Combinatorial Design Research Articles

Small examples of mosaics of combinatorial designs

We give the first example of a mosaic of three combinatorial designs with distinct parameters 2-(13,3,1), 2-(13,4,2), and 2-(13,6,5). Furthermore, we give examples of mosaics of 2-(9,3,2) designs that are not resolvable, thereby answering a question posed by M. Wiese and H. Boche. Finally, we give an example of a mosaic of projective planes of order 3 that cannot be obtained by tiling groups with difference sets.

Near regular LDPC codes based on combinatorial designs

Some new approaches for constructing near regular binary low-density parity-check (LDPC) codes free of 4-cycles are proposed using dual of certain combinatorial designs which are [Formula: see text]-configurations. The present constructions further broaden the class of code lengths. The present constructions give higher code rates of near regular LDPC codes compared to the earlier codes with respect to same code length.

Hamming distances of unsaturated orthogonal arrays

Orthogonal arrays (OAs) are applied in the statistical design of experiments, coding theory, cryptography, various types of software testing and quality control and have many connections to other combinatorial designs. The Hamming distances of OAs play a critical role in many areas such as algebraic combinatorics, quantum information theory, and wireless sensor networks. However, the calculation method of Hamming distances is difficult, especially for mixed orthogonal arrays (MOAs), since they rely on constructions or structures of OAs in many cases. In this article, by using the number of coincidences, we find some OAs with high strength and MOAs with strength 2 and 3, whose Hamming distances do not depend on their structures. We also calculate Hamming distances of a series of unsaturated asymmetrical OAs via their construction methods such as deleting columns, the expansive replacement method, and difference schemes.

Data-Driven Combinatorial Design of Highly Energetic Materials

Data-Driven Combinatorial Design of Highly Energetic Materials

Protein Engineering of Nicotinamide Riboside Kinase Based on a Combinatorial Semirational Design Strategy for Efficient Biocatalytic Synthesis of Nicotinamide Mononucleotides.

Industrial biosynthesis of β-nicotinamide mononucleotide (β-NMN) lacks a highly active nicotinamide riboside kinase for the phosphorylation process. Cumbersome preprocessing steps and excessive ATP addition contribute to its increased cost. To tackle these challenges, a docking combination simulation (DCS) semirational mutagenesis strategy was designed in this study, combining various modification strategies to obtain a mutant NRK-TRA with 2.9-fold higher enzyme activity. Molecular dynamics simulations and structural analysis demonstrate the enhancement of its structural stability. High-density fermentation was achieved through a 5 L fermentation tank, with a titer reaching 208.3 U/mL, the highest in the current report. An ATP-cycling whole-cell catalytic system was employed and optimized by introducing a polyphosphate kinase 2 (PPK2) recombinant strain, and 15.16 g/L β-NMN was obtained through a series of batch transformation experiments. This study provides a new strategy for the efficient screening of highly active enzyme variants and offers a green and promising biotransformation system for NMN production.

Biomaterials for Cell Manufacturing.

Cell therapies, potent populations of cells used to treat disease and injury, can be strategically manufactured with biomaterial intervention to improve clinical translation. In this viewpoint, we discuss biomaterial design and integration into cell manufacturing steps to achieve three main goals: scale-up, phenotype control, and selection of potent cells. Material properties can be engineered to influence the cell-biomaterial interface and, therefore, impart desirable cell behavior such as growth, secretory activity, and differentiation. Future directions for the field should capitalize on the combinatorial design of biomaterial properties to yield highly specific and potent cell populations. Furthermore, future biomaterials could contribute to novel high-throughput cell separation technologies that can individually select the most therapeutically relevant cells within a produced batch.

Construction of Asymmetric Orthogonal Arrays With High Strength

ABSTRACTOrthogonal arrays (OAs) are a key research focus in combinatorial design theory and experimental design theory. They play a very important role in an increasing number of interdisciplinary fields, such as computer science, cryptography, multipartite quantum states and quantum information. And the open problems in many fields are closely related to the construction of orthogonal arrays with high strength and large size. At present, some open problems have been solved by using orthogonal arrays. There is an urgent need for developing such orthogonal arrays. This article introduces a general method for obtaining asymmetric orthogonal arrays with high strength. The proposed method is straightforward and constructive. The constructed OAs can be utilized to generate more OAs. Some selective OAs are tabulated for practical applications.

Combinatorial design of siloxane-incorporated lipid nanoparticles augments intracellular processing for tissue-specific mRNA therapeutic delivery.

Systemic delivery of messenger RNA (mRNA) for tissue-specific targeting using lipid nanoparticles (LNPs) holds great therapeutic potential. Nevertheless, how the structural characteristics of ionizable lipids (lipidoids) impact their capability to target cells and organs remains unclear. Here we engineered a class of siloxane-based ionizable lipids with varying structures and formulated siloxane-incorporated LNPs (SiLNPs) to control in vivo mRNA delivery to the liver, lung and spleen in mice. The siloxane moieties enhance cellular internalization of mRNA-LNPs and improve their endosomal escape capacity, augmenting their mRNA delivery efficacy. Using organ-specific SiLNPs to deliver gene editing machinery, we achieve robust gene knockout in the liver of wild-type mice and in the lungs of both transgenic GFP and Lewis lung carcinoma (LLC) tumour-bearing mice. Moreover, we showed effective recovery from viral infection-induced lung damage by delivering angiogenic factors with lung-targeted Si5-N14 LNPs. We envision that our SiLNPs will aid in the clinical translation of mRNA therapeutics for next-generation tissue-specific protein replacement therapies, regenerative medicine and gene editing.

Key Pre-distribution Schemes via Certain Resolvable Block Designs

Earlier optimal key pre\(-\)distribution schemes (KPSs) for distributed sensor networks (DSNs) were proposed using combinatorial designs via transversal designs, affine, and partially affine resolvable designs. Here, nearly optimal KPSs are introduced and a class of such KPSs is obtained from resolvable group divisible designs. These KPSs are nearly optimal in the sense of local connectivity. A metric for the efficiency of KPSs is given. Further, an optimal KPS has also been proposed using affine resolvable \( L_{2} \)-type design.

Generalized Background Vector Method for Tailored Three-Dimensional Nonperiodic Woven Composite Designs

In critical aerospace applications such as Ceramic Matrix Composite structures, novel three-dimensional nonperiodic textile composite preforms hold great promise for creating advanced composite structures with strategically aligned fiber tows. However, the inherently challenging nature of determining tow locations, a large-scale combinatorial problem, presents a significant obstacle in textile architecture design. This study generalizes the previously developed Background Vector Method (BVM) to address diverse design requirements and constraints, effectively circumventing combinatorial design complexities via a game theoretic approach. This approach allows for the creation of tunable designs for woven architectures with complex geometries, such as channels and tapering features, through simple control parameter adjustments. The method demonstrates exceptional computational efficiency, making it suitable for large-scale nonperiodic textile structures. Case studies including woven sandwich and airfoil structures highlight the generalized BVM’s versatility and effectiveness in addressing complex design challenges within the aerospace sector.

CRISETR: an efficient technology for multiplexed refactoring of biosynthetic gene clusters.

The efficient refactoring of natural product biosynthetic gene clusters (BGCs) for activating silent BGCs is a central challenge for the discovery of new bioactive natural products. Herein, we have developed a simple and robust CRISETR (CRISPR/Cas9 and RecET-mediated Refactoring) technique, combining clustered regulatory interspaced short palindromic repeats (CRISPR)/Cas9 and RecET, for the multiplexed refactoring of natural product BGCs. By this approach, natural product BGCs can be refactored through the synergistic interaction between RecET-mediated efficient homologous recombination and the CRISPR/Cas9 system. We firstperformed a proof-of-concept validation of the ability of CRISETR, and CRISETR can achieve simultaneous replacement of four promoter sites and marker-free replacement of single promoter site in natural product BGCs. Subsequently, we applied CRISETR to the promoter engineering of the 74-kb daptomycin BGC containing a large number of direct repeat sequences forenhancingthe heterologous production of daptomycin. We used combinatorial design to build multiple refactored daptomycin BGCs with diverse combinations of promoters different in transcriptional strengths, and the yield of daptomycin was improved 20.4-fold in heterologous host Streptomyces coelicolor A3(2). In general, CRISETR exhibits enhanced tolerance to repetitive sequences within gene clusters, enabling efficient refactoring of diverse and complex BGCs, which would greatly accelerate discovery of novel bioactive metabolites present in microorganism.

On the Selection of Optimal Balanced Incomplete Block Design using Different Types of Designs

The choice of selecting the best among the types of balanced incomplete block designs (BIBDs) have brought about some controversies in combinatorial design. Prominent methods of constructing BIBD have been proposed by different authors, but none has been juxtaposed the designs with respect to type. In this paper, we proposed the adoption of the concept of optimality criteria such as: A-, D-, E- , and T – optimality criterion to select the best design based on their optimality values using a (15, 15, 7, 7, 3) simulated balanced incomplete block design. A dual design, residue design and derived design were selected as the major three types of BIBDs for investigation. The findings revealed that dual design is the best balanced incomplete block design based on its high optimal value. We discovered that residue and derived design obtained from the simulated balanced incomplete block design by method of block selection and intersection becomes a standard balanced incomplete block design.

On the Study of Thickness Gradients in Novel Star Honeycombs: Classical and Combinatorial Designs

Herein, a series of gradient designs are carried out to enhance further the energy absorption capacity of a novel star honeycomb. These include unidirectional and bidirectional gradient designs along the impact direction, while the gradient changes in the non‐impact direction are considered. Via the coupling of bidirectional and unidirectional directions, a combined gradient evolution method is further proposed. The in‐plane compression characteristics of these gradient honeycombs are systematically revealed based on the validated finite element method at low‐, medium‐, and high‐velocity impacts, respectively. The results show that honeycombs with gradient variations in the impact direction are realized as localized modes under both low‐ and medium‐velocity impacts, while honeycombs with gradient design only in the non‐impact direction exhibited global modes and “local + global” modes, respectively; under high‐speed impacts, honeycombs with gradient configurations in the non‐impact direction showed stepped layer‐by‐layer collapses, whereas honeycombs with gradient evolutions only in the impact direction collapsed in I‐shaped layers. Besides, the increase in compressive strength and specific energy absorption of honeycomb with combined gradient configuration can be up to 38.1% and 67.9%. This article provides a new idea of honeycomb gradient evolution, which can provide a reference for improving the energy‐absorption capacity of honeycombs.

GOLDBAR: A Framework for Combinatorial Biological Design.

With the rise of new DNA part libraries and technologies for assembling DNA, synthetic biologists are increasingly constructing and screening combinatorial libraries to optimize their biological designs. As combinatorial libraries are used to generate data on design performance, new rules for composing biological designs will emerge. Most formal frameworks for combinatorial design, however, do not yet support formal comparison of design composition, which is needed to facilitate automated analysis and machine learning in massive biological design spaces. To address this need, we introduce a combinatorial design framework called GOLDBAR. Compared with existing frameworks, GOLDBAR enables synthetic biologists to intersect and merge the rules for entire classes of biological designs to extract common design motifs and infer new ones. Here, we demonstrate the application of GOLDBAR to refine/validate design spaces for TetR-homologue transcriptional logic circuits, verify the assembly of a partial nif gene cluster, and infer novel gene clusters for the biosynthesis of rebeccamycin. We also discuss how GOLDBAR could be used to facilitate grammar-based machine learning in synthetic biology.

A survey of complex generalized weighing matrices and a construction of quantum error-correcting codes

Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and quantum computing. Objects like this also lend themselves to compelling mathematics problems, such as the Hadamard conjecture. However, complex generalized weighing matrices, which generalize Hadamard matrices, have not received anything like the same level of scrutiny. Motivated by an application to the construction of quantum error-correcting codes, which we outline in the latter sections of this paper, we survey the existing literature on complex generalized weighing matrices. We discuss and extend upon the known existence conditions and constructions, and compile known existence results for small parameters. Using these matrices we construct Hermitian self orthogonal codes over finite fields of square order, and consequently some interesting quantum codes are constructed to demonstrate the value of complex generalized weighing matrices.

Machine learning-guided multi-site combinatorial mutagenesis enhances the thermostability of pectin lyase

Enhancing the thermostability of enzymes is crucial for industrial applications. Methods such as directed evolution are often limited by the huge sequence space and combinatorial explosion, making it difficult to obtain optimal mutants. In recent years, machine learning (ML)-guided protein engineering has become an attractive tool because of its ability to comprehensively explore the sequence space of enzymes and discover superior mutants. This study employed ML to perform combinatorial mutation design on the pectin lyase PMGL-Ba from Bacillus licheniformis, aiming to improve its thermostability. First, 18 single-point mutants with enhanced thermostability were identified through semi-rational design. Subsequently, the initial library containing a small number of low-order mutants was utilized to construct an ML model to explore the combinatorial sequence space (theoretically 196,608 mutants) of single-point mutants. The results showed that the ML-predicted second library was successfully enriched with highly thermostable combinatorial mutants. After one iteration of learning, the best-performing combinatorial mutant in the third library, P36, showed a 67-fold and 39-fold increase in half-life at 75 °C and 80 °C, respectively, as well as a 2.1-fold increase in activity. Structural analysis and molecular dynamics simulations provided insights into the improved performance of the engineered enzyme.

Advancing Sustainable Construction: Discrete Modular Systems & Robotic Assembly

This research explores the SL-Block system within an architecture framework by embracing building modularity, combinatorial design, topological interlocking, machine learning, and tactile sensor-based robotic assembly. The SL-Block, composed of S and L-shaped tetracubes, possesses a unique self-interlocking feature that allows for reversible joining and the creation of various 2D or 3D structures. In architecture modularity, the high degree of reconfigurability and adaptability of the SL-Block system introduces a new element of interest. Unlike modularization strategies that emphasize large-scale volumetric modules or standardized building components, using small-scale generic building blocks provides greater flexibility in maximizing design variations and reusability. Furthermore, the serial repetition and limited connectivity of building elements reduce the efforts required for bespoke manufacturing and automated assembly. In this article, we present our digital design and robotic assembly strategies for developing dry-jointed modular construction with SL-Blocks. Drawing on combinatorics and graph theory, we propose computational design methods that can automatically generate hierarchical SL-Block assemblies from given shapes. To address the physical complexities of contact-rich assembly tasks, we develop robotics using two distinct methods: pre-programmed assembly and sensor-based reinforcement learning. Through a series of demonstrators, we showcase the ability of SL-Blocks not only to reconfigure conventional building tectonics but also to create new building configurations.

A versatile gemini amphiphile-based platform with STING-activating properties for efficient gene delivery into dendritic cells

Encouraging results from clinical trials have underscored the potential of gene-pulsed dendritic cell (DC) vaccines as a viable approach for immunotherapy. However, insufficient gene delivery and functional deficiencies in antigen presentation, migratory capacity and cytokine release of DC vaccines limited its broader clinical application. Here, a combinatorial design of cationic gemini amphiphile (GA) molecular library based on the four-component Ugi reaction (Ugi-4CR) has been developed to identify versatile non-viral vectors for gene-engineered DC vaccines. We demonstrated that the leading GA enabled robust transfection of plasmid DNA or mRNA into the DCs through the formation of minimalist binary complexes, which exhibited great advantages of low carrier/gene ratios, high gene loading efficiency and well biocompatibility. The identified GA stimulated strong type I interferon (IFN) expression via the intracellular stimulator of interferon genes (STING) pathway and enhanced DC maturation and activation, which could potentially facilitate strong immunogenicity of DC vaccines. Importantly, DC maturation and activation could be further strengthened by co-delivering maturation stimuli with mRNA/GA complexes, and adoptive transfer of gene-engineered DC vaccines elicited strong T cell responses and thus inhibited tumor growth in vivo. The further studies indicated GAs can be formulated into lipid nanoparticle (LNP)-like quinary complexes that presented 6.9-fold higher mRNA delivery efficiency on the DCs than the commercial Lipofectamine 2000. These results suggest that GA-based molecular library is a powerful platform to develop versatile gene delivery vectors for immune cell engineering.

Asymptotically Optimal Coded Distributed Computing via Combinatorial Designs

Asymptotically Optimal Coded Distributed Computing via Combinatorial Designs

Machine learning-guided co-optimization of fitness and diversity facilitates combinatorial library design in enzyme engineering

The effective design of combinatorial libraries to balance fitness and diversity facilitates the engineering of useful enzyme functions, particularly those that are poorly characterized or unknown in biology. We introduce MODIFY, a machine learning (ML) algorithm that learns from natural protein sequences to infer evolutionarily plausible mutations and predict enzyme fitness. MODIFY co-optimizes predicted fitness and sequence diversity of starting libraries, prioritizing high-fitness variants while ensuring broad sequence coverage. In silico evaluation shows that MODIFY outperforms state-of-the-art unsupervised methods in zero-shot fitness prediction and enables ML-guided directed evolution with enhanced efficiency. Using MODIFY, we engineer generalist biocatalysts derived from a thermostable cytochrome c to achieve enantioselective C-B and C-Si bond formation via a new-to-nature carbene transfer mechanism, leading to biocatalysts six mutations away from previously developed enzymes while exhibiting superior or comparable activities. These results demonstrate MODIFY’s potential in solving challenging enzyme engineering problems beyond the reach of classic directed evolution.