Triangle Motifs Research Articles

Programming crystallization kinetics of self-assembled DNA crystals with 5-methylcytosine modification

Self-assembled DNA crystals offer a precise chemical platform at the ångström-scale for DNA nanotechnology, holding enormous potential in material separation, catalysis, and DNA data storage. However, accurately controlling the crystallization kinetics of such DNA crystals remains challenging. Herein, we found that atomic-level 5-methylcytosine (5mC) modification can regulate the crystallization kinetics of DNA crystal by tuning the hybridization rates of DNA motifs. We discovered that by manipulating the axial and combination of 5mC modification on the sticky ends of DNA tensegrity triangle motifs, we can obtain a series of DNA crystals with controllable morphological features. Through DNA-PAINT and FRET-labeled DNA strand displacement experiments, we elucidate that atomic-level 5mC modification enhances the affinity constant of DNA hybridization at both the single-molecule and macroscopic scales. This enhancement can be harnessed for kinetic-driven control of the preferential growth direction of DNA crystals. The 5mC modification strategy can overcome the limitations of DNA sequence design imposed by limited nucleobase numbers in various DNA hybridization reactions. This strategy provides a new avenue for the manipulation of DNA crystal structure, valuable for the advancement of DNA and biomacromolecular crystallography.

MEGA: Machine Learning-Enhanced Graph Analytics for Infodemic Risk Management.

The COVID-19 pandemic brought not only global devastation but also an unprecedented infodemic of false or misleading information that spread rapidly through online social networks. Network analysis plays a crucial role in the science of fact-checking by modeling and learning the risk of infodemics through statistical processes and computation on mega-sized graphs. This article proposes MEGA, Machine Learning-Enhanced Graph Analytics, a framework that combines feature engineering and graph neural networks to enhance the efficiency of learning performance involving massive graphs. Infodemic risk analysis is a unique application of the MEGA framework, which involves detecting spambots by counting triangle motifs and identifying influential spreaders by computing the distance centrality. The MEGA framework is evaluated using the COVID-19 pandemic Twitter dataset, demonstrating superior computational efficiency and classification accuracy.

Depression and fatigue in active IBD from a microbiome perspective—a Bayesian approach to faecal metagenomics

BackgroundExtraintestinal symptoms are common in inflammatory bowel diseases (IBD) and include depression and fatigue. These are highly prevalent especially in active disease, potentially due to inflammation-mediated changes in the microbiota-gut-brain axis. The aim of this study was to investigate the associations between structural and functional microbiota characteristics and severity of fatigue and depressive symptoms in patients with active IBD.MethodsWe included clinical data of 62 prospectively enrolled patients with IBD in an active disease state. Patients supplied stool samples and completed the questionnaires regarding depression and fatigue symptoms. Based on taxonomic and functional metagenomic profiles of faecal gut microbiota, we used Bayesian statistics to investigate the associative networks and triangle motifs between bacterial genera, functional modules and symptom severity of self-reported fatigue and depression.ResultsAssociations with moderate to strong evidence were found for 3 genera (Odoribacter, Anaerotruncus and Alistipes) and 3 functional modules (pectin, glycosaminoglycan and central carbohydrate metabolism) with regard to depression and for 4 genera (Intestinimonas, Anaerotruncus, Eubacterium and Clostridiales g.i.s) and 2 functional modules implicating amino acid and central carbohydrate metabolism with regard to fatigue.ConclusionsThis study provides the first evidence of association triplets between microbiota composition, function and extraintestinal symptoms in active IBD. Depression and fatigue were associated with lower abundances of short-chain fatty acid producers and distinct pathways implicating glycan, carbohydrate and amino acid metabolism. Our results suggest that microbiota-directed therapeutic approaches may reduce fatigue and depression in IBD and should be investigated in future research.

CHIEF: Clustering With Higher-Order Motifs in Big Networks

Clustering network vertices is an enabler of various applications such as social computing and Internet of Things. However, challenges arise for clustering when networks increase in scale. This paper proposes CHIEF (Clustering with HIgher-ordEr motiFs), a solution which consists of two motif clustering techniques: standard acceleration CHIEF-ST and approximate acceleration CHIEF-AP. Both algorithms firstly find the maximal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-edge-connected subgraphs within the target networks to lower the network scale by optimizing the network structure with maximal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-edge-connected subgraphs, and then use heterogeneous four-node motifs clustering in higher-order dense networks. For CHIEF-ST, we illustrate that all target motifs will be kept after this procedure when the minimum node degree of the target motif is equal or greater than <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>. For CHIEF-AP, we prove that the eigenvalues of the adjacency matrix and the Laplacian matrix are relatively stable after this step. CHIEF offers an improved efficiency of motif clustering for big networks, and it verifies higher-order motif significance. Experiments on real and synthetic networks demonstrate that the proposed solutions outperform baseline approaches in large network analysis, and higher-order motifs outperform traditional triangle motifs in clustering.

Cyclic transitions between higher order motifs underlie sustained asynchronous spiking in sparse recurrent networks.

A basic—yet nontrivial—function which neocortical circuitry must satisfy is the ability to maintain stable spiking activity over time. Stable neocortical activity is asynchronous, critical, and low rate, and these features of spiking dynamics contribute to efficient computation and optimal information propagation. However, it remains unclear how neocortex maintains this asynchronous spiking regime. Here we algorithmically construct spiking neural network models, each composed of 5000 neurons. Network construction synthesized topological statistics from neocortex with a set of objective functions identifying naturalistic low-rate, asynchronous, and critical activity. We find that simulations run on the same topology exhibit sustained asynchronous activity under certain sets of initial membrane voltages but truncated activity under others. Synchrony, rate, and criticality do not provide a full explanation of this dichotomy. Consequently, in order to achieve mechanistic understanding of sustained asynchronous activity, we summarized activity as functional graphs where edges between units are defined by pairwise spike dependencies. We then analyzed the intersection between functional edges and synaptic connectivity- i.e. recruitment networks. Higher-order patterns, such as triplet or triangle motifs, have been tied to cooperativity and integration. We find, over time in each sustained simulation, low-variance periodic transitions between isomorphic triangle motifs in the recruitment networks. We quantify the phenomenon as a Markov process and discover that if the network fails to engage this stereotyped regime of motif dominance “cycling”, spiking activity truncates early. Cycling of motif dominance generalized across manipulations of synaptic weights and topologies, demonstrating the robustness of this regime for maintenance of network activity. Our results point to the crucial role of excitatory higher-order patterns in sustaining asynchronous activity in sparse recurrent networks. They also provide a possible explanation why such connectivity and activity patterns have been prominently reported in neocortex.

Quantum liquid from strange frustration in the trimer magnet Ba4Ir3O10

Quantum spin systems such as magnetic insulators usually show magnetic order, but such classical states can give way to quantum liquids with exotic entanglement through two known mechanisms of frustration: geometric frustration in lattices with triangle motifs, and spin-orbit-coupling frustration in the exactly solvable quantum liquid of Kitaev’s honeycomb lattice. Here we present the experimental observation of a new kind of frustrated quantum liquid arising in an unlikely place: the magnetic insulator Ba4Ir3O10 where Ir3O12 trimers form an unfrustrated square lattice. The crystal structure shows no apparent spin chains. Experimentally we find a quantum liquid state persisting down to 0.2 K that is stabilized by strong antiferromagnetic interaction with Curie–Weiss temperature ranging from −766 to −169 K due to magnetic anisotropy. The anisotropy-averaged frustration parameter is 2000, seldom seen in iridates. Heat capacity and thermal conductivity are both linear at low temperatures, a familiar feature in metals but here in an insulator pointing to an exotic quantum liquid state; a mere 2% Sr substitution for Ba produces long-range order at 130 K and destroys the linear-T features. Although the Ir4+(5d5) ions in Ba4Ir3O10 appear to form Ir3O12 trimers of face-sharing IrO6 octahedra, we propose that intra-trimer exchange is reduced and the lattice recombines into an array of coupled 1D chains with additional spins. An extreme limit of decoupled 1D chains can explain most but not all of the striking experimental observations, indicating that the inter-chain coupling plays an important role in the frustration mechanism leading to this quantum liquid.

Designing Higher Resolution Self-Assembled 3D DNA Crystals via Strand Terminus Modifications.

DNA tensegrity triangles self-assemble into rhombohedral three-dimensional crystals via sticky ended cohesion. Crystals containing two-nucleotide (nt) sticky ends (GA:TC) have been reported previously, and those crystals diffracted to 4.9 Å at beamline NSLS-I-X25. Here, we analyze the effect of varying sticky end lengths and sequences as well as the impact of 5'- and 3'-phosphates on crystal formation and resolution. Tensegrity triangle motifs having 1-, 2-, 3-, and 4-nt sticky ends all form crystals. X-ray diffraction data from the same beamline reveal that the crystal resolution for a 1-nt sticky end (G:C) and a 3-nt sticky end (GAT:ATC) were 3.4 and 4.2 Å, respectively. Resolutions were determined from complete data sets in each case. We also conducted trials that examined every possible combination of 1-nucleotide and 2-nucleotide sticky-ended phosphorylated strands and successfully crystallized all 16 possible combinations of strands. We observed the position of the 5'-phosphate on either the crossover (1), helical (2), or central strand (3) affected the resolution of the self-assembled crystals for the 2-turn monomer (3.0 Å for 1-2P-3P) and 2-turn dimer sticky ended (4.1 Å for 1-2-3P) systems. We have also examined the impact of the identity of the base flanking the sticky ends as well as the use of 3'-phosphate. We conclude that crystal resolution is not a simple consequence of the thermodynamics of the direct nucleotide pairing interactions involved in molecular cohesion in this system.

COMICS: a community property-based triangle motif clustering scheme.

With the development of science and technology, network scales of various fields have experienced an amazing growth. Networks in the fields of biology, economics and society contain rich hidden information of human beings in the form of connectivity structures. Network analysis is generally modeled as network partition and community detection problems. In this paper, we construct a community property-based triangle motif clustering scheme (COMICS) containing a series of high efficient graph partition procedures and triangle motif-based clustering techniques. In COMICS, four network cutting conditions are considered based on the network connectivity. We first divide the large-scale networks into many dense subgraphs under the cutting conditions before leveraging triangle motifs to refine and specify the partition results. To demonstrate the superiority of our method, we implement the experiments on three large-scale networks, including two co-authorship networks (the American Physical Society (APS) and the Microsoft Academic Graph (MAG)), and two social networks (Facebook and gemsec-Deezer networks). We then use two clustering metrics, compactness and separation, to illustrate the accuracy and runtime of clustering results. A case study is further carried out on APS and MAG data sets, in which we construct a connection between network structures and statistical data with triangle motifs. Results show that our method outperforms others in both runtime and accuracy, and the triangle motif structures can bridge network structures and statistical data in the academic collaboration area.

Trios\u2014promising in silico biomarkers for differentiating the effect of disease on the human microbiome network

Recent advances in the HMP (human microbiome project) research have revealed profound implications of the human microbiome to our health and diseases. We postulated that there should be distinctive features associated with healthy and/or diseased microbiome networks. Following Occam’s razor principle, we further hypothesized that triangle motifs or trios, arguably the simplest motif in a complex network of the human microbiome, should be sufficient to detect changes that occurred in the diseased microbiome. Here we test our hypothesis with six HMP datasets that cover five major human microbiome sites (gut, lung, oral, skin, and vaginal). The tests confirm our hypothesis and demonstrate that the trios involving the special nodes (e.g., most abundant OTU or MAO, and most dominant OTU or MDO, etc.) and interactions types (positive vs. negative) can be a powerful tool to differentiate between healthy and diseased microbiome samples. Our findings suggest that 12 kinds of trios (especially, dominantly inhibitive trio with mixed strategy, dominantly inhibitive trio with pure strategy, and fully facilitative strategy) may be utilized as in silico biomarkers for detecting disease-associated changes in the human microbiome, and may play an important role in personalized precision diagnosis of the human microbiome associated diseases.

Higher-Order Synaptic Interactions Coordinate Dynamics in Recurrent Networks.

Linking synaptic connectivity to dynamics is key to understanding information processing in neocortex. Circuit dynamics emerge from complex interactions of interconnected neurons, necessitating that links between connectivity and dynamics be evaluated at the network level. Here we map propagating activity in large neuronal ensembles from mouse neocortex and compare it to a recurrent network model, where connectivity can be precisely measured and manipulated. We find that a dynamical feature dominates statistical descriptions of propagating activity for both neocortex and the model: convergent clusters comprised of fan-in triangle motifs, where two input neurons are themselves connected. Fan-in triangles coordinate the timing of presynaptic inputs during ongoing activity to effectively generate postsynaptic spiking. As a result, paradoxically, fan-in triangles dominate the statistics of spike propagation even in randomly connected recurrent networks. Interplay between higher-order synaptic connectivity and the integrative properties of neurons constrains the structure of network dynamics and shapes the routing of information in neocortex.

Lanthanide-Organic Frameworks (LnOFs) Containing 1D Metal/Oxygen Ribbons with Cubane-like and Triangle Motifs: Synthesis, Structure, Luminescence and Slow Magnetic Relaxation

Four lanthanide-based three-dimensional(3D) complexes {[Ln5(μ2-O)(μ3-OH)5(TCA)2(NO3)(CH3COO)(H2O)2]⋅NH(CH3)2⋅DMA⋅(H2O)3}n (H3TCA=4,4′,4′′-tricarboxytriphenylamine; DMA=N,N-dimethylacetamide; Ln=Dy(1), Y(2)) and {[Ln2(μ2-OH)(μ3-OH)2(TCA)(H2O)]⋅DMA⋅H2O}n (Ln=Er(3), Yb(4)) have been hydrothermally synthesized based on a flexible tricarboxylate ligand H3TCA. Single-crystal X-ray diffraction studies reveal that complexes 1–4 exhibit a 3D framework constructed through well-isolated one-dimensional(1D) metal/oxygen ribbons. Therein, the unusual pentanuclear unit comprised of cubane-like [Ln4O4] cluster and the additional Ln (III) center can be observed in complexes 1 and 2, while lanthanide triangle motifs appear in complexes 3 and 4. Static and dynamic magnetic measurements of 1 and 3 have been performed. Both complexes reveal frequency dependence of the out-of-phase signals, suggesting the slow magnetic relaxation behavior for 1 and 3. 3 and 4 exhibit characteristic emissions of the corresponding Er3+ and Yb3+ ions in the NIR region, respectively.

Gender homophily in online dyadic and triadic relationships

Gender homophily, or the preference for interaction with individuals of the same gender, has been observed in many contexts, especially during childhood and adolescence. In this study we investigate such phenomenon by analyzing the interactions of the ∼10 million users of Tuenti, a Spanish social networking service popular among teenagers. In dyadic relationships we find evidence of higher gender homophily for women. We also observe a preference of users with more friends to connect to the opposite gender. A particularly marked gender difference emerges in signing up for the social networking service and adding the first friends, and in the interactions by means of wall messages. In these contexts we find evidence of a strong homophily for women, and little or no homophily for men. By examining the gender composition of triangle motifs, we observe a marked tendency of users to group into gender homogeneous clusters, with a particularly high number of male-only triangles. We show that age plays an important role in this context, with a tendency to higher homophily for young teenagers in both dyadic and triadic relationships. Our findings have implications for addressing gender gap issues, understanding adolescent online behavior and technology adoption, and modeling social networks.

Optimizing Protein Specificity in the Crowded Cell through Concentration Balance and Network motif Selection

Mammalian cells contain ∼21,000 genes encoding upwards to 100,000 protein types. 5-40% of cell volume is occupied by macromolecules, posing challenges for cell proteins to locate functional partners and increasing the risk of nonspecific (nonfunctional) interactions. Overexpressed proteins in particular will saturate functional partners, leaving leftovers for nonspecific binding instead. Eukaryotic cells have evolved various methods to help proteins function reliably, including compartmentalization, allostery, and structural and chemical properties of binding sites. Cells may optimize specificity as a function of their binding networks; first through concentration balance, next through network structure. Using the Gillespie algorithm, we simulated specific and nonspecific binding in 500 networks of 90-200 nodes with varying topological properties under equal, random, and stoichiometrically balanced protein concentrations. Binding affinities for all specific and nonspecific interactions were determined using a coarse-grained protein sequence model. Concentration balance significantly reduced the number of nonspecific interactions, as did local topological patterns (motifs) that allowed increased difference between specific and nonspecific binding affinities. To test if these motifs are selected for in real networks, we sampled possible interface-interaction networks (IINs) for the Clathrin-mediated endocytosis PPI network in yeast, using a Monte Carlo algorithm and a fitness function to select for features that allow increased specificity. Our fitness function reproduced several features of the real IIN, including fragmentation, a scale-free degree distribution, the presence of square motifs and low number of chain and triangle motifs. These features differed significantly from unbiased sampling. We conclude that there is selective pressure on the evolution of real IINs to avoid nonfunctional interactions, and that non-optimal features of the real IIN (chains, larger network components) likely serve a functional purpose.

Intramolecular halogen bonds in 1,2-aryldiyne molecules: a theoretical study

Intramolecular halogen bonds have been the subject of several current experimental and theoretical studies. In this work, intramolecular halogen bonds in a series of 1,2-aryldiyne molecules were investigated using density functional theory calculations at the M06-2x level of theory. For comparison, some dimeric complexes between halogenated aryldiynes and quinolinyl compounds were also considered. The calculated interatomic distances and interaction angles of intramolecular halogen bonds compare fairly well with those determined experimentally, and the triangle motifs retain almost perfectly planar in all the studied molecules. Many of the well-known properties of conventional halogen bonds are reproduced in intramolecular halogen bonds: the interaction strength tends to increase with the enlargement of the atomic radius of halogens (I > Br > Cl); the attachment of electron-withdrawing moieties to halogens leads to much stronger intramolecular halogen bonds; the X···N (quinolinyl) interactions are stronger than the X···O (carbonyl) halogen bonds. On the basis of the shorter interatomic distances and the larger values of electron densities at the bond critical points, intramolecular halogen bonds become stronger in strength than corresponding intermolecular halogen bonds. However, these interactions have similar structural, energetic, atoms in molecules (AIM), and noncovalent interaction index (NCI) characteristics to traditional halogen bonds. Therefore, these interactions can be recognized as halogen bonds that are primarily electrostatic in nature. Particularly, the formation of intramolecular halogen bonds gives rise to the essential coplanarity of the molecules, whereas the two subunits in the dimeric complexes deviate from planarity to a large degree. In addition, a small number of crystal structures containing intramolecular halogen bonds were retrieved from the Cambridge Structural Database (CSD), to provide more insights into these interactions in crystals. This work not only will extend the knowledge of noncovalent interactions involving halogens as electrophilic centers but also could be very useful in molecular design and synthetic chemistry.

132 Impact of sticky end length on the diffraction of self-assembled DNA crystals

Our laboratory has reported a self-assembled 3-D crystal based on a DNA tensegrity triangle. The tensegrity triangle is a rigid DNA motif with three-fold rotational symmetry consisting of three helices whose axes are directed along three linearly independent directions (1). The triangles form a crystalline lattice stabilized via sticky ends (2). The length of the sticky ends reported previously was two nucleotides (nt) GA:TC. Although diffracting to 4 Å resolution at the APS-ID19 beam line, they diffract only to 4.9 Å at the NSLS-X25 beam line. In the current study, we have analysed the effect of sticky end length and sequence on crystal formation and the resolution of the X-ray diffraction pattern on NSLS-X25. Tensegrity triangle motifs having 1-, 2-, and 3-nt sticky ends have all formed crystals. X-ray diffraction data from the same beam line revealed that the crystal resolution was somewhat better for the 2-nt sticky end having an AA:TT base pair (4.75 Å) than GA:CT and CC:GG (8.0 Å). Moreover, the 1-nt sticky end (C:G) yielded a diffraction pattern whose resolution (3.5 Å) compared favorably with all the three 2-nt sticky end systems. However, the triangle motif having a 1-nt sticky end with an A:T base pair did not yield any crystals. For motifs with 3-nt sticky ends, the sequence GAG:CTC produced small crystals (10–20 μm), while larger crystals (150 μm) were obtained with the sequences TAG:ATC and TAT:ATA. Our results indicate that not only do the lengths and sequences of the sticky ends define the interactions between motifs, but they also have an impact on the resulting resolution. We expect redesigned assemblies to form 3-D crystals with better resolution that can aid in the scaffolding of biological macromolecules for crystallographic structure determination. Applications in many areas of DNA nanotechnology are expected to benefit from a complete analysis of the effects of sticky end length, sequence, and free energy.

Isomorphous tetrazolate MnII and CoII compounds built on Δ-chain showing different magnetic behaviors

As a continuation of the study on using the tetrazolate ligands to construct coordination polymers, two isomorphous 3D coordination polymers built on Δ-chain topological rod-shaped SBUs have been synthesized with formulae [M(2)(μ(3)-OH)L(1)L(2)](n) (5-amino-1H-tetrazole (HL(1)), 2,3-pyrazinedicarboxylic acid (H(2)L(2)) and different 3d spin carriers (M = Mn(II), 1 and Co(II), 2)). The SBU consists of corner-sharing [M(3)(μ(3)-OH)] isosceles triangle motifs with mixed multiple (μ(4)-tetrazolyl, μ(3)-OH, syn-syn carboxylate) bridges. The SBUs were further linked by syn-anti carboxylates to form the sra net. Spin-competing was observed in the Mn(II) compound, whereas the Co(II) compound exhibits spin-canting.

Metallic Nanoparticles Used to Estimate the Structural Integrity of DNA Motifs

Branched DNA motifs can be designed to assume a variety of shapes and structures. These structures can be characterized by numerous solution techniques; the structures also can be inferred from atomic force microscopy of two-dimensional periodic arrays that the motifs form via cohesive interactions. Examples of these motifs are the DNA parallelogram, the bulged-junction DNA triangle, and the three-dimensional-double crossover (3D-DX) DNA triangle. The ability of these motifs to withstand stresses without changing geometrical structure is clearly of interest if the motif is to be used in nanomechanical devices or to organize other large chemical species. Metallic nanoparticles can be attached to DNA motifs, and the arrangement of these particles can be established by transmission electron microscopy. We have attached 5 nm or 10 nm gold nanoparticles to every vertex of DNA parallelograms, to two or three vertices of 3D-DX DNA triangle motifs, and to every vertex of bulged-junction DNA triangles. We demonstrate by transmission electron microscopy that the DNA parallelogram motif and the bulged-junction DNA triangle are deformed by the presence of the gold nanoparticles, whereas the structure of the 3D-DX DNA triangle motif appears to be minimally distorted. This method provides a way to estimate the robustness and potential utility of the many new DNA motifs that are becoming available.

Paranemic cohesion of topologically-closed DNA molecules.

Specific cohesion of DNA molecules is key to the success of work in biotechnology, DNA nanotechnology and DNA-based computation. The most common form of intermolecular cohesion between double helices is by sticky ends, but sticky ends generated by naturally occurring restriction enzymes may often be too short to bind large constructs together. An alternative form of binding is available through the paranemic crossover (PX) motif. Each of the two components of a PX motif can be a DNA dumbbell or other topologically closed species. Alternate half-turns of the dumbbell are paired intramolecularly. The intervening half-turns are paired with those of the opposite component. We demonstrate the efficacy of PX cohesion by showing that it can result in the 1:1 binding of two triangle motifs, each containing nearly 500 nucleotides. The cohesion goes to completion, demonstrating an alternative to binding nucleic acid molecules through sticky ends.