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Investigation of design principles for metal-binding and conductive protein assemblies

Throughout the lifetime of this initiative, including renewals, we focused on understanding the fundamental principles of protein-protein interface design that enable predictable and modular spatial and kinetic control of multi-component protein self-assembly in 1D, 2D, and 3D, including the interface with inorganic materials, small molecules, and metal ions. We designed individual protein components that bind specific metal ions, including REEs and transport ions across lipid membranes. We created helical 1D filaments of repeating units with programmed periodicity, pitch, and multi-component environmentally responsive self-assembling protein fibers. We showed that these filaments reversibly assemble and disassemble under specific pH conditions and created end-specific caps that independently tune the balance of attachment and detachment rates at each terminus of the filament. Using similar filaments, we succeeded in binding arrays of heme and chlorophyll molecules and assembling patterned helical coatings around carbon nanotubes in efforts to create de novo conductive nanowires. By arraying REE binding sites in a large circular tandem array with a repeat protein-based cyclic oligomer, we created a molecular scaffold for superradiance and paramagnetic quantum sensing. We created a range of one-component and two-component self-assembling 2D arrays and showed that when designed to engage cell receptors, these arrays can control cell behavior from outside the cell signal to inside the cell. We designed helical repeat proteins with variable lengths displaying charged residues in a pattern matched to the cation lattice of mica. achieved a range of ordered states with an epitaxial match to the underlying crystal lattice. We further applied the learned principles of protein-induced biomineralization to design proteins with an interface lattice matching CaCO 3 and guide the formation of specific crystal forms of CaCO 3 from solution, a significant advance toward the global need to manage carbon. In all cases of mineral lattice matching and biomineralization, we followed assembly using molecularly resolved in situ AFM imaging and extracted information about assembly pathways and energetics, applying deep learning to quantify the dynamics of protein self-organization. We developed techniques for using dynamic metal-dependent interfaces on protein nanopores for discriminatively sensing dilute REEs in solution and demonstrated the use of strong metal-binding interfaces to drive nanocage disassembly for conditional nanocompartmentalization applications. This grant supported 11 people, including Asim Bera, Evans Brackenbrough, Andrew Borst, Nikita Hanikel, Timothy Huddy, Emily Joyce, Alex Young-Seug Kang, Ryan Kibler, Joshua Morris Lubner, Harley Pyles, and Shuai Zhang. The research effort culminated in the production of published papers and theses. Electronic Thesis/Dissertation are distributed by ProQuest/UMI Dissertation Publishing and made available on an open access basis through UW Libraries ResearchWorks Service.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Controlled Enzyme Cargo Loading in Engineered Bacterial Microcompartment Shells

Bacterial microcompartments (BMCs) are nanometer-scale organelles with a protein-based shell that serve to colocalize and encapsulate metabolic enzymes. They may provide a range of benefits to improve pathway catalysis, including substrate channeling and selective permeability. Several groups are working toward using BMC shells as a platform for enhancing engineered metabolic pathways. The microcompartment shell of Haliangium ochraceum (HO) has emerged as a versatile and modular shell system that can be expressed and assembled outside its native host and with non-native cargo. Further, the HO shell has been modified to use the engineered protein conjugation system SpyCatcher–SpyTag for non-native cargo loading. Here, we used a model enzyme, triose phosphate isomerase (Tpi), to study non-native cargo loading into four HO shell variants and begin to understand maximal shell loading levels. We also measured activity of Tpi encapsulated in the HO shell variants and found that activity was determined by the amount of cargo loaded and was not strongly impacted by the predicted permeability of the shell variant to large molecules. All shell variants tested could be used to generate active, Tpi-loaded versions, but the simplest variants assembled most robustly. We propose that the simple variant is the most promising for continued development as a metabolic engineering platform.

59 BASIC BIOLOGICAL SCIENCES

Encapsulation in a Bacterial Microcompartment Shell Improves Thermal Stability of a Glycolytic Enzyme

Selective encapsulation of target enzymes is an increasingly well-studied field, with a host of potential applications for biotechnology. Natively, many bacteria utilize bacterial microcompartments (BMCs) for enzyme encapsulation to enhance catalysis. BMCs are protein shells that enable selective localization of targeted metabolic enzymes and may improve catalytic rates by colocalizing pathway enzymes and/or serve to sequester toxic or volatile intermediates. The microcompartment shell of Haliangium ochraceum (HO) is a notable BMC chassis because of its modularity and versatility; it is easily expressed and assembled outside its native host and can accept a wide array of cargo. Recently, it was demonstrated that assembly of HO BMC shells can be easily achieved in vitro. Following up on our previous work on in vivo assembly of HO-BMCs with triose phosphate isomerase (TPI) as a model enzyme cargo, here we have demonstrated the advantages of in vitro assembly (IVA) for targeted enzyme encapsulation. We achieved variable loading of BMC shells with targeted amounts of TPI and demonstrated enhanced thermal stability of encapsulated TPI versus free TPI up to 62 °C.

assays

SMR Containment Cable and Electrical Penetration Assembly System

GAIN Project CRADA Number NFE-21-08839, entitled “SMR Containment Cable and EPA System” was initiated by the partnership of Oak Ridge National Laboratory (ORNL) and Engineered Solutions Group (ESG) to test an ESG-designed Electrical Penetration Assembly and Containment Cabling System Qualified for not only SMR technologies, but also Advanced Reactors design. An Electrical Penetration Assembly (EPA) is a component used to allow electrical power and signal conductors as well as optical fiber through the nuclear reactor’s containment structure while maintaining a pressure barrier. The EPA ensures the containment's integrity both during the normal operation and also accident conditions by providing a sealed passage for power and signals. This project was undertaken to fill the equipment gap of EPA and Cabling Systems that require much more severe environmental requirements than legacy plant applications present due to their smaller containment volumes that result in high energy densities compared to legacy designs. This high energy density results in severe accident environments and also more severe normal operating conditions.This document describes cost effective approaches to qualify a unique EPA for Small Modular Reactor (SMR) technologies as legacy LWR EPA technologies will likely have inherent material performance insufficiencies. The DBA profiles for SMRs (and some Advanced Reactor Technologies) are more severe than the legacy qualification requirements making the design of the qualification testing system challenging as the temperatures and pressures can approach the limits permitted by ASME Pressure Vessel Code, as well as accident temperatures exceeding the capability of polymeric gaskets and dielectrics. Small Modular Reactors are designed to have, as the name suggests, modularity which implies sized for factory fabrication and subsequent assembly at the power plant site. SMR containment is much smaller than a legacy Light Water Reactor containment. The containment walls are likely to be comprised of stainless steel. Qualifying Electrical Penetration Assemblies (EPAs) through these steel vessels are of interest in this work. Methods are presented here that discuss critical safety and cost effectiveness for these SMR EPA’s test systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Self-assembly of wood-based shape memory composites triggered by solar-thermal energy

Transporting and assembling large, complex structures poses significant challenges due to their size, geometry, and cost. Additionally, the installation sites are often inaccessible or hazardous for humans, necessitating self-assembling capabilities in these structures. To mitigate these challenges, we propose using 3D printing materials with shape memory effect (SME) for both transport and construction. This approach involves developing 3D modular components into flat sheets for easier transportation, and then self-assembling into 3D structures on-site using solar energy. To gain a deeper understanding of the factors influencing material memory performance, we have chosen a composite PLA/WF, which is polylactic acid (PLA) with 20 wt% wood flour (WF) for this purpose, leveraging its high tensile modulus at 0.966 GPa, low cost, and sustainability. Printed shapes with this material can maintain a recovery ratio over 90% after 3 cycles. While traditional composites fillers (e.g. glass or carbon fiber) are added to enhance mechanical and thermal properties, the addition of bio-based fillers like WF accomplish similar goals without compromising sustainability. We conducted multiple experiments to demonstrate how environmental conditions (i.e. temperature) maximize the material’s SME. Although still at an early stage, this study provides initial insights into bridging the gap between the small-scale nature of shape memory polymers (SMPs) and their potential for large-scale additive manufacturing, addressing a critical need for efficient and sustainable construction. In the long term, we hope our study contributes to the design vision of utilizing SMPs for transportation, assembly, and deployment of complex structures, providing a new pathway for sustainable construction and transportation of large-scale structures to hard-to-access locations such as disaster-affected areas and remote deserts, etc.

4D printing

Interface Nucleus Templating of Modular Intermetallic Morphologies: Chemical Pressure Complementarity, Columnar Domains, and Complex Disorder in Y 13 Ag 42.7 Zn 29.7

One element of the diversity of intermetallic phases is the formation of complex structures from the assembly of fragments of simpler structures. Recently, we devised the Interface Nuclear Approach as a model for understanding such modular arrangements, in which the intergrowth of different structures is driven by chemical pressure (CP) relief at shared motifs at the domain interfaces, referred to as interface nuclei. In this Article, we present the synthesis, crystal structure, and CP analysis of a new compound that expands on this theme, Y 13 Ag 42.7 Zn 29.7 . Its hexagonal structure contains interpenetrating domains based on the CaPd 5+x and EuMg 5 types. The CaPd 5+x -based regions are reminiscent of the lamellar intergrowth structures previously observed in the Y−Ag−Zn system. In Y 13 Ag 42.7 Zn 29.7 , however, the domains have a different morphology, forming columns that adopt a hexagonal rod-packing. The geometrical features of the remaining spaces are assigned, using the program GrowDomain, to the cores of trigonal units of the EuMg 5 type, while layers of disordered atoms occur at heights along z where the parent structures are mismatched. At the CaPd 5+x -type/EuMg 5 -type interfaces, simple interface nucleus motifs with strong CP-complementarity can be identified, while their distribution within the parent structures supports the notion of templated architectures in modular intermetallics.

Chemical structure

Dynamic structural determinants in bacterial microcompartment shells

Bacterial microcompartments (BMCs) are polyhedral structures that segregate enzymatic cargo from the cytosol via encapsulation within a protein shell. Unlike other biological polyhedra, such as viral capsids and encapsulins, BMC shells can exhibit a highly advantageous structural and functional plasticity, conforming to a variety of anabolic (CO 2 fixation in carboxysomes) and catabolic (nutrient assimilation in metabolosomes) roles. Consequently, understanding the subunit properties and associated protein–protein interaction processes that guide shell assembly and function is a necessary step to fully harness BMCs as modular, biotechnological nanomachines. Here, we describe the recent insights into the dynamics of structural features of the key BMC domain (Pfam00936)-containing proteins, which serve as a structural template for BMC-H and BMC-T shell building blocks.

59 BASIC BIOLOGICAL SCIENCES

Engineered Solutions Group's SMR Containment Cable and Electrical Penetration Assembly System

GAIN Project CRADA Number NFE-21-08839, entitled “SMR Containment Cable and EPA System” was initiated by the partnership of Oak Ridge National Laboratory (ORNL) and Engineered Solutions Group (ESG) to test an ESG-designed Electrical Penetration Assembly and Containment Cabling System Qualified for not only legacy LWR designs, but also Small Modular Reactors designs currently being designed by several different suppliers. This project was undertaken to fill the equipment gap of EPA and Cabling Systems that require much more severe environmental requirements than legacy plant applications present due to their smaller containment volumes that result in high energy densities compared to legacy designs. This high energy density results in severe accident environments and more severe normal operating conditions as well. We developed two approaches to qualify Electrical Penetration Assembly (EPA) and Containment Cabling Systems for SMRs and Advanced Reactors. We take into consideration the more severe environmental parameters found with SMR designs. The system will need to meet a qualification test program addressing wear/cyclic aging, potential radiation exposure, thermal aging, vibration aging, thermal cycling, seismic qualification, electrical fault testing (per IEEE 317) and accident simulation. The equipment must meet the requirements of 10CFR50.49, GDC 50 in 10CFR50 Appendix A, and 10CFR50 Appendix J. NRC Regulatory Guides (RGs) identify an acceptable way of meeting regulatory requirements. RGs frequently endorse a standard for meeting these requirements. Specific to this review, equipment would be qualified in accordance with the following IEEE Standards. • IEEE 317-2013 (Electrical Penetration Assemblies), which is endorsed by RG 1.63, Rev. 3, • IEEE 323-2003 and the more current IEC/IEEE 60780-323 (Environmental Qualification of 1E Equipment) which is endorsed by RG 1.89. IEEE 323-2003 is endorsed by RG 1.209, • IEEE 344-2020 (Seismic Qualification. The 2013 version endorsed by RG 1.100, Rev. 4, with exceptions), • IEEE 383-2015 (Electrical Cables) (which is endorsed by RG 1.189 Rev. 4 and the -2003 version endorsed by RG 1.211 rev. 0), • IEEE 572-2019 (Electrical Connectors and Assemblies), which is endorsed by 1.156 Rev 1, and • [IEEE 1202 (endorsed by RG 1.189) would normally be applicable but the advanced cable designs are impervious to this cable flame test.] The primary goal of such a program is to provide an EPA design that can meet the qualification requirements for all legacy light water reactor plants currently operating as well as new plant designs including light water Small Modular Reactors. Thus, these requirements are applicable to plants licensed under 10CFR50 and 10CFR52. Other reactor designs may be evaluated, and this test system and qualification method applied to those applications if the requirements would satisfy the requirements of the intended plant. A secondary benefit of this work is to document some of the history and background in these requirements as there have been recent delays in an SMR licensing process due to NRC Requests for Additional Information in this subject matter area.

42 ENGINEERING

Transformative Efficiency and Automation in Modular Homes (TEAMH)

This report documents the Transformative Efficiency and Automation in Modular Homes (TEAMH) project, which evaluates the integration of advanced building envelope technologies and automation-assisted modular construction to improve residential energy performance and construction efficiency. The study investigates high-performance insulation systems, including vacuum insulation panels (VIPs), combined with light gauge steel (LGS) modular construction and factory automation. Laboratory testing, whole-building energy modeling across multiple climate zones, and factory demonstrations were conducted to assess thermal performance, energy savings, and production efficiency. Results indicate that upgraded envelope assemblies can achieve up to ~50% heating and ~34% cooling energy savings relative to IECC 2018 code-compliant homes, while automation-assisted construction can reduce wall assembly time by 24%–46% compared to conventional wood framing. The findings demonstrate the potential for scalable, high-performance modular homes that deliver significant energy savings with competitive projected costs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Robot-based Additive Manufacturing of Lego-type Modular Molds for Wind Blades

The objective of this project is to reduce the cost and lead time of horizontal wind turbine blade mold tooling and blade transportation, while maintaining the highest standards of blade quality. The solution involves a smart-design family of modular molds that are easily transportable to fabrication sites near the place of service. Key innovations include the use of additive manufacturing (AM) to integrate conformal thermal management channels, offering enhanced control over the thermal profiles tailored to specific blade materials. This approach enables in-situ quality assurance during mold fabrication, significantly improves mold life, and allows for reuse across multiple production cycles. Ultimately, the solution aims to optimize both tooling and transportation costs, contributing to the scalability of wind turbine blade production. A significant barrier to scaling up the production of large wind turbine blades lies in the high costs associated with tooling and the transportation of blades. Traditional molds are expensive, bulky, and difficult to transport, adding considerable lead time and cost to the overall manufacturing process. Additionally, transporting blades to distant locations for final assembly further exacerbates these challenges. The project aims to address these inefficiencies by demonstrating a modularized, additive-manufactured mold that meets all necessary blade specification requirements, specifically for blade lengths between 120m and 150m.

17 WIND ENERGY

Advances in genetic tools for metabolic engineering of non-conventional yeasts

Non-conventional yeasts are emerging as powerful alternatives to Saccharomyces cerevisiae for metabolic engineering, owing to their innate stress tolerance, broad substrate utilization, and distinctive metabolic capabilities. These attributes position them as promising chassis for producing biofuels, pharmaceuticals, and specialty chemicals. This review synthesizes recent advances in genetic toolkits for four such species—Pichia kudriavzevii (Issatchenkia orientalis), Starmerella bombicola, Debaryomyces hansenii, and Pachysolen tannophilus—highlighting progress across plasmid architectures (episomal and integrative), identification of autonomously replicating sequences and centromeric elements, and the development of safe-harbor genomic loci. We summarize promoter and terminator libraries enabling tunable expression, the expansion of auxotrophic and antifungal selection markers with recycling strategies, and the rapid adaptation of CRISPR-based systems (Cas9 and Cas12a) with optimized guide RNA expression, multiplex editing, and approaches that enhance homologous recombination (e.g., KU70/80 disruption). We also review landing-pad platforms for modular, repeated integrations and transposon-based tools (e.g., piggyBac) that facilitate multigene pathway assembly. Collectively, these innovations are accelerating design-build-test-learn cycles and enabling precise, scalable engineering of non-conventional yeasts. Remaining challenges—including limited species-specific episomal systems, variable transformation efficiencies, genome-stability concerns, and alternative codon usage—define clear priorities for future toolkit development. Together, these advances and open needs chart a path toward robust, sustainable biomanufacturing using diverse non-conventional yeast chassis.

59 BASIC BIOLOGICAL SCIENCES

Benefits Of Automated Construction And Energy Efficiency Measures In Modular Homes

This article builds on and adds to a Buildings XV publication that introduced the Transformative Efficiency and Automation in Modular Homes (TEAMH) project. The TEAMH project sought to develop a scalable solution for producing modular homes with 20-50% energy savings and similar cost relative to site-fabricated single-family home construction. A key aspect of the project was assessing the potential for labor cost reductions through automation-assisted construction using light gauge steel (LGS). To quantify the advantages of this approach, side-by-side comparisons were made between traditional wood-framed construction and automation-assisted LGS construction. This demonstration involved constructing one wood-framed wall and several LGS test walls, accompanied by a time-and-motion study. The results indicated that automation assistance could decrease construction time and associated labor costs by as much as 46%. High-performance envelope technologies for exterior insulation and air sealing were evaluated to compare modular homes with site-built homes that meet the International Energy Conservation Code (IECC). A key technology considered was vacuum insulation panels (VIPs) with fiberglass cores. Guarded hot box testing of multiple full-scale wall assemblies containing different combinations of exterior continuous insulation systems containing phenolic foam and VIPs. Testing on various full-scale wall assemblies revealed that, with LGS construction, cavity insulation had minimal impact on exterior wall performance. Omitting cavity insulation can reduce labor and material costs while streamlining manufacturing, as its installation is labor-intensive and not easily automated due to the need for precise placement around wiring and other internal components. Guarded hot box tests of multiple LGS test walls with foam and VIP-based exterior insulation systems achieved R-values of up to 31 hr-ft2-°F/Btu. Finally, building energy modeling of multiple modular home designs indicated that the upgraded envelope assemblies can yield heating energy savings of up to 50% and cooling energy savings of up to 30% compared to IECC 2018 standards.

Shrestha, Som [ORNL] (ORCID:0000000183993797)

Monitoring installation of partially occluded subassemblies in modular construction factories using BIM, ray tracing, and computer vision

Modular and offsite construction methods are being increasingly adopted due to the advantages they offer in terms of project completion time, quality, and energy-efficiency. Despite these advantages, the current state of monitoring systems in modular construction factories highly relies on labor-intensive, subjective, and error-prone observational methods. A large body of research has aimed to automate the monitoring process using an array of sensors, such as IMUs and RFIDs, during the past two decades. Recently, computer vision-based methods have gained increasing interest as a non-intrusive technology to monitor the process inside modular construction factories. However, partial occlusion challenges have impeded their practical application on a large scale. This challenge is specifically important for monitoring the installation of subassemblies since they can obstruct the view of the monitoring camera, especially those that enable long-term monitoring like closed-circuit television (CCTV) fixed-view surveillance cameras. Here, this paper aims to address this challenge by proposing a novel computer vision-based method to monitor the installation of new subassemblies inside modular factories in highly occluded scenes. The proposed methodology identifies the subassemblies in the CCTV video footage using computer vision, analyzes the occlusions using BIM and ray casting techniques, and estimates the progress of assembly by comparing the BIM model with the detected subassemblies in the video. The proposed methodology was successfully validated on surveillance videos captured from a volumetric modular construction factory in the U.S., achieving 93% accuracy in identifying the installation of subassemblies. The results from this research show that the integration of BIM and computer vision is a promising method for monitoring the installation processes inside modular factories under severe occlusion.

97 MATHEMATICS AND COMPUTING

Utilizing Single-Crystalline Transformations for Precise Atom Placement in Multicomponent Cluster-Based Coordination Networks

The assembly of cluster or superatom building-blocks into extended solids has revolutionized materials design, enabling the synthesis of modular semiconductors with well-defined structures and tunable electronic, magnetic or optical properties. This strategy has recently advanced the synthesis of complex metal oxides with multifunctional or emergent behaviors, but precise atom placement of multiple elements with similar chemistries or preferred coordination environments remains a significant challenge. Here, in this study, we present a strategy for synthesizing polyoxometalate (POM)-based coordination networks with up to three different cations in precisely defined positions. Our approach leverages a single-crystal-to-single-crystal (SCSC) transformation in which the spatial placement of cations is governed by their availability at distinct stages of crystallization and transformation. Specifically, [ZP 5 W 30 O 110 ] (15-n)- (Z = Na + , K + , Ca 2+ , Ag + , Bi 3+ , Y 3+ , any Ln 3+ , Th 4+ ) is coordinatively assembled with various bridging metal cations (Y 3+ , any Ln 3+ , Th 4+ ). By using the encapsulated cation (Z) to "label" the POM, we track the phase-transformation and confirm the retention of single crystallinity. The integrated use of POM labeling and SCSC transformation enables rational control over cation distribution and establishes a versatile strategy for constructing multicomponent materials with high compositional and spatial precision.

Chen, Linfeng [Univ. of California, San Diego, CA

Ion Transport in Self-Assembled Peptoid Membranes with Carbon Nanotube Porin Channels

Artificial membranes that combine high ionic selectivity with mechanical robustness remain a key challenge for next-generation separation technologies. Here, we report ion transport measurements in biomimetic membranes composed of crystalline peptoid nanosheets co-assembled with carbon nanotube porins (CNTPs). Pure peptoid sheets formed defect-free, ion-impermeable membranes, which were then suspended over small SiN x nanopore apertures for ion transport measurements. Incorporation of CNTPs into the peptoid sheet matrix made these membranes ion permeable, with ion conductance values consistent with ion transport through individual and multiple carbon nanotube channels. In conclusion, the modularity and molecular order of peptoid membranes, combined with the exceptional conductance properties of CNTPs, position this platform as a versatile framework for assembling programmable, selective, and robust nanofluidic membranes that can bridge the performance gap between biological and synthetic membrane materials.

Biotechnology

Securing Future Energy Supplies: From Renewables to Microreactors

This session will provide insight into how future energy deployments, critical to national-level programs focused on reducing carbon emissions, can be secured-by-design using lessons learned from current energy infrastructure. It will begin with an overview of current threats and risks associated with renewable energy assets and systems, primarily wind and solar, focusing on their control architecture and key system functions for both efficient and safe operations. This talk will then translate the key takeaways from current renewable infrastructure into applications for securing future energy systems, including microreactors and small modular reactors (SMRs), based on planned concepts of operations and control. Microreactors and SMRs are intended to be factory-assembled with commercially available components and deployed in more remote or distributed environments, necessitating centralized control centers, remote monitoring, and offsite maintenance and technical support. All of these factors lead these assets to a security posture and controls more similar to today's renewable energy assets than today's nuclear reactors, which represents a significant shift in mindset for the nuclear industry. This talk will provide justification for this shift as well as a path forward to motivate securing these groundbreaking technologies from the outset of their design and deployment.

22 GENERAL STUDIES OF NUCLEAR REACTORS

A stoichiometrically conserved homologous series with infinite structural diversity

Here, we describe a compositionally guided structural evolution within a stoichiometrically conserved framework, BaSbQ 3 (Q = Te 1−x S x ), where each value of x gives rise to a distinct phase. The fundamental building blocks, A 1 (BaSbSTe 2 ) and B n (Ba n Sb n S n−1 Te 2n+1 ), were composed of modular double rocksalt slabs stacked with functional polytelluride zigzag chains, with each phase differing only in the size and assembly of these blocks. Ten compounds were synthesized that maintained a coherent chemical identity that arose from this isovalent, isoelectronic substitution of Te and S. We envision that the phase formation at a molecular level unfolds in stages of extension, termination, and assembly and propose a design concept of “anionic disparity,” where phase homologies and polytelluride hierarchical networks can be controlled by leveraging differences in anion electron affinity and sizes.

Zhao, Hengdi [Argonne National Laboratory (ANL), A

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