Breathing Subjective Decision Objective

Keywords:

The neuroscience of breathing The black asterisk indicates a significant difference in the occurrence of "unseen" following stimuli presented during inhalation versus exhalation. The orange asterisk indicates a significant difference between the occurrence of "unseen" and "seen" following stimuli presented during exhalation. For clarity, as we found no significant effect of breathing mode on perceptual awareness, we pooled nasal and oral modes together on the figure. c, Subjective decision speed (i.e., mean subjective RT) as a function of breathing mode and phase.

Scan me!

  1,2* , A. Coste 1 , C-E Benoit 3 , G. Derosiere 4,5 , S. Janaqi 1 , S. Perrey 1 , A. Dupeyron1,6

Figure 1 .

 1 Figure1. Inhalation improves perceptual awareness, without affecting subjective decision speed. a, The effect of breathing mode and phase on perceptual awareness and subjective decision speed. Red arrows indicate the significant effects observed. b, Perceptual awareness (i.e., average number of subjective choices) as a function of breathing phase by subjective experience. The black asterisk indicates a significant difference in the occurrence of "unseen" following stimuli presented during inhalation versus exhalation. The orange asterisk indicates a significant difference between the occurrence of "unseen" and "seen" following stimuli presented during exhalation. For clarity, as we found no significant effect of breathing mode on perceptual awareness, we pooled nasal and oral modes together on the figure. c, Subjective decision speed (i.e., mean subjective RT) as a function of breathing mode and phase.

Figure 2 .

 2 Figure 2. Inhalation speeds up objective decision-making, without affecting accuracy. a, The effect of breathing mode and phase on objective decision speed and accuracy. The red arrow indicates the significant effects observed. b, Objective decision speed (i.e., mean objective RT) as a function of breathing mode and phase. c, Objective decision accuracy (mean percentage of correct objective choices) as a function of breathing mode and phase.

Conscious Unconscious

The neuroscience of consciousness


Elsa Fristot

Thomas Bessede

Miguel Camacho Rufino

Pauline Mayonove

Hung- Ju Chang

Ana Zuniga

Anne-Laure Michon

Sylvain Godreuil

Je ´ro ˆme Bonnet
email: jerome.bonnet@inserm.fr

Guillaume Cambray
email: cambray.guillaume@gmail.com

An optimized electrotransformation protocol for Lactobacillus jensenii

Engineered bacteria are promising candidates for in situ detection and treatment of diseases. The female uro-genital tract presents several pathologies, such as sexually transmitted diseases or genital cancer, that could benefit from such technology. While bacteria from the gut microbiome are increasingly engineered, the use of chassis isolated from the female uro-genital resident flora has been limited. A major hurdle to implement the experimental throughput required for efficient engineering in these non-model bacteria is their low transformability. Here we report an optimized electrotransformation protocol for Lactobacillus jensenii, one the most widespread species across vaginal microflora. Starting from classical conditions, we optimized buffers, electric field parameters, cuvette type and DNA quantity to achieve an 80-fold improvement in transformation efficiency, with up to 3.5�10 3 CFUs/μg of DNA in L. jensenii ATCC 25258. We also identify several plasmids that are maintained and support reporter gene expression in L. jensenii. Finally, we demonstrate that our protocol provides increased transformability in three independent clinical isolates of L. jensenii. This work will facilitate the genetic engineering of L. jensenii and enable its use for addressing challenges in gynecological healthcare.

Introduction

The vaginal mucosa defines a rich and complex ecosystem that comprises millions of microorganisms collectively referred to as the Do ¨derlein flora [START_REF] Ravel | Vaginal microbiome of reproductive-age women[END_REF]. The healthy vaginal flora is mainly composed of lactobacilli (ca. 95% of the population). These bacteria have been shown to play important roles in preventing dysbiosis in favor of other anaerobic pathogenic bacteria, fungi and viruses, which are otherwise present at low abundance. In particular, lactic acid, hydrogen peroxide and other antimicrobial substances produced by these lactobacilli have been shown to inhibit the growth of pathogenic bacteria in the vagina and reduce sexually transmitted infections [START_REF] Osset | Role of Lactobacillus as protector against vaginal candidiasis[END_REF][START_REF] Dasari | Chapter 1-Recent Findings of Lactobacillus Diversity and Their Functional Role in Vaginal Ecosystems[END_REF]. Lactobacilli belong to the order of Lactobacillales, which regroups an ensemble of functionally related but phylogenetically different bacteria [START_REF] Ruzal | Lactobacillus Genomics and Metabolic Engineering[END_REF]. They are Gram-positive, facultative anaerobic, non-spore-forming bacteria. Their capacity to ferment a wide variety of sugars into lactic acid is at the root of wide-ranging adaptation to specific niches. Commensal lactobacilli species are particularly abundant on nutrient-rich mucous membranes and in food. These bacteria are thus highly prevalent within various human microbiomes, and several have been shown to contribute to the body's defense against pathogenic microorganisms [START_REF] Dasari | Chapter 1-Recent Findings of Lactobacillus Diversity and Their Functional Role in Vaginal Ecosystems[END_REF].

Broadly speaking, lactobacilli and other lactic acid bacteria hold great promises for various biotechnological and therapeutic applications (Fig 1A) [START_REF] Mays | Synthetic biology in probiotic lactic acid bacteria: At the frontier of living therapeutics[END_REF][START_REF] Zuo | Engineer probiotic bifidobacteria for food and biomedical applications-Current status and future prospective[END_REF]. Flagship examples include the development of probiotic treatments [START_REF] Van Pijkeren | Genome Editing of Food-Grade Lactobacilli To Develop Therapeutic Probiotics[END_REF] and in situ production of mucosal vaccines [START_REF] Mercenier | Lactic acid bacteria as live vaccines[END_REF].

Although providing an effective way to widen industrial applicability, the genetic engineering of these highly diverse lactobacilli species remains limited by notorious difficulties in developing efficient biotransformation procedures [START_REF] Zuo | Engineer probiotic bifidobacteria for food and biomedical applications-Current status and future prospective[END_REF][START_REF] Aune | Methodologies to increase the transformation efficiencies and the range of bacteria that can be transformed[END_REF][START_REF] Aukrust | Transformation of Lactobacillus by electroporation[END_REF][START_REF] Luchansky | Application of electroporation for transfer of plasmid DNA to Lactobacillus, Lactococcus, Leuconostoc, Listeria, Pediococcus, Bacillus, Staphylococcus, Enterococcus and Propionibacterium[END_REF]. To a large extent, this low transformability is linked to the thick peptidoglycan layer that covers their Gram-positive membrane. As the membrane composition and properties can vary substantially between species, transformation protocols must be optimized on an ad hoc basis.

Originally described in 1969 by Gasser et al. [START_REF] Gasser | Lactobacillus jensenii sp.nov., a new representative of the subgenus Thermobacterium[END_REF], Lactobacillus jensenii is prevalent in the majority of vaginal microbiomes characterized across a diverse sample of ethnic groups worldwide [START_REF] Ravel | Vaginal microbiome of reproductive-age women[END_REF]. In most of these groups, L. jensenii consistently represents ca. 20% of the vaginal flora. As such, L. jensenii would constitute a particularly suitable chassis for engineering the vaginal microbiota. However, functional knowledge regarding this species is particularly sparse. To the best of our knowledge, only two research groups have worked on L. jensenii engineering to date: Osel Incorporation has engineered a strain to secrete therapeutic effectors capable of reducing HIV infection [START_REF] Maxmen | Living therapeutics: Scientists genetically modify bacteria to deliver drugs[END_REF] and Hervana.bio [14] engineered a strain to secrete contraceptive molecules that recently entered clinical trials. While these achievements readily demonstrate the strong potential of this bacterium, most of the tools and techniques developed in these private ventures have not been made available to the wider scientific community, thus limiting its use for further biotechnological innovations.

In this work, we aimed at developing a transformation protocol sufficiently efficient to support the construction of medium-sized genetic libraries (i.e. at least 10 3 CFUs/μg DNA)in Lactobacillus jensenii (Fig 1B). Electroporation is the only effective method for the transformation of Gram-positive bacteria in general, and lactobacilli in particular [START_REF] Aune | Methodologies to increase the transformation efficiencies and the range of bacteria that can be transformed[END_REF][START_REF] Aukrust | Transformation of Lactobacillus by electroporation[END_REF][START_REF] Luchansky | Application of electroporation for transfer of plasmid DNA to Lactobacillus, Lactococcus, Leuconostoc, Listeria, Pediococcus, Bacillus, Staphylococcus, Enterococcus and Propionibacterium[END_REF]. Here, we started from protocols widely used for related Lactobacillus species [START_REF] Berthier | Efficient transformation of Lactobacillus sake by electroporation[END_REF][START_REF] Luchansky | Genetic transfer systems for delivery of plasmid deoxyribonucleic acid to Lactobacillus acidophilus ADH: conjugation, electroporation, and transduction[END_REF] and optimized several key parameters related to competent cell preparation and electroporation procedure (Fig 1C). We defined a transformation protocol that can yield up to 3.5�10 3 CFUs per microgram of plasmid DNA and is effective on multiple strains of L. jensenii. We further identified 2 unrelated plasmids that can be maintained in L. jensenii and used to drive expression of a reporter gene.

Material and methods

Strains and media

The reference strain of Lactobacillus jensenii used in this study is a vaginal isolate [START_REF] Gasser | Lactobacillus jensenii sp.nov., a new representative of the subgenus Thermobacterium[END_REF]ATCC 25258). Three other independent clinical isolates (Strain#1 ID: 99220272882; Strain#2 ID: 99220273430; Strain #3 ID: 99220254921) of Lactobacillus jensenii were obtained from hospital bioresource bank from patient suffering vaginal dysbiosis (Bacteriology lab, Arnaud de Villeneuve University hospital, Montpellier, France). Cells were grown in liquid MRS medium (De Man, Rogosa and Sharpe, DIFCO) at 37˚C in anaerobic conditions using GasPak anaerobic jar (BD GasPak™ EZ container systems), without agitation. MRS composition is as follow: peptone proteose: 10 g/L, beef extract: 10 g/L, yeast extract: 5.0 g/L, dextrose: 20 g/L, polysorbate 80: 1.0 g/L, ammonium citrate: 2.0 g/L, sodium acetate: 5.0 g/L, magnesium sulfate: 0.1 g/ L, manganese sulfate: 0.05 g/L, dipotassium phosphate: 2.0 g/L. When appropriate, erythromycin (E6376 Sigma-Aldrich) was added to the media at 0.5 μg/mL to select for transformants.

Lactobacillus jensenii ATCC 25258 erythromycin susceptibility test

L. jensenii ATCC 25258 susceptibility to erythromycin was determined by growing cells on MRS agar plate and MRS liquid medium supplemented with a range of antibiotic concentrations (0.5 μg/mL, 1.0 μg/mL, 2.5 μg/mL, 5.0 μg/mL, 7.5 μg/mL, and 10.0 μg/mL). Cultures were incubated for two days at 37˚C under anaerobic conditions in a GasPak jar before visual evaluation of growth.

Plasmid vectors

We selected 3 shuttle vector plasmids described in the literature as being widely portable among lactobacilli. pLEM415-ldhl-mRFP11 (a gift from Sujin Bao, Addgene plasmid # 99842) is a pBLUESCRIPT derivative carrying an unnamed lactobacilli origin of replication, a highcopy version of the E. coli colE1 origin of replication, an erythromycin resistance gene and a mRFP1 expression cassette. pTRKH2 (kind gift from Rodolphe Barrangou & Todd Klaenhammer, Addgene plasmid #71312) is a theta replicative plasmid carrying a pAMβ1 origin, a p15A E. coli replication origin and an erythromycin resistance gene Erm(B). pTRK892 (kind gift from Rodolphe Barrangou & Todd Klaenhammer, Addgene plasmid #71803) is a high copy shuttle vector bearing a pWVO1 replication origin that is functional in both gram negative and positive species. pTRK892 also carries a GusA reporter cassette under ppgm promoter and erythromycin Erm(C) resistance gene.

Competent cells preparation

Optimized preparation of competent cells from L. jensenii ATCC 25258 and the three clinical isolates is performed as follows. Cells are grown overnight in 50 mL MRS at 37˚C without agitation. 98 mL of fresh MRS medium is then inoculated with 2 mL of the overnight culture and incubated at 37˚C without shaking to an OD of 0.5-0.6 (ca. 4-5 hours) in a GasPak anaerobic jar (BD GasPak™ EZ container systems). Cells are harvested a first time by centrifugation at 4,000 g for 5 min. From then on, cells are always maintained on ice or at 4˚C in refrigerated centrifuges. Supernatant is discarded and pelleted cells resuspended in 15 mL ice-cold 3X SMEB electroporation buffer (1X Sucrose Magnesium Electroporation Buffer: 298 mM sucrose, 1 mM MgCl2 in cold sterile water), and centrifuged at 4,500 g for 7 min. This procedure is repeated twice. Cell pellets are then concentrated in 1.0 mL of ice-cold 3X SMEB buffer and 200 μL aliquots can be placed at -80˚C for long term storage or alternatively used directly for electroporation up to one hour after preparation.

Electroporation

A GenePulser X Cell apparatus (Bio-rad Laboratories, Richmond, CA) was used for all electroporation experiments. The final optimized electroporation procedure is as follows: 200 μL competent cells are thawed on ice, transferred in a 0.2 cm electroporation cuvette (Bio-rad Laboratories, Richmond, CA) after addition and gentle mixing of 1 μg of DNA, and incubated on ice for 10 minutes. Cells are electroporated after drying the electrodes with a clean paper wipe using the following parameters: 12.5 kV/cm, 400 Ohm and 25 μF capacitance. Efficient electroporation events show a time constant in the 8.0-10.5 ms range. Directly after the electric pulse, cells are rapidly and gently resuspended in 800 μL antibiotic-free MRS medium preheated at 37˚C and transferred to culture tubes for a 3 hours incubation period at 37˚C without shaking in GasPak containers. 100 μL of the resulting culture is then spread on MRS agar plate (1% agar) supplemented with 0.5 μg/mL erythromycin using glass beads (0.4 cm diameter). As necessary, all cells can also be concentrated by centrifugation at 4,000 g for 5 min and gently resuspended in 100 μL MRS before spreading.

Transformation efficiencies were calculated after counting colonies upon 48 hours of incubation at 37˚C in GasPak containers. Effective transformation of L. jensenii was confirmed by liquid culture-based PCR targeted to the 16S RNA gene and to a segment of the plasmid pTRKH2, as well as by beta-glucuronidase assays for plasmid pTRK892. Primers sequences are listed in S1 Table.

Liquid culture-based PCR

Colonies were inoculated in 1 mL MRS supplemented with 0.5 μg erythromycin and grown for 24h at 37˚C in a GasPak jar without shaking. Cultures were centrifuged at 5,000 g for 5 min and the pellet resuspended in 100 μL PBS. One microliter of this concentrated culture was then used to perform verification colony PCR using the KAPA polymerase (Biosystem), following the vendor's instructions.

Beta-glucuronidase reporter assays

pTRK892 transformation was confirmed by assaying the activity of the beta-glucuronidase GusA. Colonies obtained upon electrotransformation of pTRK892 were used to inoculate 1 mL MRS culture supplemented with 0.5 μg erythromycin. Cultures were grown for 48h at 37˚C in a GasPak jar without shaking and centrifuged at 6,000 g for 5 minutes. Supernatants were discarded and pellets were resuspended in 400 μL resuspension buffer (50 mM NaH2PO4). Samples were then incubated for 30 minutes at 37˚C after addition of 25 μL permeabilization solution (9:1 acetone to toluene v/v). Beta-glucuronidase activity was evaluated qualitatively by visual observation of a green to blue coloration of the samples 30 minutes after addition of 5 μL of X-gluc stock solution (10 mg/mL in DMSO; Sigma Aldrich).

Results

Choice of plasmids and initial transformation conditions

Accurate measurements of transformation efficiency rely on the maintenance of the transformed plasmids by recipient cells, as well as the expression of phenotypes that can be used to select and/or identify transformants. As most functional genetics of L. jensenii was performed in the context of private research endeavors, little information regarding which plasmids might be suitable for this species is publicly available. We thus selected three vectors that bear replication origins that are widely functional in other lactobacilli species and that are readily available on Addgene: pTRKH2, pTRK892, and pLEM415-ldhl-mRFP1. All these plasmids comprise an expression cassette conferring resistance to erythromycin (see Table 1

, Material and Methods and S1 Fig).

We started by testing two widely used-but largely different-transformation protocols for lactobacilli initially reported by Berthier et al. [START_REF] Berthier | Efficient transformation of Lactobacillus sake by electroporation[END_REF] and Luchansky et al. [START_REF] Spangler | Broad range shuttle vector construction and promoter evaluation for the use of Lactobacillus plantarum WCFS1 as a microbial engineering platform[END_REF] using the vector pTRKH2 (Material and Methods). After growing electroporated bacteria on MRS agar plates and liquid cultures tubes supplemented with increasing concentrations of erythromycin, we determined that a working concentration of 0.5 μg/mL enabled unambiguous selection of transformant cells in MRS. In these conditions, the Luchansky protocol resulted in significantly more transformants, though the absolute number of colonies obtained remained 1). This prompted us to use the Luchansky protocol with plasmid pTRKH2 as a starting point to optimize the transformation of L. jensenii ATCC 25258.

Protocol optimization for improved L. jensenii transformation

Using a greedy hierarchical optimization strategy, we successively varied several parameters previously reported to impact electrotransformation of Lactobacilli in different sources [START_REF] Luchansky | Application of electroporation for transfer of plasmid DNA to Lactobacillus, Lactococcus, Leuconostoc, Listeria, Pediococcus, Bacillus, Staphylococcus, Enterococcus and Propionibacterium[END_REF][START_REF] Berthier | Efficient transformation of Lactobacillus sake by electroporation[END_REF][START_REF] Luchansky | Genetic transfer systems for delivery of plasmid deoxyribonucleic acid to Lactobacillus acidophilus ADH: conjugation, electroporation, and transduction[END_REF][START_REF] Chang | Guide to Electroporation and Electrofusion[END_REF]: (i) Buffer concentration, (ii) Glycine concentration, (iii) cuvette length, and (iv) strength of the electric field (Fig 1C). Using 0.1 cm electroporation cuvettes and electric field parameters as described in Luchansky et al. [START_REF] Luchansky | Genetic transfer systems for delivery of plasmid deoxyribonucleic acid to Lactobacillus acidophilus ADH: conjugation, electroporation, and transduction[END_REF], we first varied the concentration of the SMEB buffer between 1 and 3X. We found that transformation efficiency increased with concentration, yielding up to 4.8�10 2 CFUs/μg on average with the 3X buffer (an 8-fold improvement; Fig 2B). Higher concentrations led to the formation of electric arcs that killed the cells, producing no transformants.

We next investigated the addition of glycine, which is known to weaken the bacterial cell wall [START_REF] Chang | Guide to Electroporation and Electrofusion[END_REF]. Using a 3X SMEB concentration, we tested different glycine weight/volume ratio (0.0%, 0.5%, 1.0%, 1.5% and 2.0%) and observed a non-monotonic impact on transformation efficiency with a maximum average of 7.5�10 2 CFUs/μg obtained with 2.0% glycine (Fig 2C). Higher glycine titers led to markedly reduced growth rate in liquid culture (and eventually to cell death for glycine titers over 5.0%) [START_REF] Chang | Guide to Electroporation and Electrofusion[END_REF].

We next replaced the 0.1 cm cuvettes by 0.2 cm cuvettes (Fig 3A). This improved the average transformation efficiency to 1.4�10 3 CFUs/μg of plasmid on average. This 2.5-fold improvement over 0.1 cm cuvettes strikingly mirrors the increased quantity of cells loaded into the cuvette (from 80 to 200 μL of competent cells).

We then measured the impact of using increasing quantities of plasmid DNA, from 0.5 μg to 4.0 μg DNA per transformation (Fig 3B). While we observed a spectacular improvement from 0.5 μg to 1.0 μg, increasing DNA quantities over this value did not yield major improvements, but increased the likelihood of electric arc formation. Finally, we tested the impact of varying the strength of the electric field from 1.0 to 12.5 kV/cm using 1 μg DNA, and found that increasing the pulse's voltage improved transformation efficiency (Fig 3C).

Our final transformation procedure, which consists in using 3X SMEB buffer, 1 μg of DNA, 2% glycine, 0.2 cm cuvette with 12.5 kV/cm voltage, yields a transformation efficiency close to 2�10 3 CFUs/μg of plasmid, exceeding our target efficiency of 10 3 with plasmid pTRKH2. We then proceeded to re-test the transformation of the 2 other vectors: pTRK892 led to slightly better results than pTRKH2, while pLEM415 yielded a 100-fold lower transformation efficiency, indicating the origin of replication as an important choice for better transformation efficiency (Fig 4A). We thus obtained with pTRK892 a maximum transformation efficiency of 3.5�10 3 CFUs/μg plasmid. The final protocol is fully detailed in S1 Protocol.

To verify that the colonies selected upon transformation corresponded to L. jensenii ATCC 25258 bearing a plasmid, we performed PCRs targeted to the 16S RNA gene and to a segment of pTRKH2 on 16 randomly picked colonies (see Material and Methods). All putative transformants yielded amplicons of the expected sizes. We also used a beta-glucuronidase assay on isolates transformed with pTRK892. The production of a blue color from the processing of substrate X-Gluc confirmed the successful expression of the gusA reporter gene by the transformed cells (Fig 4B). Finally, in an effort to assess whether our optimized protocol is generally effective in other L. jensenii isolates, we subjected three independent clinical isolates of L. jensenii to both the original and optimized electroporation procedures. Although a lower absolute number of transformants were obtained as compared to the reference strain, our optimized protocol afforded a 28-fold increase in transformation efficiency on average across these isolates (Fig 4C). These data suggest that our protocol can be of general use for engineering clinical isolates of L. jensenii.

Discussion

In this work, we optimized the transformation of Lactobacillus jensenii, a natural resident of the vaginal microflora and promising candidate chassis for vaginal microbiome engineering. We started with the protocol originally developed by Luchansky et al. [START_REF] Luchansky | Genetic transfer systems for delivery of plasmid deoxyribonucleic acid to Lactobacillus acidophilus ADH: conjugation, electroporation, and transduction[END_REF] for the Lactobacillus group to which L. jensenii belongs, which only yielded a few dozen of clones (4.7�10 1 ). After optimization of both competent preparation and electroporation conditions, we could obtain several thousands of transformants (3.5�10 3 CFUs/μg plasmid on average with pTRK892). This improved efficiency will enable the construction and further screening of genetic libraries. Such libraries can be used for relatively high-throughput genetic engineering approaches, such as the establishment of collections of genetic elements involved in the regulation of gene expression [START_REF] Kosuri | Composability of regulatory sequences controlling transcription and translation in Escherichia coli[END_REF], or the screening of combinatorial gene circuits [START_REF] Smanski | Functional optimization of gene clusters by combinatorial design and assembly[END_REF]. Although the optimized procedure improves transformation efficiencies across unrelated strains of L. jensenii, additional fine-tuning would be necessary to maximize the absolute number of transformants obtained for any particular strain. Nevertheless, the transformation of multiple clinical isolates suggests the possibility of a personalized medicine approach for engineering microbiome therapeutics, with increased chances of successful colonization and a better resilience of the therapeutic strain in the natural flora environment.

In this work, we followed a simple greedy optimization procedure, wherein parameters are optimized sequentially using the best values identified in prior iterations. More refined Design of Experiment approaches [START_REF] Mandenius | Bioprocess optimization using design-of-experiments methodology[END_REF], which are less susceptible to converging toward local optima, could be explored in future studies to access even higher efficiencies. A major factor hindering transformation that we have not explored here is the presence of restriction-modification systems in recipient bacteria. Several approaches-such as the heterologous expression of the recipient's putative methylases in the plasmid-producing strain or the in vitro methylation of purified plasmids using a range of commercially available enzymes-could be attempted to further improve our protocol [START_REF] Zuo | Engineer probiotic bifidobacteria for food and biomedical applications-Current status and future prospective[END_REF]. Throughout this study, we observed some variation in transformation efficiencies across replicates. Some variability is expected in transformation efficiency within and mostly between different batches due to differences in growth, maintenance of the cold chain during cell preparation, storage and time before utilization. L. jensenii is microaerophilic and facultatively anaerobic. All experiments reported in this work were performed in GasPak anaerobic jars (5% CO 2 ), as we found these conditions to dramatically improve cell growth and competence. We initially attempted to culture cells in hermetic boxes with candles to create microaerophilic conditions (ca. 1-3% CO 2 ) (S2 Fig) . While these conditions led to poorer performances, they nonetheless represent a workable alternative to the expensive GasPak system. Such an alternative might not be transposable to stricter anaerobes. Best performances were obtained with freshly prepared cells. We observed a dramatic drop in efficiency after 4 months of storage at -80˚C, but only noticed a marginal decrease after 3 months. We thus recommend that cells are stored for no longer than 3 months. In these conditions, our protocol proved robust on different batches, storage conditions, consistently yielding at least a thousand transformants.

We showed that the two related plasmids pTRKH2 and pTRK892 (both developed by the Klaenhammer lab) provide good transformation efficiencies, with the latter yielding slightly more transformants (ca. 3500 vs ca. 2000). These data demonstrate that the regulatory elements driving the expression of Erm(B) (pTRKH2) and Erm(C) (pTRK892), as well as the ppgm promoter [START_REF] O'sullivan | High-and low-copy-number Lactococcus shuttle cloning vectors with features for clone screening[END_REF][START_REF] Spangler | Broad range shuttle vector construction and promoter evaluation for the use of Lactobacillus plantarum WCFS1 as a microbial engineering platform[END_REF][START_REF] Duong | Construction of vectors for inducible and constitutive gene expression in Lactobacillus[END_REF] and the ribosome binding site associated with the gusA reporter gene are all functional in L. jensenii. These elements can readily be used to express proteins of interest in future studies. The observed difference in efficiencies might be linked to differential effective activities of erythromycin resistance proteins produced from the two plasmids. Indeed, the promoter of Erm(B) is known to be positively regulated by erythromycin and might be weaker than Erm(C). The replication origin and mechanism might also play an important role, pTRKH2 carrying the pAMB1 rolling circle replication origin and pTRK892 carrying the pWVO1 theta replication origin. To the best of our knowledge, pLEM415-ldhl-mRFP1 is the most frequently used plasmid reported as functional in L. jensenii [START_REF] Chang | Inhibition of HIV infectivity by a natural human isolate of Lactobacillus jensenii engineered to express functional two-domain CD4[END_REF]. Interestingly, it could only be transformed with moderate efficiency in our hands. Since it is approximately the same size as other plasmids tested in this work, this low performance could be attributed to a poorly functional replication origin, which is more difficult to assess as it has not been well described [START_REF] Bao | Distribution dynamics of recombinant Lactobacillus in the gastrointestinal tract of neonatal rats[END_REF].

While our work provides a first step towards enabling routine engineering of L. jensenii, many additional tools must be developed. For example, parts collections to control gene expression (such as promoters and RBS libraries with different strengths) will be needed to engineer genetic circuits operating reliably and with high precision [START_REF] Mutalik | Quantitative estimation of activity and quality for collections of functional genetic elements[END_REF][START_REF] Guiziou | A part toolbox to tune genetic expression in Bacillus subtilis[END_REF]. Chromosomal integration toolkits are also necessary to ensure stable genetic circuit maintenance without antibiotic selective pressure [START_REF] Zuo | Inducible Plasmid Self-Destruction (IPSD) Assisted Genome Engineering in Lactobacilli and Bifidobacteria[END_REF]. Finally, biocontainment, ethical and societal issues will need to be addressed before the use of stably engrafted engineered microbes becomes widespread. By enabling efficient plasmid transformation, our work provides a means to tackle these and other challenges in Lactobacillus jensenii.

Fig 1 .

 1 Fig 1. Potential applications to vaginal microbiota engineering and electroporation optimization. A. Potential applications of engineering the vaginal microbiota.B. L. jensenii is a candidate to develop genetically engineered probiotics for the vaginal microflora. Electrotransformation is the most effective method to transform DNA into Lactobacillus spp. C. Parameters described as important to optimize electroporation in lactic acid bacteria that were tested in this study. https://doi.org/10.1371/journal.pone.0280935.g001

Fig 2 .

 2 Fig 2. Optimization of competent cells preparation for L. jensenii ATCC25258 using pTRKH2. A. Comparison of widely used electroporation protocols for Lactobacillus spp. Shown are transformation efficiency of Lactobacillus jensenii observed using original protocols described by Luchansky et al. (protocol 1) [22] and Berthier et al. (protocol 2) [21]. B. Increasing buffer concentration improves transformation efficiency. Shown are transformation efficiency of electrocompetent L. jensenii prepared at 1, 2 or 3X the concentration described in Luchansky et al. [16]. More concentrated buffers led to arcing. C. Addition of glycine improves transformability. Shown are transformation efficiency of electrocompetent L. jensenii prepared in 3X buffer with increasing titers of glycine (expressed as weight to volume percentage). Titers higher than 2.0% lead to markedly reduced growth rate. All electroporation were performed with 1 μg pTRKH2 in 0.1 cm electroporation cuvettes and electric parameters as follows: voltage: 6.5 kV/cm, resistance: 600 Ohm, capacitance: 25 μF. 3 biological replicates of 3 technical replicates were performed on different days (data are shown in S2 Table). Technical replicates are shown in the same color. (Wilcoxon signed-rank test p-value, ns p > 0.05, � p < = 0.05, �� p < = 0.01, ��� p < = 0.001 and ���� p < = 0.0001). https://doi.org/10.1371/journal.pone.0280935.g002

Fig 3 .

 3 Fig 3. Optimization of electroporation procedure for L. jensenii 25258 using pTRKH2 vector. A. Increasing electroporation cuvette size yields a 2.5-fold increase in transformation efficiency. Shown are transformation efficiency of electrocompetent L. jensenii in 0.1 cm or 0.2 cm cuvette gap size. B. Increasing DNA quantity impacts transformation efficiency in a step-like manner. Shown are transformation efficiency of electrocompetent L. jensenii electroporated in 0.2 cm cuvettes with different DNA quantities, as indicated. Quantities above 4 μg (or volume above 5 μL) frequently result in electric arcs. C. Increasing electric pulses' voltage improves transformation efficiency. Shown are transformation efficiencies for electrocompetent L. jensenii electroporated in 0.2 cm cuvettes with 1 μg DNA at different voltage intensities, as indicated. Increasing the voltage above 12.5 KV/cm causes arcing and kills the cells. All electroporations were carried with vector pTRKH2, 3X SMEB, 2% glycine, 6.5 kV/cm voltage (unless otherwise indicated), 400 O resistance, 25 μF capacitance. 3 biological replicates of 3 technical replicates were performed on different days (data are shown in S2 Table). Technical replicates are shown in the same color. (Wilcoxon signed-rank test p-value, ns p > 0.05, � p < = 0.05, �� p < = 0.01, ��� p < = 0.001 and ���� p < = 0.0001). https://doi.org/10.1371/journal.pone.0280935.g003

Fig 4 .

 4 Fig 4. Optimized transformations of various vectors and unrelated L. jensenii strains. A. Transformation efficiency of different plasmids using the optimized protocol. Shown are transformation efficiencies obtained for plasmids pTRKH2, pTRK892 and pLEM415-ldhl-mRFP1. While pTRKH2 and pTRK892 yield similarly high efficiencies, the unrelated pLEM415 yields a measurable but moderate number of transformants. Numbers above bars represent the average number of transformants. B. Beta-glucuronidase assay with Lactobacillus jensenii pTRK892 transformants showed blue coloration after addition of X-GLU substrate. C. The optimized electroporation procedure is efficient across unrelated strains of L. jensenii. Shown is a comparison of transformation efficiencies obtained with the Luchansky [22] and optimized procedure with different clinical isolates. All electroporations were carried with 1.0 μg of DNA, 3X SMEB, 2% glycine, in 0.2 cm cuvettes and electric parameters as follows: voltage: 12.5 kV/cm, resistance: 400 O, capacitance: 25 μF. 3 biological replicates of 3 technical replicates were performed on different days (data are shown in S2 Table). Technical replicates are shown in the same color. (Wilcoxon signed-rank test p-value, ns p > 0.05, � p < = 0.05, �� p < = 0.01, ��� p < = 0.001 and ���� p < = 0.0001). https://doi.org/10.1371/journal.pone.0280935.g004

Table 1 . Designation, characteristics and transformation frequency of plasmids tested in Lactobacillus jensenii ATCC 25258.

 1 We next attempted electroporation of the two other vectors, but could only obtain transformants with pTRK892, even under lower antibiotic pressure (Table

	Plasmid	Resistance	Copy number	Size	Origin	Source	Ref	Average transformation frequency
								before optimization	After optimization
	pTRKH2	Erm B	High copy	6,719	pAMβ1	Addgene	21	4.7 x 10 1	2.0 x 10 3
	pTRK892	Erm C	High copy (gram -)	6,470	pWV01	Addgene	22, 23	3.2 x 10 1	3.5 x 10 3
			Low copy (gram +)
	pLEM415-ldhl-mRFP1	Erm	High copy	7,357	L. fermentum	Addgene	24, 25	1.2 x 10 1	3.3 x 10 1

Abbreviation: Erm, erythromycin 0.5 μg/mL in Lactobacillus jensenii. Transformation efficiency are expressed as erythromycin resistant colonies forming unit per μg of plasmid (CFUs/μg). https://doi.org/10.1371/journal.pone.0280935.t001 relatively low (4.7�10 1 CFUs/μg plasmid on average; Fig 2A).

PLOS ONE | https://doi.org/10.1371/journal.pone.0280935February 17, 2023

Acknowledgments

We thank Pascale Serror (Micalis, Jouy-en-Josas, France) for insightful advice on lactobacilli. We thank members of our research groups and the CBS for fruitful discussions. We also thank the iGEM team Montpellier 2018, whose Vagineering project originally motivated this study. The team was composed of Le ´a Meneu, Elsa Fristot, Tamara Yehouessi, Younes Babaaziz, Marie Peras, Julien Mathieu, Leo Carrillo, Miguel Camacho Rufino, and Maxime Heintze

´.

JB acknowledges support from the INSERM Atip-Avenir program (https://www. inserm.fr/en/about-us/atip-avenir-program) and the Bettencourt-Schueller Foundation (https:// www.fondationbs.org). GC acknowledges support from the CNRS Atip-Avenir program (https://www. insb.cnrs.fr/fr/atip-avenir). The CBS acknowledges support from the French Infrastructure for Integrated Structural Biology (FRISBI, https://frisbi. eu/; ANR-10-INSB-05-01). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

All relevant data are within the paper and its Supporting Information files.

Supporting information

Methodology: Elsa Fristot, Hung-Ju Chang, Ana Zuniga, Je ´ro ˆme Bonnet, Guillaume Cambray.

Project administration: Pauline Mayonove, Je ´ro ˆme Bonnet, Guillaume Cambray.

Resources: Anne-Laure Michon, Sylvain Godreuil, Je ´ro ˆme Bonnet, Guillaume Cambray.

Supervision: Je ´ro ˆme Bonnet, Guillaume Cambray.

Validation: Je ´ro ˆme Bonnet, Guillaume Cambray.

Visualization: Elsa Fristot, Je ´ro ˆme Bonnet, Guillaume Cambray.

Writing -original draft: Elsa Fristot, Je ´ro ˆme Bonnet, Guillaume Cambray.

Writing -review & editing: Elsa Fristot, Je ´ro ˆme Bonnet, Guillaume Cambray.


Krzysztof K Dudek

Julio A Iglesias Martínez

Gwenn Ulliac

Laurent Hirsinger

Lianchao Wang

Vincent Laude

Muamer Kadic
email: muamer.kadic@femto-st.fr

Micro-scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation

Keywords: Mechanical Metamaterials, Auxetics, Micro-scale, Phonons, Band-gaps, Stimuli-responsive

The ability to significantly change the mechanical and wave propagation properties of a structure without rebuilding it is currently one of the main challenges in the field of mechanical metamaterials. This stems from the enormous appeal that such tunable behavior may offer from the perspective of applications ranging from biomedical to protective devices, particularly in the case of microscale systems. In this work, a novel micro-scale mechanical metamaterial is proposed that can undergo a transition from one type of configuration to another, with one configuration having a very negative Poisson's ratio, corresponding to strong auxeticity, and the other having a highly positive Poisson's ratio. The formation of phononic band gaps can also be controlled concurrently which can be very useful for the design of vibration dampers and sensors. Finally, it is experimentally shown that the reconfiguration process can be induced and controlled remotely through application of a magnetic field by using appropriately distributed magnetic inclusions.

Introduction

Over the years, the importance of functional materials [1,2,3,4,5,6,7,8,9,10,11] has increased rapidly in our everyday lives. Most prominently in the span of the last two decades, different classes of these structures have been successfully implemented in numerous industries including biomedical [12,13] and protective devices [14,15,16], sports equipment [17] as well as electronics [18,19]. One of the most promising fields of study relating to such easily-applicable functional materials is that of mechanical metamaterials [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. Mechanical metamaterials are rationally designed structures that can exhibit counterintuitive mechanical properties based primarily on their design rather than their chemical composition. The most studied cases and well-known examples of metamaterials with extraordinary mechanical properties pertain to those with negative properties such as a negative Poisson's ratio (auxetic behavior) [20,38,39,40,41], negative stiffness [42,43,44,45] and negative compressibility [42,46,47,48]. Most notably, auxetic mechanical metamaterials have been proven to exhibit superior indentation resistance [49], energy absorption [50,51] and wave attenuation [14,52] in comparison to many conventional non-auxetic materials. However, despite the numerous advantages offered by mechanical metamaterials characterized by a negative value of Poisson's ratio, the vast majority of such structures share an important limitation. Namely, once typical auxetic metamaterials are manufactured, it is very difficult to change their mechanical characteristics without rebuilding the system. This, in turn, diminishes their applicability in fields where a variable response of the material is required. Nevertheless, as reported in recent years, this shortcoming can be addressed by the use of active mechanical metamaterials in the form of stimuli responsive structures.

Active mechanical metamaterials are structures that can exhibit a tunable mechanical behavior which depends on the application of an external stimulus. In recent years, it has been demonstrated that in the case of multi-material structures, the mechanical properties of the system can be adjusted remotely in a process that does not require reconstruction of the system. In the case of macroscopic systems, one of the most promising approaches used corresponds to the use of appropriately distributed inclusions in a form of magnets that respond to the application of an external magnetic field [53,54]. However, this task becomes much more challenging at small scales. In these cases, one of the more feasible approaches which may be used is to utilise composite materials incorporating magnetic nanoparticles dis-persed within a non-magnetic matrix [10,55,56,57]. Another possible approach involves the use of several materials with different thermal expansion coefficients. In such a case, the behavior of the structure can be modified by changing the external temperature [56,58]. This method, however, often does not allow one to obtain a very significant variation in the mechanical properties. In addition, the corresponding reconfiguration process tends to be quite slow. Last but not least, it is worth noting that it is possible to construct an active metamaterial composed of only one type of residual material that, to some extent, can undergo a change in its mechanical properties with a deformation pattern based solely on the variation of the mechanical stimulus, e.g. the rate of mechanical compression. A prime example of this approach corresponds to hierarchical metamaterials [59,[START_REF] Cho | Proc. Natl. Acad. Sci[END_REF][START_REF] Tang | [END_REF]62,63,64,65], where different hierarchical levels can deform independently of each other. Despite several notable achievements, studies devoted to active mechanical metamaterials are still in their infancy and a far more in-depth analysis is required to fully harness their potential. First of all, it is important to emphasize that for a significant number of known active mechanical metamaterials, although it is possible to change one of their properties without rebuilding the system; this is very difficult to achieve whilst retaining control over the other properties. This problem is exacerbated further at small scales, such as the micro-scale, where the manufacturing process is often not only very difficult but also fairly expensive. On the other hand, despite these challenges, the ability to achieve simultaneous tunable control over multiple properties of a micro-scale system without the need for reconstruction is a very appealing concept that could be utilized in fields such as programmable robotics, vibration dampers / sensors and effective biomedical devices. In fact, in the literature [66], there are some rare examples demonstrating the possibility of simultaneously controlling several properties of micro-scale mechanical metamaterials. Some of the most promising studies describe the possibility of controlling Poisson's ratio [64] as well as wave propagation properties with an emphasis on tunable band gap formation [52,67,68]. However, despite their numerous advantages, such studies typically focus on complex hierarchical structures where the deformation process is not easily recoverable nor controlled due to the presence of multiple independently-deforming hierarchical levels. Furthermore, in most cases, it is also not possible to observe a large tunable change in the Poisson's ratio of the system, which significantly decreases the applicability of these systems.

In this work, a novel mechanical metamaterial is proposed that can be defined in the form of two distinct configurations. The considered structure can undergo a transition from one type of configuration to another during which the Poisson's ratio varies very significantly; without the need to rebuild the system. Namely, the change occurs from a structure possessing a positive Poisson's ratio to a strongly auxetic structure and vice versa. In addition, it is shown that a change in the configuration of the system can be used to achieve control over the formation of a phononic band gap. Finally, it is shown that all configurations of the considered system are realizable at the micro-scale, with experimental tests demonstrating a possibility of the reconfiguration of the structure through the use of an external magnetic field.

Results and Discussion

In this work, a novel mechanical metamaterial composed of triangle-shaped structural elements is proposed in order to assess its potential to exhibit versatile mechanical and wave propagation properties. As shown in Fig. 1a, the considered system can occur in two very different configurations, hereafter referred to as Type A and Type B structures. In the case of the Type A configuration, the system consists of two types of isosceles triangles connected to each other at the vertices. Due to this specific connectivity, the geometry is characterized by three different types of apertures. In contrast, the configuration denoted as Type B has a more regular design and consists of only one type of isosceles triangles. In fact, it resembles a lattice of mutually connected star-shaped elements where each of these elements consists of six triangles. The two configurations were designed in this specific manner in order to ensure that during mechanical deformation they would exhibit very different Poisson's ratios. This concept is depicted schematically in Fig. 1a, where qualitatively, Type A and Type B structures exhibit strongly negative (auxetic behavior) and positive Poisson's ratio, respectively.

In order to investigate the mechanical properties of the two considered configurations and to demonstrate that the proposed concept can be utilized in the case of microscopic applications, experimental prototypes were constructed at the micro-scale (see Methods section). More specifically, as shown in Fig. 1b, in order to assess the effect of the geometric parameters on the behavior of the structures, three different prototypes were fabricated for each configuration; labeled A1, A2, A3 and B1, B2, B3. In fact, the only difference between the three Type A structures is the value of the d parameter. Similarly, the only difference between the Type B prototypes is the value of the b parameter. All prototypes are composed of 5 × 3 unit-cells, where the bottom part of the system is clamped as a result of the manufacturing process (see Methods section).

Mechanical Properties

To determine the Poisson's ratio of the considered systems, the microscopic experimental prototypes were compressed by a flat external indenter along the y-axis, with the bottom part of each sample re-maining fixed in space. Thus, to qualitatively estimate the Poisson's ratio of the system, one can follow the changes in the horizontal dimension of the topmost part of each structure. More specifically, for all prototypes, the topmost section is unaffected by the bottom constraint due to being very far from the substrate on top of which samples were printed. Hence, the expansion or shrinkage of the x dimension of the fabricated prototypes subjected to the compression along the y-axis indicates the sign of Poisson's ratio. From the optical images of the experiment presented in Fig. 2a, one can note from the qualitative analysis that prototypes corresponding to Type A and Type B exhibit very different behaviors. Namely, the x dimension for all the prototypes with a Type A configuration decreases significantly during the compression process which is an indication of strong auxetic behavior. In contrast, for the Type B structures, the horizontal dimension of the samples slightly increases during the deformation process. Such behavior is an indication of a weakly positive Poisson's ratio. This means that Type B configurations exhibit a non-auxetic behavior unlike the Type A samples. At this point, it should be emphasized that the non-uniform deformation of the entire system originates from the fact that the experimental samples remain attached to the substrate after the 3D printing process. However, if one was to consider the deformation of the detached sample, the extent of non-uniformity would be significantly smaller. Nonetheless, mechanical testing could potentially become unreliable in such a scenario due to the very small size of the system. It is also worth emphasizing that if fabricated through the use of appropriate materials, the considered system can maintain its properties over numerous deformation cycles (see Fig. S1 in the Supplementary Information). This, in turn, further enhances its appeal from the perspective of potential applications.

In addition to the qualitative description of the behavior of the system, it is important to conduct a quantitative analysis in order to determine the range of Poisson's ratio values and to assess its usefulness in the case of specific applications. To this aim, in order to calculate the Poisson's ratio for each structure, the central unit-cell was taken into consideration. This stems from the fact that the mechanical behavior of this specific unit-cell is the least affected by edge effects contributing to the uneven deformation pattern. More specifically, the deformation of the central unit-cell is not significantly affected by the bottom part of the system being attached to the substrate. In addition, its behavior is also mostly unaffected by the unbounded left and right-hand sides of the structure as well as any friction imparted through contact of the topmost part of the system with the indenter inducing the deformation. As shown in Fig. 2b, all of the Type A structures exhibit strong auxetic behavior throughout the entire deformation process. In fact, the largest extent of auxeticity can be observed for the A3 sample corresponding to the largest value of d. In this case, for a relatively large strain of around 0.07, the Poisson's ratio assumes the value of approximately -1.4. Furthermore, one can note that the extent of auxeticity can be adjusted by the value of d. In contrast, the behavior of the analyzed samples of type B is very different. Namely, all type B samples tend to exhibit a positive Poisson's ratio that in most cases, becomes gradually less positive as strain increases. Notably, the sample that exhibits the largest values of Poisson's ratio throughout the majority of the deformation process is structure B3 that possesses the largest value of b from amongst the considered samples. Thus, taking all of these results into account, there are significant differences between the Poisson's ratios of type A and type B structures. In addition, the range of Poisson's ratio for each configuration can be adjusted through a variation of the geometric parameters.

In addition to experimental studies, another interesting aspect of the analysis corresponds to the investigation of the Poisson's ratio of the system through the FEM (Finite Element Method) computer simulations. In this case, both the structure and the corresponding boundary conditions were designed to closely match the experiment (see Methods section). As shown in Fig. 2c, the trends observed for computational results were qualitatively identical to those of the conducted experiments. More specifically, in the case of these two approaches, type A configurations exhibited a strong auxetic behavior throughout the entire deformation process while type B configurations exhibited positive values of this parameter. Of course, in terms of the quantitative analysis, there are some discrepancies between the two approaches that originate from multiple reasons. In the case of the experiment, the effect of the bottom constraint and edge effects on the effective Poisson's ratio is not fully negligible, however it is evident that, through the use of multiple cells in the design of the system and the selection of only the central unit-cell for analysis purposes, these influences are certainly significantly diminished. Thus, based on the provided results, it is clear that the two approaches confirm a very significant difference in the Poisson's ratio exhibited by the two types of analyzed configurations.

Effect of Reconfiguration on the Properties of the Structures

In addition to the Poisson's ratio, another interesting direction of study is the analysis of phononic band gap formation associated with phonon dispersion. Such analysis provides valuable information about the ranges of frequencies for which elastic waves are not transmitted through a given configuration of the system. Hence, in addition to applications related explicitly to a tunable Poisson's ratio, this information can be used for the design of microscopic vibration dampers / sensors.

From the perspective of applications, it is very important to check what happens to the mechanical and wave propagation properties once the system is subjected to a reconfiguration process. In other words, it is essential to assess the properties of the system during a reconfiguration process induced by an external stimulus that does not involve reconstruction of the structure. An example of such a reconfiguration process is presented in Fig. 3a, where the initial configuration of type A corresponds to angle θ 0 = 80 • . In this case, all triangles are the same and correspond to the b/a = 1.5 aspect ratio. Furthermore, as the reconfiguration process begins, the magnitude of the angle θ 0 starts increasing until it reaches the value θ 0 = 120 • . At this point, the system assumes a configuration of type B, where there are only two types of apertures. In order to describe what happens to the properties of the system throughout the reconfiguration process, we focus on the three representative configurations depicted schematically in Fig. 3a, where θ 0 is equal to 80 • , 100 • and 120 • respectively.

According to Fig. 3b, the phononic band structures for all three considered configurations are relatively similar. Most notably, the first non-negligible band gap occurring in the case of the system characterized by θ 0 = 80 • has a size of 2.95 MHz. As the value of θ 0 increases and assumes the values of 100 • and 120 • , the size of the band gap increases and is equal to 4.03 MHz and 4.13 MHz respectively. However, even though the size of the band gap changes as a result of the reconfiguration process, one could say that such variations are not very significant. This, in turn, is in agreement with the observations made for other complex mechanical metamaterials subjected to a reconfiguration process that were reported in the literature [66]. At this point, it is also important to note that whereas for Fig. 3 a structure cor-responding to a specific value of the b/a ratio was taken into account, in general, the change in width of the first significant band gap may look different when considering the deformation of structures characterized by different values of b/a. More specifically, as described in the Supplementary Information, if one was to consider the deformation of the structure with b/a = 2 from the configuration where θ 0 = 80 • to the configuration corresponding to θ 0 = 120 • , the magnitude of the change in the band gap width would be very different from the former case. In this scenario, the relative change in the band gap width is only equal to 0.149 MHz. In contrast, for the structure with b/a = 1.5, the change in the band gap width equals 1.18 MHz. Thus, a relatively small variation in the aspect ratio of structural elements may lead to a considerable difference in the magnitude of the change in the width of the band gap during the continuous reconfiguration process. Of course, this is due to the fact that structures corresponding to certain values of b/a lead to considerably different band gaps compared to other systems. Hence, it follows that the change in their magnitude is also considerably different.

Contrary to the results related to band gap formation, it is evident that the reconfiguration process strongly influences the Poisson's ratio of the system. As shown in Fig. 3c, configurations associated with θ 0 = 80 • and θ 0 = 120 • assume very different values of Poisson's ratio. Namely, in the case of the system where θ 0 = 80 • , the structure exhibits strong auxetic behavior throughout the entire deformation process. On the other hand, for θ 0 = 120 • , the value of the Poisson's ratio is predominantly positive. These two results are in accordance with the expectations based on the results of the mechanical testing of different configurations of Type A and Type B. However, it is very interesting to see what happens when the Type A configuration becomes very similar to a Type B configuration. Such a scenario can be observed in the case of the intermediate configuration corresponding to θ 0 = 100 • . For this configuration, even though Poisson's ratio is initially positive, it quickly assumes strong negative values upon increasing strain. All of these results are very interesting since they indicate that a relatively simple reconfiguration process of the considered system makes it possible to very significantly change its Poisson's ratio.

Once the effect of the reconfiguration of the system on its properties has been determined, it is also interesting to have a closer look at band gap formation for the Type B system. As shown in Fig. 3b, the largest first significant band gap is observed during the reconfiguration process. In order to investigate this factor further, the influence of changing the aspect ratio of the isosceles triangles constituting the Type B structure while keeping the dimension a constant, was analyzed.

The three specific configurations of the system chosen for this analysis are illustrated in Fig. 4a. In fact, the only difference between them is the value of b. Hence, to refer to a specific configuration assumed by the structure, one can use a particular value of the b/a coefficient. According to Fig. 4b, the variation in the value of b/a has a very significant effect on the phonon dispersion and on the size of the first significant band gap. More specifically, in the considered range of frequencies, one can note that for the structure associated with b/a = 0.7, the first non-negligible band gap is relatively small. In contrast, once the geometric dimensions of the structure are modified to correspond to b/a = 1.0, the appearance of a very significant band gap can be observed. Furthermore, upon increasing the magnitude of this coefficient up to a value of 1.3, the size of the first significant band gap is reduced in relation to the configuration with b/a = 1.0. This means that at relatively low frequencies, one should expect the largest band gap to be observed for this specific configuration. Hence, as shown in Fig. 4c, an analysis of the size of the first three band gaps was conducted for a larger number of possible structures corresponding to the b/a coefficient ranging between 0.7 and 1.3. The results show that the width of the first significant band gap gradually increases until it reaches its maximum value at b/a = 1.0. For configurations with b/a exceeding this value, the band gap gradually decreases. Finally, it should be noted that an experimental validation confirming the capability of controlling the width of band gaps through the change in the value of b/a is provided in Fig. S2 in the Supplementary Information.

Active Control

Up to this point, it has been shown that the properties of the proposed mechanical metamaterial can be controlled as a result of the reconfiguration process. However, such reconfiguration was merely a theoretical concept and thus far, it has not been explicitly demonstrated how it could be achieved without reconstructing the system. Thus, in this section, it is demonstrated how such active control over the configuration assumed by the system and the resulting mechanical properties can be attained. Furthermore, since the concept proposed in this work is fully scalable and all results can in general be reproduced irrespective of the size of the system, active control over the reconfiguration process was demonstrated through the use of a macroscopic prototype (see Fig. 5).

As shown in Fig. 5a, the system selected to demonstrate the active reconfiguration process corresponds to a 3D-printed (see Methods section) prototype associated with the Type B configuration that was inserted into the uniform magnetic field induced by two large parallel electromagnets. The response of the structure to the application of the external magnetic field was made possible due to the use of magnetic inclusions in the form of very small neodymium magnets (see Methods section) that were embedded within some of the structural triangle-like elements constituting the system. The concept of active reconfiguration corresponding to this structure is schematically demonstrated in Fig. 5b, where for the sake of clarity, only a fragment of the considered structure is presented. As can be seen, the structure is initially at rest in the Type B configuration, where θ 0 = 120 • . Once the external magnetic field is switched on, the magnetic dipole moments of the magnets attempt to align with the external magnetic field. Of course, depending on the magnitude of the external field, this might not be possible since for the triangles to rotate, the applied torques must be large enough to overcome the resistance and the restoring forces corresponding to the elastic non-magnetic material.

As shown in Fig. 5c, the considered structure deforms significantly and assumes a configuration corresponding to θ 0 ≈ 84 • upon being subjected to a relatively strong external magnetic field having a magnitude of 0.24 T (see Supplementary Video 1 to observe the gradual reconfiguration process where the magnetic field was changed with increments of 0.01 T). In other words, the structure undergoes a transition from Type B to Type A configuration. Based on the computational results provided in Fig. 5d, one can note that these two configurations correspond to a very different Poisson's ratio. Thus, the application of the external magnetic field makes it possible to significantly modify the properties of the structure without the need to rebuild it. In addition, after switching off the external magnetic field, the structure returns to its initial configuration, which means that after the transition it is possible to recover the initial properties of the system. These results are very important as they prove that the mechanical metamaterial proposed in this work can be used to exhibit a versatile Poisson's ratio that can be controlled remotely via the magnitude and orientation of the external magnetic field. Of course, in this case, due to the scale of the prototype, the controllable behavior was achieved thanks to the use of magnetic inclusions in the form of neodymium magnets. However, at much lower scales, this approach should be replaced for example by the use of single domain superparamagnetic nanoparticles dispersed within the resin prior to the polymerization process [69,70]. Another approach that could be used to achieve control over the behavior of the system through the use of an external magnetic field, is to use a selective magnetic coating applied for example by sputtering following the 3D printing fabrication process [71,72]. At this point, we emphasize that the results of this work are scale independent. Depending on the size of the system, however, they can be better suited for specific applications.

The results show that the proposed system can exhibit two very useful properties at the same time that are controllable remotely via an applied external magnetic field without the need for reconstructing the system. Specifically, it was shown that the considered structure can undergo a transition from positive to highly negative Poisson's ratio solely as a result of a reconfiguration process that can be invoked and controlled remotely. In addition, after the transition, the system maintains a stable mechanical behaviour for relatively large strains. Such active and reversible control over mechanical properties, combined with the observation of a very significant variation of Poisson's ratio, is seldom observed in mechanical metamaterials and can be very useful for numerous applications. Furthermore, what makes these results even more appealing, is the fact that it is demonstrated that the highly versatile Poisson's ratio of the considered system can be observed for samples fabricated at the micro-scale. In addition, from the perspective of multifunctional devices, the proposed system exhibits two highly useful properties at once: controllable Poisson's ratio and adjustable phononic band gap. The latter property prevents waves in a specific range of frequencies from propagating through the system. Mechanical metamaterials exhibiting such band gap formation combined with fully controllable Poisson's ratio are extremely rare. In a few known instances where control over both aspects was attempted to some extent [56], the studies were limited to structures at the macro / millimetre scale and typically only one of these properties was quantitatively assessed.

As mentioned above, the reconfiguration process leading to the transition in the properties of the system is fully reversible and can be achieved in an active manner that does not require rebuilding the system. This means that the ability of the mechanical metamaterial to exhibit a tunable Poisson's ratio could be used at the macroscale or the millimeter scale in the design of smart protective devices that could adjust their mechanical response depending on the specific impacting body, e.g. active car bumpers. Similarly, at the microscale, the controllable Poisson's ratio can lead to the design of materials characterized by the programmable extent of their micro-indentation resistance. In addition, should somebody use magnetic inclusions to control the properties of the structure, then by distributing them in a non-uniform manner, it would be possible to observe a situation where the initially uniformly-designed structure exhibits a very different Poisson's ratio in different parts of the system. Such behavior, as demonstrated in another study [64], could enable the system to exhibit complex shape morphing upon being subjected to a mechanical deformation or through the application of an external magnetic field. Especially at the micro-scale, and among other applications, such shape morphing may be useful for the design of smart stents that would provide local support to specific parts of a blood vessel, where the location of the support could be changed throughout treatment. Finally, it was also demonstrated that in addition to control over the Poisson's ratio, one can form band gaps that are almost unaffected by the reconfiguration process. Thus, while changing the mechanical response of the sample, it would be possible to prevent waves corresponding to a specific range of frequencies from being transmitted through the system. Such ability could be very interesting from the perspective of the design of multifunctional vibration-damping protective devices. Alternatively, should the need arise, the band gap could be adjusted by a variation in geometric parameters of the system. In addition, for specific values of the b/a parameter, the change in the width of the band gap induced by mechanical deformation is considerable.

Conclusion

In this work, a novel micro-scale mechanical metamaterial was proposed. It was demonstrated that depending on the assumed configuration, the system can exhibit very different Poisson's ratios ranging from strongly negative to positive values at relatively large strains. In addition, it was shown that such control over the mechanical behavior of the system can be achieved as a result of active reconfiguration, i.e. a process that does not require rebuilding the system. The transiton of properties of the structure following the reconfiguration process is recoverable and the extent of changes can be controlled by means of an external stimulus, such as a magnetic field. Furthermore, in addition to control over Poisson's ratio, it was demonstrated that during the reconfiguration process one can approximately retain the band gap formation corresponding to the system. Alternatively, band gap formation can be also tailored by an appropriate variation in the geometric parameters. All of these results indicate that the proposed mechanical metamaterial can be very useful in a plethora of applications ranging from smart protective to biomedical devices.

Methods

Fabrication

The Poisson's ratio of the considered system was assessed based on micro-scale experimental prototypes produced through the use of a commercial 3D printer (Photonic Professional GT+, Nanoscribe GmbH). The 3D printer used in this work operates based on the two-photon lithography method. All samples were printed with a resolution of around 2 µm which was possible thanks to use of the negative tone IP-S photoresin (Nanoscribe GmbH). Prior to the printing process, a drop of resin was deposited on an ITO-coated soda-lime glass substrate having the following dimensions: 25 Ö 25 Ö 0.7 mm 3 . After deposition, specific fragments of the drop were photopolymerized by means of a 25X-objective with a femtosecond laser that was operating at λ = 780 nm. Furthermore, the standard printing parameters were set as follows: a galvanometric scanning speed of 100 mm/s, a laser power at the level of 90% and slicing as well as hatching distances equal to 1 µm and 0.5 µm respectively. Once the printing process was finished, each sample was developed for 25 min in a solution of PGMEA (Propylene Glycol Methyl Ether acetate). This step of the procedure allows to remove the nonpolymerized photoresist. Subsequently, the resulting structure was rinsed for a duration of three minutes in isopropyl alcohol (IPA) in order to remove the developer solution.

In the case of the macroscopic experimental prototype, the structure was 3D printed by means of a commercial FDM 3D-printer (Ultimaker) by means of the elastic TPU 95A material. Furthermore, in each of the star-shaped segments of the structure, there were two apertures with magnetic inclusions in the form of 3 neodymium magnets of the N42 type. Each of the magnets had a cylindrical shape with a height of 1 mm and a base diameter equal to 1 mm. The remanent induction of each magnet was estimated to be equal to 0.613 T. The geometric dimensions of the initial structure were set to be the following: a = 6 mm, b = 9 mm, l 1 = 0.7 mm, l 2 = 0.43 mm, l 3 = 0.36 mm, l 4 = 0.8 mm and l 5 = 0.55 mm.

Mechanical Compression Testing

The experimental samples considered in this work were tested mechanically in order to assess their Poisson's ratio. To this aim, all samples were subjected to a mechanical compression induced by a flat external indenter. The speed of the indenter was constant and was set to 1 µm s -1 . At the same time, the bottom part of each sample was fixed in place by adhesion to the substrate on top of which they were printed. Throughout the experiment, the deformation process was recorded by means of an optical camera with magnification factor x20. The working distance, i.e. the distance between the lens of the camera and the sample, was approximately equal to 11 mm. Based on the recorded pictures, the Poisson's ratio of the system was determined based on the central topmost unit-cell (see Supplementary Information). To track the position of vertices that could be used to calculate the Poisson's ratio of the selected unit-cell, the digital image correlation method implemented in the MATLAB software was used.

In the case of the results presented in Fig. 5, the macroscopic experimental prototype was inserted into the uniform external magnetic field that was induced by two parallel electromagnets. The magnitude of the applied field was varied in a range between 0 T and 0.24 T with steps of 0.01 T in order to induce the reconfiguration process (see Supplementary Video 1). The deformation of the structure was recorded by means of a standard optical camera.

FEM simulations

To determine the Poisson's ratio of the considered finite structurs resembling experimental prototypes presented in Fig. 2, FEM simulations were conducted by means of the commercial software COMSOL Multiphysics. To this aim, for each of the structures considered in Fig. 2, it was assumed that geometric parameters characterizing the structure are the same as in the case of the experimental samples. Furthermore, to match the boundary conditions used in the experiments, it was assumed that the bottom part of each of the systems is fixed in space. In addition, the deformation of the structure was induced by means of contact with a large flat indenter in order to match the deformation process observed in the experiments as closely as possible. Mechanical properties of the simulated material were set as E = 4 GPa, ν = 0.4 and ρ = 1200 kg m -3 . In addition, geometrical nonlinearities were implemented to make simulations more realistic under large strains. Finally, it should be emphasized that a specific method related to the calculation of the Poisson's ratio is provided in the Supplementary Information.

In order to determine the phonon band structure, Bloch boundary conditions were implemented and used via an eigenvalue solver assuming real wave vectors in the Bloch conditions and searching for real eigenfrequencies of the system. This research was funded by the Polish Minister of Education and Science under the program "Regional Initiative of Excellence" in 2019-2023, project No. 003/RID/2018/19, funding amount PLN 11 936 596.10.

Figure 1 :

 1 Figure 1: a) Diagrams showing the two types of structures considered in this work. b) Experimental prototypes corresponding to specific examples of the Type A and Type B structures that are analyzed from the point of view of their mechanical properties. Parameters that remain the same for all structures are the following: a = 40 µm, l 1 = 4.8 µm, l 2 = 2.4 µm, l 3 = 2.4 µm, l 4 = 3.6 µm, and l 5 = 6.7 µm. In addition, parameters that remain the same for type A structures are b = 80 µm and c = 40 µm. Parameters that assume unique values both for type A and type B systems are as follows: d = 28 µm (A1), d = 40 µm (A2), d = 60 µm (A3) and b = 40 µm (B1), b = 60 µm (B2), and b = 80 µm (B3). The outof-plane thickness l for all of the structures is equal to 300 µm.

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Figure 2 :Figure 3 :

 23 Figure 2: a) Optical images of a compression test along the y-axis of the three micro-scale experimental prototypes corresponding to Type A and Type B configurations. b) Poisson's ratio estimated from experimental samples. c) Poisson's ratio estimated with FEM (Finite Element Method) computer simulations that was calculated based on the deformation of the central unit-cell of the considered finite samples.

Figure 4 :

 4 Figure 4: Effect of the elongation of the isosceles triangles corresponding to Type B of the system on the band gap formation. a) Diagrams showing three different configurations of the system, where the value of a is kept constant. b) Phonon band structures corresponding to the analyzed structures. c) The first three band gaps associated with structures corresponding to different values of the b/a ratio. The geometric parameters used for all of the structures were set to be the following: a = 200 µm, l 1 = 8 µm, l 2 = 4 µm, l 3 = 4 µm, l 4 = 4 µm, l 5 = 9 µm

Figure 5 :

 5 Figure 5: Active reconfiguration and transition in the properties of the system induced by the application of an external magnetic field. a) Picture of the investigated sample placed between two parallel electromagnets that produce an approximately uniform magnetic field. b) Diagram showing the concept of the reconfiguration of the magneto-mechanical structure. c) A change in the configuration of the system induced by the variation in the magnitude of the external magnetic field. d) Mechanical deformation of different configurations assumed by the system during the active reconfiguration.

Acknowledgements

This work was partly supported by the french RENATECH network and its FEMTO-ST technological facility. K.K.D. acknowledges the support of the Polish National Science Centre (NCN) in the form of the grant awarded as a part of the SONATINA 5 program, project No. 2021/40/C/ST5/00007 under the name "Programmable magneto-mechanical metamaterials guided by the magnetic field".

Supporting Information

Supporting Information is available from the Wiley Online Library or from the corresponding author upon request.