HMP2) metabolomes, using a newly developed methodology for bioactive compound prioritization from microbial communities. This suggested >1000 metabolic features as potentially bioactive in IBD and associated ~43% of prevalent, unannotated features with at least one well-characterized metabolite, thereby providing initial information for further characterization of a significant portion of the fecal metabolome. Prioritized features included known IBD-linked chemical families such as bile acids and short-chain fatty acids, and less-explored bilirubin, polyamine, and vitamin derivatives, and other microbial products. One of these, nicotinamide riboside, reduced colitis scores in DSS-treated mice. The method, MACARRoN, is generalizable with the potential to improve microbial community characterization and provide therapeutic candidates.

AtML: An Arabidopsis thaliana root cell identity recognition tool for medicinal ingredient accumulation.

Arabidopsis thaliana synthesizes various medicinal compounds, and serves as a model plant for medicinal plant research. Single-cell transcriptomics technologies are essential for understanding the developmental trajectory of plant roots, facilitating the analysis of synthesis and accumulation patterns of medicinal compounds in different cell subpopulations. Although methods for interpreting single-cell transcriptomics data are rapidly advancing in Arabidopsis, challenges remain in precisely annotating cell identity due to the lack of marker genes for certain cell types. In this work, we trained a machine learning system, AtML, using sequencing datasets from six cell subpopulations, comprising a total of 6000 cells, to predict Arabidopsis root cell stages and identify biomarkers through complete model interpretability. Performance testing using an external dataset revealed that AtML achieved 96.50% accuracy and 96.51% recall. Through the interpretability provided by AtML, our model identified 160 important marker genes, contributing to the understanding of cell type annotations. In conclusion, we trained AtML to efficiently identify Arabidopsis root cell stages, providing a new tool for elucidating the mechanisms of medicinal compound accumulation in Arabidopsis roots.

Platelet C3G: a key player in vesicle exocytosis, spreading and clot retraction.

C3G is a Rap1 GEF that plays a pivotal role in platelet-mediated processes such as angiogenesis, tumor growth, and metastasis by modulating the platelet secretome. Here, we explore the mechanisms through which C3G governs platelet secretion. For this, we utilized animal models featuring either overexpression or deletion of C3G in platelets, as well as PC12 cell clones expressing C3G mutants. We found that C3G specifically regulates α-granule secretion via PKCδ, but it does not affect δ-granules or lysosomes. C3G activated RalA through a GEF-dependent mechanism, facilitating vesicle docking, while interfering with the formation of the trans-SNARE complex, thereby restricting vesicle fusion. Furthermore, C3G promotes the formation of lamellipodia during platelet spreading on specific substrates by enhancing actin polymerization via Src and Rac1-Arp2/3 pathways, but not Rap1. Consequently, C3G deletion in platelets favored kiss-and-run exocytosis. C3G also controlled granule secretion in PC12 cells, including pore formation. Additionally, C3G-deficient platelets exhibited reduced phosphatidylserine exposure, resulting in decreased thrombin generation, which along with defective actin polymerization and spreading, led to impaired clot retraction. In summary, platelet C3G plays a dual role by facilitating platelet spreading and clot retraction through the promotion of outside-in signaling while concurrently downregulating α-granule secretion by restricting granule fusion.

Discovery and Validation of a Volatile Signature of Eosinophilic Airway Inflammation in Asthma.

Rationale: Volatile organic compounds (VOCs) in asthmatic breath may be associated with sputum eosinophilia. We developed a volatile biomarker signature to predict sputum eosinophilia in asthma. Methods: VOCs emitted into the space above sputum samples (headspace) from patients with severe asthma (n = 36) were collected onto sorbent tubes and analyzed using thermal desorption gas chromatography-mass spectrometry (GC-MS). Elastic net regression identified stable VOCs associated with sputum eosinophilia ⩾ 3% and generated a volatile biomarker signature. This VOC signature was validated in breath samples from: 1) patients with acute asthma according to blood eosinophilia ⩾0.3 × 109cells/L or sputum eosinophilia of ⩾3% in the UK EMBER (East Midlands Breathomics Pathology Node) consortium (n = 65) and 2) U-BIOPRED-IMI (Unbiased Biomarkers in Prediction of Respiratory Disease Outcomes Innovative Medicines Initiative) consortium (n = 42). Breath samples were collected onto sorbent tubes (EMBER) or Tedlar bags (U-BIOPRED) and analyzed by GC-MS (GC × GC-MS for EMBER or GC-MS for U-BIOPRED). Measurements and Main Results: The in vitro headspace identified 19 VOCs associated with sputum eosinophilia, and the derived VOC signature yielded good diagnostic accuracy for sputum eosinophilia ⩾3% in headspace (area under the receiver operating characteristic curve [AUROC] 0.90; 95% confidence interval [CI], 0.80-0.99; P < 0.0001), correlated inversely with sputum eosinophil percentage (rs = -0.71; P < 0.0001), and outperformed fractional exhaled nitric oxide (AUROC 0.61; 95% CI, 0.35-0.86). Analysis of exhaled breath in replication cohorts yielded a VOC signature AUROC (95% CI) for acute asthma exacerbations of 0.89 (0.76-1.0) (EMBER cohort) with sputum eosinophilia and 0.90 (0.75-1.0) in U-BIOPRED, again outperforming fractional exhaled nitric oxide in U-BIOPRED (0.62 [0.33-0.90]). Conclusions: We have discovered and provided early-stage clinical validation of a volatile biomarker signature associated with eosinophilic airway inflammation. Further work is needed to translate our discovery using point-of-care clinical sensors.

Symmetric tangled Platonic polyhedra.

Conventional embeddings of the edge-graphs of Platonic polyhedra, {f, z}, where f, z denote the number of edges in each face and the edge-valence at each vertex, respectively, are untangled in that they can be placed on a sphere ([Formula: see text]) such that distinct edges do not intersect, analogous to unknotted loops, which allow crossing-free drawings of [Formula: see text] on the sphere. The most symmetric (flag-transitive) realizations of those polyhedral graphs are those of the classical Platonic polyhedra, whose symmetries are *2fz, according to Conway's two-dimensional (2D) orbifold notation (equivalent to Schönflies symbols Ih , Oh , and Td ). Tangled Platonic {f, z} polyhedra-which cannot lie on the sphere without edge-crossings-are constructed as windings of helices with three, five, seven,… strands on multigenus surfaces formed by tubifying the edges of conventional Platonic polyhedra, have (chiral) symmetries 2fz (I, O, and T), whose vertices, edges, and faces are symmetrically identical, realized with two flags. The analysis extends to the "θz " polyhedra, [Formula: see text] The vertices of these symmetric tangled polyhedra overlap with those of the Platonic polyhedra; however, their helicity requires curvilinear (or kinked) edges in all but one case. We show that these 2fz polyhedral tangles are maximally symmetric; more symmetric embeddings are necessarily untangled. On one hand, their topologies are very constrained: They are either self-entangled graphs (analogous to knots) or mutually catenated entangled compound polyhedra (analogous to links). On the other hand, an endless variety of entanglements can be realized for each topology. Simpler examples resemble patterns observed in synthetic organometallic materials and clathrin coats in vivo.