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Structural and compositional complexities of hierarchical self-assembly: A hypergraph approach

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. In this work, we introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

36 MATERIALS SCIENCE

Characterization of switchgrass ( Panicum virgatum L.) PvKSL1 as a levopimaradiene/abietadiene‐type diterpene synthase

Abstract The diverse class of plant diterpenoid metabolites serves important functions in mediating growth, chemical defence, and ecological adaptation. In major monocot crops, such as maize (Zea mays), rice (Oryza sativa), and barley (Hordeum vulgare), diterpenoids function as core components of biotic and abiotic stress resilience. Switchgrass (Panicum virgatum) is a perennial grass valued as a stress‐resilient biofuel model crop. Previously we identified an unusually large diterpene synthase family that produces both common and species‐specific diterpenoids, several of which accumulate in response to abiotic stress. Here, we report discovery and functional characterization of a previously unrecognized monofunctional class I diterpene synthase (PvKSL1) viain vivoco‐expression assays with different copalyl pyrophosphate (CPP) isomers, structural and mutagenesis studies, as well as genomic and transcriptomic analyses. In particular, PvKSL1 convertsent‐CPP intoent‐abietadiene,ent‐palustradiene,ent‐levopimaradiene, andent‐neoabietadiene via a 13‐hydroxy‐8(14)‐ent‐abietene intermediate. Notably, although featuring a distinctent‐stereochemistry, this product profile is near‐identical to bifunctional (+)‐levopimaradiene/abietadiene synthases occurring in conifer trees. PvKSL1 has three of four active site residues previously shown to control (+)‐levopimaradiene/abietadiene synthase catalytic specificity. However, mutagenesis studies suggest a distinct catalytic mechanism in PvKSL1. Genome localization ofPvKSL1distant from other diterpene synthases, and its phylogenetic distinctiveness from known abietane‐forming diterpene synthases, support an independent evolution of PvKSL1 activity. Albeit at low levels,PvKSL1gene expression predominantly in roots suggests a role of diterpenoid formation in belowground tissue. Together, these findings expand the known chemical and functional space of diterpenoid metabolism in monocot crops.

Plant Sciences

Lithographic crystallinity regulation in additive fabrication of thermoplastics (CRAFT)

For semicrystalline polyolefin thermoplastics, the balance between interconnected ordered crystalline and disordered amorphous regions is paramount to their performance and processability. However, contemporary manufacturing strategies, from injection molding to three-dimensional (3D) printing, result in monolithic objects, unable to spatially encode crystallinity. We develop a light-based approach for fabricating mechanically robust polyolefin thermoplastics with microscopic control over crystallinity in 3D space. Light dosage governs polymer stereochemistry giving access to a continuum of materials, from strong rigid plastics, such as high-density polyethylene, to more extensible materials akin to low-density polyethylene, all at the flick of a switch. Leveraging this finding in lithographic grayscale 3D printing enables rapid multimaterial fabrication with voxel-level control over optical and mechanical properties, opening avenues in information storage, soft robotics, and energy damping.

36 MATERIALS SCIENCE

Catalytic Difunctionalization of Cyclic Dienes: Direct Entry to Novel ROMP Monomers

We developed a catalytic platform to convert simple hydrocarbon feedstocks into valuable, tunable materials by leveraging nickel-catalyzed difunctionalization of cyclic dienes to access a novel class of cyclic alkene monomers. These monomers undergo ring-opening metathesis polymerization (ROMP) to yield sequence-controlled polymers with defined stereochemistry. Through mechanistic studies and catalyst optimization, we established a scalable, gram-level synthesis for selective diarylation, and expanded the reaction scope to include arylalkylation through rationally tuning the organoboron coupling partner. The resulting polymers were systematically studied to understand how steric, electronic, and stereochemical features influence polymerization behavior and bulk material properties. Functionalized derivatives bearing sulfonated groups were explored as proton-exchange membranes, and chemical recycling pathways were developed to recover monomers from the final materials. This work bridges small-molecule catalysis and macromolecular design, enabling access to tunable, recyclable polymers from abundant hydrocarbon starting materials.

36 MATERIALS SCIENCE

Ames interactive molecular model building system - A 3-D computer modelling system applied to the study of the origin of life

The investigation of specific interactions among biological molecules must take into consideration the stereochemistry of the structures. Thus, models of the molecules are essential for describing the spatial organization of potentially interacting groups, and estimations of conformation are required for a description of spatial organization. Both the function of visualizing molecules, and that of estimating conformation through calculations of energy, are part of the molecular modeling system described in the present paper. The potential uses of the system in investigating some aspects of the origin of life rest on the assumption that translation of conformation from genetic elements to catalytic elements would have been required for the development of the first replicating systems subject to the process of biological evolution.

Coeckelenbergh, Y.

From inanimate matter to living systems

Since the early part of this century, the Genesis account of the origin and evolution of life has been explained as an extrapolation of astronomical and geochemical processes. The essence of the answer to date is a protoreproductive protocell of much biochemical and cytophysical competance. The processes of its origin, molecular ordering, and its functions are described. A crucial understanding is that of the nonrandomness of evolutionary processes at all stages (with perhaps a minor statistical component). In this way, evolution conflicts with statistical randomness; the latter is a favorite assumption of both scientific and creationistic critics of the proteinoid theory. The principle contribution of the proteinoid theory to the understanding of general biology is to particularize the view that evolutionary direction is rooted in the shapes of molecules, in stereochemistry. After molecules of the right kind first assembled to protocells, life in its various stages of evolution was an inevitable consequence. It is molecules that continue to assemble as part of living process and, in the role of enzymes, continue to direct life cycle of the cell.

Fox, S. W.

Biochemical changes in bone in a model of weightlessness

The amounts of nonmineralized and mineralized collagen in bone from control, immobilized, and immobilized reambulated monkeys were examined. In order to understand structure function relationships of bone collagen and the reponse of a variety of conditions on control of the three dimensional structure of the collagen fibril, the stereochemistry of the cross-linking reactions as well as the stereospecific packing of the collagen molecules were studied.

Mechanic, Gerald L.

Macromolecular recognition: Structural aspects of the origin of the genetic system

Theoretical simulation of prebiotic chemical processes is an invaluable tool for probing the phenomenon of evolution of life. Using computational and modeling techniques and guided by analogies from present day systems we, seek to understand the emergence of genetic apparatus, enzymatic catalysis and protein synthesis under prebiotic conditions. In one possible scenario, the RNA enzymatic reaction plays a key role in the emergence of the self-replicating and offers a clue to the onset of enzymatic catalysis prior to the existence of the protein biosynthetic machinery. Our ultimate goal is to propose a simple RNA segment which contains the specificity and catalytic activity of the contemporary RNA enzyme and which could emerge in a primordial chemical environment. To understand the mechanism of ribozyme catalyzed reactions, ab initio and semi-empirical (ZINDO) programs were used to investigate the reaction path of transphosphorylation. A special emphasis was placed on the possible catalytic and structural roles played by the coordinated magnesium cation. Both the inline and adjacent mechanisms of transphosphorylation have been studied. Another important aspect of this reaction is the identity of the functional groups which are essential for the acid base catalysis. The structural characteristics of the target helices, particularly a possible role of G center dot T pair, is under examination by molecular dynamics (MD) simulation technique. Modeling of the ancestral aminoacyl-tRNA synthetases (aRS) may provide important clues to the emergence of the genetic code and the protein synthetic machinery. Assuming that the catalytic function evolved before the elements of specific recognition of a particular amino acid, we are exploring the minimal structural requirements for the catalysis of tRNA aminoacylation. The molecular modeling system SYBYL was used for this study based on the high resolution crystallographic structures of the present day tyrosyl-adenylate:tyrRS and tRNA(Gln): ATP:glnRS complexes. The trinucleotide CCA of the 3'-end tRNA is placed into the active site pocket of tyrRS, based on the scheme of interaction between tRNA(Gln) and glnRS, and upon the stereochemistry of the tyrRS:tRNA:Tyr-AMP transition state. This provides a model of the non-specific recognition of a tRNA's 3'-end by an aRS, which might be similar to that of the ancestral aRS's. In the next step, modeling of the rest of the acceptor stem of tRNA (Tyr) with tyrRS is carried out.

Rein, Robert

Double layer hydroxide minerals as host structures for bioorganic molecules

A central problem in molecular evolution concerns the selective concentration from dilute, multicomponent solution of source molecules into a reactive environment, where formation of larger molecular assemblages can take place. Minerals consisting of positively charged, separable metal hydroxide sheets have proven capable of these functions. This common structural type is represented by minerals such as pyroaurite (Mg-Fe(3+) hydroxide), hydrotalcite (Mg-Al), green rust Fe(2+)-Fe(3+) and others. Effective interlayer sorption is demonstrated for orthophosphate and condensed phosphates, anionic alkyl compounds, polypeptides, nucleic acids, cyanide complexes and glycolaldehyde phosphate, the latter shown to readily oligomerize to form and selectively retain racemic hexose -2, 4, 6-phosphates, preferentially of altrose (Pitsch, et al, 1993). The selective aldomerization and retention effects correlate with the charge distribution in the host mineral structure and the stereochemistry of the substrate molecules. Interaction between nucleic acid bases, and between the cyanide groups of glycolaldehyde phosphate nitrile at the low water activity in the mineral interlayer is indicated by doubling of the monomeric separation of the hydroxide mineral sheets.

Lee, Ton

A Structural and Molecular Approach for the Study Biomarkers

Investigation of the nucleation and growth of crystals in both abiotic and biotic systems is critical to seemingly diverse disciplines of geology, biology, environmental science, and astrobiology. While there are abundant studies devoted to the determination of the structure and composition of inorganic crystals, as well as to the development of thermodynamic and kinetic models, it is only recently that research efforts have been directed towards understanding mineralization in biological systems (i.e., biomineralization). Biomineralization refers to the processes by which living organisms form inorganic solids. Studies of the processes of biomineralization under low temperature aqueous conditions have focused primarily on magnetite forming bacteria and shell forming marine organisms. Many of the biological building materials consist of inorganic minerals (calcium carbonate, calcium phosphate, silica or iron oxide) intricately combined with organic polymers (like proteins). More recently, efforts have been undertaken to explore the nature of biological activities in ancient rocks. In the absence of well-preserved microorganisms or genetic material required for the polmerase chain reaction (PCR) method in molecular phylogenetic studies, using biominerals as biomarkers offers an alternative approach for the recognition of biogenic activity in both terrestrial and extraterrestrial environments. The primary driving force in biomineralization is the interaction between organic and inorganic phases. Thus, the investigation of the ultrastructure and the nature of reactions at the molecular level occurring at the interface between inorganic and organic phases is essential to understanding the processes leading to the nucleation and growth of crystals. It is recognized that crystal surfaces can serve as the substrate for the organization of organic molecules that lead to the formation of polymers and other complex organic molecules, and in discussions of the origins of life, is referred to as organic synthesis on mineral surfaces. Furthermore, it is suggested that the interaction between mineral surfaces and simple organic molecules resulted in the formation of amino acids, RNA, and perhaps other more complex molecules such as proteins. On the other hand, in natural systems, it is recognized that functional groups on cell walls or membranes of microorganisms serve as sites of nucleation and crystallization. The precise replication of biominerals with controlled structure, morphology, size and texture is not confined to higher organisms as it also occurs in primitive prokaryotic cells such as magnetotactic bacteria and cyanobacteria. This suggests that the principal strategies of biomineralization were established early on in the evolutionary history of organisms. It is critical, therefore, to search for common mechanisms within diverse biological systems. One such common factor is the capability for organization and self-assembly. Organic macromolecules such as proteins and lipids can aggregate and polymerize forming membranes or extracellular matrix. At the organic-inorganic interface, several factors such as lattice geometry, polarity, stereochemistry and topography may act in concert to control nucleation and growth of crystals. Although several models have been proposed that discuss the significance of these factors for biomineralization, no comprehensive experimental data are available. In contrast to crystallization in exclusively inorganic systems, the kinetics of reaction and structural relationships between organic and inorganic phases in biominerals or biomimetic material is poorly understood. For example, it is not clear if the concept of epitactic growth (geometrical matching of unit cells at the interface of a secondary crystal growing on a primary crystal) applies to organic-inorganic systems. In contrast to inorganic templates that often have a smooth and rigid surface that promotes epitactic growth, biological substrates are usually rough and result in a large degree of mismatch. It is apparent that factors controlling the reaction at the crystal-matrix interface are strongly dependent upon the nature of the substrate. Therefore, characterization of the assembled organic surface and surface structure of the inorganic phase is crucial to understanding the processes of biomineralization. The focus of our research is the investigation of the processes leading to the nucleation and growth of crystals on both natural and synthetic systems through an interdisciplinary approach that integrates molecular biology, morphology and mineralogy using advanced preparation and analytical techniques. We have studied run-products, particularly magnetite, siderite and other carbonates, that resulted from extracellular biomineralization by extremophiles isolated from a variety of extreme environments ranging from permafrost to hydrothermal vent systems. The results of this study are critical to recognizing biomarkers in terrestrial and extraterrestrial environments.

Thomas-Keprta, Kathie

Chirality of Meteoritic Free and IOM-Derived Monocarboxylic Acids and Implications for Prebiotic Organic Synthesis

The origin of homochirality and its role in the development of life on Earth are among the most intriguing questions in science. It has been suggested that carbonaceous chondrites seeded primitive Earth with the initial organic compounds necessary for the origin of life. One of the strongest pieces of evidence supporting this theory is that certain amino acids in carbonaceous chondrites display a significant L-enantiomeric excess (ee), similar to those use by terrestrial life. Analyses of ee in meteoritic molecules other than amino acids would shed more light on the origins of homochirality. In this study we investigated the stereochemistry of two groups of compounds: (1) free monocarboxylic acids (MCAs) from CM2 meteorites LON 94101 and Murchison; and (2) the aliphatic side chains present in the insoluble organic matter (IOM) and extracted in the form of monocarboxylic acids (MCAs) from EET 87770 (CR2) and Orgueil (CI1). Contrary to the well-known ee observed for amino acids in meteorites, we found that meteoritic branched free and IOM-derived MCAs with 5-8 carbon atoms are essentially racemic. The racemic nature of these compounds is used to discuss the possible influence of ultraviolet circularly polarized light (UVCPL) and aqueous alterations on the parent body on chirality observed in in carbonaceous chondrites. 2014 Elsevier Ltd. All rights reserved.

monocarboxylic acids

Effect of salinity on the preservation of biomarkers in hypersaline microbial mat kerogens

Kerogen is the residue that remains after the minerals and organic compounds have been extracted from a rock using acid and organic solvents, respectively [1]. It is not only the largest organic carbon sink in the geological record but the best-preserved fraction due to its recalcitrance and ability to retain syngenetic source information during deposition [2]. Due to the complex, macromolecular, cross-linked polymeric structure of kerogen, it is difficult to analyse intact, often requiring breakdown into smaller subunits through thermal (pyrolysis) or chemical treatment (chemolysis) [3]. Saline and hypersaline environments host diverse microbial communities, which can trap and bind organic matrices such as cellular components (e.g., extracellular polymeric substances, cell wall, peptidoglycan, sheath material, etc.) with sediments, forming layered, laminated structures called microbial mats. Here we present depth profiles of two hypersaline cores through a microbial mat with differing total salinities. We looked at the composition of organic compounds released from kerogen during high temperature, hydrogen-assisted, pyrolysis to understand the effect of salinity on the composition and timing of their incorporation [4]. Field Site: The Exportadora del Sal S. A. (ESSA) saltern of Guerrero Negro (Baja California Sur, Mexico) lies within a typical sabhka environment adjacent to Laguna Ojo de Liebre. Note the spatial extent of the 13 major ponds of the ESSA system. The GN ponds thrive under well-monitored and stable conditions with steady state accretion and degradation of mat layers (around 0.5–1.4 cm per year). Organic mats typically attain up to 10 cm in thickness, depending on the location, which represents about 60 years of growth since these ponds were established. Sedimentation rate is rapid in these non-lithifying and non-mineralising mats, 1–1.5 cm per year. This environment is ideal for investigating in situ lipid preservation and diagenesis without the influence of constantly changing physical parameters. Methods: P4n5 and P5AB cores were collected as ~9 cm and 6.5 cm fresh cores, respectively, in June 2001 and September 2010, respectively from the ESSA saltern. The P4n5 core (9-9.1% salinity) was taken from Pond 4 near 5 and sub-divided into 10 layers. The P5AB core (11.2% salinity) was taken from Pond 5A near 5B and sub-divided into 8 layers. Lyophilised microbial mat powders were solvent-extracted using a modified Bligh-Dyer method and analysed by gas chromatography-mass spectrometry (GC-MS). Additionally, a subset of layers—layer 4 and layer 7—which represented active biomass and sediment-processed, respectively, were subjected to mild-acid methanolysis. The respective residues from conventional solvent extraction and acid methanolysis were loaded with a molybdenum sulfide catalyst and placed into a stainless-steel reactor. Samples were run on the hydropyrolysis set up (heated to 500 °C with 13-15 MPa of H2 pressure), extracted, and analysed by GC-MS. Results: Molecular profiles from the two ponds were significantly different and reflect the contributions of different photosynthetic and respiratory microbial communities to preserved organic matter. For example, the higher salinity P5AB core showed evidence of greater archaeal inputs (similarly observed in lab culture experiments [5]) as well as potential kerogen-bound carotenoids/carotenoid rearranged products or fragments. A hydrophobic emulsion formed during the acid methanolysis processing of layer 4 from both P4n5 and P5AB and layer 7 of P5AB. Hydropyrolysis of this hydrophobic residues released a greater abundance of polycyclic lipids relative to the pre-extracted control. Implications and Future Work: Catalytic hydropyrolysis of kerogen can rapidly generate abundant saturated pyrolysate products from the bound biomarker pool without altering the structures or stereochemistries of the products [6]. Chemical processing of solvent-extractable residues indicated that cellular matrices such as extracellular polymeric substances (EPS) may play a role in the sequestration of polycyclic lipid biomarkers such as steranes and hopanes. Their higher relative abundance compared to the pre-extracted control in the higher salinity layers and cores preliminarily aligns with this hypothesis, although further experiments are required to confirm this. It has been well-documented that EPS plays an important role in mineralisation, specifically carbonate formation, in microbial ecosystems. EPS can enhance calcium carbonate precipitation by providing diffusion-limited sites that create alkalinity gradients in response to microbial processes [7]. It has been experimentally demonstrated that salinity influences the total amount of EPS (both loosely- and tightly-bound) which increases with increasing salinity [8]. The higher salinity at Guerrero Negro switches the microbial population from filamentous Microcoleus to being dominated by Phormidium, Oscillatoria, and unicellular cyanobacteria. We demonstrated that lipid binding into kerogen via strong covalent linkages occurs at the very earliest stages of sedimentary diagenesis. We are currently investigating the influence of salinity on organic preservation through experimental and modelling approaches. Understanding how key biomarkers transform into preserved organic matter (i.e., from precursor biolipids to bound geolipids) in brine ecosystems will aid the search for organic biosignatures on other planetary bodies, especially Icy Moons and modern Mars.

hypersaline

Stereochemically‐Controlled Fluorinated Copolymers for Selectively Permeable Barrier Applications

Selective oxygen permeability coupled with low water vapor transmission is essential for biomedical and packaging applications requiring controlled oxygen flux under humid conditions. However, most high‐performance barrier polymers depend on perfluoroalkyl substances (PFAS), whose persistence and regulatory restrictions limit their long‐term applicability. We designed a series of stereocontrolled thiol‐yne‐based polyesters, including both fluorinated and non‐fluorinated variants, for selective oxygen permeability with considerable water barrier performance. Tailoring polymer crystallinity and morphology tuned both oxygen transport and mechanical properties. Fluorinated polymers demonstrated enhanced hydrophobicity and water resistance while maintaining oxygen diffusivity within a range relevant to oxygen‐sensing applications. Structure–property relationships were elucidated through small‐ and wide‐angle X‐ray scattering, revealing semi‐crystalline domains influenced by fluorine content and dithiol chain length. Barrier performance was rigorously evaluated via water vapor transmission rate and dynamic vapor sorption, showing reduced water uptake with increasing dithiol monomer length and crystallinity. In conclusion, this work introduces a PFAS‐free alternative to conventional barrier materials and establishes a tunable materials platform with potential relevance for biomedical devices and packaging systems requiring controlled oxygen permeability.

36 MATERIALS SCIENCE

A compact catenane with tuneable mechanical chirality

Catenanes are formed by the mechanical interlocking of two or more rings. Enantiomers of a catenane can exist even if the rings themselves are achiral. Here we demonstrate that two achiral rings, each featuring a polarized cavity and two mirror planes, in addition to a two-fold axis of symmetry, can form a catenane with mechanical chirality. The catenane has been designed using an isostructural desymmetrization strategy, enabling the catenane to adopt a compact co-conformation similar to that of its achiral isostructural counterpart. Mechanical chirality in the catenane occurs when its two rings become interlocked in the compact co-conformation, leading to the loss of the two planes of symmetry present in its individual rings. The resulting enantiomers, which both have two-fold axes of symmetry, exist as a racemic modification in the solid state. Dynamic 1 H NMR spectroscopy carried out in acetonitrile-d 3 reveals a barrier of 16.4 kcal mol −1 to racemization between the two enantiomeric catenanes, the equilibrium of which can be influenced by the addition of chiral disulfonate anions, which support induced chirality and exhibit optical activity. One of the salts crystallizes to give only one diastereoisomer in the solid state. Furthermore, this research highlights the potential of using the isostructural desymmetrization strategy to create and study mechanical chirality along with its properties.

Interlocked molecules