Discussions on what psychological resilience is, its operationalizations, and approaches to measuring it have occupied the scientific community for decades. This manuscript (1) provides an overview of psychometric methods used to assess resilience, including key characteristics, and (2) evaluates resilience scales through a preregistered, content-analytical evaluation of items based on expert ratings. Items from 83 resilience scales were empirically categorized using a literature-based framework with three main categories (resilience as a process, traits, and environmental factors) and 12 corresponding subcategories. Across all scales, 31.79% of items reflected resilience as a process, 51.95% reflected five-factor model traits, and 16.26% reflected environmental factors. An additional analysis weighted results according to citation frequency, showing how operationalizations influence the current research practice: From this perspective, 60.17% of the items relate to process-related content, 34.59% to trait-related content, and 5.24% to environment-related content. This weighting reflects the prevalence and influence of specific scales in the field. The inter-rater agreement across four raters was κ = .68. Overall, existing questionnaires predominantly cover trait-based content, whereas widely used instruments tend to operationalize resilience as a dynamic process. We derive conceptually grounded recommendations for scale selection to improve clarity and comparability in future research.
This work introduces reverse EXAFS analysis (REA), a novel, ab initio framework that transforms extended X-ray absorption fine structure (EXAFS) spectroscopy from a complementary local probe into a primary tool for de novo crystal structure determination. By integrating iterative FEFF simulations with a reverse-fitting algorithm, REA directly extracts full crystallographic parameters, lattice constants, space group and atomic positions, from EXAFS oscillations, without requiring the user to supply an initial structural model from X-ray diffraction; instead, candidate models are retrieved from crystallographic databases and evaluated against EXAFS data. Validated on LiCrO2 and CuFeO2, REA uncovered unexpected phase complexities in CuFeO2, identifying secondary CuFe2O4 and CuFe5O8 phases undetected by conventional methods. This paradigm shift enables accurate structure solving in disordered, nanostructured and novel materials where diffraction fails, establishing EXAFS as a stand-alone crystallographic technique.
Amyloid fibrils are intrinsically polymorphic protein assemblies that form distinct structural strains linked to diverse biological and pathological outcomes. Yet, the principles governing how sequence encodes diverse fibril architectures, and the extent to which a given fold constrains underlying amino-acid sequence compatibility, remain poorly understood. Here, we apply generative protein design to directly interrogate the sequence-structure relationship of defined fibril architectures, using α-synuclein (αS), a protein known to form highly polymorphic amyloid fibrils, as a model system. Sampling sequence space under structural constraints reveals a continuous compatibility manifold in which diverse sequences encode a common amyloid architecture. De novo designed sequences assemble into fibrils, often with enhanced aggregation efficiency relative to αS. A subset exhibits strain-like behaviour, including similar morphologies, efficient cross-templating, and induction of αS cellular propagation, thereby functionally validating structural compatibility with the native fibril fold. Energetic analysis shows that stability is achieved through distinct but compensatory interactions, supporting a non-unique mapping between sequence and structure. Together, our results define a continuous and constrained compatibility landscape underlying amyloid strains, providing a framework for understanding the determinants of polymorphism and establishing generative protein design as a strategy to access this space, interrogate amyloid sequence-structure relationships, and engineer fibrillar protein assemblies and functional biomaterials.
In industrial production, the yield of desired targets derived from carbon sources is frequently diminished by the competitive influence of cellular metabolism within microbial cell factories. The bioproduction of l-valine exemplifies a classic process that is confronted with such a dilemma, substantially hindering its economic industrial-scale production. In this study, we aim to engineer a cell factory capable of efficiently synthesizing l-valine with high yield by minimizing the consumption of its precursor pyruvate through the TCA cycle under oxygen-limited conditions. Metabolic engineering-based adaptive laboratory evolution (ALE) under oxygen-limited conditions resulted in the development of an evolved strain ALE2-40 with better cell growth and enhanced l-valine yield. Through comparative omics analysis and validation experiments, it was uncovered that during the ALE process, both pyruvate dehydrogenase activity and NADH availability were significantly improved. Moreover, beneficial targets have the potential to contribute to the NADH and ATP pools, thereby further promoting l-valine synthesis. Based on these results, reverse engineering of the evolved strain ALE2-40 was further conducted. Ultimately, the final strain VAL19 demonstrated remarkable performance, achieving an impressive l-valine titer of 93.7 g/L within 28 h in a 5-L bioreactor under oxygen-limited conditions, with a remarkable yield of 60.4% from glucose-equivalent to 92.9% of the theoretical yield-and a productivity of 3.35 g/L/h. These results set a new benchmark for the fermentative production of l-valine, with the highest yield and productivity reported so far.
The 2D dendritic structure of stream networks within fluvial catchments has not previously been linked to reach-scale channel processes. Existing extensions of 2D network models to 3D landscapes yield only pixelized landscapes, without resolving channels or their properties. At-a-point relations for hydraulic geometry alone provide no insight into how fluvial processes sculpt 3D landscapes in which channels are embedded. We provide this insight by reverse-engineering generic fluvial landscapes with scalable dimensions for all attributes. We do this by coupling a) a 2D network generator, b) dimensionless, physically grounded relations for gravel-bed river hydraulic geometry, and c) a simplified hillslope model. Catchment hypsometric curve and relief, as well as relations between local channel properties and basin structure, cannot be predicted with just one of these components. Our model predicts in specific, dimensioned terms not only how attributes such as hypsometric curve change with changing bed grain size, precipitation and catchment area, but also why, because each model element can be interrogated individually or jointly. Our method offers a tool for studying the effect of varied mean annual precipitation and intensity on catchment structure. Our central application is to tectonically inactive, quasi-equilibrium, low-relief montane landscapes on Earth. We underline the insight provided by our formulation through application to analogous planetary fluvial landscapes. We implement this for Mars and Titan using appropriate values for gravitational acceleration and sediment submerged specific gravity, both freely variable in our model. Our reverse-engineering methodology indicates why and how an analogous class of landscapes should differ in different planetary settings.
Developing additive manufacturing (AM) aluminum alloys with high temperature strength remains a formidable scientific challenge, primarily due to the strengthening precipitates coarsening above 200°C. Conventional heat-resistant alloy design strategies aim to hinder the precipitate coarsening by incorporating low diffusive alloying elements. However, such approaches remain ineffective against thermally driven defect mobilization, especially for vacancy diffusion and dislocation climbing, which are dominant drivers of high temperature weakening. As a result, most AM Al alloys exhibit a rapid decline in strength within this critical temperature range. Through reverse-engineering of intrinsic atom-defect/atom attraction, we employ an intrinsic attraction (IA) strategy to trigger multi-dimensional defect confinement mechanisms. This approach achieves: divacancy clusters anchoring free vacancies; solute atmospheres capturing mobile dislocations and suppressing creep deformation; specific segregation forming nanostructures at precipitate interfaces and interiors to inhibit coarsening. The AM heat-resistant Al alloy demonstrates satisfactory high temperature performance, exhibiting yield strengths of ~305 MPa at 300°C, ~190 MPa at 400°C, coupled with creep resistance at 200-400°C ( ε °  < 10-7/s) and prominent processability for large-size bladed disk. This strategy transcends the conventional empirical paradigm by engineering elemental segregation tendencies at specific sites, provides a universal design approach for the development of aluminum alloys or other high temperature structural materials.
Food composition databases are fundamental for rigorous dietary assessment, yet they often include information only for generic foods. This study aimed to estimate the full nutrient composition of packaged foods using natural language processing (NLP) and optimization modeling. Nutrition Facts tables (NFTs) and ingredient lists for 5371 packaged foods collected by the food quality observatory across 17 food categories available in Québec, Canada, were used. First, an NLP algorithm matched individual ingredients from packaged foods to the closest equivalents in the Canadian Nutrient File 2015, which contains full nutrient profiles for over 5690 ingredients and foods in Canada. Match quality was assessed using cosine similarity scores. Second, an optimization model estimated the proportion of all ingredients (grams per 100 g) from the packaged foods, enabling the reverse-engineering of nutrient composition data found on the NFT. Model performance was assessed using relative errors comparing estimated with known nutrient values reported on NFTs. Over 55% of ingredients were matched to the Canadian Nutrient File with cosine similarity scores ≥0.9, indicating high-quality matches. Across all food categories combined, the median relative error for the estimates of energy and the 10 nutrients reported on NFTs was <|20%|, consistent with Health Canada's accepted variance for NFT declarations, suggesting reliable estimations. Six food categories showed strong results, with all nutrient estimates having median relative errors <|20%|. Eight food categories obtained moderate results, with all nutrient estimates having median relative errors <|20%|, but with a broader range of error values. Three food categories obtained poor results, with several nutrient estimates having relative errors beyond the |20%| threshold. A method based on NLP and optimization modeling can reliably estimate ingredient proportions of a wide variety of packaged foods, allowing for the generation of complete nutrient profiles.
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite data, which introduces systematic errors. A comprehensive understanding of these errors in the context of finite data remains elusive. To address this gap, we study the error in growth rate estimates across different models. We show that under the usual bias-variance decomposition, the bias can be decomposed into a finite-time bias and nonlinear averaging bias. We demonstrate that finite-time bias, which dominates at short times, can be mitigated by fitting its monotonic behavior. In contrast, at longer times, nonlinear averaging bias becomes the predominant source of error, leading to a phase transition. This transition can be understood through the Random Energy Model, a mean-field model of disordered systems, where a few lineages dominate the estimator. Applying these methods to experimental data demonstrates that correcting for biases in lineage-based approaches yields consistent results for the long-term growth rate across multiple methods and enables the reverse-engineering of dynamic models. This new framework provides a quantitative understanding of growth rate estimators, clarifies the conditions under which they can be effectively applied to finite data, and introduces model-free approaches for studying the connections between physiology and cell growth.
This study applies a forensic-science-based approach combined with three-dimensional CFD simulations to reconstruct a large-scale explosion at a chemical plant and to evaluate the plausibility of candidate accident scenarios. A joint on-site investigation and document review were first used to reconstruct a baseline scenario for butane leakage, vapor cloud formation, and ignition. FLACS simulations were then conducted to examine whether a range of assumed leak volumes could reproduce the observed damage pattern, with particular emphasis on overpressure at a reference building located 93 m from the explosion center. The National Disaster Management Research Institute (NDMI) led the investigation, which included on-site inspections and document analysis. Based on physical evidence such as major structural damage, fragment distribution, and gas detector activation data, the location and dispersion range of the leak were estimated. A 3D simulation of the incident process was performed using the FLACS software. Alongside theoretical leak estimations, a reverse-engineering simulation approach considering actual damage patterns confirmed the possibility of a butane release exceeding 11,000 kg. The simulation results quantitatively matched the measured damage radius and verified that the calculated overpressure levels met established damage thresholds. This study scientifically reconstructed the accident scenario using quantitative simulation methods, demonstrating the effectiveness and applicability of forensic-based disaster investigations. The proposed methodology may serve as foundational data not only for identifying the root causes of disasters but also for informing prevention policies, institutional reforms, and legal liability assessments.
Acute kidney injury (AKI) is a complex disease driven by the dynamic coupling of multiple pathological mechanisms. Current treatments remain primarily supportive, making it difficult to achieve precise regulation at key pathological junctures. In recent years, cell-derived nanomaterials (CdNMs) have demonstrated unique advantages in renal-targeted delivery, biocompatibility, and multi-mechanism synergistic regulation, due to their retention of the native biological properties of the source cells. This offers a novel technical pathway to overcome the limitations of traditional nanodelivery systems in AKI treatment. This review systematically summarises the construction strategies and application progress of CdNMs - including exosomes, cell membrane-coated nanoparticles (CM-NPs), and engineered extracellular vesicles (eEVs) - with a focus on core AKI pathological processes. It further discusses their potential applications in multimodal synergistic therapy and integrated diagnosis-treatment approaches. More importantly, this review proposes a research paradigm in which the design principles of CdNMs are systematically coupled with AKI's pathological dynamics, therapeutic timing, and efficacy evaluation dimensions. This paradigm, driven by a reverse-engineering strategy from pathological mechanisms to material construction and functional assessment, provides methodological references for achieving precise intervention, predictable efficacy evaluation, and optimised clinical translation pathways for AKI.
Biochar from biomass residues has emerged as a sustainable alternative to conventional nanocarbon materials for electrochemical biosensors. Due to its low cost and adjustable physicochemical properties, significant progress has been made in developing biochar-based electrochemical sensors. However, the lack of a systematic mechanistic understanding of how interconnected biochar properties influence electrochemical performance limits rational electrode design. This study evaluates the correlation between physicochemical properties of different biomass feedstocks and their electrochemical performance, using quantitative structure-performance relationships to provide an in-depth mechanistic understanding. It was observed that electrochemical performance is governed by the collective interplay of multiple biochar physicochemical properties. With a reverse-engineering approach, it is demonstrated that biochars derived from Grass biomass feedstocks achieve superior electrochemical performance by balancing properties from moderate height particle irregularity (Ra = 0.79-3.31 nm), controlled microporosity (< 25.78%), sufficient hydrophilicity (low C/O < 4.19, moderate inorganic content 4.29-6.84%), and good carbon crystallinity (high sp2 > 10.76% and low d002 < 3.80 Å). This enables smooth-to-moderate interfacial electrode surface roughness for efficient electrode-electrolyte contact and rapid electron-transfer pathways. Therefore, this understanding shows that intentional feedstock selection based on grass classification can serve as a controllable strategy to engineer the electrode-electrolyte interface for advanced biosensing.
Internal states such as motivation and task engagement influence cognitive functions. Working memory, which maintains information over time, is an essential component of cognition and is modulated by motivation. Here, we show motivational states modulated attractor dynamics that supported working memory. Combining population recordings from mouse medial prefrontal cortex (mPFC) with data-constrained recurrent neural network (RNN) modeling, we found task engagement selectively modulated attractor dynamics within a memory-maintenance subspace, while stimulus-evoked responses remained intact. Reverse-engineering the RNNs revealed that task engagement reorganized the dynamical landscape by stabilizing memory-specific attractors. Specifically, task engagement modulated interactions between neurons to change the attractor dynamics. Finally, gradual changes in behavioral engagement were predicted by continuous modulation of attractor geometry in RNNs and mPFC. Together, these results suggest that internal state modulate working memory function by controlling the dynamical regime of mPFC circuits, providing a mechanistic link between internal state, neural dynamics, and cognitive function.
Traditional electrochemical DNA sensors for Hg2+ rely on target-induced conformational changes of Hg2+-binding DNA probes, which often suffer from limited signal output and complex probe design. To address these issues, this study introduces a novel ratiometric electrochemical DNA sensor based on a "reverse-engineering" strategy, where the signal molecule is pre-immobilized on the electrode instead of the Hg2+-binding DNA. The double-helix DNA intercalator Nile blue (NB) with excellent redox activity was covalently grafted onto a gold electrode to generate an intense inherent signal. In addition, in a solution containing target Hg2+, the polythymine DNA modified onto gold nanoparticles (AuNP@polyT) undergoes a conformational transition to a double-helix structure via specific T-Hg2+-T chemistry. Then the AuNP@polyT-Hg2+ is captured onto the electrode surface through intercalation between NB and the Hg2+-induced DNA duplex, leading to a decrease in the NB electrochemical signal. Subsequently, another intercalator, methylene blue (MB), is adsorbed into the remaining base pair space of polyT-Hg2+, generating a new indicating signal. A ratiometric response for Hg2+ is thus achieved through the decrease in the NB signal and the increase in the MB signal. Within the Hg2+ concentration range of 0.1 nM to 100 μM, log(INB/IMB) exhibits a favorable double logarithmic linear relationship with the logarithm of Hg2+ concentration, achieving a detection limit as low as 40 pM. The sensor was successfully applied to Hg2+ analysis in actual water and tea samples. By combining T-Hg2+-T coordination chemistry with a dual-intercalator ratiometric readout, the proposed reverse-engineered ratiometric electrochemical sensor eliminates complex DNA probe immobilization, improves accuracy and anti-interference capability, and shows great promise for on-site monitoring of Hg2+ in environmental water and tea samples.
Aromatics are important building blocks for polymers, pharmaceuticals, and advanced materials, but their current production relies on petrochemical processes. Biotechnological de novo production from renewable bio-based feedstocks with microbial cell factories provides a sustainable alternative. In this study, we enhanced 4-coumarate production in Pseudomonas taiwanensis from glucose and glycerol compared to previously published producers. This was achieved through heterologous expression of tyrosine ammonia-lyase (TAL) from Rivularia sp. PCC7116, which debottlenecked the specific deamination of tyrosine. Moreover, deletion of the phosphoenolpyruvate carboxylase-encoding gene ppc further increased the production. Subsequently, the substrate spectrum for efficient aromatics production was expanded to include the abundant pentoses, xylose and arabinose. Heterologous non-oxidative assimilation pathways were integrated into P. taiwanensis GRC3 chassis strains and growth on xylose and arabinose was improved through adaptive laboratory evolution, whole-genome sequencing, and reverse engineering. Optimized catabolic modules were then transferred to producer strains to enhance or enable 4-coumarate production from xylose and arabinose. Notably, the product yield on xylose increased approximately 3.5-fold with the non-oxidative xylose isomerase pathway compared to the oxidative native Weimberg pathway, without compromising yields on glucose. For the final strain, P. taiwanensis GRC3Δ6-TYR2Δppc-REXA-attTn7::P14f-RpcTAL, product yields were significantly higher on xylose (38.2% (Cmol/Cmol)) and arabinose (39.7% (Cmol/Cmol)) than on glucose (26.0% (Cmol/Cmol)). 4-Coumarate production was characterized on mixtures of glucose, xylose, and arabinose to mimic lignocellulosic hydrolysate feedstocks, with the best reverse-engineered xylose- and arabinose-metabolizing 4-coumarate producer significantly outperforming the reference strain.
Although abolishing the Crabtree effect in Saccharomyces cerevisiae through a pyruvate dehydrogenase bypass eliminates carbon loss through ethanol overflow metabolism, it compromises growth rates. While the Crabtree effect has been a valuable natural adaptation, it is energetically inferior to respiration and is generally undesirable in cell factories engineered to produce assimilatory compounds. Restoring growth efficiency in Crabtree-negative strains remains a central challenge. Through adaptive laboratory evolution of the engineered strain (sZJD23) and subsequent reverse engineering, a variant (sZJD28) with markedly improved growth was identified. This improvement is driven primarily by a mutation in MED2 (encoding a Mediator complex subunit) and, to a lesser extent, a mutation in GPD1 (encoding glycerol-3-phosphate dehydrogenase). By integrating quantitative proteomics with enzyme-constrained genome-scale modelling, we demonstrate that these mutations jointly enable a more efficient mode of oxidative stress adaptation and energy utilization. The GPD1 mutation suppresses a protein-costly, suboptimal NAD⁺-recycling strategy reliant on glycerol synthesis, while the MED2 mutation reshapes the oxidative stress response towards peroxisomal detoxification. Collectively, these adjustments optimize metabolic flux distribution and reduce protein costs in energy metabolism, thereby increasing ATP availability. Our findings reveal how coordinated mutations in regulatory and metabolic genes restore growth fitness in engineered Crabtree-negative yeast.
(1) Purpose: To compare the fabrication accuracy, internal fit, and marginal adaptation of three-unit definitive resin fixed dental prostheses (FDPs) produced by subtractive milling and additive manufacturing. (2) Materials and Methods: A typodont mandible was prepared for a three-unit FDP, with full crown preparations on teeth mandibular left canine and mandibular left second premolar featuring 1 mm chamfer finish lines. The FDP was designed with a 16 mm2 connector and a 100 µm cement gap. Two milling materials (Ambarino High-Class, IPS e.max CAD) and two experimental 3D printing hybrid resins (3D-1, 3D-2) were used. All restorations were scanned using an intraoral scanner and compared to the original STL using reverse engineering software for surface trueness and deviation analysis. The internal fit was evaluated using the triple-scan method, while marginal fit was assessed via micro-CT imaging. Statistical analysis was conducted using one-way ANOVA and Kruskal-Wallis tests (α = 0.05). (3) Results: Milled groups demonstrated a lower prevalence of external, marginal, and overall surface deviations (p < 0.001), while 3D-1 exhibited comparable deviations within the internal region with M-E (p = 0.067). Milled groups had average gap values that were similar to 3D-1 (p > 0.08), but significantly lower than 3D-2 (p < 0.002). In marginal adaptation evaluated by micro-CT, the M-A and M-E groups provided significantly lower gaps, while the 3D-1 and 3D-2 groups exhibited wider marginal and axial gaps. (4) Conclusions: These results indicate that while milling remains a more reliable manufacturing method for achieving external and marginal precision, position 3D-1 is a compelling, chairside alternative to milling.
The discovery of high-performance thermoelectric materials requires models that are both accurate and interpretable. Traditional machine learning approaches, while effective at property prediction, often act as black boxes and provide limited physical insight. In this work, we introduce Kolmogorov–Arnold Networks (KANs) for the prediction of thermoelectric properties, focusing on the Seebeck coefficient and band gap. Compared to multilayer perceptrons (MLPs), KANs achieve comparable predictive accuracy while offering explicit symbolic representations of structure-property relationships. This dual capability enables both reliable predictions and physically interpretable functional forms, providing insight into the governing mechanisms of thermoelectric behaviour. Benchmarking against literature baselines highlights their robustness and generalisability, demonstrating that KANs constitute a practical framework for reverse engineering materials with targeted thermoelectric performance and bridging the gap between predictive power and scientific interpretability.
Recent advances in mitochondrial network dynamic and signalling highlight mitochondria as key therapeutic targets across diverse diseases. Yet, high drug development failure rates reflect an incomplete understanding of upstream molecular regulators of mitochondrial fate. Here, we address this gap by reverse engineering of the BH3-only protein BNIP3. Structural modelling and sequence-function analyses of its N-terminus identify a critical functional domain and amino acid hotspots that directly activate BCL-2 executioner proteins, triggering mitochondrial cell death. Leveraging these insights, we develop a BNIP3 antagonist peptide (B-017) that disrupts interactions between BNIP3 and BCL-2 executioner proteins, preserving mitochondrial integrity. B-017 demonstrates target specificity, a favourable safety profile, and robust suppression of cell death signalling in human cells. In clinically relevant animal models, it reduces tissue damage in the heart, brain, and liver. Together, these findings position B-017 as a promising therapeutic candidate targeting mitochondrial dysfunction.
To investigate the impact of spatial positions of the transfer fork registration markers on the accuracy of generating a virtual dentofacial patient. An in vitro study was conducted using a mannequin head with a standard maxillary dentition model. Radiopaque gauge markers were fixed on the face and dentition of the mannequin head. CBCT was performed and the distance and angle between the dentition and facial markers were measured in the CBCT as reference values. Intraoral scanners were used to obtain 3D morphological data of the maxilla. Two types of transfer fork were designed and fabricated. The registration markers on transfer fork A were positioned in the midline area, while those on transfer fork B were located at the corners of the mouth on both sides. The transfer forks were digitised and connected to the maxillary dentition within the mannequin head, and facial scanning was performed using a facial scanner five times in each group. A virtual dentofacial patient was built through matching and integration of digital dentition, face and transfer fork data using 3D reverse engineering software (Geomagic Wrap 2021, 3D Systems, Rock Hill, SC, USA). Measurement values including feature lengths and feature angles between six facial gauge markers and three dentition gauge markers were obtained in the virtual patients. The mean trueness and precision of linear difference for virtual patients established using transfer fork A were -1.00 ± 0.11 mm and 0.27 ± 0.02 mm and the angle deviation was -1.88 ± 0.27 degrees, whereas for transfer fork B, the mean trueness and precision of linear difference were 2.66 ± 0.25 mm and 0.83 ± 0.06 mm, and the angle deviation was 3.74 ± 0.87 degrees. There is an overall significant difference in the trueness values of feature lengths (t = -13.963, P = 0.000) and angles (t = -5.985, P = 0.004) between transfer fork groups A and B, with group A showing better trueness and precision. Linear and angular errors will be introduced in the process of building up a virtual dentofacial patient using a transfer fork. The trueness and precision of the transfer fork with the matching markers at the centre of the lips are more precise than the transfer fork, with matching markers on both sides of the mouth.
Metamaterials can achieve extraordinary properties unattainable in natural materials through sophisticated artificial structural design. This study constructs novel tri-periodic minimal surface configurations based on fundamental structures. By employing surface boundary capture techniques to capture infinitely continuous and smooth surfaces, corresponding fusion functions are derived. New configurations are then established: one fused with rod elements and another featuring smooth fusion of multiple fundamental structures. By integrating the advantages of these configurations, novel metamaterials with both excellent load-bearing and heat transfer properties can be designed. Transition fusion functions are employed to derive implicit function construction methods for each new configuration. Through homogenisation analysis of all novel configurations, this study obtains their mechanical vector data. Combined with the implicit function expressions, this configuration and design methodology establishes a novel theoretical approach for reverse-engineering mechanical metamaterials according to specific requirements.