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At least 361 records · Page 20

X‐ray scattering reveals disordered linkers and dynamic interfaces in complexes and mechanisms for DNA double‐strand break repair impacting cell and cancer biology

Abstract Evolutionary selection ensures specificity and efficiency in dynamic metastable macromolecular machines that repair DNA damage without releasing toxic and mutagenic intermediates. Here we examine non‐homologous end joining (NHEJ) as the primary conserved DNA double‐strand break (DSB) repair process in human cells. NHEJ has exemplary key roles in networks determining the development, outcome of cancer treatments by DSB‐inducing agents, generation of antibody and T‐cell receptor diversity, and innate immune response for RNA viruses. We determine mechanistic insights into NHEJ structural biochemistry focusing upon advanced small angle X‐ray scattering (SAXS) results combined with X‐ray crystallography (MX) and cryo‐electron microscopy (cryo‐EM). SAXS coupled to atomic structures enables integrated structural biology for objective quantitative assessment of conformational ensembles and assemblies in solution, intra‐molecular distances, structural similarity, functional disorder, conformational switching, and flexibility. Importantly, NHEJ complexes in solution undergo larger allosteric transitions than seen in their cryo‐EM or MX structures. In the long‐range synaptic complex, X‐ray repair cross‐complementing 4 (XRCC4) plus XRCC4‐like‐factor (XLF) form a flexible bridge and linchpin for DNA ends bound to KU heterodimer (Ku70/80) and DNA‐PKcs (DNA‐dependent protein kinase catalytic subunit). Upon binding two DNA ends, auto‐phosphorylation opens DNA‐PKcs dimer licensing NHEJ via concerted conformational transformations of XLF‐XRCC4, XLF–Ku80, and LigIV BRCT –Ku70 interfaces. Integrated structures reveal multifunctional roles for disordered linkers and modular dynamic interfaces promoting DSB end processing and alignment into the short‐range complex for ligation by LigIV. Integrated findings define dynamic assemblies fundamental to designing separation‐of‐function mutants and allosteric inhibitors targeting conformational transitions in multifunctional complexes.

59 BASIC BIOLOGICAL SCIENCES↗

Differences in the dynamics of the tandem-SH2 modules of the Syk and ZAP-70 tyrosine kinases

The catalytic activity of Syk-family tyrosine kinases is regulated by a tandem Src homology 2 module (tSH2 module). In the autoinhibited state, this module adopts a conformation that stabilizes an inactive conformation of the kinase domain. The binding of the tSH2 module to phosphorylated immunoreceptor tyrosine-based activation motifs necessitates a conformational change, thereby relieving kinase inhibition and promoting activation. We determined the crystal structure of the isolated tSH2 module of Syk and find, in contrast to ZAP-70, that its conformation more closely resembles that of the peptide-bound state, rather than the autoinhibited state. Hydrogen–deuterium exchange by mass spectrometry, as well as molecular dynamics simulations, reveal that the dynamics of the tSH2 modules of Syk and ZAP-70 differ, with most of these differences occurring in the C-terminal SH2 domain. Our data suggest that the conformational landscapes of the tSH2 modules in Syk and ZAP-70 have been tuned differently, such that the autoinhibited conformation of the Syk tSH2 module is less stable. This feature of Syk likely contributes to its ability to more readily escape autoinhibition when compared to ZAP-70, consistent with tighter control of downstream signaling pathways in T cells.

59 BASIC BIOLOGICAL SCIENCES↗

Structural and functional validation of a highly specific Smurf2 inhibitor

Smurf1 and Smurf2 are two closely related member of the HECT (homologous to E6AP carboxy terminus) E3 ubiquitin ligase family and play important roles in the regulation of various cellular processes. Both were initially identified to regulate transforming growth factor‐β and bone morphogenetic protein signaling pathways through regulating Smad protein stability and are now implicated in various pathological processes. Generally, E3 ligases, of which over 800 exist in humans, are ideal targets for inhibition as they determine substrate specificity; however, there are few inhibitors with the ability to precisely target a particular E3 ligase of interest. In this work, we explored a panel of ubiquitin variants (UbVs) that were previously identified to bind Smurf1 or Smurf2. In vitro binding and ubiquitination assays identified a highly specific Smurf2 inhibitor, UbV S2.4, which was able to inhibit ligase activity with high potency in the low nanomolar range. Orthologous cellular assays further demonstrated high specificity of UbV S2.4 toward Smurf2 and no cross‐reactivity toward Smurf1. Structural analysis of UbV S2.4 in complex with Smurf2 revealed its mechanism of inhibition was through targeting the E2 binding site. In summary, we investigated several protein‐based inhibitors of Smurf1 and Smurf2 and identified a highly specific Smurf2 inhibitor that disrupts the E2–E3 protein interaction interface.

59 BASIC BIOLOGICAL SCIENCES↗

RrA, an enzyme from Rhodospirillum rubrum , is a prototype of a new family of short‐chain L‐asparaginases

Abstract L‐Asparaginases (ASNases) catalyze the hydrolysis of L‐Asn to L‐Asp and ammonia. Members of the ASNase family are used as drugs in the treatment of leukemia, as well as in the food industry. The protomers of bacterial ASNases typically contain 300–400 amino acids (typical class 1 ASNases). In contrast, the chain of ASNase from Rhodospirillum rubrum , reported here and referred to as RrA, consists of only 172 amino acid residues. RrA is homologous to the N‐terminal domain of typical bacterial class 1 ASNases and exhibits millimolar affinity for L‐Asn. In this study, we demonstrate that RrA belongs to a unique family of cytoplasmic, short‐chain ASNases (scASNases). These proteins occupy a distinct region in the sequence space, separate from the regions typically assigned to class 1 ASNases. The scASNases are present in approximately 7% of eubacterial species, spanning diverse bacterial lineages. They seem to be significantly enriched in species that encode for more than one class 1 ASNase. Here, we report biochemical, biophysical, and structural properties of RrA, a member of scASNases family. Crystal structures of the wild‐type RrA, both with and without bound L‐Asp, as well as structures of several RrA mutants, reveal topologically unique tetramers. Moreover, the active site of one protomer is complemented by two residues (Tyr21 and Asn26) from another protomer. Upon closer inspection, these findings clearly outline scASNases as a stand‐alone subfamily of ASNases that can catalyze the hydrolysis of L‐Asn to L‐Asp despite the lack of the C‐terminal domain that is present in all ASNases described structurally to date.

59 BASIC BIOLOGICAL SCIENCES↗

Structural studies of intrinsically disordered MLL -fusion protein AF9 in complex with peptidomimetic inhibitors

AF9 (MLLT3) and its paralog ENL(MLLT1) are members of the YEATS family of proteins with important role in transcriptional and epigenetic regulatory complexes. These proteins are two common MLL fusion partners in MLL -rearranged leukemias. The oncofusion proteins MLL-AF9/ENL recruit multiple binding partners, including the histone methyltransferase DOT1L, leading to aberrant transcriptional activation and enhancing the expression of a characteristic set of genes that drive leukemogenesis. The interaction between AF9 and DOT1L is mediated by an intrinsically disordered C-terminal ANC1 homology domain (AHD) in AF9, which undergoes folding upon binding of DOT1L and other partner proteins. We have recently reported peptidomimetics that disrupt the recruitment of DOT1L by AF9 and ENL, providing a proof-of-concept for targeting AHD and assessing its druggability. Intrinsically disordered proteins, such as AF9 AHD, are difficult to study and characterize experimentally on a structural level. In this study, we present a successful protein engineering strategy to facilitate structural investigation of the intrinsically disordered AF9 AHD domain in complex with peptidomimetic inhibitors by using maltose binding protein (MBP) as a crystallization chaperone connected with linkers of varying flexibility and length. The strategic incorporation of disulfide bonds provided diffraction-quality crystals of the two disulfide-bridged MBP–AF9 AHD fusion proteins in complex with the peptidomimetics. These successfully determined first series of 2.1–2.6 Å crystal complex structures provide high-resolution insights into the interactions between AHD and its inhibitors, shedding light on the role of AHD in recruiting various binding partner proteins. We show that the overall complex structures closely resemble the reported NMR structure of AF9 AHD/DOT1L with notable difference in the conformation of the β-hairpin region, stabilized through conserved hydrogen bonds network. These first series of AF9 AHD/peptidomimetics complex structures are providing insights of the protein–inhibitor interactions and will facilitate further development of novel inhibitors targeting the AF9/ENL AHD domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Crystal structures of Salmonella enterica FraB deglycase reveal a conformational heterodimer with remarkable structural plasticity at the active site

Abstract Thefralocus ofSalmonella entericaencodes five genes for metabolism of fructose‐asparagine, an Amadori product formed by condensation of asparagine with glucose. In the last step of this pathway, the FraB deglycase cleaves 6‐phospho‐fructose‐aspartate into glucose‐6‐phosphate and aspartate. In homology models, FraB forms a homodimer with two equivalent active sites located at the dimer interface. E214 and H230, two invariant residues essential for catalysis, project into each active site cleft from opposing subunits of the dimer. Here, we have determined six crystal structures of FraB, three of a variant containing an N‐terminal His 6 tag and two mutations needed for crystallization (hereafter referred to as WT′), two with additional mutations to active site residues (E214A and P232A), and one of a variant with C‐terminal residues 313–325 deleted. Surprisingly, in the WT′ FraB structure, the two catalytic residues, E214 (general base) and H230 (general acid), are positioned ~22 Å apart. In the E214A and C‐terminus‐truncated FraB variants, however, a conformational change in the E214‐residing helix brings E214 and H230* to ~7 Å (* indicates residue from the second protomer that creates the inter‐subunit catalytic center). The loop bearing H230 also exhibits significant variation, ranging from being completely disordered to adopting open or closed states, with the nearby P232* residue being eithercisortrans. The C‐terminal residues 313–325 form a flexible “C‐tail” that can be fully disordered, bind in the active site to block access of substrate, or angle across the active site to wrap across the other subunit of the dimer and potentially close over substrate. Collectively, these structures reveal that FraB is a conformational heterodimer with two chemically identical subunits that are constrained to adopt different structures as they come together for catalysis. This plasticity likely involves correlated opening and closure of the two active sites for their respective binding and release of substrates and ligands.

Biochemistry & Molecular Biology↗

Molecular dynamics analysis of the binding of human interleukin-6 with interleukin-6 α-receptor

Human interleukin-6 (hIL-6) is a multifunctional cytokine that regulates immune and inflammatory responses in addition to metabolic and regenerative processes and cancer. hIL-6 binding to the IL-6 receptor (IL-6Rα) induces homodimerization and recruitment of the glycoprotein (gp130) to form a hexameric signaling complex. Anti-IL-6 and IL-6R antibodies are clinically approved inhibitors of IL-6 signaling pathway for treating rheumatoid arthritis and Castleman's disease, respectively. There is a potential to develop novel small molecule IL-6 antagonists derived from understanding the structural basis for IL-6/IL-6Rα interactions. In this work, we combine homology modeling with extensive molecular dynamics (MD) simulations to examine the association of hIL-6 with IL-6Rα. A comparison with MD of apo hIL-6 reveals that the binding of hIL-6 to IL-6Rα induces structural and dynamic rearrangements in the AB loop region of hIL-6, disrupting intraprotein contacts and increasing the flexibility of residues 48 to 58 of the AB loop. In contrast, due to the involvement of residues 59 to 78 in forming contacts with the receptor, these residues of the AB loop are observed to rigidify in the presence of the receptor. The binary complex is primarily stabilized by two pairs of salt bridges, Arg181 (hIL-6)- Glu182 (IL-6Rα) and Arg184 (hIL-6)- Glu183 (IL-6Rα) as well as hydrophobic and aromatic stacking interactions mediated essentially by Phe residues in both proteins. An interplay of electrostatic, hydrophobic, hydrogen bonding, and aromatic stacking interactions facilitates the formation of the hIL-6/IL-6Rα complex.

59 BASIC BIOLOGICAL SCIENCES↗

Improving protein tertiary structure prediction by deep learning and distance prediction in CASP14

Abstract Substantial progresses in protein structure prediction have been made by utilizing deep‐learning and residue‐residue distance prediction since CASP13. Inspired by the advances, we improve our CASP14 MULTICOM protein structure prediction system by incorporating three new components: (a) a new deep learning‐based protein inter‐residue distance predictor to improve template‐free (ab initio) tertiary structure prediction, (b) an enhanced template‐based tertiary structure prediction method, and (c) distance‐based model quality assessment methods empowered by deep learning. In the 2020 CASP14 experiment, MULTICOM predictor was ranked seventh out of 146 predictors in tertiary structure prediction and ranked third out of 136 predictors in inter‐domain structure prediction. The results demonstrate that the template‐free modeling based on deep learning and residue‐residue distance prediction can predict the correct topology for almost all template‐based modeling targets and a majority of hard targets (template‐free targets or targets whose templates cannot be recognized), which is a significant improvement over the CASP13 MULTICOM predictor. Moreover, the template‐free modeling performs better than the template‐based modeling on not only hard targets but also the targets that have homologous templates. The performance of the template‐free modeling largely depends on the accuracy of distance prediction closely related to the quality of multiple sequence alignments. The structural model quality assessment works well on targets for which enough good models can be predicted, but it may perform poorly when only a few good models are predicted for a hard target and the distribution of model quality scores is highly skewed. MULTICOM is available at https://github.com/jianlin-cheng/MULTICOM_Human_CASP14/tree/CASP14_DeepRank3 and https://github.com/multicom-toolbox/multicom/tree/multicom_v2.0 .

59 BASIC BIOLOGICAL SCIENCES↗

The N‐terminal intrinsically disordered region of Ncb5or docks with the cytochrome b 5 core to form a helical motif that is of ancient origin

Abstract NADH cytochromeb 5 oxidoreductase (Ncb5or) is a cytosolic ferric reductase implicated in diabetes and neurological conditions. Ncb5or comprises cytochromeb 5 (b 5 ) and cytochromeb 5 reductase (b 5 R) domains separated by a CHORD‐Sgt1 (CS) linker domain. Ncb5or redox activity depends on proper inter‐domain interactions to mediate electron transfer from NADH or NADPH via FAD to heme. While full‐length human Ncb5or has proven resistant to crystallization, we have succeeded in obtaining high‐resolution atomic structures of theb 5 domain and a construct containing the CS andb 5 R domains (CS/b 5 R). Ncb5or also contains an N‐terminal intrinsically disordered region of 50 residues that has no homologs in other protein families in animals but features a distinctive, conserved L 34 MDWIRL 40 motif also present in reduced lateral root formation (RLF) protein in rice and increased recombination center 21 in baker's yeast, all attaching to ab 5 domain. After unsuccessful attempts at crystallizing a human Ncb5or construct comprising the N‐terminal region naturally fused to theb 5 domain, we were able to obtain a high‐resolution atomic structure of a recombinant rice RLF construct corresponding to residues 25–129 of human Ncb5or (52% sequence identity; 74% similarity). The structure reveals Trp 120 (corresponding to invariant Trp 37 in Ncb5or) to be part of an 11‐residue α‐helix (S 116 QMDWLKLTRT 126 ) packing against two of the four helices in theb 5 domain that surround heme (α2 and α5). The Trp 120 side chain forms a network of interactions with the side chains of four highly conserved residues corresponding to Tyr 85 and Tyr 88 (α2), Cys 124 (α5), and Leu 47 in Ncb5or. Circular dichroism measurements of human Ncb5or fragments further support a key role of Trp 37 in nucleating the formation of the N‐terminal helix, whose location in the N/b 5 module suggests a role in regulating the function of this multi‐domain redox enzyme. This study revealed for the first time an ancient origin of a helical motif in the N/b 5 module as reflected by its existence in a class of cytochromeb 5 proteins from three kingdoms among eukaryotes.

Biochemistry & Molecular Biology↗

Insight into the autoproteolysis mechanism of the RsgI9 anti‐σ factor from Clostridium thermocellum

Abstract Clostridium thermocellum is a potential microbial platform to convert abundant plant biomass to biofuels and other renewable chemicals. It efficiently degrades lignocellulosic biomass using a surface displayed cellulosome, a megadalton sized multienzyme containing complex. The enzymatic composition and architecture of the cellulosome is controlled by several transmembrane biomass‐sensing RsgI‐type anti‐σ factors. Recent studies suggest that these factors transduce signals from the cell surface via a conserved RsgI extracellular (CRE) domain (also called a periplasmic domain) that undergoes autoproteolysis through an incompletely understood mechanism. Here we report the structure of the autoproteolyzed CRE domain from the C. thermocellum RsgI9 anti‐σ factor, revealing that the cleaved fragments forming this domain associate to form a stable α/β/α sandwich fold. Based on AlphaFold2 modeling, molecular dynamics simulations, and tandem mass spectrometry, we propose that a conserved Asn‐Pro bond in RsgI9 autoproteolyzes via a succinimide intermediate whose formation is promoted by a conserved hydrogen bond network holding the scissile peptide bond in a strained conformation. As other RsgI anti‐σ factors share sequence homology to RsgI9, they likely autoproteolyze through a similar mechanism.

Takayesu, Allen↗

Functional Relevance of CASP16 Nucleic Acid Predictions as Evaluated by Structure Providers

ABSTRACT Accurate biomolecular structure prediction enables the prediction of mutational effects, the speculation of function based on predicted structural homology, the analysis of ligand binding modes, experimental model building, and many other applications. Such algorithms to predict essential functional and structural features remain out of reach for biomolecular complexes containing nucleic acids. Here, we report a quantitative and qualitative evaluation of nucleic acid structures for the CASP16 blind prediction challenge by 12 of the experimental groups who provided nucleic acid targets. Blind predictions accurately model secondary structure and some aspects of tertiary structure, including reasonable global folds for some complex RNAs; however, predictions often lack accuracy in the regions of highest functional importance. All models have inaccuracies in non‐canonical regions where, for example, the nucleic‐acid backbone bends, deviating from an A‐form helix geometry, or a base forms a non‐standard hydrogen bond (not a Watson‐Crick base pair). These bends and non‐canonical interactions are integral to forming functionally important regions such as RNA enzymatic active sites. Additionally, the modeling of conserved and functional interfaces between nucleic acids and ligands, proteins, or other nucleic acids remains poor. For some targets, the experimental structures may not represent the only structure the biomolecular complex occupies in solution or in its functional life cycle, posing a future challenge for the community.

Biochemistry & Molecular Biology↗

Modeling Protein–Protein and Protein–Ligand Interactions by the ClusPro Team in CASP16

ABSTRACT In the CASP16 experiment, our team employed hybrid computational strategies to predict both protein–protein and protein–ligand complex structures. For protein–protein docking, we combined physics‐based sampling—using ClusPro FFT docking and molecular dynamics—with AlphaFold (AF)‐based sampling, followed by AF‐based refinement. Our method produced numerous high‐accuracy complex models, including cases where AF alone failed, underscoring the critical role of physics‐based sampling alongside deep learning‐based refinement. For protein–ligand docking, we integrated the ClusPro LigTBM template‐based approach with a machine learning‐based confidence model for rescoring. The method preserves conserved interaction fragments derived from homologous complexes, followed by local resampling using physics‐based sampling and a diffusion model. Our template‐based strategy achieved a mean lDDT‐PLI of 0.69 across 233 targets, which was highly competitive. These results demonstrate that combining physics‐based modeling with AI‐driven refinement can significantly enhance the accuracy of both protein–protein and protein–ligand structure predictions.

Ashizawa, Ryota [Department of Applied Mathematics↗

Design and Development of Stable Nanocrystalline High‐Entropy Alloy: Coupling Self‐Stabilization and Solute Grain Boundary Segregation Effects

Abstract Grain growth is prevalent in nanocrystalline (NC) materials at low homologous temperatures. Solute element addition is used to offset excess energy that drives coarsening at grain boundaries (GBs), albeit mostly for simple binary alloys. This thermodynamic approach is considered complicated in multi‐component alloy systems due to complex pairwise interactions among alloying elements. Guided by empirical and GB‐segregation enthalpy considerations for binary‐alloy systems, a novel alloy design strategy, the “ pseudo‐binary thermodynamic ” approach, for stabilizing NC‐high entropy alloys (HEAs) and other multi‐component‐alloy variants is proposed. Using Al 25 Co 25 Cr 25 Fe 25 as a model‐HEA to validate this approach, Zr, Sc, and Hf, are identified as the preferred solutes that would segregate to HEA‐GBs to stabilize it against growth. Using Zr, NC‐Al 25 Co 25 Cr 25 Fe 25 HEAs with minor additions of Zr are synthesized, followed by annealing up to 1123 K. Using advanced characterization techniques— in situ X‐ray diffraction (XRD), scanning/transmission electron microscopy (S/TEM), and atom probe tomography, nanograin stability due to coupling self‐stabilization and solute‐GB segregation effects is reported in HEAs up to substantially high temperatures. The self‐stabilization effect originates from the preferential GB‐segregation of constituent HEA‐elements that stabilizes NC‐Al 25 Co 25 Cr 25 Fe 25 up to 0.5 T m ( T m –melting temperature). Meanwhile, solute‐GB segregation originates from Zr segregation to NC‐Al 25 Co 25 Cr 25 Fe 25 GBs; this results in further stabilization of the phase and grain‐size (≈14 nm) up to ≈0.58 and ≈0.64 T m , respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Genomic variation within the maize stiff-stalk heterotic germplasm pool

The stiff-stalk heterotic group in Maize (Zea mays L.) is an important source of inbreds used in U.S. commercial hybrid production. Founder inbreds B14, B37, B73, and, to a lesser extent, B84, are found in the pedigrees of a majority of commercial seed parent inbred lines. We created high-quality genome assemblies of B84 and four expired Plant Variety Protection (ex-PVP) lines LH145 representing B14, NKH8431 of mixed descent, PHB47 representing B37, and PHJ40, which is a Pioneer Hi-Bred International (PHI) early stiff-stalk type. Sequence was generated using long-read sequencing achieving highly contiguous assemblies of 2.13-2.18 Gbp with N50 scaffold lengths >200 Mbp. Inbred-specific gene annotations were generated using a core five-tissue gene expression atlas, whereas transposable element (TE) annotation was conducted using de novo and homology-directed methodologies. Compared with the reference inbred B73, synteny analyses revealed extensive collinearity across the five stiff-stalk genomes, although unique components of the maize pangenome were detected. Comparison of this set of stiff-stalk inbreds with the original Iowa Stiff Stalk Synthetic breeding population revealed that these inbreds represent only a proportion of variation in the original stiff-stalk pool and there are highly conserved haplotypes in released public and ex-Plant Variety Protection inbreds. Despite the reduction in variation from the original stiff-stalk population, substantial genetic and genomic variation was identified supporting the potential for continued breeding success in this pool. The assemblies described here represent stiff-stalk inbreds that have historical and commercial relevance and provide further insight into the emerging maize pangenome.

59 BASIC BIOLOGICAL SCIENCES↗

Cell-Free Protein Synthesis for High-Throughput Biosynthetic Pathway Prototyping

Biological systems provide a sustainable and complimentary approach to synthesizing useful chemical products. Metabolic engineers seeking to establish economically viable biosynthesis platforms strive to increase product titers, rates, and yields. Despite continued advances in genetic tools and metabolic engineering techniques, cellular workflows remain limited in throughput. It may take months to test dozens of unique pathway designs even in a robust model organism, such as Escherichia coli. In contrast, cell-free protein synthesis enables the rapid generation of enzyme libraries that can be combined to reconstitute metabolic pathways in vitro for biochemical synthesis in days rather than weeks. Cell-free reactions thereby enable comparison of hundreds to thousands of unique combinations of enzyme homologs and concentrations, which can quickly identify the most productive pathway variants to test in vivo or further characterize in vitro. Furthermore, this cell-free pathway prototyping strategy provides a complementary approach to accelerate cellular metabolic engineering efforts toward highly productive strains for metabolite production.

59 BASIC BIOLOGICAL SCIENCES↗

A Topological Approach for Motion Track Discrimination

Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the scene. Moreover, this lack of spatial information also disqualifies the use of most state-of-the-art deep learning image-based classifiers. Here, we use characteristics of target tracks extracted from video sequences as data from which to derive distinguishing topological features that help robustly differentiate targets of interest from confusers. In particular, we calculate persistent homology from time-delayed embeddings of dynamic statistics calculated from motion tracks extracted from a wide field-of-view video stream. In short, we use topological methods to extract features related to target motion dynamics that are useful for classification and disambiguation and show that small targets can be detected at range with high probability.

Emerson, Tegan H.↗

Hyperbolic string vertices

The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of string vertices and their uniqueness up to canonical transformations. Using hyperbolic metrics on surfaces with geodesic boundaries we give an exact construction of string vertices as sets of surfaces with systole greater than or equal to L with L ≤ 2 arcsinh 1. Intrinsic hyperbolic collars prevent the appearance of short geodesics upon sewing. The surfaces generated by Feynman diagrams are naturally endowed with Thurston metrics: hyperbolic on the vertices and flat on the propagators. For the classical theory the length L is arbitrary and, as L → ∞hyperbolic vertices become the minimal-area vertices of closed string theory

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗