Neurospora crassa CDH. The effect of linker lengthand its domain attachment on electron transfer rates has been determinedby biochemical and electrochemical methods, while distances betweenthe domains of CDH variants were computed. This study elucidates theregulatory mechanism of the interdomain linker on electron transferby determining the minimum linker length, observing the effects ofelongated linkers, and testing the covalent stabilization of a linkerpart to the flavodehydrogenase domain. The evolutionary guided, rationaldesign of the interdomain linker provides a strategy to optimize electrontransfer rates in multidomain enzymes and maximize their bioelectrocatalyticperformance.Direct bioelectrocatalysis applied in biosensors, biofuelcells,and bioelectrosynthesis is based on an efficient electron transferbetween enzymes and electrodes in the absence of redox mediators.Some oxidoreductases are capable of direct electron transfer (DET),while others achieve the enzyme to electrode electron transfer (ET)by employing an electron-transferring domain. Cellobiose dehydrogenase(CDH) is the most-studied multidomain bioelectrocatalyst and featuresa catalytic flavodehydrogenase domain and a mobile, electron-transferringcytochrome domain connected by a flexible linker. The ET to the physiologicalredox partner lytic polysaccharide monooxygenase or, ex vivo, electrodesdepends on the flexibility of the electron transferring domain andits connecting linker, but the regulatory mechanism is little understood.Studying the linker sequences of currently characterized CDH classeswe observed that the inner, mobile linker sequence is flanked by twoouter linker regions that are in close contact with the adjacent domain.A function-based definition of the linker region in CDH is proposedand has been verified by rationally designed variants of  For instance, Phanerochaete sordida CDH was employed in the design of a direct electron transfer (DET)-basedlactose biosensor in 2005, followed by a DET glucose biosensor basedon Corynascus thermophilus CDH in 2011.5 Similarly, Dichomera saubinetii CDHwas used in 2008 to fabricate a noncompartmentalized, mediator-freeglucose–oxygen biofuel cell based on adsorbed enzymes exhibitingdirect bioelectrocatalysis.6 Additionally,the first self-charging chemical supercapacitor based on pseudocapacitanceused C. thermophilus CDH as an anodicbioelement.7 In these examples, the electrontransfer rate of CDH was the limiting factor in the generated current,rather than the catalytic rate.Direct bioelectrocatalysis is an emergingfield based on interdisciplinaryresearch in electrochemistry, materials science, biochemistry, andmolecular biology. Enzymes play a fundamental role in bioelectrocatalyticdevices such as biosensors, biofuel cells, biosupercapacitors, andbioelectrosynthetic reactors, enabling efficient catalysis of substrate-specific,regiospecific, and stereospecific redox reactions on electrodes.8 In bioelectrochemical applications,this cytochrome (CYT) domain is considered a built-in redox mediatorthat facilitates DET to the electrode.9 To optimize DET in this field focuses not only on the developmentof electrode materials,10 nanostructures,11 and protein immobilization strategies12 but also on protein engineering strategies.One approach involves fusing a CYT domain onto a single-domain enzymeto mimic the function of CDH.14 Establishing a CYTlibrary expands the potential for utilizing CYT as an electron shuttlefor a wider range of biocatalysts.16 In this andother enzyme engineering approaches, maintaining or improving DETwhile optimizing the interdomain electron transfer (IET) is crucial.18 The basis for these strategies lies in the structures of two ascomyceteCDHs from Crassicarpon hotsonii  and Neurospora crassa (4QI7), which feature a closed-stateand an open-state conformation of the domains, respectively.19 The mobility of the CYT domain significantlyaffects the IET and DET. The switch between the open-state and closed-stateconformation of the enzyme depends on the steric and electrostaticinterface complementarity as well as the length of the protein linker.21 In the most productive side-on orientation of CDH relative to aflat surface, e.g., an electrode, the linker plays a key role in IETand DET.22 To enhance the electrochemicalperformance of CDH as a bioelectrocatalyst, linker optimization strategiesshow promising potential.CDH possesses a noncatalyticelectron-transferring domain thattransfers electrons in vivo to lytic polysaccharide monooxygenase(LPMO).23 In fusionprotein design, designed linkers typically consist of a combinationof flexible (GGGS) and rigid (EAAAK) linker units.24 Early studies on FMN-dependent flavocytochrome b2 investigated the relationship between linkerlength and enzymatic function. The variants created with either ashorter linker or an elongated linker  showed a decreased IET, suggesting that the linkerlength in the natural enzyme is evolutionarily optimized.25 Although several characterized CDHs can achieveDET on various types of electrodes, the linker length and compositionare quite different together with reported IET rates ranging from0.003 to 66 s–1.9Limited research has been conductedon linker engineering in oxidoreductases,particularly with respect to optimizing electron transfer. One studyon the interdomain linker region of cellulase 5A demonstrated thata certain degree of linker rigidity and interdomain spacing is criticalfor proper enzyme function.N. crassa CDH IIA  were constructed,produced, and characterized using fast biochemical and electrochemicalmethods. Steered molecular dynamics (MD) simulations were performedto test the hypothesis and compare the results with experimental data.In this study, we explore from an evolutionary perspective howthe interdomain linker differs between CDHs. Although the length andamino acid composition of the linker vary, there are some generalrules that allow for their classification. Based on the sequence andstructural information of different CDH classes, we have defined linkerregions with different functions. To assess their postulated functionsand the effect on IET and DET, variants of 26 For this study,we only considered the well-studied basidiomycete Class I CDH sequencesand ascomycete Classes II CDH sequences. Together with previouslyreported crystal structures,19 we redefinedthe boundaries of the CDH linker. A highly conserved Tyr195 initiatesthe last, C-terminal secondary structure element of the CYT domain,a short α-helix, which in the available crystal structures isin contact with the domain. Since this Tyr195 is conserved in allsequences it is a well-suited position to define the N-terminal startof the linker, contrary to the end of the helix, which is not clearlydefined in sequence alignments. The C-terminal end of the linker isdefined by the highly conserved 229Tyr/Phe-Asp-Tyr231 motif, which is, according to the crystal structures, alsofirmly connected with the DH domain. We include these residues inthe linker for reasons that will be discussed later. From all available cdh sequences, 190 Class I CDH linkers and 501 Class IICDH linkers were extracted . Very few linkersare shorter than 30, or longer than 60 amino acids. The linkers areformed by mostly hydrophilic amino acids, the percentage is higherin Class I linkers and the percentage is increasing with linker length.Hydrophobic amino acids occur more often in Class II linkers. Thepercentage of amino acids with a potential structural function suchas Gly, Pro, Cys is relatively high in linkers of both CDH classes.Some frequently occurring amino acids like Ser, Thr, and Asp as wellas Tyr, Trp, and Cys are strongly conserved.CDHs form a diverse enzymefamily within the glucose–methanol–choline (GMC)-oxidoreductasesuperfamily. Based on the latest phylogenetic analysis, CDHs can bedivided into four classes.xtracted 1. Most o27 and used to group CDH linker sequences . At an alignment score of 1 ×10–10, 150 Class II linker sequences could be assignedinto 6 independent groups. A subsequent phylogenetic analysis withthose 150 full sequences resulted in similar clades and confirms anevolutionary relationship between the groups . However, the positions of a few CDHs of Group1 differed between the phylogenetic tree and the SSN network, dueto the explicit evolutionary model used for phylogenetic analysis.29 To visualize the sequence properties of the linker Groups 1–6,sequence logos were generated (S5). Based on the sequencelogos and crystal structures, three linker segments were defined.The middle segment, which showed the highest sequence variation istermed mobile linker and the flanking segments are termed attachedlinkers. Attached linker segments typically feature a conserved Cys,which can form a disulfide bond to the CYT domain, or a Pro-Val-Promotif, which interacts with the dehydrogenase (DH) domain. In contrast,the mobile linker typically comprises many hydrophilic amino acidsand Gly for increased flexibility. The mobile linker also containsa high percentage of Ser and Thr, which are potential O-glycosylation sites.20 In addition tothe six groups shown, the remaining 351 CDHs of Class II were groupedfurther by SSN using a lower threshold. The resulting additional eightgroups can be assigned to the six groups with minor differences .A multiple sequence alignment showed that especiallyClass I linkersvary greatly in length and sequence composition. Structure similaritynetwork (SSN) analysis was therefore used to discover interrelationshipsbetween linkers as a collection of pairwise alignments between sequencesenerated 2 and S5.NcCDHIIA (Group 3) variantswere designed , which favors the formation of a disulfide bond. An additionalinsertion of four amino acids (ATAT) in LNK_S=S + 4 increasesthe length of the mobile linker segment  gives CYT a higher mobilityrange which, interestingly, increases the cytochrome NcCDHIIA and its linker variants showthe same spectra in the oxidized state . Although the spectra were originally measured to showthe purity of the prepared enzymes, the spectra of the reduced statethat were measured 30 s after the addition of cellobiose also indicatethe changes in the IET. For the wild-type CDH and most variants, thetypical Soret band shift was observed from 420 to 430 nm, while theheme β- and α-peaks appeared at 533 and 563 nm, respectively.However, for LNK–2 and LNK–4, no CYT reduction was observedindicating the loss of IET, which was also observed in the measurementswith the cytochrome c assay or no heme reduction at all  comparedto the wild-type CDH and variants with an elongated linker. LNK +4, LNK_S=S and LNK_S=S + 4 showed a similar or slightlyhigher heme reduction rate than wild-type CDH. The about three timesreduced heme reduction rate of LNK+8 demonstrates that a too-longlinker allows a wide separation of the domains and slows down theIET. A moderate elongation by only four amino acids seems not to interferewith the frequent formation of the IET-competent closed state of CDH.This slight elongation of the linker might, however, add some flexibilityto the CYT domain to interact with an external redox partner and increasethe interprotein electron transfer to LPMO or the DET to an electrode.UV–Visspectra of ed state S9. Altho c assay 2, even mcdh sequences. The analysis of amino acids at the interfacearea showed that the interface residues are not conserved betweendifferent CDHs . The transientinteraction between the two domains is dominated by weak hydrophobicinteractions. The precise fit of the two domains mainly depends onspatial complementarity. The mostly weak interactions between thedomains ensure the freedom of movement of the CYT domain between theclosed and open states. Modeled structures of wild-type NcCDHIIA, LNK–1, LNK–2, and LNK–4 using the closed-statecrystal structure of CDH (PDB ID 4QI6) as a template showed that the linkerregion was more stretched with reduced linker length . For LNK–4, no modeled structureof the closed state could be obtained, indicating that the NcCDHIIA linker is already at a minimum length and any reductiondistorts the closed state which reduces the IET (and therefore thecytochrome c activity) by changing the interfaceregion and involving new amino acids into the interface. This alsoalters the electrostatic interactions between the domains that aresusceptible to pH.To investigatethe molecular reasons for the effect of the linker length on the IETand the pH profile of the IET, we investigated the interface of various Table S3). The largest distances between the COG of the DH and CYT domainswere observed for the two variants with an extended linker: LNK+4and LNK+8. The increased movement radius of the CYT domain reducesthe frequency of forming the electron transfer competent closed state.As expected, the COG distance between the DH and CYT domains graduallydecreased for variants with a shortened linker. For reference, theCOG distance between the DH and CYT domains was 35.6 Å when thetwo domains were in the closed-state conformation (modeled after PDBID: 4QI6). Thesolvent-accessible surface area (SASA) of the linker corresponds withthe linker elongation .Steered MD simulations were performed toexplore the maximum distance that the linker of the different variantscan stretch. In these simulations, the CYT domain was constantly pulledaway from the DH domain. Despite the low pulling force, a distortionof the CYT domain could be observed after some time. This distortionwas monitored via the distance between the CYT center of geometry(COG) and the Cα of Cys211. The MD simulations were cut offafter the distortion measurement within the CYT domain reached 11Å, a value that was considered appropriate after a visual inspectionof the individual MD simulations (NcCDHIIA numbering) remained relatively confined for theLNK_S=S (Δ 1.2 Å) and LNK_S=S + 4 (Δ2.3 Å), whereas the wild-type CDH and the other variants shownno stabilization and a detachment of the attached linker from theDH domain (average Δ = 20.4 ± 1.8 Å). This highlightsthe stabilizing effect of the disulfide bond on the attached linkerand domain interaction. Elongating the LNK_S=S linker by 4amino acids could bring the COG distance of LNK_S=S + 4 backto that of the wild-type CDH, which should result in an increasedCYT mobility that could be beneficial for the interaction with macromolecularelectron acceptors such as cytochrome c, lytic polysaccharidemonooxygenase, and electrodes.The computed COG distance of LNK_S=S was over 20 Åsmaller than for the wild-type model 5a. Sincec, or its physiological redoxpartner LPMO. The interprotein electron transfer (IPET) step fromCYT to the type-2 copper center of LPMO was determined by measuringthe reoxidation rate of heme b in the CYT domain(k2563) in the presence of NcLPMO9C. We found little difference between the wild-typeCDH (15.6 ± 0.7 s–1), LNK + 4 (13.6 ±2.4 s–1), and LNK_S=S + 4 (18.4 ± 0.4s–1), which indicates that a moderate elongationof the linker does not restrict the CYT domain movement between theopen and closed state or improves the interaction with the terminalelectron acceptor. However, in another study, a much longer linkerreduced the IET in CDH greatly.21The last electron transfer step of CDH starts from the reduced CYTdomain and delivers a single electron either to the nonnatural electronacceptor cytochrome –1) of LNK–1 together with the decreased IET rate reveal a significantchange in the transition between the open and closed states. LNK-1is much more likely to maintain the open state with an exposing heme b cofactor that increases the interaction with NcLPMO9C but reduces IET.However, the increased IPET rate (34.3 ± 2.4 sS13). The plot of peak current vs the square root of the scan speedshowed a linear trend for all CDHs, which indicates that the systemis in a freely diffusing mode .32 The anodic and cathodic peak currents increasedgradually with an increased scan rate (2–500 mV s–1) . After determining theoptimal scan speed, the midpoint redox potential of the heme b was measured at pH 5.5 with a scan rate of 25 mV s–1. No significant deviations between the midpoint redoxpotential of the wild-type enzyme (111 mV vs SHE) and the linker variants(106–116 mV vs SHE) were found.Besides LPMO, anotherimportant terminal electron acceptor for CDH is an electrode. Here,the reduced CYT domain delivers a single electron directly to theelectrode, which is described as direct electron transfer (DET). Inthis context, DET does not indicate a direct electron transfer fromthe FAD to the electrode. To investigate the DET of the CYT domainof wild-type CDH and the linker variants, cyclic voltammetry witha 1-thiogycerol-modified gold electrode was performed 5 and S13–2), which is 14% higher thanthe wild-type CDH (13.9 μA cm–2) and supportsthe data from steady-state and presteady-state experiments that indicatean increased CYT domain flexibility after stabilization of the attachedlinker. The reduced CYT domain mobility expected in LNK_S=Sis also obvious from the lower current density of 10.2 μA cm–2. Elongated linkers do neither increase IET nor DETLNK + 8 (8.8 μA cm–2) and LNK + 4 (7.1 μAcm–2), which a reduced linker length introducesa greatly reduced IET which is demonstrated by LNK–1 (5.1 μAcm–2).The observed currentdensities (measured at 250 mV vs SHE) are a result of the combinationof differing IET and DET rates 6b. The h40 More variations appear in Class II CDH linker sequences that weregrouped into six groups. Here, highly conserved sites were found.In almost all linker N-termini a Tyr defines the start of the linker,which forms an α-helix with other four or five amino acids.This structure is common and conserved in all analyzed CDH structures.16 The next highly conserved position is a Cysresidue in the N-terminal attached linker, that forms a disulfidebridge with the CYT domain, which has been confirmed by previous LC–MS/MSanalyses (Cys167-Cys211 in Crassicarpon hotsonii CDH).20 After this Cys, the mobile linkerregion starts. The length of the mobile part is between 15 and 30amino acids in Class II linkers. The abundance of Gly and Ser residuesgives the linker a high flexibility, which also leads to the difficultiesof full-length enzyme crystallization.19 Other studies reported O-glycosylation on Ser andThr residues in the mobile linker of C. hotsonii CDH.20O-glycans are also oftenfound in the hinge regions of matrix metalloproteinases and lgA antibodies.33 The abundant Ser and Thr residues in the ClassII linker groups 1, 3, and 6 provide many potential O-glycosylation sites.20 The highly conservedPro-Val-Pro motif or a conserved Cys residue at the correspondingposition is the start of the next attached linker segment. Its C-terminalendpoint is given by the highly conserved Tyr/Phe-Asp-Tyr motif. Alook at other GMC-oxidoreductases, such as flavocytochrome b2 lactate dehydrogenase (PDB ID: 1FCB), flavohemoglobin(PDB ID: 4G1V), flavocytochrome p-cresol methylhydroxylase (PDBID: 1DII), flavocytochrome c sulfide dehydrogenase (PDB ID: 1FCD), and flavocytochrome c3 (PDB ID: 1QJD), which shows no sign of such motifs and reflectsthe evolutionary uniqueness of the linker in CDH. Most characterizedascomycetous Class II CDHs from Chaetomium atrobrunneum, Hypoxylon hemeatostroma, N. crassa, and Stachybotrys bisbyi have linkers that belong to linker Group 1, 2, or 3. The linkerof C. thermophilus CDH is a representativeof Group 4, and the CDH linker from D. saubinetii is a typical Group 6 type linker. For those characterized CDHs,which show DET on electrodes, the length of mobile linker varies from10 to 22 amino acids, and the pH-dependent activity varies from acidicto alkaline.34Multiple sequence analysis revealed notablefeatures of CDH linkers,where were not apparent from prior studies. The definition of theflanking linker regions that are most often attached to the CYT orDH domain and a mobile central linker region allows a better understandingof the linker function based on its amino acid composition. The mobilelinker region of Class I CDHs shows a consistent composition richin Gly, Ser, and Thr. The high-sequence similarity was reflected inbeing below the minimum grouping threshold for SSN analysis.c activity and the pH shiftas well as the reduced IET rates directly obtained from stopped-flowmeasurements result from the shortened linker variant LNK–1,which hinders the two domains to form the optimal closed-state. ThepH shift originates from the sterically distorted interface due tothe shorter linker and a mismatch of electrostatic interactions. Theinteraction of attractive and repulsive electrostatic charges at theinterface is crucial for the formation of the transient CYT/DH complex,but also for the following fast dissociation of both domains. A shorteningof the linker leads to the different positioning of the CYT domainat the DH interface and can shift the pH profile to a lower pH whenmore repulsive electrostatic interactions due to the pairing of negativelycharged Asp side chains are formed. The interface conservation analysisshowed that the interface area is not conserved in CDHs, which requiresthe evaluation of each individual CDH interface. The amino acid pairsof NcCDHIIA at the interface was positioned and mostlyweak interactions ensures the freedom of conformational switch. Modeledstructures of wild-type NcCDHIIA, LNK–1, LNK–2,and LNK–4 showed that the linker region was stretched obviouslywith reducing of linker length. Especially, for LNK–4, themodeled structure cannot be successfully built using a closed-statecrystal structure, resulting in an open-state structure. These resultsrevealed that the natural linker is already optimized for the shortestlength.The reduced cytochrome b2 have been reported, the changes in the length of theinterdomainhinge region result in severe disruption of heme reduction.25 A study on the linker length of GH5-CBM3 cellulasesfrom Paenibacillus genus showed variantwith a linker two times longer than that of the wide-type proteinattained the highest catalytic performance, and other variants withexcessively long or short linkers were equally detrimental to catalysis.23 All these studies show that the optimizationof the spatial distance of multidomain enzymes is feasible and worthwhile.Similar results in flavocytochrome NcCDHIIA was changed from a one Cys linker type to a doubleCys linker type, thereby attaching the linker covalently to a correspondingcysteine on the DH domain to prevent linker dissociation. However,presteady-state experiments with LPMO showed no significantly differentIPET rates for the LNK_S=S + 4 with the attached linker orLNK_+4 with a slightly elongated attached linker. This shows thatthe CYT domain does not need to move a great distance to make efficientcontact with a molecule like LPMO. In contrast, the slight shorteningof the linker in LNK–1 had a positive effect and increasedthe IPET more than 2-fold. The modeled structures of shortened linkervariants show that the linker region was stretched with reduced linkerlength; therefore, open conformation is prior.Steered MD simulations suggest that the weaker nonbonded interactionsbetween the C-terminal attached linker and the DH allow the attachedlinker segment to dissociate from the DH. This dissociation resultsin a two-step length change of the interdomain linker during the open/closedconformational switch, which could be important for the IPET to itsnatural redox partner LPMO. To test this hypothesis, the linker of D. saubinetii CDH, which has a quite good electron transfer efficiency.6 This insertion promoted DET of LNK_S=S+4,which may be because the longer mobile linker increases the possibilityof open conformation compared with LNK_S=S. For LNK+4 and LNK+8,the longer mobile linker has a better IET but reduced DET, which confirmedthat the mobility of linker and the frequency of the switch betweenopen and closed state is the rate-limiting steps. These results areconsistent with previous studies showing that IET is dependent onthe mobility of the CYT domain, and the mobility of the CYT domainis affected by the orientation of the DH domain and the length ofthe interdomain linker.22 Another study investigatedchimeric CDH variants and found that the occurrence of IET highlydepends on a close distance between the FAD and heme b cofactors, respectively, the DH and CYT domains, the mobility ofthe linker, and the correct orientation of the CYT domain in respectto the DH domain.24 Steric mismatches betweenthe domain surfaces or repulsive electrostatic interactions at theinterface hinder a successful IET.The effect ofthe different linkers changes when applied to anelectrode. Here, preventing the dissociation of the linker in theLNK_S=S variant, resulted in an enhanced IET but still reducedDET rate on the electrode. The variants of LNK_S=S+4, LNK+4,and LNK+8 have an insert Ala-Thr-Ala-Thr in the mobile liker (betweenThr216_Thr217). This insert was designed to increase the length ofthe linker which could form a coil without a special function. Ala-Thr-Ala-Thralso exist in the mobile linker of 22 A previous study has shown that the mobility of CYT domaindetermines the IET from FAD to heme b and the DETfrom heme b to the electrode surface.22 The bioelectrocatalytically best-performing variant LNK_S=S+4showed a combination of optimized IET and DET. The rational designfrom an evolutionary point of view is a promising strategy for optimizingdirect electron transfer rates of multidomain enzymes, as well asfor other fusion proteins that might be of interest in bioelectrocatalytisapplications.The CDH linker variants showeddifferent trends in kinetic studiesand electrochemical measurements. For example, compared with the wild-typeenzyme, LNK_S=S had a higher IET but lower DET. This revealedthe electron transfer between the enzyme and electrode was limited,most likely due to the reduced frequency of open-close conformationswitch by the extra disulfide bond. In this study, proteins diffusedfreely on the electrode surface with an unordered orientation, soit is not optimal to reach the best DET orientation.cdh sequences  oxidoreductase family) were collected from the NCBI and UniprotKBdatabases (accessed in 2021). The linker part is extracted accordingto the new definition, and sequence similarity networks (SSNs) wereused to group all potential cdh linker sequencesand only Class I and II enzyme sequences with characterized exampleswere selected at an alignment score of 10–10 inthis study.26 The multiple sequence alignmentwas performed by MUSCLE for both classes. Sequence LOGOs were madeby WebLogo (https://weblogo.berkeley.edu/logo.cgi). In order to analyzethe linker diversity, repeated sequences were deleted. Different aminoacid compositions and linker lengths were counted, hydrophilic aminoacids including serine, threonine, glutamic acid, aspartic acid, asparagine,glutamine, histidine, lysine, and arginine. Leucine, isoleucine, valine,alanine, tyrosine, phenylalanine, and tryptophan were considered hydrophobicamino acids. Special cases were glycine, proline, and cysteine.All available The full sequencesof Class I and Class II were imported into MEGA (version 11) respectively,and aligned with MUSCLE. Evolutionary relationships were inferredwith the maximum likelihood method (JTT model). The bootstrap consensustree is based on 1000 replicates. Different clades were defined dependingon linker sequence types.NcCDHIIA were determinedone by one in PyMOL software according to different bond screeningprinciples for hydrophobic force, hydrogen bonding, and electrostaticinteraction. The Consurf software was used to analyze the overallsequence conservation (https://consurf.tau.ac.il/). The multiple sequencealignment of all CDH sequences from Class I and Class II CDHs wasperformed by MEGA 4.0, and binding sequence spectra were drawn usingthe sequence logo.The interacting amino acidsin domain interfaces of –1 peptone fromcasein, 5 g L–1 yeast extract, 5 g L–1 NaCl, and in the LS-LB selection plates has additional 15 g L–1 agar and 25 mg L–1 zeocin) wasprepared for Escherichia coli. Thebacteria were cultivated at 37 °C. The KM71H (MutS) yeast strains were cultivated at 30 °C in YPD medium . Media components were dissolvedin highly pure water and autoclaved for 20 min at 121 °C and1 bar.All chemicals and mediacomponents were purchased in the highest purity from Sigma Aldrich, Fluka , Roth and VWR  or Bio-Rad . Low-saltLuria Bertani (LS-LB) broth was used for linker variants cloning. The Pichia pastoris strain KM71H (MutS), supplied by Invitrogen , was used for the expression of all the linker variants. Thevector of wild-type pPIC_NcCDHIIAwas used as a template to design and clone all linker variants onthe linker region. Primers were synthesized by Microsynth , and all PCR primers used in the construction of plasmidsfor linker variants of NcCDHIIA protein overexpressionare listed in Table S4. The correct sequencesof plasmids were confirmed via DNA sequencing by Microsynth .NEB DH5-alpha competent P. pastoris KM71H cells by electroporation. Then,several single colonies were selected on zeocin antibiotic (100 mgL–1)-containing YPD agar plates for 96-deep-wellscreening. The colony with the highest activity of variants was usedfor fermentation. The fermentation was performed in shaking flasksaccording to the manual of the Pichia fermentationprocess guidelines . The bufferedglycerol-complex medium (BMGY) and buffered methanol-complex medium(BMMY) were used for preculture and acculturation, respectively. Theyeast cultures were harvested after 120 h of cultivation. NcCDH linker variants were purified from the supernatantby a two-step chromatographic procedure The supernatant was stabilizedwith 30% (v/v) ammonium sulfate before the first purification step,which was performed using a Butyl Sepharose 4FF column . The columnwas equilibrated with a 50 mM sodium acetate buffer pH 5.5 containing30% (satd.) ammonium sulfate. The variants were eluted by a lineargradient from 30 to 0% ammonium sulfate in 5 column volumes at a flowrate of 10 mL min–1 and collected in 5 mL fractions.The active fractions were determined with activity assays (describedhere below) and a buffer exchange to 10 mM HEPES pH 7.5 was performedwith a Sephadex G-25 desalting column after concentrating the samples.The conductivity was below 1.5 mS cm–1. The enzymesolution was applied to a Source 30 Q resin (52 mL) equilibrated with10 mM HEPES buffer, pH 7.5. the enzymes were eluted by a linear gradientin 10 column volumes from 0 to 1 M NaCl at a flow rate of 5 mL min–1. The proteins were collected in 3 mL fractions andpooled according to activity and SDS-PAGE. The pooled fractions wereconcentrated and a buffer exchange to 50 mM acetate acid pH 5.5 wasperformed with Amicon Ultra centrifugal filters cutoff of 10 kDa.The SDS-PAGE analysis of all preparations in this study is displayedin The encodingcDNA for CDH linker variants was ligated with the expression vectorpPICZαA and transformed into electrocompetent 520 = 6.9mM–1 cm–1) or 50 μM cytochrome c from equine heart (ε550 = 19.6 mM–1 cm–1). Assay reactions were performedin 100 mM potassium phosphate, pH 6.0. The activity was measured with30 mM lactose as the saturating substrate. Assay reactions were monitoredfor 180 s at 30 °C at 520 nm in a LAMBDA 35 UV–vis spectrophotometerequipped with a temperature-controlled 8-cell changer (PerkinElmer).To cover the wide pH range from 3.0 to 8.0 for activity profiles,the McIlvaine buffer system was used. The protein concentration ofwild-type and linker variants was determined with the absorbance at280 nm. One unit of enzyme activity was defined as the amount of enzymenecessary to reduce 1 μmol lactose per min under the assay conditions.The presence of free thiols in proteins was quantified through theuse of the chromogenic reagent 5,5′-dithiobis-(2-nitrobenzoic)acid (DTNB), 100 μM DTNB and pure proteins (more than 10 μMin the reaction cuvette) in 100 mM Tris buffer pH 8.0, the opticalabsorbance were measured at 412 nm after 5 min incubation.35Theactivity of the CDH variants was determined by the concomitant reductionof 0.03 mM DCIP  inthe aging loop for 30 s until the second electron on the FAD usedup according to the literature.21 Whenthe heme b in the CYT domain was oxidized to about 70 to 80%, we combineit with NcLPMO9C (20 μM) to measure the reoxidationof heme b. The trace of the absorbance at 563 nmwas fit to a single exponential curve. All experiments were performedin 50 mM sodium acetate buffer pH 5.5 at 30 °C.Fast kinetic of wild-type CDH and linker variants weredetermined with a stopped-flow spectrometer . Measurements were performed with 5 μM protein and100 mM cellobiose as substrate. Absorbance changes were recorded from0 to 30 s. The redox state of the FAD cofactor was monitored at 449nm, while the heme The cyclic voltammetry andchronoamperometry were performed with an Autolab PGSTA204 potentiostat(Metrohm) using thiol-glycerol modified gold electrodes . A SAM was assembled by immersing the cleaned gold electrodeinto a 10 mM 1-thioglycerol solution for at least 1 h at room temperature.Voltametric measurements were performed in McIlvaine buffer at pH5.5 containing 100 mM KCl as a supporting electrolyte. All solutionshad been degassed sufficiently. To maintain an oxygen-free atmospherethroughout the procedure, nitrogen was circulated into the solutions.20 μL of the enzyme was placed in a Teflon holder on top ofthe electrode as a container for the protein at a concentration of80 μM. A filter membrane with a cutoff of 3.5 kDa keeps thefluid confined. It is possible to restrict the enzyme in the membrane,enabling low molecular weight substrates and products to pass through.4QI6) or the NcCDHIIA crystal structure (PDB ID: 4QI7) as templates.36 The residues I218, N459 in the wild-type crystalstructure, and I223, N464 in the LNK+4 homology model were substitutedwith cysteines using the “Mutagenesis” tool in open-sourcePyMOL  to generate the LNK_S=Sand LNK_S=S + 4 variants, respectively. The cysteine side chainrotamers were chosen such that the sulfur atoms were as close as possible.Homology models for the LNK+4,LNK+8, LNK–1 LNK–2, and LNK–4 variants were generatedusing the SWISS-MODEL online tool and the SWISS-MODEL web interface(ProMod3 3.2.1) with the close-state CDH crystal structure . The preparation included the removalof all solvent molecules, glycans, and cofactors. Also, the modelswere aligned such that the center of mass of the DH domain is at the coordinates, the Cα atom of residue V806 (wild-type numbering)is at coordinates , and the CYT center ofmass is at coordinates .Subsequently, GROMACS topology files were created with pdb2gmx forthe cleaned models using the simple point charge (SPC) water modeland the OPLS-AA force field. Definitions for restraining the positionsof the DH domain atoms with a force constant of 104 kJ mol–1 were manually added to the topology files. Then, the models werecentered at  coordinates  in a box with  dimensions . Once the models were solvated in SPC water and 0.1 M NaClwas added on top of neutralizing counterions with genion, a steepestdescent energy minimization was performed with a convergence criterionof 103 kJ mol–1 nm–1. Thereafter,an NPT equilibration of 100 ps (5 × 104 with a step size of 2 × 10–3) was performedwith initial velocities generated from a Maxwell–Boltzmanndistribution. To maintain a constant temperature of 310 K and a constantpressure of 1 bar, a weak coupling scheme with coupling times τT = 0.1 and τP = 2 ps, and isothermal compressibilityof 4.5 × 10–5 bar–1 was used.The LINCS algorithm was used to constrain all bond lengths. A Verletcutoff scheme was used and a new neighbor list was generated every5 steps with a short range, electrostatic, and van der Waals cutoffof 1.4 nm. The Particle-Mesh Ewald (PME) method was used with PMEorder = 4 and Fourier spacing = 0.16 nm to treat long-range electrostatics.Subsequently, a steered MD simulation was performed with some modifications.Here, a new neighbor list was generated every 20 steps. Also, theNose–Hoover method was used for the temperature coupling withτT = 1 ps, and the Parrinello–Rahman methodwas used for the pressure coupling with τP = 2 ps,and isothermal compressibility of 4.5 × 10–5 bar–1. During the steered MD simulations, positionrestraints 104 kJ mol–1 nm–2 wereimposed on the DH domain and the CYT was constantly pulled away fromthe DH domain with a force constant of 500 kJ mol–1 nm–2 along the x-axis. Finally,the trajectories were analyzed with the tools provided in the GROMACS2021.4 biomolecular simulation package. The data was then furtherprocessed using the python packages matplotlib, numpy, and scipy.A Savitzky–Golay filter, as implemented in scipy, was appliedto the distance data with a filter window length of 101 and a polynomialof the second order.MD simulations settings. MD simulations were performed with theGROMACS 2021.4 biomolecular simulation package.


This study simulated the deformation of a hot runner manifold and nozzle assembly during operation, aiming to address potential leaks and premature failure. Both thermal and mechanical models were used simultaneously to accurately capture system behavior. A simplified set of boundary conditions was proposed for efficient problem-solving. Analysis of the simulation results revealed that thermal deformation posed a risk of catastrophic failures and leaks. Deformation from melt pressure was relatively small compared to thermal loading, not exceeding 12%. The study provided design recommendations based on the simulation findings, guiding the development of hot runner systems for improved reliability. The demand for mass-produced plastic parts through injection molding is steadily rising. There is also a growing emphasis on achieving high dimensional stability and appearance quality in these products. However, there is increasing pressure to reduce unit prices, making it challenging to maintain profitability in injection production.Consequently, the injection molding industry is increasingly adopting hot runner systems to enhance process efficiency and cost-effectiveness. The tight nature of the molding process has led to growing concerns regarding material waste. Furthermore, modern injection molded parts strive to minimize the need for reprocessing scraps.At times, the construction practices of hot runner systems deviate from established theories or protocols due to the differing intuitions of tooling designers or manufacturers ,2,3. MolThe difficulties with hot runners arise from the fact that they are machined and assembled at room temperature but must be operated at high temperatures. Moreover, this assembly includes a connection by bolts, and this connection by bolts constrains deformation at high temperatures to an unexpected form. If bolts are applied only for strong fastening without a close examination based on mechanical principles, thermal deformation occurs mainly in areas where fastening is weak. Due to the nature of the hot runner, a huge temperature gradient is generated between the parts, which causes strain of a size that cannot be handled only by simple fastening. In a hot runner, the plates are kept cold, but the manifolds and nozzles are exposed to difficult thermal conditions that must be heated close to the melt temperature. Therefore, the fastening between the high-temperature part and the low-temperature part should be performed in consideration of thermal expansion in an operating situation. At this time, where and how to fasten is an important task, and for this, it is essential to three-dimensionally predict the deformation. This work presents a novel method for simulating the structural deformation of hot runner systems. While previous studies have explored deformation in injection molds ,5,6,7, tThis study aims to develop a suitable thermal and mechanical model for the hot runner system, considering its structural aspects. The model should achieve a balance between accuracy and simplicity. To accurately capture the behavior of the hot runner system, a three-dimensional model is crucial. The model primarily focuses on the manifold and nozzle, which are essential components of the system. Detailed modeling is carried out for these parts, while the remaining components are represented in a more general manner.While the simulation does not incorporate the melt flow due to its minimal impact on deformation, it assumes a static pressure applied to the contact surface with the melt. The simulation results obtained under these conditions will be presented and analyzed to provide valuable insights for manifold design.This study focuses on a simplified hot runner system consisting of a manifold connected to two nozzles, as illustrated in Designing the manifold to achieve both thermal insulation and structural integrity under high melt pressure poses a significant challenge in hot runner systems. Fixing the manifold to the mold plates without compromising thermal performance is particularly challenging. Over the years, mold manufacturers and individuals have patented various ideas related to this issue ,19,20,21The design depicted in The number of fastenings in the manifold can contribute to the formation of temperature gradients, leading to thermal bridges. These bridges can disrupt temperature control and create uneven heating, resulting in hot and cold spots. Moreover, the constraints imposed by boltings and bushings can induce deformation in the overall structure. One of the critical consequences of manifold deformation is the failure of heat control, as it can cause melt leakage due to misalignment of the nozzle and manifold connections.Hence, it is crucial to ensure intimate contact between the nozzle and manifold interface. It is important to effectively control the deformation of the manifold to ensure that the interface does not become excessively deformed. The bending deformation occurs due to the constraints, causing the manifold to deviate from parallel alignment with the surrounding plates. Unfortunately, in many cases, attempts to address resin leaks involve mistakenly tightening the parts further. In this study, we will investigate and discuss the characteristics of the associated deformation, using simulations as a basis.ti, si, Li, and di. Some of the detailed dimensions around the nozzle and the sprue are suppressed. The dimension in the figure is for the operational condition. Let us denote the dimensions at the reference temperature of machining by At the operation temperature, the gap would change toi-th section.Ideally, x. Then, Hooke’s law combined with thermal strain describes the stress asE, G, and ν are Young’s modulus, shear modulus, and Poisson’s ratio, respectively. The thermal strain is of the formT is the processing temperature at which the hot runner is under operation. This work assumes a simple steady simulation of an elastic deformation involving linear thermal expansion. The Equation of equilibrium isT, the thermal problem by the energy equation should be solved together with a set of proper boundary conditions. The heat transfer in the hot runner system can be simplified to a heat conduction problem of the formk, the specific heat capacity, c, and the density ρ should be specified. In addition, heat generation In order to determine the temperature field, n is the direction normal toward the outside of the surface. Moreover, in the domain enclosed by the manifold and the surrounding structures containing it, the surface-to-surface radiation, as well as the convective boundary condition, has been taken into consideration for accurate simulation. The mathematical description of the radiation has been suppressed in this work since it is quite bulky to fully describe here. This is a very stable calculation that can be easily achieved without great numerical concern. However, the imposition of the proper boundary condition is not always easy. The boundaries of exposed air are treated asThis work addresses a conjugate problem by considering both heat conduction and static deformation in the simulation. The heat conduction analysis incorporates boundary conditions that account for both convection heat transfer and surface-to-surface radiation.Realistically simulating the hot runner system depicted in D is the signed distance between the surfaces considering the outward normal vector.Here, It is important to note that the sprue is treated as blocked and subject to constant static pressure. As mentioned before, no flow is considered in this simulation. Therefore, the sprue is treated under the condition that normal stress is applied to the wall surface. This work employs SolidWorks Simulation to accommodate all of the factors described above. SolidWorks Simulation is a viable option for this simulation because it is capable of handling these factors without great burden. The heat generation is estimated by obtaining the integrated energy input required to maintain the target temperature in the simulation system. This has been performed by trial and error.pT, while the plates and space block are at rT. Moreover, the properties of the insulation pad are obtained from the manufacturer. The values for the simulations are presented in The simulation requires several material properties, such as Young’s modulus, Poisson’s ratio, thermal conductivity, and heat capacity. A hot runner assembly is considered built of the AISI H13 tool steel. The manifold and nozzles are maintained at a temperature of A large injection molding machine such as Engel ES4550, which is capable of 10,000 kN clamping, can generate a melt pressure of up to 218 MPa. The maximum pressure can instantaneously rise over the pressure in the specification. The ratio of possible excess rise is considered to reach 0.382, which is the first number in the set of Fibonacci-derived ratios . In the pT = 500 K while the rT is set as 320 K, considering the fairly high environmental temperature in injection molding facilities. In addition, the dimensions of the tested hot runner are specified in It has been set that the hot runner is controlled at A large value is shown near the nozzle, which is associated with a very large temperature gradient near the nozzle and the cross-sectional change of the runner. Although localized on the surface of the runner, the value is slightly above the known yield strength of AISI H13 steel at high temperatures (1200 MPa at 425 °C). It can also be seen that the locations in the supporting plate adjacent to the fastening points are all highly stressed. Inevitably stresses are concentrated on certain locations, which might render the hot runner further fatigued.The hot runner system is stressed since deformation is restrained by enclosing structures. Inevitably, there is not enough structural support to prevent the bending. As shown in the figure, slight bending is also observed. The manifold near the nozzle is curved upward, forming a very mild cup-like shape. Note that the deformation in the figure is magnified 20 times.z-direction in y-direction in To clearly visualize this, the deflection has been further magnified and shown in The design guide considering the thermal expansion of the pin guide bush or insulation pads is quite well described in the literature . The impz cannot be eliminated because it is affected by multi-dimensional effects such as horizontal thermal expansion.The temperature rise of the space block can be regarded as Despite the necessity of the gap, according to mold builders, the manufacturers do not want to provide a hot runner with gaps. In theory, an intentional gap is required, but the design does not accommodate the gap in practice. The counterargument against the gap is that prestress can resist the possible force opening the connection between the nozzle and the manifold.In a scenario where there is no thermal deformation and the deformation is solely caused by pressure, the resulting deformation depicted in When the gap by Equation (12) is applied, the stress around the pin guide bush is dramatically reduced, as shown in In this study, the theoretical numerical methodology needs experimental verification through the fabrication of actual hot runners. However, conducting experiments in high-temperature environments with assembled hot runners is challenging. A long-term usage method or an alternative approach involving the fabrication of experimental hot runners with exposed structures and observation of deformation and connection states could be considered, but this would incur significant costs. Despite the lack of experimental verification, the study’s results provide numerical evidence for previously theoretical design guidelines, such as Equation (1), enhancing confidence in their use.The study assumes uniform maintenance of the surrounding thermal environment and the absence of heater failure as boundary conditions. Although the temperature distribution of the hot runner structure may not change significantly outside these conditions, actual hot runner failures often occur due to heater overheating, usually resulting from thermal bridges caused by resin leakage. Therefore, the design method proposed in this study has the potential to prevent control failures by addressing resin leakage. A simulation based on a more comprehensive model would offer detailed results that go beyond what this work provides. This is particularly relevant when considering a manifold that possesses intricate mechanical and thermal connections with the surrounding plates. When the deformation of surrounding plates becomes critical, such a model would be necessary to capture these complex interactions accurately.This study focuses on simulating the deformation of a hot runner manifold and nozzle assembly. The deformation arises from thermal loading caused by temperature control, which is determined by calculating steady-state heat generation. Additionally, the melt pressure is accounted for, assuming a uniform pressure across the runner wall, gate, and sprue cross sections.The simulation provides accurate predictions for the gap between the manifold and the nozzle bushing. While a simple calculation of thermal strain can serve as a reasonable approximation for design purposes, a simulation-based approach offers enhanced safety. It has been found that the deformation by the melt pressure does not exceed 12% of that by the thermal loading. This work has proposed how the gap can be set based on the simulation. By employing the gap, the stress can be reduced at the interface. As a result, the risk of catastrophic failures such as leaks or overheating can be mitigated. To facilitate the widespread adoption of the gap design, it is crucial to provide supporting experimental evidence.


There is accelerating demand for energy-absorbing structures fabricated from lightweight materials with idealized, near-constant force responses to simultaneously resolve the engineering challenges of vehicle mass reduction and improved occupant safety. A novel compounded energy dissipation system composed of AA6061-T6 and AA6061-T4 tubing subjected to hybrid cutting/clamping and H130, H200 and H250 PVC foam compression was investigated utilizing quasi-static experiments, finite element simulations and theoretical modeling. Identical structures were also subjected to axial crushing to compare with the current state of the art. The novel cutting/foam crushing system exhibited highly stable collapse mechanisms that were uniquely insensitive to the tube/foam material configuration, despite the disparate material properties, and exceeded the energy-absorbing capacity and compressive force efficiency of the axial crushing mode by 14% and 44%, respectively. The simulated deformation profiles and force responses were consistent with the experiments and were predicted with an average error of 12.4%. The validated analytical models identified numerous geometric/material configurations with superior performance for the compounded AA6061/PVC foam cutting/foam crushing system compared to axial crushing. An Ashby plot comparing the newly obtained results to several findings from the open literature highlighted the potential for the compounded cutting/foam crushing system to significantly outperform several alternative lightweight safety systems. The field of structural crashworthiness has experienced considerable growth both in terms of the community size and extent of contributions since its inception in the 20th century ,2,3. LarCrash boxes filled with structural foam cores represent one of the most thoroughly studied enhancements for the universally implemented axial crushing energy dissipation mode ,21,22,23Hybrid energy absorbers, which subject the same thin-walled structures to more ideal cutting, splitting and tearing-based deformation modes ,35,36, h®  internal foam cores. Closed-cell polyvinyl chloride (PVC) foams have also shown promise for enhancing many lightweight structural applications, including various energy absorbers [The concept of introducing structural foam cores to further enhance the mechanical performance of these novel alternative deformation modes has received some attention in recent years ,50. Nearbsorbers ,55,56, absorbers  and hybrbsorbers  with higbsorbers ,3,18.The present study contains comprehensive experimental, numerical and analytical investigations on the influence of extruded material annealing and foam core density on the energy-absorbing capacity, efficacy and limitations for AA6061/H-series PVC foam-filled energy-absorbing structures subjected to axial crushing and 10-bladed cutting/clamping. Extruded AA6061 tubing, in both T6 (as-received) and T4  temper conditions, was considered to assess the extent and severity of brittle material fracture for PVC foam cores with relative densities between 0.092 and 0.171. Experiments and numerical modeling were performed for the hollow and PVC foam-filled structures subjected to compounded, 10-bladed cutting/foam crushing. Complementary axial crushing tests and simulations allowed for direct comparisons between the newly proposed energy absorber and the current state of the art. The novel compounded axial cutting/foam crushing mode displayed significant benefits over the traditional axial crushing mode, especially with respect to energy-absorbing capacity and stability during collapse, for every considered tube/foam core pair. The novel compounded cutting/foam crushing remained uniquely stable during collapse regardless of the disparate material pairings. The numerical models accurately replicated the experimentally observed force/displacement responses and deformation profiles. A theoretical study model was utilized to newly identify a wider range of material pairings and critical structural dimensions which benefited most significantly from the compounded cutting/foam crushing mode.The following section provides details on the composite AA6061/PCV foam energy-absorbing structures, including the fundamental material properties, critical details for each constitutive component and fixture, experimental testing and numerical modeling procedures and the performance metrics necessary to analyze the data. A parametric scope emphasizing the influence of the tubing/foam core material pair is also presented.oσ, utilized in the theoretical studies presented in Yε and fε represent the strains to yielding and fracture, respectively, and Seamless AA6061-T6 tubing  with a 63.5 mm outer diameter and 1.588 mm wall thickness was (rough) saw-cut into specimens with nominal lengths of 200 mm, followed by end milling to remove chips and burrs. This geometry was selected based on nominal material sizes/availability and because the tube ratio, m design ,21,36. TThe parametric scope considered extruded tubing in the mentioned T6 temper condition and an annealed T4 temper condition with a lower flow strength but significantly improved strain-to-failure. The latter specimens were obtained by heat-treating a portion of the as-received (T6 temper condition) samples per ASM Handbook guidelines . Charact3, 181.2 kg/m3 and 235.6 kg/m3, respectively. Representative quasi-static compressive stress/strain responses for each material are provided in The internal foam cores were composed of H-series, closed-cell PVC foam in H130, H200 and H250 configurations  with structural densities of 126.7 kg/mve model :(2)σfε=KThe necessary material coefficients, obtained via regression analysis, and critical mechanical properties are summarized in ® with the arbor removed from rectangular sheets, consistent with previous studies [The AA6061 tubes were combined concentrically with internal PVC foam cores, the latter were obtained from 25.4 mm-thick rectangular sheets utilizing a hole saw to match the inner profile of the extruded tubing. The cylindrical foam cores were fabricated utilizing a hole saw mounted to a Bridgeport studies ,57,64. AThe sacrificial AA6061/PVC foam composite structures were subjected to a traditional axial crushing deformation mode and a novel, in-house designed, engineered and fabricated 10-bladed hybrid cutting/clamping mode, shown in ® 1204-13A load cell  and 300 mm-range AR700-12 Acuity® non-contact laser displacement transducer . All measurements were synchronized using an NI CompactDAQ system (cDAQ-9174) operating at 2 kHz . The test frame was operated at 10 mm/min, limiting the nominal compressive strain rate within the foam cores to 10−3 s−1, for 125 mm of displacement .Experimental testing was completed utilizing apparatuses consistent with the schematics from The scope of experimental testing was selected to characterize the influence of the tube/foam core material pairing on the energy-absorbing capacity, effectiveness and structural stability of the traditional axial crushing (AC) and novel 10-bladed hybrid cutting/clamping (C10) deformation modes. The results were identified with the naming convention: EM/FC- DM-#, where EM/FC indicated the tubing material/foam core pairing, DM the deformation mode and # the individual test number or type of model . The full parametric scope is summarized in Representative finite element meshes for the axial crushing and compounded cutting/foam crushing systems are provided in K, defined as the coefficient of proportionality was implemented. The material parameters and exponential constants for each temper condition are summarized in The AA6061 tubing was modeled utilizing a simplified Johnson–Cook relationship as defined in Equation (3), since the present study considered quasi-static loading where thermal effects such as thermal softening are negligible. To that end, a simple linear polynomial equation of state with the bulk modulus, A Johnson–Cook model with damage parameters was defined for the AA6061-T6 tubing, with damage parameters widely utilized in the open literature ,67,68, s3 and 0.3, respectively. The rigid material assumption was necessary to mitigate the computation requirements of each developed model and was assumed to be reasonable since no deformation, tool wear or similar degradation was observed between tests.The remaining metallic, hardened 4140 steel fixtures  were modeled as rigid entities with an assumed elastic modulus, density and Poisson’s ratio of 207 GPa, 7830 kg/m®, Livermore Software Technology Corporation, Livermore, CA, USA)) was utilized to replicate the quasi-static compressive stress/strain responses of the H-series PVC foam cores with the data originally presented in An orthotropic crushable foam model εIPD=Note that the force was halved due to symmetry conditions. This expression was applied as the nonlinear force response in the translational spring to account for the axial force associated with in-plane foam core restriction, which was omitted in recent modeling efforts  and thus®, release R12.1 . Compression of the composite AA6061/PVC foam structures was simulated by positioning a rigidly fixed platen at the upper ends of the apparatus and applying a 1 mm/ss displacement rate to the lower platen (crushing) and cutter assembly (cutting). Half-symmetry was invoked for the 10-bladed cutting/clamping model shown in The compounded energy dissipation systems were simulated utilizing a double precision massive parallel processing (MPP) version of LS-DYNAC, defined in Equation (6), with an anticipated ideal value of zero [Tδ). Average cumulative errors of 0.057 and 0.190 were calculated for the axial cutting and 10-bladed cutting/foam crushing deformation modes, respectively. These values were consistent with approximately 88% correlation between the numerical modeling and experiments.The numerically predicted force/displacement responses,  of zero . This meTEA, was defined asTδ represent the reaction force during axial collapse at a given displacement, x, and the total displacement, respectively. The specific energy absorbed, SEA, per unit mass of the sacrificial structure is defined as Equation (8); the mass, EAm, of a circular tubing packed with solid foam cores can be calculated utilizing Equation (9).k = 0 if hollow and k = 8 if foam-filled. The mean force, mF, over the force/displacement response was determined as follows:Several performance metrics were utilized to evaluate the experimental and theoretical results. The total energy absorbed, CFE, quantifies the fluctuation between the average and the peak reaction forces:The compressive force efficiency, ψ, quantifies the TEA capacity, structural stability and material utilization for a sacrificial structure normalized with respect to the TEA for an equal volume of material, oσ and P,foamσ are the flow stress of the extruded material and foam plateau stress, respectively, and fε is the extruded material fracture strain.The energy-absorbing effectiveness factor (EAEF),  tension :(12)ψ=Fmoσ, blade friction coefficients, bμ, etc.) were originally provided in A parametric study was also conducted for the AA6061/PVC foam energy absorbers to assess the influence of key engineering parameters, especially critical tube/foam dimensions, on the efficacy of these composite structures subjected to the novel 10-bladed cutting and traditional axial crushing modes and is presented in m,crushF, experienced by foam-filled tubes can be predicted asfρ and sρ are the density of a given foam configuration and its base material, respectively.The plastic deformation mechanisms for foam-filled metallic tubing were considered in numerous theoretical studies that linked axisymmetric lobe formation in unfilled structures ,73 with Pσ, can be related to the density, sρ, and yield strength, Y,sσ, of the base material [3 and 55 MPa, respectively. The peak crushing force associated with initial lobe formation is the product between the flow strength and cross-sectional area of the tubing, The peak crushing force, material :(14)σP=1TEA since the lobes form and collapse with complete/intact hinges before fracturing.These models were previously validated for AA6061 tubing in both T6 and T4 temper conditions ; brittlecfcF, can be generically stated as [bn-bladed cutter imparts resistive forces due to plastic deformation, PF, which also influence the frictional forces at the cutting interface, and the foam cores experience axial compression, foamF, and interactions with the inner wall of the tubing, interF. The remaining geometric parameters are introduced in cutF, present with elastically dominated wedge indentation, EF, followed by plastic wedge penetration, wF, and steady-state cutting/clamping, ssF:x, utilizing Equation (18) through Equation (20), respectively [The accepted standard approach for analytically modeling unfilled ,75 and Ptated as (16)Fcfcectively .(18)FExThe forces associated with PVC foam compression and tubing/foam interactions include the bulk out-of-plane resistance to crushing by the closed foam cells, in-plane/volumetric resistance from the inner walls of the tubing and relative sliding at the interface , expressmaxδ, such that The mechanical properties of the various PVC foam cores in the rise and in-plane directions  were initially given in mF, CFE and EAEF) defined in The parametric scope for this theoretical study, summarized in TEA, SEA, etc.) as defined in The following section summarizes the experimental observations, including the observed deformation profiles, force/displacement responses and average performance metrics  mode was characterized by significantly improved consistency in the force/displacement response, even for the unfilled case presented in TEA capacity, 10% to 104% increases in CFE and improved structural stability during collapse when comparing similar tubing/foam core pairs.The performance metrics obtained from the experimental force/displacement responses are summarized in The following section contains analyses of the findings from DMR, in a given performance metric, Q, for the 10-bladed cutting (C10) mode compared to axial crushing (AC) was calculated for a specific tubing/foam pair asThe analyses in this section begin with a direct comparison  of the performance metrics obtained for the traditional axial crushing mode to the novel, compound 10-bladed cutting/foam crushing deformation mode. The relative change, TEA capacity refers to the average enhancement in TEA and mF since the DMR for these metrics, per the definitions from mF is essentially a scale factor of the TEA and thus should experience identical relative changes).The average values for this metric, which were referred to as enhancements since the 10-bladed cutting/clamping mode eclipsed the performance observed for axial crushing, are summarized in CFE, with peak values of 104% and 61% for the unfilled AA6061-T6 and AA6061-T4 tubes, respectively. The enhancements reduced but still remained above 10% for the considered scope, with the inclusion of H200 and H250 PVC foam cores since these configurations promoted tubing/foam interaction effects which disproportionately influenced the peak cutting forces. The overall effectiveness (EAEF), ψ, experienced an opposing trend of greater enhancements for the foam-filled configurations compared to the hollow tubes, with average values of 55% and 26%, respectively. The improvements in effectiveness were greater for the AA6061-T6 test groups, reflecting the ability of the novel 10-bladed cutting to eliminate the extensive brittle fractures observed for axial crushing. The increased TEA capacity and improved lateral stability for test groups considering AA6061-T4 tubing yielded 10% to 25% lower enhancements in effectiveness since the lateral kinking observed during the axial crushing test was less detrimental than the brittle fracture associated with the (higher-strength) T6 temper condition.The most dramatically improved performance metric for both temper conditions was the The temper condition of the extruded tubing significantly influenced the stability of the composite AA6061/PVC foam energy absorbers subjected to crushing, with structures containing the T4 temper condition influenced by uneven foam compression and subsequent lateral kinking. Sectioned views of a representative specimen post-test and the corresponding simulated profile are provided in The mentioned improvements in structural stability for the 10-bladed cutting/foam crushing deformation mode and consistency between T4 and T6 temper conditions are evident from an examination of the deformed cross-sections provided in EMR, in a given performance metric, Q, for energy absorbers composed of AA6061 tubes in the annealed, T4 temper condition compared to the as-received T6 temper condition can be quantified asThe relative change, CFEs, between 10% and 27%, due to the elimination of brittle lobe fracture. The TEA capacity of test groups composed of AA6061-T4 tubing was reduced, however, by only 9% on average, in contrast to the 35% difference between flow strengths for the T6 and T4 temper conditions. The tubes subjected to 10-bladed cutting/clamping exhibited more consistent behavior, with little difference  between CFE values when comparing temper conditions, further confirming the insensitivity of this deformation mode to the material pair. The EAEF and TEA capacity were reduced by 12% to 21% for the lower-strength T4 temper condition, with little variation between test groups, since brittle fracture did not occur for AA6061-T6 tubing subjected to the novel cutting/foam crushing deformation mode.The average values are summarized in FCR, were considered for a given test group/material pairing by assessing the evolution in each performance metric for the foam-filled tubing with respect to the unfilled, reference test case:The relative contributions associated with the presence of the PVC foam cores, TEA capacity increased by approximately 81% for the H250 foam-filled cases compared to the unfilled tubing, for the 10-bladed cutting mode compared to a corresponding 96% relative increase for the axial crushing mode. This relative difference was expected since the 10-bladed cutting/clamping mode was associated with higher energy-absorbing capacity , discussed further in The evolutions in this metric with increasing foam core density are summarized in CFE experienced a moderate decrease of approximately 20% for H250 foam-filled tubing subjected to the 10-bladed cutting/clamping  cases, since the collapse mechanisms remained stable for the considered tube/foam material pairs. Relative enhancements in the EAEF with increasing foam core density were highly similar between structures composed of T6 and T4 tempered extrusions  and H130, H200 and H250 foam-filled AA6061-T6 (as-received) tubing are provided in The interaction effects for composite structures composed of AA6061-T4 tubing subjected to 10-bladed cutting/clamping are provided in iE:Eη, defined in Equation (26), such that The total energy absorption for the composite AA6061/PVC foam structures in the present study can be generally expressed in terms of the following principal deformation mechanisms, The relative contributions of each principal deformation mechanism for the hollow and foam-filled AA6061 extruded tubing subjected to axial crushing (AC) and 10-bladed cutting/clamping (C10) are summarized in foamη, experienced a 78% relative increase across all test configurations with respect to an 86% increase in density. Relative contributions due to tube/foam interactions were notably less consistent between test groups. The composite structures composed of AA6061-T6 tubing presented with an initially marginal average contribution of 8% when subjected to axial crushing for the H130 foam-filled case and increased to 14% between the H200 and H250 groups, as shown in The axial compression of the foam cores presented with quasi-linear increases in the relative contribution toward TEA capacity which was nominally proportionate to the increasing density. For example, comparing the H130 and H250 foam-filled configurations, the contribution due to foam compression, The annealed, T4 temper condition  or exceeded by significant margins for the H130 foam-filled configurations. The relative enhancements in TEA capacity for composite AA6061/PVC foam structures subjected to 10-bladed cutting versus axial crushing increased, in all theoretical groups, with decreasing wall thickness and tube diameter. The mean force increased by a factor of 2 or greater when considering the lowest diameter/thickness pairs in all groups  and was marginally lower, between 5% and 20% reductions, for the groups with the largest tube geometry . High sensitivity to thin wall thicknesses and larger diameters, especially the trend of relative comparison metrics approaching equivalence with increasing tube profile/cross-section size, suggests that a greater presence of internal PVC foam cores diminishes the enhancing effect on TEA capacity. Furthermore, the relative enhancements were lower for tubes in the T6 temper condition since this material configuration experiences mean axial crushing forces which are not hindered/reduced by strain hardening, in contrast to the annealed T4 temper condition.The mean force anticipated for the 10-bladed cutting/clamping mode was either near-equivalent  anticipated for the 10-bladed cutting/clamping mode to absolute values well below 80%. The highest-density, H250 foam-filled composite structures correspondingly exhibited CFE values that were near-identical between the cutting and crushing deformation modes for the T6 temper condition  ratio of the composite structures subjected to 10-bladed cutting/clamping was found to increase compared to the traditional axial crushing mode for every considered case of AA6061-T6 tubing with H130, H200 and H250 foam fillers, illustrated by The data from the current study, obtained (in part) with a thoroughly validated analytical model , were suRecall from the previous subsection that the composite AA6061/PVC foam structures subjected to the compounded cutting/clamping deformation mode can also eclipse the mechanical performance of complementary structures subjected to axial crushing, which represents the current state of the art. A broad range of mean forces and specific energy absorptions were noted, with upper limits exceeding 100 kN and 50 kJ/kg, respectively. These high-capacity metrics can be achieved with ideal, near-constant reaction forces, and furthermore, the desired mechanical response, including the distribution of energy dissipation between the (cut) tubing and (crushed) foam cores, can be precisely engineered utilizing the numerical and theoretical modeling approaches from The impetus of this study was to assess the influence of extruded/foam core material pairing on the energy-absorbing capabilities, structural stability and overall effectiveness of a novel compounded axial cutting/foam crushing energy dissipation system utilizing composite AA6061/PVC foam structures, with complementary axial crushing experiments to enable direct comparisons to the current state of the art. The tubing was considered in as-received and annealed configurations to observe the potential extent and severity of brittle fracture during collapse, especially when interacting with newly considered, high-density  foam cores. The experimental testing and numerical modeling identified trends of increased energy-absorbing capacity and worsening structural stability with increasing foam core density for the AA6061/PVC foam structures subjected to axial crushing. The tubes with T6 temper conditions experienced brittle hinge fracture during collapse with a correspondingly more erratic force/displacement response. The observed fractures were generally more severe when PVC foam cores were added since lobe formation could not occur within the inner profile, diminishing the benefits that would be anticipated for this higher-strength material configuration. The complementary tubing in an annealed, T4 temper condition mitigated the lobe fracture but experienced lateral kinking and unstable shifting of the tube axes.TEA capacity, CFE and overall effectiveness (EAEF) of 14%, 44% and 52%, respectively, over the considered scope. The compounded cutting/foam crushing mode also efficiently mitigated erratic interaction effects since the extruded material remained intact above the cutters during collapse, promoting more consistent interactions.In contrast, the experimentally observed and numerically predicted deformation mechanisms for the 10-bladed cutting mode were highly consistent, exhibited no evidence of unstable/brittle fracture which is often characteristic of sacrificial aluminum structures and were nearly indistinguishable between each test group. This insensitivity to the extruded material/foam core pairing is a unique capability of the compounded cutting/foam crushing system, which is highly advantageous to structural safety applications, especially since the notoriously brittle nature of lightweight alloys can be effectively eliminated. The performance metrics observed for the 10-bladed cutting/clamping mode eclipsed corresponding values obtained for the axial crushing mode, with average relative enhancements in the mF, and compressive force efficiency, CFE, respectively, compared to the axial crushing mode. The improvements in TEA capacity were greater for composite structures composed of AA6061-T4 tubing since the annular support provided by the PVC foam cores promoted a higher-strength cutting response from this annealed alloy while the complementary T6 temper condition experienced greater CFE enhancements due to the elimination of brittle fracture. With a limited scope of geometries, particularly H250 foam-filled tubing with outer diameters exceeding 50.8 mm, the efficacy of the proposed 10-bladed cutting/foam crushing system was diminished. These limitations were associated with pronounced tube/foam interactions, which eliminated CFE enhancements, and excessive energy dissipation by the foam cores, reducing the role of the extruded material on TEA capacity. An Ashby plot summarizing the present results with respect to alternative technologies demonstrated the potential for the proposed compounded cutting/foam cutting system to significantly extend the loading envelope  for lightweight safety systems.A theoretical parametric study considering 294 individual material/geometric configurations promoted comprehensive comparisons between the compounded cutting/clamping and axial crushing deformation modes. The composite structures subjected to 10-bladed cutting/clamping could promote up to 90% and 185% enhancements in the mean force, To conclude, this study highlighted the versatility of the proposed 10-bladed cutting/foam crushing energy dissipation system by considering multiple geometries, extruded tubing/foam core material pairs and a thorough comparison to the traditional axial crushing deformation mode. The analyses are supported by experimental, numerical and analytical evidence which, most significantly, demonstrate that the compounded cutting/foam crushing system can achieve high-capacity energy absorption with idealized, near-constant reaction forces for a broad range of sacrificial material selections with disparate constitutive properties. This latter point is bolstered by the unique ability of this apparatus to absorb energy without imparting widescale brittle fracture on the lightweight, AA6061 extruded materials despite their moderate ductility. This novel ability to promote more stable collapse in lightweight materials is especially critical since many proposed energy dissipation modes cannot reliably transition away from traditional  materials due to this previous limitation. Therefore, these findings represent an important contribution toward the current state of the art which can more effectively enable the adoption of lightweight constitutive materials within sacrificial safety systems across numerous industrial sectors.