Margaret Chern

Chloé Grazon

Allison M Dennis

C Grazon

Chloe Grazon

Phase Transfer and DNA Functionalization of Quantum Dots Using

Keywords: Quantum dots, zwitterion, DNA labeling, surface functionalization, copper-free click chemistry, biofunctionalization, nanoparticle, carboxybetaine, poly(isobutylene-alt-maleic anhydride), PIMA 1

QDs often employ an amphiphilic polymer that encapsulates the QD with its original organic ligands. While quite stable, their large hydrodynamic size can negatively affect energy transfer [START_REF] Chern | Shell thickness effects on quantum dot brightness and energy transfer[END_REF][START_REF] Dennis | Surface ligand effects on metal-affinity coordination to quantum dots: Implications for nanoprobe self-assembly[END_REF] and the robustness of the steric coating precludes the use of histidine-based selfassembly of peptides and proteins to the QD, the simplest way to make QD bioconjugates. [START_REF] Dennis | Surface ligand effects on metal-affinity coordination to quantum dots: Implications for nanoprobe self-assembly[END_REF][START_REF] Medintz | Optimizing Protein Coordination to Quantum Dots with Designer Peptidyl Linkers[END_REF] Ligand exchange strategies that displace the native organic ligands create smaller particles. The first iterations of this method used small molecule ligands, but reports have shown that increasing the number of chemical handles to bind to the QD surface improves stability. [START_REF] Zhan | Multidentate zwitterionic ligands provide compact and highly biocompatible quantum dots[END_REF][START_REF] Mattoussi | Synthesis of compact multidentate ligands to prepare stable hydrophilic quantum dot fluorophores[END_REF] Building on that knowledge, several groups have reported the synthesis of multidentate polymers [START_REF] Ma | Multidentate Polymer Coatings for Compact and Homogeneous Quantum Dots with Efficient Bioconjugation[END_REF][START_REF] Susumu | A new family of pyridine-appended multidentate polymers as hydrophilic surface ligands for preparing stable biocompatible quantum dots[END_REF][START_REF] Wang | Photoligation of an Amphiphilic Polymer with Mixed Coordination Provides Compact and Reactive Quantum Dots[END_REF] for QD water-solubilization that provide excellent colloidal stability. The Mattoussi group has developed a particularly compelling strategy using a poly(anhydride maleicalt-isobutylene) (PIMA) as a polymer backbone for facile functionalization with primary amines. [START_REF] Mattoussi | Multifunctional and multicoordinating amphiphilic polymer ligands for interfacing semiconducting, magnetic, and metallic nanocrystals with biological systems[END_REF] They have shown effective grafting of amine bearing imidazole, lipoic acid, and phosphonates for anchoring the polymer to the QD surface, as well as sulfobetaine and polyethylene glycol (PEG) derivatives for water solubilization. [START_REF] Du | A Versatile Coordinating Ligand for Coating Semiconductor, Metal, and Metal Oxide Nanocrystals[END_REF][START_REF] Wang | A multifunctional amphiphilic polymer as a platform for surface-functionalizing metallic and other inorganic nanostructures[END_REF][START_REF] Wang | Published in Quantum Dots -Applications in Biology Springer Protocols 2020 Imidazole and Zwitterion Motifs as a Biocompatible Compact Coating for Quantum Dots[END_REF] Interest in zwitterionic or charge-based surface coatings, like the PIMA variant displaying sulfobetaine, is high as the surface charges are reported to confer excellent colloidal stability and reduce protein adsorption or opsonization. [START_REF] Wang | Multifunctional and High Affinity Polymer Ligand that Provides Bio-Orthogonal Coating of Quantum Dots[END_REF] Unfortunately, synthesizing and handling sulfobetaine or a similar zwitterionic molecule carboxybetaine with a primary amine is non-trivial, as is the synthesis of Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020 zwitterionic polymers from zwitterionic monomers. To expand access to those who are not organic chemists, we outline a straightforward protocol for preparing a low-cost, charged polymer (3.1) and using it in a straightfoward ligand exchange (3.2) to obtain an aqueous colloidal solution of bright, small, and stable QDs. [START_REF] Grazon | A versatile and accessible polymer coating for functionalizable zwitterioinic quantum dots with high DNA grafting efficiency[END_REF] Rather than using polyethylene glycol (PEG; expensive) or sulfobetaine (difficult to synthesize) derivatives to functionalize the PIMA, we use a commercially available quaternary amine ((2aminoethyl)trimethylammonium chloride (Me3N + -NH2)) to impart a persistent positive charge.

Combined with the carboxylic acid produced on each PIMA moiety formed during the amide coupling between the maleic anhydride and the primary amine-containing molecules, the Me3N + -NH2 produces a carboxybetaine-like zwitterionic coating without the need to synthesize a zwitterionic agent. Histamine, used as the anchoring group mediating the interaction between the QD surface and the polymer, is also readily available. To make the polymer relevant to a variety of biological applications, we include dibenzocyclooctyne-amine (DBCO-amine), which can react with any azido biomolecule of interest (e.g., derivatives of ligands like folic acid or biotin as well as larger peptides or proteins). Specifically, we detail our purification-free protocol for grafting DNA to the QD surface (3.3). Research in creating QD-DNA conjugates is ongoing, and historically, methods have been low-yield with the highest grafting efficiencies reaching only ~65% (9, 18) necessitating downstream purification steps. [START_REF] Banerjee | Quantum dots-DNA bioconjugates: Synthesis to applications[END_REF] The protocol we provide is simple and highly efficient (>95%) precluding the need for purification and increasing the overall yield of the QD-DNA conjugates obtained.

Materials

Anhydrous dimethylsulfoxide (DMSO) (see Note 2).

4. Polymer precipitation solution: Pre-weigh two 50 mL conical tubes, taking care to mark which lid belongs to which tube. Prepare 50 mL of ethyl acetate/diethyl ether (1/1) by mixing 25 mL of ethyl acetate and 25 mL diethyl ether and divide between the two tubes.

Mixing the ethyl acetate and diethyl ether in one of the tubes and pouring half into the other is precise enough for this purpose and ensures that the solvent ratio is the same in both tubes.

Methanol (MeOH).

6. Deuterium oxide (D2O). All synthesis steps should be carried out under air-free conditions (https://www.chemistryviews.org/details/education/4360441/Tips_and_Tricks_for_the_Lab_Air-Sensitive_Techniques_3.html). Either nitrogen or argon can be used as the inert gas in this protocol.

This procedure is specific to preparing a polymer for ligand exchange that is functionalized with 45% histamine, 45% Me3N + -NH2, and 10% DBCO-NH2 (Scheme 1). Different grafting percentages can be obtained by adjusting the molar ratios of each reagent. Additional or different functional groups can be included as long as they contain a primary amine (R-NH2). It can be convenient to prepare a table (Table 1) for calculating the amount of each reagent needed. For PIMA with MW ~ 6,000 g/mol there are on average ~39 monomers (MW = 154 g/mol) per polymer. We calculate our molar equivalents by assuming 40 monomers/polymer in order to provide slight excess of amine bearing reagents. 2. Centrifuge the 50 mL conical tube (~7,000 RPM, 5 -15 mins) to obtain a pellet of the PIMA polymer (see Note 7). Discard the supernatant containing unreacted amines and triethylamine.

3. Set the conical tubes upside down on a laboratory wipe and let sit for ~ 5 mins to dry the pellet.

4. Add MeOH (~1-5 mL) directly to each tube to re-disperse the polymer pellet (see Note 8).

Precipitate the polymer from MeOH by adding ethyl acetate until the solution becomes

turbid (~10 -20 mL).

6. Centrifuge to obtain a pellet of the purified polymer and discard the supernatant. 7. Dry the purified polymer under vacuum. Septa (24/40 or 29/32) can be used to seal the 50 mL conical vials and attached to the vacuum/gas manifold with a syringe and needle.

Alternatively, a vacuum desiccator can be used, if available.

8. The mass of the polymer is obtained by weighing the tube with polymer and subtracting the original weight of the tube. The chemical yield is estimated by dividing the end weight by the original total mass of the reaction. The yield should be higher than 70%. 9. After purification and drying, a white powder is obtained and should be stored at 4°C in the dark for further use. [START_REF] Susumu | A new family of pyridine-appended multidentate polymers as hydrophilic surface ligands for preparing stable biocompatible quantum dots[END_REF]. Acquire an infrared spectrum of the powder using an attenuated total reflection (ATR) probe on a Fourier-transform infrared (FTIR) spectrophotometer to confirm the disappearance of the C=O stretch of the anhydride at 1770 cm -1 and appearance of the C=O stretch of carboxylic acid and amide at 1710 cm -1 and 1650 cm -1 , respectively (Figure 1). 11. Transfer to a centrifuge tube and centrifuge at 3000 rpm for 1 min to obtain two nicely separated phases (Figure 3) and precipitate any aggregates. Separate the supernatant and collect the top, aqueous layer containing QDs in 0.1 M NaOH.

12. Filter the QDs in 0.1 M NaOH on a 0.1 m (or 0.25 m) PVDF syringe filter into a 100 kDa centrifugal filter (0.5 mL capacity) (see Note 20).

13. Wash the QDs with 0.5 mL of 0.1 M NaHCO3 and centrifuge at 10,000 rpm for 2 min.

14. Discard the flow-through and refill the centrifugal filter with 0.1 M NaHCO3.

15. Centrifuge at 10,000 rpm for 2 mins. [START_REF] Wang | Multifunctional and High Affinity Polymer Ligand that Provides Bio-Orthogonal Coating of Quantum Dots[END_REF]. Repeat steps 14 and 15 at least two more times. 17. Recover the QDs in a minimal amount of buffer (now in 0.1 M NaHCO3) and store concentrated at 4°C in the dark. Beer-Lambert Law:

𝐴 = 𝜀 ⋅ 𝑐 ⋅ 𝑙
where A is absorbance at wavelength , ε is molar extinction coefficient (M -1 cm -1 ) at wavelength , c is concentration (M), and l is pathlength (cm).

2. Subtract the absorbance before ligand exchange from absorbance after ligand exchange to obtain DBCO absorbance. Use the value of the absorbance at 309 nm to calculate DBCO concentration using the Beer-Lambert Law.

3. Divide DBCO concentration by QD concentration to obtain DBCO/QD ratio (Figure 4).

The DNA grafting reaction relies on DBCO-azide coupling, so the DBCO/QD ratio can be used to ensure that there are a sufficient amount of biofunctional handles on the QD.

Centrifuge with a table top centrifuge for ~ 1 min to pellet any aggregates (see Note 22).

Collect the supernatant.

DNA hybridization:

1. Add 4 nmol (i.e., an equimolar amount) of the DNA complement to the QD/ssDNA conjugates (see Note 23).

2. Heat to 95 °C for 2 minutes and gradually cool. A cooling ramp can be used, but simply transferring samples from a heat block/water batch to bench-top at room temperature is usually sufficient (see Note 24).

3. The QD-dsDNA can now be stored at 4 °C in the dark for further use. Do not freeze.

Verification of hybridization:

1. For simple verification of hybridization, a small aliquot of the QD-DNA should be hybridized with a biotinylated complement (available from IDT) (QD-dsDNA-bt), and hybridization can be verified in a simple bead pull-down assay.

2. Aliquot ~ 200 µL of streptavidin-agarose beads into a 500 µL PCR tube.

3. Centrifuge for 30 s using a tabletop centrifuge (~ 6,000 rpm, 2,000 g) to pellet beads at the bottom of the tube. 4. Although many labs, including ours, have wash bottles of commonly used solvents available for convenience, we find that using ethanol freshly aliquoted from the reagent bottle has a significant effect on maintaining the brightness of the final QD product.

Ethanol is hygroscopic and will draw water out of the air, gradually contaminating the solvent.

5. Consider the inner diameter of the tubing on the manifold and roughly match to the outer diameter of a plastic syringe, likely either the 1 mL or 3 mL size. Remove and discard the syringe plunger. Cut the syringe barrel just below the flanges on the back end to produce a plastic tube with a needle connection. Insert the straight barrel of the cut syringe into the manifold tubing; attach a needle and insert needle into septum.

6. If vacuum/inert gas cycling is used to degas the flasks relatively quickly, be sure to gradually switch from nitrogen to vacuum, as sudden introduction can cause the PIMA powder to fly about and potentially be drawn up the vacuum line.. 9. If purification by precipitation does not yield high purity, the polymer can be further purified by dialysis ( < 10 kDa membrane). This should be done after FTIR as any unreacted maleic anhydride rings will open in this process and confound FTIR results.

Resuspend the product in a minimal amount of water and load into dialysis tubing or cassette. Place in a beaker filled with milli-Q water (100 -1,000 mL); add a couple drops of 1 M NaOH to the dialysis bath to help swell the polymer and remove impurities. Let dialysis proceed for at least 1 hr (longer is not harmful to the product, but will extend the time of the procedure). Replace the dialysis bath with milli-Q water and again allow the dialysis to proceed for at least one hour. The dialysis bath should be replaced at least 5 times with milli-Q water to remove all impurities. 10. Sometimes extra washing steps (re-dispersing in decane (or hexanes) and repeating step 2 in section 3.2) can help if the ligand transfer does not work for a specific QD sample. It is very important to remember to perform step 5 (section 3.2) if several QD precipitations are done because QDs will start to aggregate as more organic ligands are cleaned from their surface.

11. QDs that have not been successful in ligand transfer may benefit from a post-synthesis treatment with zinc stearate. After step 3 (section 3.2), the QD pellet can be re-dispersed directly in a small amount (~1 mL) of zinc stearate dissolved in ODE (0. Alternatively, the Smith group outlines several additional surface treatments and can be referred to for those who are more comfortable with chemistry. [START_REF] Ma | Multidentate Polymer Coatings for Compact and Homogeneous Quantum Dots with Efficient Bioconjugation[END_REF] 12. The rest of the QDs can be stored in a tightly sealed vial at 4°C in the dark for up to a week or long term (~2 months) at -20 °C. Be sure to syringe filter and check the QD concentration by UV-vis. absorption the solution before ligand transfer. [START_REF] Du | A Versatile Coordinating Ligand for Coating Semiconductor, Metal, and Metal Oxide Nanocrystals[END_REF]. For samples that are sensitive to oxidation, the vial can be septum capped and nitrogen gently bubbled through the solution (~5 mins) while stirring. Dip the vial in an ice bag to avoid evaporation of the CHCl3.

14. If nanoparticle size is known, scaling to nanoparticle surface area instead can help to reduce waste of polymer. We find that ~300 anchoring groups (imidazoles) per nm 2 QD (QD concentration multiplied by the surface area of 1 QD) consistently works.

15. 1 hour is normally sufficient for ligand exchange to have occurred. However, overnight ligand exchange it has been qualitatively observed to impart better stability at the cost of decreased quantum yield. [START_REF] Wang | Multifunctional and High Affinity Polymer Ligand that Provides Bio-Orthogonal Coating of Quantum Dots[END_REF]. Alternatively, the QDs can first be precipitated from the DMSO/CHCl3 solution by addition of ethyl acetate and centrifugation (10,000 rpm, ~ 5 mins). The supernatant should then be discarded and the pellet recovered directly into 0.1M NaOH. 17. Sometimes a white precipitate is seen at the solvent interface. This can be pelleted through centrifugation and discarded.

18. If the phase transfer failed and QDs are in the bottom organic phase, they can be recollected and the ligand exchange re-attempted. The QD solution should be first filtered through a 0.1 µm PVFD syringe filter to get rid of any aggregates that may have formed and a higher polymer/QD ratio should be used. 19. If the QDs are stuck between the water and organic phases, sometimes they can be recovered. Remove the CHCl3/DMSO layer with a syringe and pour off the water layer + QDs into a 2 mL centrifuge tube. This can be gently sonicated to disperse the QDs in the water phase. Once relatively dispersed, hexanes can be added to the tube to wash off any excess organic ligands that may have gotten "stuck" between the polymer and QD during ligand exchange. The tube should then be sonicated (~5 mins) and centrifuged (~3,000 rpm for 1 min). QDs in the water phase (bottom) can be collected and used. If this does not work, the ligand transfer should be repeated from the beginning, using freshly prepared QDs in CHCl3 and a higher polymer ratio.

20. Sometimes at step 12 (section 3.2), the QDs are lost on the PVDF filter, indicating that large aggregates were solubilized rather than single QDs. Double check that the QD concentration in CHCl3 is ~100 nM; if the solution is too concentrated, multiple QDs can be wrapped together during ligand exchange. Alternatively, increasing the CHCl3/DMSO ratio by using a ligand solution at 20 mg/mL rather than 10 mg/mL can help to avoid QD aggregation during DMSO addition. 21. Higher or lower DNA/QD ratios can be used, but the DBCO/DNA ratio should be higher than 2:1 22. We have consistently seen that using the conditions described in the DNA conjugation methods provides near complete reaction efficiency of the DNA to the QDs (> 95%).

Most downstream applications do not need further purification. For applications extremely sensitive to free DNA, dialysis or centrifugal filters can be used to separate QD-DNA conjugates from free DNA.

Phase

  Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020 2.1 Polymer Synthesis, Purification, and Characterization 1. Polymer backbone: Poly(isobutylene-alt-maleic anhydride) (PIMA; molecular weight (MW) ~ 6,000 g/mol). PIMA has been largely shelf-stable in our experience, but since water can hydrolyze the rings needed for functionalization, long-term storage in a desiccator or in a glove box at room temperature is preferred. 2. Primary amine-containing molecules to functionalize polymer: (2-aminoethyl) trimethylammonium chloride hydrochloride (Me3N + -NH2) and triethylamine (Et3N) for solubilization; histamine; dibenzocyclooctyne-amine (DBCO-NH2) (see Note 1).

2. 2

 2 Quantum Dot Preparation and Ligand Exchange 1. Quantum dots (see Note 3).

2 .

 2 Organic solvents: chloroform (CHCl3), hexanes (Hex), methanol (MeOH), ethanol (EtOH) (see Note 4). Optional: Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020  0.2 M zinc stearate in octadecene (ODE): weigh 6.3233 g of zinc stearate and load into a 100 mL round bottom flask. Add a stir bar. Heat while stirring under vacuum to 80 C until fully dissolved. Once dissolved, fill the flask with nitrogen and stir for 15 mins before switching back to vacuum and degassing for 15 mins. Do at least 3 vacuum / nitrogen cycles to ensure that the solution is air-free.  0.1 M sodium bicarbonate (NaHCO3): mix 8.401 g of NaHCO3 with 1 L diH20.  0.1 M sodium hydroxide (NaOH).

2. 3

 3 DNA Labeling and Characterization 1. Azide-modified oligonucleotides (ssDNA-N3) and their complement strands, plain and biotinylated (csDNA & csDNA-bt), can be custom ordered, for example from IDT Technologies).

2. 1 x

 1 Duplex Buffer: 100 mM Potassium Acetate, 30 mM HEPES, pH 7.5, available from IDT Technologies. 3. Streptavidin-coated agarose beads. 4. 2 M sodium chloride (2 M NaCl): Add 1.17 g of NaCl to graduated cylinder and raise the volume to 10 mL with diH20. Add stir bar and leave on a stir plate until completely dissolved (~1 min).

  Preparation Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

1 .

 1 Prepare Solution 1: a. Weigh 0.240 g of PIMA into a 25 mL round bottom flask equipped with a magnetic stir bar and sealed with a septum. b. Insert a needle (see Note 5) in the septum and degas either by i) actively flowing nitrogen through the flask (using a second needle to allow nitrogen to escape, creating flow) while gently stirring the powder for 20 min or ii) applying 3 cycles of vacuum / nitrogen for 5 seconds each (see Note 6). c. Add 6 mL of anhydrous DMSO to the dry powder with a syringe. The PIMA should dissolve easily in DMSO. Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020 d. Heat Solution 1 to 45 °C while stirring. 2. Prepare Solution 2: a. In a separate septum-sealed container (glass vial or round bottom flask), combine histamine (80 mg), Me3N + -NH2 (126 mg), and DBCO-NH2 (44 mg) at 18, 18, and 4 molar equivalents to PIMA, respectively. Include a magnetic stir bar. b. Add Et3N at a 2:1 molar ratio to Me3N-NH2 (200 µL) to help solubilize Me3N + in DMSO. c. Insert a needle in the septum and degas by either i) actively flowing nitrogen through the flask while gently stirring the mixture for 5 min or ii) applying 3 cycles of vacuum / nitrogen for 5 seconds each. Be careful not to evaporate the triethylamine. d. Add anhydrous DMSO with a syringe such that the final concentration of all reagents in solution is 260 mM (11.5 mL).e. Heat Solution 2 to 50 °C while stirring to fully dissolve reagents.

3 .

 3 Add Solution 2 to Solution 1 (stirring at 45 °C) dropwise with a syringe.4. Allow the mixture to stir overnight at 45 °C.

3. 1 . 2

 12 Polymer Purification and Characterization 1. Add the polymer/DMSO solution (18 mL total) dropwise to the two pre-weighed 50 mL conical tubes each containing ~25 mL of precipitating solvent (~9 mL polymer solution in each tube). The solution will become turbid (cloudy), indicating that the polymer is precipitating. Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

  Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020 11. Run 1 H NMR in D2O to confirm the purity of the polymer and its molar composition (example calculations provided in Figure 2; see Note 9).

3. 2

 2 Quantum Dot (QD) Preparation and Phase Transfer 1. Aliquot ~150 µL of QDs in organic solution into a 2 mL centrifuge tube and add ~150 µL of hexanes. Commercially sourced QDs ship at ~1 µM. The QDs used in this procedure started at 4.8 µM. 2. Add EtOH until the solution becomes cloudy. 3. Centrifuge to obtain a pellet of the "cleaned" QDs (see Notes 10 & 11).4. Re-disperse the QDs in CHCl3 to a final concentration of ~100 nM (7 mL).

5 .

 5 Syringe filter (0.1 µm, PVDF) and transfer the 1 mL of the QDs in CHCl3 to a glass vial with a stir bar (seeNotes 12 & 13).

6 .

 6 Prepare ligand solution: Weigh polymer in a glass vial and add anhydrous DMSO such that the final concentration is 10 mg/mL. Use ~10 mg of polymer per nmol of QD (~800:1 molar excess of polymer) (seeNote 14). Heating with a heat gun or at 50 °C in an oil or water bath is usually required to fully dissolve the polymer.7. Add the ligand solution dropwise to the QD solution while stirring at room temperature. For 1 mL of QDs at 100 nM, 100 µL of polymer at 10 mg/mL should be added. The final solution should consist of 10:1 CHCl3:DMSO. 8. Purge the vial with nitrogen and allow the solution to stir for at least 1 hour at room temperature and protected from light (foil wrapped) (see Note 15).

9 .

 9 For transfer to water, add 0.5 mL of 0.1 M NaOH to the QD/PIMA/DMSO/CHCl3 mixture while stirring (see Note 16). Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 202010. Turn off stir plate and allow the aqueous phase and organic phases to separate. Successful ligand exchange is indicated by QDs being in the top (aqueous) phase (Figure3). (see

3. 3

 3 DNA Functionalization 3.3.2 DBCO stoichiometry determination 1. The number of DBCO moieties per QD can be estimated with UV-Vis absorbance.DBCO absorbs strongly in the UV and has a molar extinction coefficient (ε) of 12,000 M - 1 cm -1 at 309 nm. Scale QD absorbance before ligand exchange to the absorbance spectra of the QD after ligand exchange at 400 nm. Calculate QD concentration using the Beer-Lambert Law and the QD molar extinction coefficient given by the vendor or using published size-dependent molar extinction coefficient formulas.(20) Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

3. 3 . 2

 32 DNA conjugation and hybridization 1. Add PIMA-coated QDs (0.2 nmol; 70 µL at ~ 3µM) and DNA-N3 (4 nmol; 20 µL at ~ 200 µM) to a 500 µL PCR tube at a DNA:QD ratio of 20:1(see Note 21).

2 .

 2 Add NaCl to the QD/DNA mixture to obtain a final NaCl concentration of 1 M (90 µL of 2 M NaCl).

3 .

 3 Wrap the tube in aluminum foil and shake on an agitation plate for 4 days at room temperature. Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

4 .

 4 Pull off the supernatant (~ 100 µL) with a pipette and add 100 µL of 0.1 M NaHCO3. Pipette up and down 5 -10 times to mix. 5. Repeat steps 3 & 4 two more times to fully wash the streptavidin beads. 6. Split bead slurry into two 500 µL PCR tubes (100 µL each). Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020 7. To one tube (Tube 1) add 2-10 µL of the QD-dsDNA. Pipette up and down 5 -10 times to mix. 8. To the other tube (Tube 2) add 2-10 µL of the QD-dsDNA-bt. Pipette up and down 5 -10 times to mix.9. Centrifuge for 30 s using a tabletop centrifuge (~ 6,000 rpm, 2,000 g) to pellet beads at the bottom of the tube. 10. Repeat steps 3 & 4 two times to wash unbound QDs from the slurry. 11. Check for fluorescence under UV illumination (lamp, flashlight, etc.) The QD-dsDNA should not bind to the beads, so Tube 1 should be non-fluorescent, while the opposite is true of QD-dsDNA-bt (Figure5).

4 . Notes 1 . 3 .

 413 photoluminescent once transferred into water. If using QDs synthesized in house, it is

7 .

 7 If the polymer does not precipitate easily, place the conical tubes in the freezer (-20 °C) for 1 hr and re-centrifuge. If a refrigerated centrifuge is available, centrifuge at -20 °C. 8. If the polymer does not dissolve readily, gentle sonication, gentle heating (warning: boiling point of MeOH is 65°C), or adding acetonitrile can help. Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

  2 M, heated to ~80°C). Transfer the QD/Zn solution to a septum-fitted glass vial with a stir bar. Degas the solution by bubbling nitrogen through the solution. Heat while stirring at 240°C for 2-3 hours. The QDs should then be precipitated from solution by addition of hexane and ethanol and centrifuging. Extra washing steps are necessary when doing zinc treatment. Phase Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

Phase

  Transfer and DNA Functionalization of Quantum Dots Using an Easy-to-Prepare, Low-Cost Zwitterionic Polymer M. Chern, C. Grazon, A. M. Dennis Published in Quantum Dots -Applications in Biology Springer Protocols 2020

Figures Scheme 1 .

 1 Figures

Figure 1 .

 1 Figure 1. FTIR spectra of the as-shipped (grey) and functionalized PIMA polymer (blue). The

Figure 2 .

 2 Figure 2. Analysis of 1 H NMR of the polymer in D2O. The isobutyl group is used as reference (6

Figure 3 .

 3 Figure 3. Quantum dots ligand exchanged with the functionalized PIMA. Successful ligand

Figure 4 .

 4 Figure 4. DBCO/QD Analysis. Absorbance spectra of the QDs in CHCl3 is normalized at 400 nm

  Me3N + and 10% DBCO-NH2. a Molar equivalents obtained by multiplying desired grafting fraction by the number of monomer/PIMA polymer (~40). b Millimoles (mmol) of each reagent needed, calculated by multiplying N by the number of mmol of PIMA. PIMA is first weighed and the number of mmol calculated by dividing mass (m) d in mg by MW c .Tables:

Table Captions :Table 1 .

 Captions1 Calculation of reagent amounts needed for a reaction consisting of 45% histamine, 45%

Table 1 :

 1

	Reagent	Reagent	Molar	Moles b	MW c	Mass d	Density	Volume	[Final]	DMSO
		Fraction	Equiv. a	(mmol)	(g/mol)	(mg)	(g/mL)	(µL)	(mM)	(mL)
	PIMA		1	0.04	6000	240			6.7	6
	histamine	0.45	18	0.72	111.15	80			260	11.5
	Me3N + -NH2	0.45	18	0.72	175.10	126
	DBCO-NH2	0.1	4	0.16	276.33	44
	Et3N		36	1.44	101.49	146	0.73	200


Ouafae Karmouda

Jeremie Boulanger

Remy Boyer

SPEEDING UP OF KERNEL-BASED LEARNING FOR HIGH-ORDER TENSORS

Keywords: Tensor classification, HOSVD, subspaces, Grassman manifold, Tensor Train

Supervised learning is a major task to classify datasets. In our context, we are interested into classification from highorder tensors datasets. The "curse of dimensionality" states that the complexities in terms of storage and computation grow exponentially with the order. As a consequence, the method from the state-of-art based on the Higher-Order SVD (HOSVD) works well but suffers from severe limitation in terms of complexities. In this work, we propose a fast Grassmannian kernel-based method for high-order tensor learning based on the equivalence between the Tucker and the tensortrain decompositions. Our solution is linked to the tensor network, where the aim is to break the initial high-order tensor into a collection of low-order tensors (at most 3-order). We show on several real datasets that the proposed method reaches a similar accuracy classification rate as the Grassmannian kernel-based method based on the HOSVD but for a much lower complexity.

INTRODUCTION

Nowadays, data needs more and more dimensions to be described [START_REF] Cichocki | Tensor decompositions for signal processing applications: From two-way to multiway component analysis[END_REF]. A natural way to represent such data is to use multidimensional arrays called tensors [START_REF] Sidiropoulos | Tensor decomposition for signal processing and machine learning[END_REF]. Tensors of order Q [START_REF] Kolda | Tensor decompositions and applications[END_REF] are multiway arrays of Q dimensions. They generalize the notions of vectors (first order tensors) and matrices (second order tensors). A prominent tensor decomposition is the High-Order SVD (HOSVD) [START_REF] Lathauwer | A multi-linear singular value decomposition[END_REF] but this decomposition suffers from the well-known "curse of diemnsionality" meaning that the storage and computational costs grow exponentially with the order of the tensor. This is a severe limitation for tensors with Q > 3 [START_REF] Cichocki | Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions[END_REF][START_REF] Zniyed | High-order tensor estimation via trains of coupled third-order cp and tucker decompositions[END_REF]. In the context of supervised classification, Support Vector Machines (SVMs) [START_REF] Christopher | A tutorial on support vector machines for pattern recognition[END_REF][START_REF] Smola | A tutorial on support vector regression[END_REF] have been widely used due to their solid theoretical foundations, their performances and their easy implementation. Despite only processing linear classification, they can be modified to treat non linear problems via a kernel method. The main idea is to map data that are initially non linearly separable into a higher dimensional space (an RKHS) where it becomes linearly separable using a mapping φ. In practice (thanks to the kernel trick), the explicit computation is φ is not required as long as an expression for the kernel: k(., .) =< φ(.), φ(.) > exists. The exploitation of the HOSVD and SVMs to tensorial data has been introduced in [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF]. The proposed method, denoted FAKSETT (Fast Kernel Subspace Estimation based on Tensor Train decomposition) shows good classification performance at the price of higher computational complexity due to the use of the HOSVD. The main idea of this work is to decrease this complexity using a recent theoretical result giving an algebraic link between the Tucker and Tensor-Train format [START_REF] Zniyed | High-order tensor estimation via trains of coupled third-order cp and tucker decompositions[END_REF].

For the remaining part of this work, scalar will be denoted by lower case letters (e.g: a), matrix will be denoted by upper case letters (e.g: A) while tensors will be denoted by calligraphic letters (e.g: A)). The order of a tensor will generally be denoted by Q and we will consider the case when Q > 3. The q-th unfolding for A is a matrix and will be denoted A <q> whose elements are given by:

A <q> (i q , i 1 ...i q-1 i q+1 ...i Q ) = A i1 , ... , i Q .
The n-product between A and B will be denoted by × n according to

(A × n B) i1 , ... , i Q = i A ... , in-1 , i , ... B i , in .
The contraction product × m n between A and B is a tensor constructed similarly by summing over the n-th index on A and over the m-th index from B.

KERNEL FOR DATA TENSORS

We focus on supervised classification problems where data are high order tensors. Kernel-based classification methods [START_REF] Newman | Image classification using local tensor singular value decompositions[END_REF][START_REF] Peeters | Analysis of Distance/Similarity Measures for Diffusion Tensor Imaging[END_REF] require a similarity measure. It is standard [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF] to consider a kernel between two tensors X and Y as for instance the RBF Gaussian kernel :

k(X , Y) = exp(-γ||X -Y|| 2 F ) (1)
where γ > 0 is the bandwidth and ||.|| F is the Frobenius norm. However, this kernel does not consider the multidimensional structure of data tensors.

HOSVD Decomposition

Definition: Tucker decomposition. A tensor X follows a Tucker Decomposition (TD) if it can be written as [START_REF] Lathauwer | A multi-linear singular value decomposition[END_REF]:

X = G × 1 U 1 × 2 ... × Q U Q (2)
where U q are of size

I × R q , 1 ≤ q ≤ Q and G is the core tensor of size R 1 × • • • × R Q . The multi-linear ranks (m- ranks) of X is the Q-uplet {R 1 , ..., R Q }.
Definition: HOSVD. An important constrained format of the TD is the HOSVD. In the latter, the factors U q are orthonormal and the core tensor G is all-orthogonal. In order to compute the HOSVD presented in Equation ( 2), [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF] consider the R q left dominant singular vectors from the q-th unfolding X <q> . The complexity of the HOSVD for a cubic Q-order tensor of size

I 1 × • • • × I Q is evaluated to O(QRI Q
) where I = max q {I q } and R = max q {R q } is the maximal multilinear rank. We can see that the HOSVD complexity grows linearly and exponentially with respect to the order Q. For low-order tensor [START_REF] Papastergiou | Tensor decomposition for multiple-instance classification of high-order medical data[END_REF][START_REF] Makantasis | Tensorbased classification models for hyperspectral data analysis[END_REF], this complexity remains acceptable but this limitation becomes rapidly severe for high-order tensors (Q > 3).

Tensor-based Kernel on HOSVD factors

In order to take account of the multidimensional structure of input data tensors, an idea presented in [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF] consists in decomposing each tensor into its HOSVD:

X = G × 1 U 1 × 2 ... × Q U Q (3) Y = H × 1 V 1 × 2 ... × Q V Q (4)
The kernel-based part of the proposed method is

k(X , Y) = Q q k q (U q , V q ) (5)
where k q (., .) is a positive definite kernel defined on the matrices R I×Rq × R I×Rq .

Kernel on a Grassmann manifold

It shall be noted that the decompositions from Equation ( 3) are not unique [START_REF] Kolda | Tensor decompositions and applications[END_REF]. The output class will be affected by this lack of non-uniqueness. To mitigate this issue in the learning context, one can consider the subspaces spanned by the factors {U q , ..., U q } and {V 1 , ..., V Q }. Indeed, the subspace spanned by the factor U q , q ≤ N (respectively V q ) are invariant to any right multiplication by a non-singular matrix. Therefore, let consider the sub-kernels k q in the form:

k q (U q , V q ) = kq (span(U q ), span(V q )) (6)
where kq is a kernel defined on the Grassman manifold G(R q , I), i.e the subspaces from R I with dimension R q .

Fig. 1. Illustration of the angle θ q from Equation ( 7)

A popular choice for kq that gives rise to a positive definite kernel and used in [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF] is given by:

k q (U q , V q ) = exp -γ sin 2 (θ q ) (7)
where θ q is the principal angle between span(U q ) and span(V q ). It should be noted that despite θ q being the geodesic distance in the Grassman manifold between the two subspaces, the expression sin(θ q ) is considered instead, making the kernel k q definite positive (therefore, SVM methods can be used for classification) [START_REF] Jayasumana | Kernel methods on riemannian manifolds with gaussian rbf kernels[END_REF]. Readers can refer to [START_REF] Jayasumana | Kernel methods on riemannian manifolds with gaussian rbf kernels[END_REF] for explicit ways of computing the principal angles. In our case, it is possible to directly use the projectors:

sin 2 (θ q ) = 2 U q U T q -V q V T q 2 F . (8)
The principal angle θ q is illustrated in Figure 1.

THE FAKSETT METHOD : A FAST ALTERNATIVE TO THE METHOD OF [9]

In order to decrease the complexity of the HOSVD discussed in Section 2.2, we propose to use a fast multiLinear projection method proposed in [START_REF] Zniyed | High-order tensor estimation via trains of coupled third-order cp and tucker decompositions[END_REF]. The theoretical foundations of this method are based on the Tensor Network theory [START_REF] Cichocki | Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions[END_REF] and in particular on the equivalence between the Tucker and Tensor-Train formats introduced in [START_REF] Zniyed | High-order tensor estimation via trains of coupled third-order cp and tucker decompositions[END_REF] and described in the following. We will first begin with a definition of Tensor Train decomposition (TTD).

Definition: Tensor-Train Decomposition (TTD). A Tensor X admits a TTD with TT-ranks (R 1 , . . . , R Q-1 ) if it can be expressed as:

X = G 1 × 1 2 G 2 × 1 Q-1 G Q-1 × 1 Q G Q (9)
where the size of each core is:

• G 1 ∈ R I×R 1 • G q ∈ R R q-1 ×I×R q , ∀q : 1 < q < Q Fig. 2.
In the case of R q = 2 with U q = [U 1 q , U 2 q ]: Despite giving different factors, HOSVD and FAKSETT gives factors that span the same subspace.

• G Q ∈ R R Q-1 ×I
and where (R 1 , R 2 , ..., R Q-1 ) are the TT-ranks. To estimate the core tensors, we can use the TT-SVD algorithm [START_REF] Ivan | Tensor-train decomposition[END_REF] or its generalization [START_REF] Zniyed | A tt-based hierarchical framework for decomposing high-order tensors[END_REF]. Assume that a tensor X follows a TD of m-ranks {R 1 , • • • R Q } with orthonormal factor U q . An equivalence between TD and TTD is presented in [START_REF] Zniyed | High-order tensor estimation via trains of coupled third-order cp and tucker decompositions[END_REF]. Each core extracted from the TD given by Equation ( 9) follows a 3-order Tucker model with two latent matrices in its first and third dimensions. In the second dimension, we have the interesting property that R q left dominant singular vectors from the second unfolding spans the same subspace as U q . As a consequence, we have for 2 ≤ q ≤ Q -1:

span(U q ) = span (G q<2> ) . ( 10
)
This property is illustrated on Figure 2 and span(U 1 ) = span(G 1 ), span(U Q ) = span(G T Q ). Therefore, the expression from Equation ( 7) can be obtained from a the computation of the left dominant singular vectors thanks to the SVD associated to Q -2 cores. The m-ranks and TT-ranks verify the following relation:

R q = min q p=1 R p , Q p=q+1 R p .
The last step of the FAKSETT method is to compute the kernel defined in Equations ( 5) and [START_REF] Christopher | A tutorial on support vector machines for pattern recognition[END_REF].

EXPERIMENTS

For the following datasets, a classification task is realized via SVM [START_REF] Christopher | A tutorial on support vector machines for pattern recognition[END_REF]. This relies on the similarity matrix obtained using the kernel defined previously. The kernel is computed with FAKSETT and is compared to the native method of [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF].

Classification performance

In this section, we report on numerical experiments where we use accuracy as a performance measure.

Both the SVM regularization parameter and the kernel bandwidth γ from Equation [START_REF] Christopher | A tutorial on support vector machines for pattern recognition[END_REF] are selected from the grid of values {2 -9 , 2 -8 , ..., 2 8 , 2 9 } by a 5 fold cross validation. All the experiments are conducted on a computer with Intel Core i7 9th generation 2.6 GHZ processor and 32 Go RAM memory running Windows 10. Computations of SVDs are realised using optimised TensorLy (Tensor Learning in Python) library.

• Table 1 and Table 2 show very close accuracy scores between FAKSETT and method of [START_REF] Signoretto | A kernel-based framework to tensorial data analysis[END_REF] for classification tasks on both real database. This indicates that the FAKSETT method operates as efficiently as the stateof-art method. Reducing the size of the training data set (i.e training with less data) does not impact significantly the performances.

• However, it is noticeable from Table 3

CONCLUSION

Recently, supervised kernel-based learning for tensors based on a Grassmannian metric between subspaces extracted from HOSVD has been proposed. Despite a good classification accuracy, this method suffers from a high complexity cost in particular for datasets associated to Q-order tensors when Q > 3. In this work, we exploit some recent algebraic link between the HOSVD and the TTD to speed up the native method. We call this new supervised leaning scheme FAK-SETT for Kernel-based Fast Multilinear Projection. On real datasets, we show that the FAKSETT scheme reaches a very similar classification accuracy as the state-of-art method but for a running time considerably reduced on real datatsets.

Fig. 3 .

 3 Fig. 3. Three classes from Extended Yale Database.

Fig. 4 .

 4 Fig. 4. Two classes from UCF11 Database.

4. 1

 1 . Datasets • UCF11 dataset: This dataset [17] contains 1600 video clips belonging to 11 human actions such as: diving, trampoling jumping, walking, shooting... Two human actions are chosen: trampoling jumping and walking, presented in Figure 4. They will represents 2 classes for the classification. Sequence that contains the first 240 frames from each clip video where the resolution of each RGB frame is 320 × 240 are considered. These clip videos can be interpreted as tensors of order 4 with dimensions 240 × 240 × 320 × 3. A total of 109 tensors are present in each class. Randomly selecting 60% of them constitutes the training set. The rest is left for the test. • Extended Yale dataset B: This dataset [18] contains 28 human subjects. For each subject, there are 576 images of size 480 × 640 taken under 9 poses. Each pose is taken under 64 different illuminations. In that case, 3 subjects, represented in Figure 3 represents 3 classes for a classification problem. In order to construct the training and the test set, we break the tensor of each subject in 16 tensors by considering each 4 illuminations in a tensor of size 9 × 480 × 640 × 4.

Table 1 .

 1 that FAKSETT reduces significantly the running time for the computation of the factors, despite working with only Q = 4 order tensors. Higher orders would lead to an even higher running time gain between the two methods. Mean accuracy (standard deviation) on test data for

	s%	m-ranks FAKSETT method of [9]
	%50 [2,2,2,2] 0.72(10 -2 ) 0.73(10 -2 )
	%60 [3,3,3,3] 0.7(10 -2 )	0.7(10 -2 )
	%80 [3,3,3,3] 0.76(10 -2 ) 0.77(10 -2 )
	UCF11 database
	s%	m-ranks	FAKSETT	method of [9]
	%50 [1,3,2,1]	0.98(10 -2 )	0.99(10 -2 )
	%60 [1,2,2,1] 0.99(10 -2 ) 0.99(10 -2 )

Table 2 .

 2 Mean accuracy (standard deviation) on test data for

	Extended Yale database
	Database	m-ranks	FAKSETT	method of [9]
		[2,2,2,2]	14(0.42)	69(3)
	UCF11	[3,3,3,3]	15(0.63)	104(5)
	Extended Yale [1,2,2,1] 2.56(0.09)	9.47(0.1)

Table 3 .

 3 Mean time (standard deviation) on seconds consumed to compute HOSVD for different databases w.r.t to different values of multi-linear ranks.


Jérémy Lemaire
email: jeremy.ca.lemaire@gmail.com

Paco Bustamante

Olivier Marquis

Stéphane Caut

François Brischoux

Influence of sex, size and trophic level on blood Hg concentrations in Black caiman, Melanosuchus niger (Spix, 1825) in French Guiana

Keywords: Crocodilians, Trace metals, Tropical ecosystems, Diet, Bioaccumulation

Mercury (Hg) is a contaminant that is impacting ecosystems worldwide. Its toxicity is threatening wildlife and human populations, leading to the necessity of identifying the most affected ecosystems. Therefore, it is essential to identify pertinent bioindicator organisms to monitor Hg contamination. In this study, we determined the stable carbon ( 13 C) and nitrogen ( 15 N) isotope ratios in the red blood cells (RBCs), and the total Hg concentration in total blood of 72 Melanosuchus niger in French Guiana. The goals of our study were to assess the level of Hg contamination in total blood of Black caimans and to further investigate the influence of individual traits (i.e., sex, size/age, diet) on Hg concentrations. Mercury concentration in total blood of Black caimans ranged from 0.572 to 3.408 µg.g -1 dw (mean ± SD is 1.284 ± 0.672 µg.g - 1 dw) and was positively correlated to individual body size and trophic position (𝛿 15 N). We did not find any sexual or seasonal effects on Hg concentrations in the blood. The use of blood of M. niger is relevant to determine Hg concentrations within the population and suggests that this species can be used as a bioindicator for environmental contamination. In addition, our results emphasize trophic position as a major source of Hg variation and further suggest that it is essential to take trophic position ( 15 N) into account for future studies.

Introduction

Mercury (Hg) is one of the major contaminants that affect human and wildlife around the world with increasing levels due to anthropogenic activities [START_REF] Ericksen | Accumulation of atmospheric mercury in forest foliage[END_REF][START_REF] Scheuhammer | Recent advances in the toxicology of methylmercury in wildlife[END_REF]Hsu-Kim et al., 2018). In anoxic conditions, microorganisms can transform inorganic Hg into methylmercury (MeHg), the most toxic and bioavailable form of Hg (Compeau and Barta, 1985;[START_REF] Benoit | Geochemical and biological controls over methylmercury production and degradation in aquatic ecosystems[END_REF]. Because of its strong bioavailability, MeHg is highly absorbed and retained in biota. Hence, it accumulates within organisms during their lifetime and biomagnifies through food webs, resulting in an increasing Hg contamination level throughout most living organisms [START_REF] Mason | Bioaccumulation of mercury and methylmercury[END_REF][START_REF] Atwell | Biomagnification and bioaccumulation of mercury in an artic marine food web: insights from stable nitrogen isotope analysis[END_REF][START_REF] Power | Mercury accumulation in the fish community of a sub-Artic lake in relation to trophic position and carbon sources[END_REF].

Due to their life history traits, crocodilians (caimans, true crocodiles, alligators, gharials) are potentially good bioindicators of environmental contamination. Indeed, they are long-lived predators, resulting in the accumulation of Hg over a lifespan of several decades. As ectothermic vertebrates, crocodilians display relatively low metabolic rates, but relatively high tissue conversion rates; two features that are expected to favor the bioaccumulation of significant levels of Hg (Cook et al., 1989;[START_REF] Camus | Elevated lead levels in farmed American alligators Alligator mississipiensis consuming nutria Myocastor coypus meat contaminated by lead bullets[END_REF][START_REF] Jagoe | Mercury in alligators (Alligator mississipiensis) in the southeastern United States[END_REF][START_REF] Twining | Osteoderms of estuarine crocodiles record their enhanced Pb exposure in Kakadu National Park[END_REF][START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF][START_REF] Lázaro | Non-lethal sampling for mercury evaluation in crocodilians[END_REF][START_REF] Nilsen | Trace element biodistribution in the American alligator (Alligator mississippiensis)[END_REF]. Maternal transfer, an elimination pathway of Hg, which is already known from a variety of reptiles, can also be found in crocodilians (Sakai et al., 2000;[START_REF] Day | Monitoring mercury in loggerhead sea turtle, Caretta caretta[END_REF][START_REF] Nilsen | Examining maternal and environmental transfer of mercury into American alligator eggs[END_REF]. However, some studies reported similar Hg concentrations in males and females, whereas females that have already reproduced should theoretically have lower concentrations than males [START_REF] Burger | Metals and metalloids in tissues of American Alligators in Three Florida Lakes[END_REF][START_REF] Eggins | Mercury concentrations in different tissues of turtle and caiman species from Rio Purus, Amazonas, Brazil[END_REF][START_REF] Nilsen | Examining maternal and environmental transfer of mercury into American alligator eggs[END_REF].

The geographic range of caimans is altered by intense gold mining, an anthropogenic activity that is a major source of Hg deposition to the aquatic ecosystems of equatorial South America, and represents approximately 70% of local Hg emissions that are increasing the availability throughout food webs [START_REF] De Lacerda | Updating global Hg emissions from small-scale gold mining and assessing it environmental impacts[END_REF][START_REF] Rocha | Impact of fold mining associated with mercury contamination in surface soil of San Martin de Loba, south of Bolivar (Colombia)[END_REF][START_REF] Ottenbros | Knowledge and awareness of health effects related to the use of mercury in artisanal and small-scale gold mining in Suriname[END_REF].

Contrarily to highly mobile individuals such as migratory birds or fishes [START_REF] Fréry | Gold-Mining activities and mercury contamination of Native Amerindian communities in French Guiana: Key role of fish in dietary uptake[END_REF][START_REF] Fort | Spatial Ecotoxicology: Migratory Arctic Seabirds Are Exposed to Mercury Contamination While Overwintering in the Northwest Atlantic[END_REF], crocodilians are rather sedentary [START_REF] Hutton | Movement, Home Range, Dispersal and the Separation of Size Classes in Nile Crocodiles[END_REF][START_REF] Magnusson | The ecology of a cryptic predator, Paleosuchus trigonatus, in a tropical rainforest[END_REF][START_REF] Fujisaki | Home range and movements of American alligator (Alligator mississippiensis) in an estuary habitat[END_REF][START_REF] Caut | The dark side of the black caiman: Shedding light on species dietary ecology and movement in Agami Pond, French Guiana[END_REF]. Hg concentrations in their tissues reflect the contamination of their environment at a relatively small and precise spatial scale when measured in the blood.

In equatorial South America, this taxon could provide the opportunity to assess environmental Hg contamination due to its wide distribution. In addition, sample collection from crocodilians is rather uncomplicated as there is sufficient tissue (i.e., blood, scutes, claws) that can be sampled with comparatively little impact on individuals.

Stable carbon and nitrogen isotope analyses provide information on the diet composition and the trophic position of organisms via the variation of δ 13 C and δ 15 N levels. Carbon stable isotopes (δ 13 C) are used as a proxy to discriminate different types of habitat and to provide information on primary production [START_REF] Pinnegar | Contribution of stable-isotope data to elucidating food webs of Mediterranean rocky littoral fishes[END_REF][START_REF] Post | Using stable isotopes to estimate trophic position: models, methods, and assumptions[END_REF]. Nitrogen stable isotopes (δ 15 N) are discriminating the trophic position, as consumers are predictably enriched in 15 N in relation to their diet [START_REF] Minagawa | Stepwise enrichment of 15 N along food chains: further evidence and the relation between ∂ 15 N and animal age[END_REF]Wada, 1984, Post, 2002;[START_REF] Vanderklift | Sources of variation in consumer-diet ∂15N enrichments: a meta-analysis[END_REF]. Among crocodilians, it has been shown that increased values of δ 15 N reflect a change in the trophic position, linked to a change in their diet [START_REF] Radloff | Characterising ontogenetic niche shifts in Nile crocodile using stable isotope (∂ 13 C, ∂ 15 N) analyses of scute keratin[END_REF][START_REF] Bontemps | Diet of the nonnative spectacled caiman (Caiman crocodilus) in Puerto Rico[END_REF][START_REF] Caut | The dark side of the black caiman: Shedding light on species dietary ecology and movement in Agami Pond, French Guiana[END_REF]. Therefore, adding analyses of stable carbon and nitrogen isotopes to the quantification of Hg levels is extending information on the feeding habitat and trophic positions.

In this study, we assessed Hg concentrations in the only known population of Black caimans (Melanosuchus niger) in French Guiana [START_REF] De Thoisy | Genetic structure, population dynamics, and conservation of black caiman (Melanosuchus niger)[END_REF]. This French territory suffers from illegal, artisanal, small-scale gold mining. The goals of our study were to determine the levels of Hg contamination in the blood of Black caimans and the factors influencing the Hg concentrations. We investigated a potential variation between seasons, and the influence of size, sex and foraging ecology on the individual contamination level.

Material and Methods

Study area

The study was conducted in the Nature Reserve "Réserve Naturelle Nationale de Kaw-Roura", French Guiana (4°36'N, 52°07W) (Fig. 1), a 94.700 ha protected area situated approximately 90 Km southwest of the city of Cayenne. Animals were captured in "Agami Pond", an area situated in the middle of the Nature Reserve, (04°38'N, 52°09'W), a patchwork of herbaceous savannah, swamp forest and open water. Black caimans were sampled during three sampling periods: once during dry season (October 2013), and two samplings during rainy season (May 2014 andMay 2015). Caimans were located at night between 19:00pm to 04:00am, using a head lamp, and further captured with a noose.

Sample collection

A total of 72 individuals were captured, among which 49 adults and subadults were sexed with a ratio of 30 males and 19 females. The body (from the tip of the snout to the cloaca) and total length (including the tail) of each individual were measured with a flexible ruler. We collected a blood sample (~2 ml) through occipital venous sinus puncture, using a syringe with a 30 gauge heparinized needle (heparin sodium). Black caimans were released at the location of their capture directly after biometric measurements and sample collection were performed.

Blood samples were separated as following: 1 mL of each blood sample was centrifugated in order to separate the red blood cells (RBCs) and plasma for isotopic analyses (see below), an additional 1 mL of the total blood was kept in 70 % alcohol until further processed at the laboratory for Hg assays. Samples were initially collected to investigate the dietary ecology of Black caimans [START_REF] Caut | The dark side of the black caiman: Shedding light on species dietary ecology and movement in Agami Pond, French Guiana[END_REF]. We took the opportunity to further use this sampling set to investigate the Hg concentration in the blood of Melanosuchus niger. As a result, the protocol that had been originally applied did not allow us to assess water blood content, and Hg values are therefore presented as dry weight (dw) of the total blood (see below).

Mercury analysis

One mL of each total blood sample was freeze-dried and grounded to a fine powder. Total Hg concentration (hereafter Hg) in the blood was determined by direct measurement using an atomic absorption spectrometer AMA-254 (Advanced Mercury Analyser-254; Altec®).

Analyses were made on at least two replicates of ~3.0 mg dry weight (dw) for each individual.

The reproducibility for duplicate samples was approved when Relative Standard Deviation (RSD) was below 10%. The method was validated by the analyses of certified reference material (CRM) produced by the National Research Council of Canada: TORT-2 (Lobster hepatopancreas; certified Hg concentration: 0.27 ± 0.06 µg.g -1 dw) and TORT-3 (Lobster hepatopancreas; certified Hg concentration: 0.29 ± 0.02 µg.g -1 dw). CRMs were analyzed at the beginning and at the end of the analytical cycle, and between every 10 samples [START_REF] Chouvelon | Hg concentrations and related risk assessment in coral reef crustaceans, molluscs and fish from New Caledonia[END_REF]. Recovery rates of certified reference material were 97.3 ± 1.0 % for TORT-2 (n=4) and 102.0 ± 1.5 % for TORT-3 (n=5). Blanks were included at the beginning of each analytical run and the limit of quantification was 0.05 ng. Hg concentrations in caiman blood are presented in µg.g -1 dw.

Stable isotope analysis

An analysis of nitrogen and carbon stable isotopes was conducted on red blood cells (RBCs) separated from plasma by centrifugation. RBC samples were freeze-dried and then grounded to a fine powder. Aliquots of 0.3-0.4 mg were placed in tin capsules. Stable isotopes were analyzed using a mass spectrometer (IsoPrime 100, Isoprime, UK) associated to a C-N-S elementary analyser (vario MICRO cube, Elementar, Germany). Stable carbon and nitrogen isotope ratios are expressed as 𝛿 15 N or 𝛿 13 C = [(Rsample/Rstandard)-1]x1000, where R is 15 N/ 14 N or 13 C/ 12 C for 𝛿 15 N or 𝛿 13 C. IAEA-CG-6 (-10.4‰) was used as a standard reference for carbon, and IAEA-N1 (+0.4‰) for nitrogen. Ten replicate assays of internal laboratory standards indicated maximum measurement errors (SD) of ± 0.2‰ and ± 0.15‰ for the nitrogen and carbon isotope measurements, respectively. Further details on isotope analysis are available in Caut et al., 2019.

Statistical analyses

All analyses were performed using the software R, v.3.2.4 (R development Core Team 2013).

The data was first checked for normality and homogeneity of variances. The relationship between Hg concentration and animal total length was assessed by parametric linear regression. Paired t-tests were used to compare Hg concentrations between the sex, and the season. A linear regression model was used to determine the relationship between Hg concentrations, 𝛿 15 N and 𝛿 13 C values and to further determine the relationship between caiman length and 𝛿 15 N and 𝛿 13 C values. The significance for statistical analyses was always set at p < 0.05.

Results

The Hg concentrations in the 72 sampled individuals ranged from 0.299 to 3.408 µg.g -1 dw (Table 1). There was a significant, positive relationship between Hg concentration and total body length (Linear regression, F1,70 = 92.37, p < 0.0001, r² = 0.56, Fig. 2). Adult females and males had a similar size range, respectively 162.9 ± 60.4 cm and 171.0 ± 53.1 cm (Paired t-test, t = 0.48, p = 0.64) and displayed similar Hg concentrations, respectively 1.660 ± 0.694 µg.g -1 dw and 1.459 ± 0.502 µg.g -1 dw (Paired t-test, t = 1.09, p = 0.28, Fig. 3).

Seasons (dry and rainy) did not influence Hg concentration (Paired t-test, t = 0.38, p = 0.70), with values of 1.499 ± 0.440 µg.g -1 dw for dry season and 1.559 ± 0.661 µg.g -1 for rainy season.

The 𝛿 15 N was significantly and positively related to caiman total length (linear regression, F1,70 = 68.33, p < 0.0001, r² = 0.49) and Hg concentration (linear regression, F1,70 = 58.74, p < 0.0001, r² = 0.45, Fig. 4a). However, the 𝛿 13 C was not related to caiman total length (linear regression, F1,70 = 0.86, p = 0.36, r² = -0.002) nor Hg concentration (linear regression, F1,70 = 1.13, p = 0.27, r² = -0.003, Fig. 4b).

Discussion

Our results show that Black caimans in French Guiana bioaccumulate Hg. As a consequence, Hg concentration increases with body size and is further linked to their trophic position (𝛿 15 N).

We did not find any sexual or seasonal correlation with the Hg concentration.

Blood is a universally used matrix to measure Hg exposure in a wide array of organisms [START_REF] Lommel | Organochlorine pesticides, octachlorostyrene, and mercury in the blood of Elb River residents, Germany[END_REF][START_REF] Henny | Nineteenth century mercury: hazard to wading birds and cormorants of the Carson River, Nevada[END_REF], Eggins et al., 2015). Our results show a significant positive relationship between the total length of Black caiman and the Hg concentration in the blood (Fig. 2). Mercury is being transported through the blood to different tissues, such as those involved in detoxification (mainly the liver), storage (muscles), excretion (kidneys) and elimination (keratinized tissues). In reptiles, Hg concentrations of blood are related to Hg concentrations of internal tissues because of the dynamic transfer between these matrices [START_REF] Burger | Metals levels in blood, muscle and liver of water snakes (Nerodia spp.) from New Jersey, Tennessee and South Carolina[END_REF][START_REF] Eggins | Mercury concentrations in different tissues of turtle and caiman species from Rio Purus, Amazonas, Brazil[END_REF][START_REF] Nilsen | Trace element biodistribution in the American alligator (Alligator mississippiensis)[END_REF]. Therefore, Hg values in the blood reflect an overall Hg concentration in the internal tissues. Our results also confirm the usefulness of blood to determine the Hg contamination in caimans [START_REF] Eggins | Mercury concentrations in different tissues of turtle and caiman species from Rio Purus, Amazonas, Brazil[END_REF][START_REF] Marrugo-Negrete | Mercury levels and genotoxic effect in caimans from tropical ecosystems impacted by mining[END_REF].

Several studies in crocodilians already reported a linear increase of Hg with age in various tissues [START_REF] Yanochko | Tissue mercury concentrations in alligators (Alligator mississipiensis) from the Florida Everglades and the Savannah River site, South Carolina[END_REF][START_REF] Burger | Metals and metalloids in tissues of American Alligators in Three Florida Lakes[END_REF][START_REF] Rumbold | Levels of mercury in alligators (Alligator mississipiensis) collected along a transect trough the Florida Everglades[END_REF][START_REF] Schneider | Mercury concentration in the spectacled caiman and black caiman (Alligatoridae) of the Amazon: implications for human health[END_REF]. Age and size are generally correlated (i.e. [START_REF] Eaton | Estimating age from recapture data: integrating incremental growth measures with ancillary data to infer age-at-length[END_REF]), yet, in wild populations, detailed information on age is rarely available. The relationship between crocodilian size and Hg concentration in tissues such as blood, scutes, claws, muscles and liver shows that Hg is bioaccumulated across the life of an individual [START_REF] Burger | Metals and metalloids in tissues of American Alligators in Three Florida Lakes[END_REF][START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF][START_REF] Lázaro | Non-lethal sampling for mercury evaluation in crocodilians[END_REF][START_REF] Marrugo-Negrete | Mercury levels and genotoxic effect in caimans from tropical ecosystems impacted by mining[END_REF]. Although the Hg concentration in various tissues and the body size are positively correlated in some crocodilian species (i.e., Alligator mississippiensis, Caiman crocodilus, Melanosuchus niger, Caiman yacare), we emphasize that this pattern has not been detected in other species (i.e., Crocodylus acutus, Crocodylus moreletii, [START_REF] Yanochko | Tissue mercury concentrations in alligators (Alligator mississipiensis) from the Florida Everglades and the Savannah River site, South Carolina[END_REF][START_REF] Burger | Metals and metalloids in tissues of American Alligators in Three Florida Lakes[END_REF][START_REF] Rainwater | Metals and organochlorine pesticides in caudal scutes of crocodiles from Belize and Costa Rica[END_REF][START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF][START_REF] Lázaro | Non-lethal sampling for mercury evaluation in crocodilians[END_REF][START_REF] Marrugo-Negrete | Mercury levels and genotoxic effect in caimans from tropical ecosystems impacted by mining[END_REF]. Such divergent findings may highlight the importance of relatively large sample sizes associated with significant body size ranges in order to robustly assess the relationship between Hg and individual traits. Mercury concentrations are significantly linked to 𝛿 15 N values (a proxy used to discriminate the trophic level) (Fig. 4a). Results indicate that the Hg concentration is depending on the ontogenetic change in the trophic position in M. niger [START_REF] Caut | The dark side of the black caiman: Shedding light on species dietary ecology and movement in Agami Pond, French Guiana[END_REF].

Our results do not show a relationship between Hg concentration and 𝛿 13 C (a proxy used to discriminate different types of habitat) for M. niger (Fig. 4b). This result shows that the ontogenetic change in the foraging ecology of M. niger does not induce a change in foraging habitats in the studied population. We did not find any seasonal influence on Hg concentrations, suggesting that the trophic ecology of M. niger at our study site does not significantly vary across seasons.

We did not find any variation in Hg concentrations between males and females (Table 1, Fig. 3). A possible mechanism of Hg elimination in females is the maternal transfer of Hg to the eggs: Females use their energy storage (e.g. body fat and proteins) during vitellogenesis, which may induce a transfer of the Hg stored in their tissues towards their eggs [START_REF] Nilsen | Examining maternal and environmental transfer of mercury into American alligator eggs[END_REF] as reported for birds for instance (e.g., [START_REF] Lewis | Mercury levels in eggs, tissues, and feathers of herring gulls Larus argentatus from the German Wadden Sea Coast[END_REF]. This process would lead to lower concentrations in the blood of females that recently laid eggs, compared to males. Therefore, our results suggest that either 1), Hg remobilization did not occur, or more likely, 2) this process is not significant enough to be detected in the blood of female Black caimans.

Future studies should investigate the level of Hg transfer to the eggs during vitellogenesis in female M. niger, as well as in other crocodilian species.

It is important to emphasize that the relatively low turn-over rates of erythrocytes in crocodilians may have obscured putative influences of sex and season on Hg levels. Indeed, blood is known to reflect short-time Hg exposure in birds or mammals [START_REF] Bearhop | Dynamics of mercury in blood and feathers of great-skuas[END_REF].

For instance, the lifetime of erythrocytes is up to two months in birds and up to four months in mammals (reviewed in [START_REF] Rodnan | The life span of the red blood cell and the red blood cell volume in the chicken, pigeon and duck as estimated by the use of Na2, Cr 51 O4: with observations on red cell turnover rate in the mammal, bird and reptile[END_REF][START_REF] Monteiro | Kinetics, Dose-Response, and Excretion of Methylmercury in Free-Living Cory's Shearwaters[END_REF]. In crocodilians, the lifetime of erythrocytes can last up to 3 years [START_REF] Cline | Effect of temperature on red cell survival in the alligator[END_REF]. Future studies are required to assess whether low turn-over rates of erythrocytes in crocodilians influence short-scale, temporal variations in Hg concentrations.

Mercury concentrations in the blood of M. niger in French Guiana (1.284 ± 0.672 µg.g -1 dw) are higher than in other South American species with a maximum value of 0.325 ± 0.105 µg.g - 1 dw (Table 2; Marugo-Negrete et al., 2019). However, limited data is available from this geographic area (Table 2). The values we report in the blood of M. niger are similar to what has been determinated in the muscle of the same species in Brazil (Table 2). This is especially interesting as Hg concentrations in the muscle usually tends to be higher than in the blood [START_REF] Schneider | Mercury concentration in the spectacled caiman and black caiman (Alligatoridae) of the Amazon: implications for human health[END_REF]. Insufficient data on Hg in crocodilians from the Americas make comparison difficult, except for the United States where the American alligator is well documented (Table 2). Clearly, future studies are required in order to provide a complete background to perform substantial comparisons. In addition, the use of other tissues where sampling is less invasive (i.e.., claws and scutes, [START_REF] Lázaro | Non-lethal sampling for mercury evaluation in crocodilians[END_REF][START_REF] Marrugo-Negrete | Mercury levels and genotoxic effect in caimans from tropical ecosystems impacted by mining[END_REF], should be considered, for it is already a conventional method in other reptile species (e.g., [START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF][START_REF] Lemaire | Determinants of mercury contamination in viperine snakes, Natrix maura, in Western Europe[END_REF][START_REF] Beau | Environmental causes and reproductive correlates of mercury contamination in European pond turtles (Emys orbicularis)[END_REF].

Conclusion

Overall, the use of blood of M. niger is informative regarding the Hg concentration and it extends the use of Crocodilians to monitor the environmental Hg contamination. To do so, precise individual information (e.g., size and diet or trophic position) is required. For instance, the change of the trophic position has a significant impact on the level of Hg contamination between juveniles (feeding on low trophic level prey) and adults (feeding mostly on high trophic level prey). Therefore, it is essential to take their diet into account to compare levels of Hg contamination between different sites or populations. Additionally, future studies are required to assess whether the concentrations of Hg we have found in M. niger pose a threat to the species.

Acknowledgments

We are grateful to the authorities of Conseil Scientifique Régional du Patrimoine Naturel (CSRPN) and La Direction de l'Environnement, de l'Aménagement et du Logement de Guyane (DEAL), who authorized our fieldwork. We would also like to thank M. Bacques, V.

Figure 1 .

 1 Figure 1. Geographic location of the study site in South America (A), French Guiana (B), Kaw-Roura Nature Reserve (C).

Figure 2 .Figure 3 .Figure 4 .

 234 Figure 2. Relationship between the total length (in cm) and Hg concentration (µg.g -1 dw) measured in the blood of Black caiman Melanosuchus niger from French Guiana (Linear regression, F1,70 = 92.37, p < 0.0001, r² = 0.56).

Table 1 .

 1 Sex, total length (cm) and blood Hg concentration (µg g -1 dw) of the Black caiman, Melanosuchus niger, from French Guiana.

		N (Males/Females)	Total Length		Hg concentrations
			Mean ± SD	Min-Max	Mean ± SD	Min-Max
	Season
	Dry	18 (11/7)	155.8 ± 35.8	114 -278	1.499 ± 0.440	0.741 -2.432
	Rainy	31 (19/12)	174.9 ± 63.8	95 -320	1.559 ± 0.661	0.572 -3.408
	Sex
	Male	30	171.0 ± 53.1	109 -320	1.459 ± 0.502	0.717 -2.894
	Female	19	162.9 ± 60.4	95 -254	1.660 ± 0.694	0.572 -3.408

Table 2 .

 2 Review of Hg concentration (µg.g -1 dw) reported in crocodilians. TL stands for Total Length and SVL for Snout-Vent-Length (cm). ( a Original data reported in wet weight, transformed in dry weight with a factor 3.8 calculated by[START_REF] Jeffree | Element concentrations in the flesh and osteoderms of Estuarine Crocodiles (Crocodylus porosus) from the Alligator Rivers Region, Northern Australia: Biotic and Geographic Effects[END_REF] for muscles; b original data reported in wet weight, transformed in dry weight using a factor 5).

	Species	Location	Tissue	n	Length (cm)	Hg (µg.g -1 dw)	Reference
					Mean ±SD	Min-Max	Mean ±SD	Min-Max
	Black caiman	Rio Purus, Brazil Muscles	11	107.5 ± 31.4 (SVL)	75.3 -190.9 (SVL) 1.93 a	0.69 -4.06 a	Schneider et al., 2012
	Melanosuchus niger
	Black caiman	Rio Purus, Brazil Muscles	16	102 ± 27 (SVL)	75 -191 (SVL)	0.669 ± 0.369 a	-	Eggins et al., 2015
	Melanosuchus niger
	Black caiman	Mamirauá	Muscles	60	107 -309 (TL)	107 -309 (TL)	1.457 ± 0.433 a	-	Correia et al., 2014
	Melanosuchus niger	Reservoir, Brazil
	American Alligator	South Carolina	Total Blood	-	-	-	2.19 ± 0.38	-	Jagoe et al., 1998
	Alligator mississippiensis
	American Alligator	Florida	Total Blood	37	92.1 ± 31.6 (SVL)	43.9 -153.5 (SVL) 0.965 b	0.280 -6.900 b	Nilsen et al., 2017
	Alligator mississippiensis
	Spectacled Caiman	La Mojana,	Total Blood	22	57.2 ± 3.5 (TL)	-	0.325 ± 0.105 b	-	Marrugo-Negrete et al., 2019
	Caiman crocodilus	Colombia
	Spectacled Caiman	La Mojana,	Total Blood	23	57.5 ± 6.8 (TL)	-	0.07 ± 0.04 b	-	Marrugo-Negrete et al., 2019
	Caiman crocodilus	Colombia
	Black caiman	Kaw, French	Total Blood	72	143.2 ± 61.3 (TL)	46 -326 (TL)	1.284 ± 0.672	0.30 -3.41	Our study
	Melanosuchus niger	Guiana