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Identifying and Validating Tankyrase Binders and Substrates: A Candidate Approach

The poly(ADP-ribose)polymerase (PARP) enzyme tankyrase (TNKS/ARTD5, TNKS2/ARTD6) uses its ankyrin repeat clusters (ARCs) to recognize degenerate peptide motifs in a wide range of proteins, thereby recruiting such proteins and their complexes for scaffolding and/or poly(ADP-ribosyl)ation. Here, we provide guidance for predicting putative tankyrase-binding motifs, based on the previously delineated peptide sequence rules and existing structural information. We present a general method for the expression and purification of tankyrase ARCs from Escherichia coli and outline a fluorescence polarization assay to quantitatively assess direct ARC–TBM peptide interactions. We provide a basic protocol for evaluating binding and poly(ADP-ribosyl)ation of full-length candidate interacting proteins by full-length tankyrase in mammalian cells.

Introduction
Poly(ADP-ribosyl)ation (PARylation) constitutes a striking posttranslational modification (PTM) catalyzed by poly(ADP-ribose) polymerase (PARP) enzymes, which serially transfer ADP-ribose from NAD + onto substrate proteins [1]. The resulting long, strongly negatively charged PAR chains provide attachment sites for proteins endowed with PAR-binding modules or directly affect substrate function [2]. PAR can thus act as a scaffolding component as well as a regulatory PTM. PARylation is most commonly associated with nuclear events such as gene regulation and DNA damage repair, but PAR is found in both the nucleus and the cytoplasm [1,3]. The PARP tankyrase, of which there are two human paralogs (TNKS/ ARTD5, TNKS2/ARTD6, see Fig. 1a), contributes to both the nuclear and cytoplasmic pools of PAR [4,5]. The biological roles of the two tankyrases are largely redundant [6], pointing to shared  [31]). (b) and (c) Examples for ARC-TBM interactions studied by X-ray crystallography. (b) Human TNKS2 ARC4 is shown in surface representation with bound TBM peptides from 3BP2 and MCL1 shown in stick representation with the core TBM octapeptide colored purple and orange, respectively, and by heteroatom. TBM amino acid positions (1)(2)(3)(4)(5)(6)(7)(8) and sequences shown. The figure was generated by superimposing the ARCs of the ARC4-3BP2 and ARC4-MCL1 crystal structures (PDB accession codes 3TWR and 3TWU, respectively) onto each other and showing ARC4 of the former [7]. The colored surface areas represent different contact areas, as indicated, that mediate binding of the TBM peptides (Modified from [7] with permission from Elsevier/Cell Press). (c) ARC2 (from ARC2-3) of murine Tnks bound by the N-terminus of murine Axin1 (PDB accession code 3UTM), which contains two TBMs [11]. Each TBM binds one copy each of ARC2 in a dimeric ARC2-3 assembly. The figure was generated by superimposing the two ARC2-3 copies onto each other; the surface of ARC2 bound by the first TBM is shown. TBMs are shown and labeled as in (b). The first TBM, shown in magenta, consists of a continuous stretch of eight amino acids. In the second TBM, shown in green, the Arg at position 1 is followed by a seven-amino-acid insertion (positions +1 to +7), as indicated in the sequences shown. The peptide insertion forms a loop. (d) TBM sequence rules represented by a sequence logo. (Reprinted from [7] with permission from Elsevier/Cell Press.) (e) Sequence alignment of known example TBMs ( [7] and references therein, [11,22,23,[37][38][39]), colored by identity with conservation graph, generated with ClustalX and Jalview [40,41]. UniProt IDs are indicated [24]. The asterisk indicates insertion sequences in AXIN1 and AXIN2. The TBMs of 3BP2, TRF1 (TERF1_HUMAN), and MERIT40 (BABA1_HUMAN), studied as model TBMs here, are highlighted molecular mechanisms. The recruitment of tankyrase to different protein complexes associated with specific cellular processes and situated at different subcellular locations defines its diverse functions. All tankyrase binders characterized to date bear a tankyrasebinding motif (TBM), which in its simplest form consists of six to eight consecutive amino acids [4,7,8]. TBMs are recognized by tankyrase's ankyrin repeat clusters (ARCs) [7,9,10]. Out of the five ARCs, the central one (ARC3) is devoid of a known peptidebinding function while the other four (ARCs 1, 2, 4, and 5) each feature a highly conserved peptide-binding pocket with similar specificities [7,10] (Fig. 1a). Given four peptide-binding ARCs, tankyrase recognizes its binders multivalently.
The TBM has been characterized extensively and a consensus sequence of R-x-x-[small hydrophobic or G]-[D/E]-G-[no P]-[D/E] identified through positional scanning and evaluation of known TBMs [7] (Fig. 1d and e). Paired with structural information from ARC-peptide complexes [7,[11][12][13], these "sequence rules" provide a valuable tool for identifying tankyrase binders/substrates. Fig. 1b-e gives examples for X-ray crystal structures describing TBM-ARC interactions, summarize the experimentally derived TBM sequence rules, and list known TBMs. Within the motif, the Arg residue at position 1, bound in an extensive "Arg cradle," is essential, as is Gly at position 6, owing to its unique geometry that is adopted when the residue is sandwiched between two aromatic side chains in the ARC (Fig. 1b, d). At positions 2 and 3, where side chains point away from the ARC, a wide range of amino acids is tolerated. At position 4, a small and/or hydrophobic residue binds a tight hydrophobic sub-pocket. Gly, Pro, Ala, and Cys (in this order of preference) have been found suitable by positional scanning [7], and known TBMs mostly feature Pro and Gly, followed by Ala, Val, Leu, and Cys ( Fig. 1e). At position 5, Asp is clearly preferred, with Glu ranked second, but Val, Gln, Tyr, Ile, and Cys were all allowed in positional scanning experiments (Fig. 1b, d) [7]. In line with these observations, Asp and Glu are found at position 5 in the vast majority of known TBMs, followed by Gln, Pro, Ile, and Val (Fig. 1e). Positions 7 and 8 tolerate a wide range of amino acids, with the exception of Pro at position 7, where Pro causes an unfavorable distortion of the peptide backbone ( Fig. 1d). At position 8, Asp and Glu are most favored, owing to an electrostatic contact with the ARC, and can balance out the negative contribution made by suboptimal residues at other positions (Fig. 1b, d) [7]. Recent structural and biophysical studies suggest that the spatial organization of the five ARCs and the positioning of multiple TBMs within a subset of tankyrase binders encode another determinant of tankyrase binding [13].
Among the tankyrase-substrate relationships most extensively studied to date are those with AXIN (axis inhibition protein, AXIN1, AXIN2), scaffolding proteins involved in Wnt signaling [11,14], the telomeric protein TRF1 (telomeric repeat-binding factor 1, official gene name TERF1) [12,15], and the signaling adaptor protein 3BP2 (SH3 domain-binding protein 2, official gene name SH3BP2) [7,16]. Many more tankyrase binders/substrates have been identified, and the list of known interactors keeps expanding [5]. An in silico prediction of tankyrase binders gives reason to anticipate a broad involvement of tankyrase in a wide range of biological functions [7]. To understand the complex biological roles of tankyrase, also in light of the considerable interest in tankyrase as a potential therapeutic target [5,17], we require insights into the complement of tankyrase-binding proteins in the proteome.
Here, we outline a hierarchical three-step candidate approach for identifying tankyrase binders and substrates, providing further experimental detail on the method reported previously [7]. Step 1 constitutes TBM prediction, step 2 the evaluation of TBMs as direct ARC binders by fluorescence polarization (FP), and step 3 the validation of tankyrase binding and tankyrase-dependent PARylation in the full-length protein context. We chose two model proteins: the first identified tankyrase binder, TRF1 [15], and a novel tankyrase binder, MERIT40 (Mediator of RAP80 interactions and targeting subunit of 40 kDa, official gene name BABAM1), which was identified by the approach presented here [7]. The TBM from 3BP2 serves as an additional example in the FP assay [7]. As part of step 2, we present a general method for the expression and purification of TNKS and TNKS2 ARCs from Escherichia coli Table 1 Human tankyrase (TNKS/TNKS2) ARC constructs for biophysical assays. The proteins include a non-native, vector-derived GAMGS sequence at the N-terminus that is retained upon cleavage of the affinity tag [ (Table 1). ARCs 1, 4, and 5 can be produced as individual domains. ARCs 2 and 3 are insoluble when produced independently; however, they can be produced as a double ARC2-3 construct. Moreover, the entire tankyrase N-termini with all five ARCs can be generated [7,13]. Proteins are expressed with a cleavable N-terminal His 6 -GST tag, which enables simple affinity purification, minimally followed by size exclusion chromatography upon tag removal. The subsequent FP assay uses a candidate TBM peptide, synthesized with a fluorescent label such as fluorescein, to directly measure the binding affinity to a tankyrase ARC or a set of ARCs. In this assay, the fluorescent peptide probe is excited by polarized light. The light emitted by an unbound probe loses most of its polarization due to its rapid motion in solution. When bound to an ARC, movement of the peptide is slowed down and a high degree of polarization retained in the emitted light. Titration of tankyrase ARCs at a constant probe concentration allows the dissociation constant (K d ) to be determined [7,[18][19][20]. Upon confirmation of the isolated TBM, further validation of the candidate tankyrase binder requires an assessment of tankyrase binding and substrate PARylation using full-length proteins (step 3). We present details for a straightforward assay based on co-expression in HEK293T cells, co-immunoprecipitation and the detection of PAR in the immunoprecipitates, using PAR-binding antibodies [7].

Materials
Unless the supplier is explicitly mentioned, chemicals are typically obtained from Sigma-Aldrich. 6. Fluorescently tagged peptide corresponding to TBM of potential tankyrase binder/substrate, 2× stock (50 nM for a final assay concentration of 25 nM) in FP assay buffer. In the present examples (3BP2, MERIT40, TRF1), fluorescein and 5(6)-carboxyfluorescein are used as fluorophores. The peptides have been described previously [7]. We recommend peptides of minimally the TBM octapeptide with one flanking amino acid on either side. The peptides used here are longer (see Fig. 3b for peptide sequences). The fluorescein fluorophore is linked via β-Ala, which also provides an additional linker to minimize potential steric interference of the fluorophore with the peptide-ARC interaction (see Note 8).
22. Vacuum pump with inlet trap and collection flask for aspirating buffer.
24. Electrophoresis apparatus for the above and appropriate power supply.
28. Wet transfer Western blotting apparatus and appropriate power supply. 29. Ponceau S solution.
33. X-ray film for Western blot detection or alternative ECL detection setup.

Methods
The details of many standard experimental methods not addressed here can be found in [21].
Experimental approaches such as yeast-two-hybrid analysis [22] or co-immunoprecipitation coupled with tandem mass spectrometry [23] have been used to identify proteins present in complexes with tankyrase. It is desirable to pinpoint those proteins that directly interact with tankyrase. The existence of putative TBMs is the most reliable known indicator for direct interaction. Based on previously identified TBM sequence rules and structural information, we provide a guide to identifying strong TBM candidates for further validation. A previously generated list of ranked octapeptide motifs across the entire human proteome can be used [7]. Here, we recapitulate a simple step-by-step approach for identifying candidate TBMs without the need for specialized bioinformatics beyond the use of established programs and databases.
1. Screen your protein of interest for potential TBMs. In an initial step, a search for Arg and Gly spaced 6 amino acids apart (i.e., with four amino acids in between, RxxxxG) will suffice. See step 4 below for atypical TBMs.
2. Using UniProt (http://www.uniprot.org), assess the topology of the protein and whether the candidate motif would be located in the cytoplasm or nucleoplasm, accessible to tankyrase [24]. The relevant information can be found under Subcellular location > Topology.
3. Assess the occurrence of disordered stretches in your protein of interest. TBMs must be present in unstructured regions of the protein to be accessible to tankyrase and must not be part of a stable α-helix or β-strand. Secondary structure information, obtained from the Protein Data Bank [25], is available in UniProt (http://www.uniprot.org) under Structure > Secondary structure [24]. It remains possible that TBMs are present within loops of structured protein domains. If no structural information is available, a disorder predictor such as IUPred (http://iupred.enzim. hu) may be used to obtain an indication of protein disorder [26].

Predicting Tankyrase Binders
4. Assess the short-listed sequences for their suitability as TBMs. REAGDGEE has been found to be the optimal 8-amino-acid TBM by positional scanning [7], but many TBMs only span six amino acids (positions 1-6). While the sequence rules from positional scanning prove valuable in predicting TBMs, it should be noted that some of their aspects may be specific to the context of the 3BP2 TBM peptide, which positional scanning was performed on [7]. Whereas Arg and Gly at positions 1 and 6, respectively, are essential, other residues are important as well, with the exception of positions 2 and 3, which can likely be ignored since they do not contribute to binding and mainly fulfil spacing roles (Fig. 1b, d).
Please refer to the motif description under Subheading 1 for the assessment. Of note, a large or strongly charged amino acid at position 4 very likely disqualifies the TBM candidate as a genuine tankyrase binder. Furthermore, Asp and Glu at position 8 can compensate for unfavorable amino acids at other positions [7], as seen in one of the TBMs of AXIN1/2, where a suboptimal Val at position 4 appears to be counterbalanced by a Glu at position 8 ( Fig. 1e) [7,11]. Interestingly, a second TBM in AXIN1/2 shows that the Arg, normally at position 1, can be placed further N-terminal, resulting in looping-out of the "inserted" residues ( Fig. 1c, e). Likewise, the E3 ubiquitin ligase RNF146 has been proposed to contain numerous atypical TBMs with a nonconventional positioning of the Arg [27], and it is possible that a distal Arg is required for weak binding of the TBM of GRB14 to tankyrase (Fig. 1e) [7,8,28]. Thus, the possibility of a distal Arg residue should be taken into consideration. It is likely that such extended TBMs display a weaker affinity for tankyrase. Numerous tankyrase binders contain multiple TBMs, such as AXIN1/2 [11] and MERIT40 [7] (see below). Since avidity effects likely contribute to binding of these proteins to tankyrase, the affinity of some of these individual TBMs for the ARC may be lower, and this may be reflected in deviations from the "optimal" sequence.
cDNA sequences encoding TNKS or TNKS2 ARC constructs are cloned into a pETM-30-2 expression vector (or similar vector) to generate fusion proteins with an N-terminal His 6 -GST tag followed by a TEV protease cleavage site (ENLYFQG) [7]. See Table 1  A similar procedure is followed for the purification of all tankyrase ARCs. All buffers are ice-cold, and work is performed at 4 °C or on ice throughout. In the first step, the protein is affinity-purified by immobilized metal affinity chromatography (IMAC) using a Ni 2+ affinity column. The affinity tag is then cleaved overnight using TEV protease, under simultaneous dialysis to remove imidazole from the elution step. A second Ni 2+ affinity chromatography step separates the cleaved tag from the protein. An optional anion exchange chromatography step removes further impurities. Finally, size exclusion chromatography yields high-quality purified protein for downstream applications. The general procedure is applicable to all TNKS and TNKS2 ARCs with small changes ( Fig. 2a; see Note 11). 2. Break cells by using a large-tip sonicator at 40% amplitude output, using a 5 s on, 5 s off pulse, for a total of 5 min "on" time.

Purification of Tankyrase ARCs
Keep cells on ice continuously to avoid overheating (see Note 12). Take a sample of the total lysate for subsequent analysis by SDS-PAGE (9 μL lysate + 3 μL 4× SDS sample buffer). 5. Decant the supernatant into a beaker, and sonicate on ice, 5 s on, 5 s off for a total of 20 s "on" time to further break up genomic DNA and avoid clogging the filter in the next step.
6. Filter the supernatant through 5.0 μm syringe filter units. Take a sample of the soluble lysate for subsequent analysis by SDS-PAGE (9 μL lysate + 3 μL 4× SDS sample buffer). Load the cleared lysate on the equilibrated HisTrap column using the peristaltic pump as before (see Note 13). The His 6 -GST-tagged protein will bind to the immobilized Ni 2+ ions. Wash the column with 20 CV of buffer A (100 mL) to remove unbound contaminants. Collect lysate flow-through and the wash buffer in case the protein was not bound or was released during the wash, and take samples for analysis by SDS-PAGE (9 μL flowthrough or wash + 3 μL 4× SDS sample buffer).
7. Attach the HisTrap column to an FPLC system, and elute the His 6 -GST-ARC protein with the following three-step protocol, at a flow rate of 2 mL/min, collecting 1.5 mL fractions in a 96-deep-well block: step 1: 100% buffer A for 2 CV. step 2: gradient from 0-100% buffer B over 20 CV. step 3: 100% buffer B for 4 CV.
8. Take samples of each peak elution fraction (9 μL of eluate + 3 μL 4× SDS sample buffer). Analyze the samples taken in steps 2 and 6 (2 μL of sample for lysates and flow-through, 5 μL of sample for wash) and the peak elution fractions (5 μL of sample) by SDS-PAGE (Fig. 2b). 9. Pool fractions containing ARC fusion protein. Take a sample of the pooled fractions (9 μL of protein + 3 μL 4× SDS sample buffer). Add TEV protease (approximately 100 μL of 5 mg/ mL stock for every 25 mL fusion protein solution) to cleave the tag. 10. Soak dialysis tubing (3500 Da MWCO) in dialysis buffer, and seal one end with a dialysis membrane clip. Transfer the protein into the dialysis tubing and seal the other end. More than one dialysis tube may be required. Dialyze overnight in a 2 L glass beaker containing dialysis buffer, with gentle stirring at 4 °C. Avoid contact between the stirrer bar and the dialysis tubing to prevent rupture.
11. Pour content of dialysis tubing into 50 mL Falcon tubes. Centrifuge at 3200 × g for 15 min to remove any precipitate that may have formed. Take a sample of the protein post-TEV cleavage (9 μL of protein + 3 μL 4× SDS sample buffer). White precipitate often forms overnight with the change to low-salt buffer. SDS-PAGE analysis of the precipitate reveals it to be enriched in a contaminant (not shown).

Meanwhile, wash a 5 mL HisTrap column with 10 CV of H 2 O.
Next, equilibrate the column in 10 CV of dialysis buffer. Filter the supernatant through a 0.22 μm syringe filter and load it onto the equilibrated HisTrap column using the low-pressure peristaltic pump. Collect the flow-through. The untagged ARC protein will pass through, while the cleaved tag (or residual His 6 -GST-ARC fusion protein) will be retained on the column (see Note 14). Wash with 2 CV of dialysis buffer to fully remove all ARC protein from the column, collecting the wash. Take samples of the flow-through and wash (9 μL of protein + 3 μL 4× SDS sample buffer).
13. Analyze 5 μL of the pre-TEV sample, post-TEV sample and flow-through/wash samples from the second Ni 2+ column by SDS-PAGE to assess successful tag removal and separation (Fig. 2c).
14. Take the protein-containing samples (flow-through/wash) and concentrate the protein to about 20 mL by centrifuging in a 3000 Da MWCO spin concentrator at 3200 × g for 30 min at a time in a swinging bucket rotor. Mix by gently pipetting up and down to prevent a steep concentration gradient from forming in the concentrator. Take a sample of the concentrated protein (9 μL of protein + 3 μL 4× SDS sample buffer).
15. The following anion exchange chromatography step is optional, but was found to increase the purity of ARC proteins, especially TNKS2 ARC5, by removing a higher-molecular-weight impurity. Using the peristaltic pump at 2 mL/min, wash a 5 mL HiTrap Q HP column with 5 CV of H 2 O, followed by 5 CV of buffer B for Q column, and then equilibrate with 10 CV of buffer A for Q column. Pass the concentrated protein over the column, and collect the flow-through. Wash the column with 2 CV of buffer A for Q column, also collecting the flowthrough. ARCs do not bind to the Q column; however, the impurity does and will be retained on the column (see Note 15). Take a sample of the combined flow-through and wash (9 μL of protein + 3 μL 4× SDS sample buffer). Analyze 5 μL of the samples from step 14 and this step by SDS-PAGE as above (Fig. 2d). 16. Concentrate the protein as in step 14, to ≤2 mL.
17. Centrifuge protein in a microcentrifuge tube at 18,000 × g for 10 min to remove any particles before size exclusion chromatography.
18. Load the concentrated protein onto an equilibrated size exclusion column connected to an FPLC system, using a 2 mL sample loop (see Note 4). Elute the protein isocratically, using 1.2 CV of size exclusion buffer. Collect 1 mL fractions in a 96-deep-well block.
19. Take samples of the input material and peak fractions (9 μL input or fraction + 3 μL 4× SDS sample buffer). Analyze 5 μL of the samples by SDS-PAGE (Fig. 2e). 20. Combine fractions containing pure protein. Wash the membrane of a spin concentrator by spinning through one concentrator volume of H 2 O to remove any stabilizing agents such as glycerol and azide. Now concentrate the protein using the prewashed spin concentrator as described above (step 14) until a concentration of >0.5 mM is achieved (solubility of multi-ARC constructs can be lower). The concentration can be determined by measuring the UV absorbance at 280 nm and using the molar extinction coefficient calculated by ProtParam (http://web.expasy.org/protparam/) [29].
21. Aliquot the protein into small volumes in thin-walled PCR tubes and flash-freeze them in a liquid nitrogen bath. Frozen protein aliquots can be stored at −80 °C until future use.
This assay measures the direct binding of a fluorescently labeled TBM candidate peptide to a tankyrase ARC [7]. The ARC protein is titrated at a constant peptide probe concentration, and the change in polarization (ΔFP) is measured and plotted. Plotting ΔFP values against [ARC] enables a dissociation constant (K d ) to be calculated. In the present example, we use fluorescein-based peptide labels, but the general method can be adapted for different fluorophores.
1. Ensure the plate reader is set up for fluorescence polarization, with the correct filters for the fluorophore. The fluorescein

Fluorescence Polarization Assay for TBM Validation
example uses a 485 nm excitation filter and two 520 nm emission filters, one parallel and one perpendicular to the plane of the linearly polarized light used for excitation.
2. Dissolve the lyophilized peptide probe in FP assay buffer, to approximately 100 μM. The concentration can be measured spectrophotometrically (see Note 16). Here, we measure the absorbance of the peptide stock at 492 nm and use a molar extinction coefficient for fluorescein of ε 492 = 83,000/M/cm [30]. The concentrated probe can then be aliquoted into small volumes (5-10 μL) and flash-frozen in liquid nitrogen for long-term storage at −80 °C, to be thawed when required.
3. Determine the optimal probe concentration to use. This will depend on the sensitivity of the plate reader. FP values should be independent of the probe concentration used, and give a robust signal window for an unbound vs. protein-bound peptide. Make 2× stocks of a twofold dilution series of probe in FP buffer, from 0-800 nM (10 concentrations + no peptide). It is often easier to make a 1/100 dilution of the concentrated peptide stock to avoid pipetting small volumes. Total sample volumes per well are either 15 or 50 μL (see step 5 below).
4. Prepare a 2× protein stock solution, by diluting tankyrase ARC protein in FP buffer to 20 μM (10 μM final protein concentration). The protein concentration should be in vast excess over the peptide probe to obtain a first impression of the anticipated signal window between free and protein-bound peptide probe.
5. Plate out the assay samples in technical duplicate (see Table 2, Note 17). Small-volume plates will require 15 μL per well (7.5 μL of each stock), standard-volume plates 50 μL per well (25 μL of each stock). Mix the probe stock solution 1:1 with either FP buffer for the peptide probe-only titration or protein F_parallel and F_perpendicular denote the fluorescence intensities parallel and perpendicular to the plane of the linearly polarized light used for excitation. mP, millipolarization units. 8. Export the FP data and raw fluorescence intensity values. Plot the data (average FP vs. [probe]) using GraphPad Prism or your data analysis program of choice (Fig. 3a).
9. Determine the minimum probe concentration required. Raw fluorescence intensity values of >10× the blank reading are necessary to calculate accurate FP values. In the example shown in Fig. 3a, fluorescence intensity values measured with probe concentrations below 6.25 nM were too low and therefore excluded.
10. Determine the maximum probe concentration. The FP values will drop sharply when the signal overloads the detectors. In this case, both detectors reach saturation, so the fluorescence intensities registered in the parallel and perpendicular channels will be identical, and hence the FP calculated will be zero. In the example shown in Fig. 3a, 50 nM is the maximum usable peptide probe concentration. FP readings between 6.25 and 50 nM probe are approximately constant.
11. Peptide probe concentrations should be kept as low as reasonably possible. Thus, the peptide concentration can be ignored in K d calculations. 25 nM probe was chosen for the protein 12. Set up a binding experiment for K d determination. Mix the probe and protein stock solution 1:1 to give a final well volume of 15 μL (7.5 μL of each stock solution, small-volume plates). Centrifuge the plate as in step 5 above. Incubate the plate in the dark at room temperature for 30 min to achieve equilibrium before measurement.
13. Calculate FP as in step 7 above and export the raw fluorescence and calculated FP values. units; Background denotes the baseline ΔFP value, which should be zero. Although it is possible to constrain the background to zero, it is advisable to retain the background term since the baseline is defined by more values than that from the zero-protein sample.

Enter the individual FP values into GraphPad
Non-binding peptides will give a straight line of nonspecific binding. Binding peptides will give a logarithmic curve (Fig. 3b). This analysis will yield a K d value. 16. Repeat the experiment to obtain pooled data from (typically three) separate experiments. In each separate experiment, technical duplicates are combined into a single data point. Error bars (SEM) are calculated for the mean data points from the separate experiments (Fig. 3b). The peptides from 3BP2, TRF1, and MERIT40 (two peptides) bind TNKS2 ARC5 with the indicated affinities, while no binding is detectable for the G6R negative control peptide from 3BP2 (Fig. 3b).
This final section outlines a step-by-step approach to assess and validate the full-length candidate protein interaction with fulllength tankyrase and the extent of its tankyrase-dependent PARylation. Mammalian expression constructs for MYC 2 -tagged TNKS2 (pLP-dMYC SD-TNKS2) and FLAG-or FLAG 3 -tagged candidate interacting proteins (pCMV-FLAG-MERIT40 and pLP-tripleFLAG SD-TRF1) are generated. Standard site-directed mutagenesis is performed to mutate the Gly at position 6 of the FP-validated TBMs to Arg. The FLAG-tagged candidate proteins and corresponding TBM mutant derivatives are next used as "baits" in co-immunoprecipitation experiments, to assess their binding to and their PARylation by MYC 2 -TNKS2, using catalytically inactive TNKS2 (G1032W) as control [31].
1. Grow a sufficient number (here two) 15 cm cell culture plates of HEK293T cells to a cell density of ≈90% confluence in standard DMEM media supplemented with 10% FBS.
2. Remove the media and gently rinse the cell culture plates with 10 mL of Versene to remove residual media, which could impede the efficient dissociation of the cells by trypsin.
3. Add 3 mL of trypsin-Versene to each plate and place the plates back in the incubator for 2 min. Gently tap the side of the plates to help the cells detach from the plate and dissociate from each other.
4. Add 10 mL of DMEM media with 10% FBS to each plate; the FBS will inactivate the trypsin. Pipette the cell suspension up and down a few times to ensure proper dissociation of cell clumps into a homogenous cell suspension.
5. Measure the cell density, using either a hemocytometer or automated cell counter. Add 6 × 10 6 cells each to the required number of 10 cm cell culture plates for the cotransfection of different DNA constructs (Table 3). Add 10 mL of DMEM media with 10% FBS to each plate and incubate cells overnight.
6. The next day, co-transfect cells with 5 μg of each DNA construct (thus 10 μg total) per plate (  6. Gently settle the resin by centrifugation at 800 × g for 5 min at 4 °C and remove supernatant using a vacuum pump. Table 3 Chart for co-transfection of HEK293T cells for co-immunoprecipitation. The indicated FLAG/FLAG 3tagged constructs (5 μg) are used as baits in co-immunoprecipitation with the indicated MYC 2tagged TNKS2 constructs (5 μg). The G-to-R mutation at position 6 of the TBM efficiently abolishes the ARC-TBM peptide interaction [7]. A G1032W mutation abolishes both poly-and mono(ADPribosyl)ation by TNKS2 [31]. Each "+" sign denotes a single co-transfection setup

Co-immunoprecipitation
Wash the resin by adding 1 mL of RIPA buffer to each sample and incubating microcentrifuge tubes for 5 min on a rotating wheel at 4 °C.
8. Settle the resin as before (step 6) and repeat the wash step four more times. 9. After the last wash step, gently remove as much of buffer as possible and add 25 μL of 2× SDS sample buffer. Boil samples at 95 °C for 5 min, collect briefly by centrifugation and store at −20 °C until analysis, if required (immunoprecipitate (IP) samples).
1. Resolve 10 μL of the boiled input (step 4 above) and IP (step 9 above) samples on a pre-cast 4-15% Tris-glycine polyacrylamide gradient gel for SDS-PAGE analysis.
2. Transfer proteins from the gel onto a nitrocellulose membrane using a wet-transfer blotting system. Ponceau S can be used to assess the transfer quality.
3. Incubate the nitrocellulose membrane for at least 1 h at room temperature on a horizontal shaking platform in 5% dry milk powder in PBS to block the membrane to reduce nonspecific binding of antibodies during the subsequent immunodetection steps.
5. Wash the membrane three times for 5 min with copious amounts PBS + 0.1% Tween 20 on a horizontal shaking platform.
6. As required, incubate the membrane with the matching HRPcoupled secondary antibody, here diluted 1:5000 in 5% milk/ PBS for 1 h at room temperature on a horizontal shaking platform (see Note 20).

Develop Western blot by incubating membrane with ECL
Western blotting substrate following the manufacturer's instructions.
9. Detect chemiluminescence signal by exposing membrane to X-ray film in a dark room and develop the film with an X-ray film developer (see Note 21). Fig. 4 shows the TBMdependent interaction of FLAG 3 -TRF1 and FLAG-MERIT40 with MYC 2 -TNKS2, and the TNKS2-dependent PARylation of both TNKS2 interactors, in addition to TNKS2 auto-PARylation (see Note 22). Both MERIT40 TBMs contribute to tankyrase binding (Fig. 4b).

Notes
1. We recommend using vectors with a kanamycin selection marker. Ampicillin hydrolysis by secreted β-lactamase and under low pH increases the proportion of cells lacking the plasmid, which decreases protein yield [33].

Fig. 4
Assessing tankyrase binding and PARylation by tankyrase in the full-length protein context. (a) FLAG 3 -TRF1, either in its wild-type form or as a G18R TBM mutant ("mut."), was co-expressed with the indicated MYC 2 -TNKS2 constructs, either in wild-type form or as a G1032W PARP-inactive mutant ("GW") [31]. FLAG-TRF1 was immunoprecipitated and input and immunoprecipitate (IP) samples analyzed by SDS-PAGE and Western blotting as indicated. "•" in the anti-PAR blot labels a high-molecular-weight PARylated species that appears to be antagonized by MYC 2 -TNKS2 overexpression. "*" in the anti-PAR blot denotes a nonspecific band. (b) Same analysis as in (a) with FLAG-MERIT40, either in wild-type form or as a G33R ("mut. 1"), G53R ("mut. 2"), or GG33/53RR ("mut. 1 + 2") TBM mutant. MERIT40 appears as a doublet, most likely reflecting differentially phosphorylated species [32]. See Note 22 on attributing PAR signals to candidate proteins 2. RIL cells contain additional tRNAs for codons of Arg, Ile, and Leu that are otherwise rare in E. coli. The plasmid bearing these genes contains a chloramphenicol selection marker.
3. We recommend using one 5 mL column per 4 L expression culture. If using larger volumes, connect additional column(s) in series. Ni 2+ affinity columns can easily be reconstituted by stripping from and re-charging with Ni 2+ as per the manufacturer's instructions. 4. Use a Superdex 200 column for ARC1-5 constructs. All other ARC constructs are sufficiently small for the Superdex 75 column.
5. TCEP is more stable than DTT and not volatile, unlike β-mercaptoethanol or DTT. However, TCEP is acidic and will affect the final pH of the buffer unless the 0.5 mM stock solution is pH-adjusted with NaOH. To keep costs down, TCEP is only used in the final purification step.
6. HEPES is preferred for the final protein and in experiments due to its lower temperature dependency compared with Tris [34]. Tris was chosen for the affinity purification step due to its weak interaction with Ni 2+ , which would help decrease background (contaminant) binding [35]. If HEPES buffer is used in the affinity purification step, the imidazole concentration may need to be increased to achieve comparably low background binding.
7. Detergent is used to reduce nonspecific binding and surface tension that may interfere with fluorescence intensity readings in the plate format. The choice of detergent and its concentration is empirical. We have also had good experience with using 100 μg/mL bovine serum albumin (BSA), but use CHAPS here since it is more effective at reducing nonspecific binding.
8. Keeping the fluorescently labeled peptides as short as possible increases the ΔFP signal window between the bound and unbound states. Ideally, peptides should be HPLC-purified; however, this is not always realistically achievable, especially if large numbers of peptides are to be compared and no access to in-house solid-state peptide synthesis is available. To save costs, peptides can be used at non-HPLC-purified grade, in which case a capping step is strongly recommended after each amino acid coupling reaction to prevent peptide synthesis intermediates from being linked to the fluorophore in the final coupling step and affecting the assay [7].
9. Alternatively, fluorescently labeled antibodies can be used for detection with appropriate fluorescence imaging systems. Instead of the anti-PAR antibody, an anti-pan-ADP-ribose or anti-poly(ADP-ribose) binding reagents (MABE1016 and MABE1032, respectively, Millipore) may be explored. 10. Compared to LB, TB is richer and enables higher cell densities in the log phase of growth. Cooling the cultures before IPTG induction slows down expression, thereby facilitating correct protein folding and increasing protein solubility.
11. For ARC2-3 and ARC1-5 constructs described here, a minimal NaCl concentration of 300 mM needs to be maintained, compared to 100 mM for all single-ARC constructs, and glycerol may further help stabilize the protein [7].
12. For large volumes, it may be easier to lyse cells in two batches. Alternative disruption techniques can be used, such as homogenization by an Avestin EmulsiFlex homogenizer.
13. If available with the FPLC setup, a superloop or, preferably, a sample pump can be used to load the column.
14. Depending on the ARC construct and the final concentration of imidazole in the dialysis buffer, ARCs can bind weakly to the Ni 2+ column even after tag cleavage. They can be eluted with a further imidazole gradient. While this adds one more step to the purification protocol, it enables even higher purities to be achieved.
15. The Q column step can also be performed before concentration, directly using the flow-through from the second Ni 2+ affinity column; however, prior concentration saves time in loading the column. 16. Confirm the pH of the peptide stock solution before measuring the concentration. Acidity, for example due to residual trifluoroacetic acid from the peptide synthesis, will strongly affect fluorophore absorption.
17. We recommend leaving wells in the outermost rows and columns empty to reduce the microplate "edge effect," a discrepancy in readings between the central and peripheral wells [36].
18. It is important to add the different transfection reagents in the specified order to ensure proper calcium phosphate-DNA particle formation.
19. Avoid using micropipette tips to transfer the cell suspension after scraping. The small opening of the tips can cause cells to break due to shearing. You can cut off the tips to avoid this risk.
20. For directly HRP-coupled antibodies, azide as a preservative should be avoided as it inhibits HRP activity. 21. The Western blot protocol can be adapted for film-free chemiluminescence detection or fluorescence-based detection. 22. Attributing a PAR signal to a particular protein by molecular weight may be challenging, in part due to possible PAR-induced mobility shifts in SDS-PAGE. Since the tankyrase substrate can-didates are immunoprecipitated from cell lysates, it is possible that the observed PAR signal corresponds to other PARylated proteins in a protein complex. Ultimate confirmation of substrates can be obtained from experiments with purified proteins or PAR site mapping by mass spectrometry, for example.
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extfieldsofstudy: Biology Medicine

text:
Epigenetic DNA Methylation Mediating Octopus vulgaris Early Development: Effect of Essential Fatty Acids Enriched Diet

The common octopus, Octopus vulgaris, is a good candidate for aquaculture but a sustainable production is still unviable due to an almost total mortality during the paralarvae stage. DNA methylation regulates gene expression in the eukaryotic genome, and has been shown to exhibit plasticity throughout O. vulgaris life cycle, changing profiles from paralarvae to adult stages. This pattern of methylation could be sensitive to small alterations in nutritional and environmental conditions during the species early development, thus impacting on its health, growth and survival. In this sense, a full understanding of the epigenetic mechanisms operating during O. vulgaris development would contribute to optimizing the culture conditions for this species. Paralarvae of O. vulgaris were cultured over 28 days post-hatching (dph) using two different Artemia sp. based diets: control and a long chain polyunsaturated fatty acids (LC-PUFA) enriched diet. The effect of the diets on the paralarvae DNA global methylation was analyzed by Methyl-Sensitive Amplification Polymorphism (MSAP) and global 5-methylcytosine enzyme-linked immunosorbent assay (ELISA) approaches. The analysis of different methylation states over the time revealed a global demethylation phenomena occurring along O. vulgaris early development being directly driven by the age of the paralarvae. A gradual decline in methylated loci (hemimethylated, internal cytosine methylated, and hypermethylated) parallel to a progressive gain in non-methylated (NMT) loci toward the later sampling points was verified regardless of the diet provided and demonstrate a pre-established and well-defined demethylation program during its early development, involving a 20% of the MSAP loci. In addition, a differential behavior between diets was also observed at 20 dph, with a LC-PUFA supplementation effect over the methylation profiles. The present results show significant differences on the paralarvae methylation profiles during its development and a diet effect on these changes. It is characterized by a process of demethylation of the genome at the paralarvae stage and the influence of diet to favor this methylation loss.

INTRODUCTION
One of the cephalopod species with a great potential for intensive aquaculture diversification is the common octopus, Octopus vulgaris, since it fulfills many of the criteria for this purpose: a short life cycle, fast growth, good food conversion rate, high reproduction performance, fast adaptation to life in captivity, high nutritional value and market price. Unfortunately, while great efforts have been put into raising octopuses in captivity, the sustainable production of this species is still unviable due to the mass mortality during the planktonic paralarvae phase (Vaz-Pires et al., 2004;Iglesias and Fuentes, 2014). Factors, such as: water quality, temperature, light exposure or nutrition; directly influence on growth, health, and ultimately, survival. In addition, octopus paralarvae from distinct geographical origins could have different behavior under similar culturing conditions, suggesting an interaction between paralarvae adaptability to captivity and genotype (Garrido et al., 2017).
Nutrition has been identified as one of the most critical factors influencing octopus paralarvae viability and survival in captivity conditions . In contrast to the standard feeding protocols based on live Artemia sp. prey, experimental enriched diets supplemented with long chain polyunsaturated fatty acids (LC-PUFAs) and phospholipids have been shown to be beneficial in terms of growth and survival (Guinot et al., 2013a;Garrido et al., 2016a). LC-PUFAs are known to modulate gene expression by provoking local and global effects over DNA methylation in several organisms (see Burdge and Lillycrop, 2014 for review). DNA methylation, the addition of a methyl group to the C-5 position of a cytosine nucleotide by a DNA methyltransferase (Jin et al., 2011), is the most widely studied epigenetic mechanism. Increasing evidence points out DNA methylation as a mechanism with an important role in gene expression regulation in the eukaryotic genome (Wu and Zhang, 2014). Unprogrammed alterations on the methylation profiles triggered by diet and environmental stressors would lead to aberrant gene expression associated with spurious consequences (Faulk and Dolinoy, 2011). This is particularly true during the early development, when DNA methylation is crucial on genomic reprogramming. These early acquired epigenetic landmarks may affect the phenotype, provoke diseases at the adulthood or cause premature mortality (Faulk and Dolinoy, 2011). Moreover, they may persist throughout the entire animal life and even be transmitted to the following generations by genomic imprinting, conditioning their offspring (Feil and Berger, 2007). Considering the direct impact on gene expression and potential heritability, the analysis of methylation profiles should become a valuable tool, if not essential, for biomonitoring the physiological status of cultured specimens in aquaculture (Moghadam et al., 2015).
Although there is wide evidence demonstrating an interaction between epigenetic mechanisms and environment in mammals, research on invertebrates is still ongoing (Sarda et al., 2012). One of the most representative examples of this phenomenon is found in the honeybee Apis melifera, with diet-controlled larvae differentiation into either queen or worker casts positively correlating with their brain methylomes (Lyko et al., 2011). Equally, DNA methylation on the crustacean Daphnia magna is labile to exposure to toxic pollutants, conditioning fertility and affecting their future offspring by genome imprinting (Vandegehuchte et al., 2009a,b). DNA methylation research in mollusks is scarce and limited to a few species by using methylation-specific restriction enzymes (Petrović et al., 2009;Díaz-Freije et al., 2014;Sun et al., 2014), quantification by LC-MS (Fneich et al., 2013) and ELISA approaches (Rivière et al., 2013) and genome-wide bisulfite sequencing (Gavery and Roberts, 2013). Gavery and Roberts (2010) confirmed the presence of intragenic CpG island methylation in Crassostrea gigas, demonstrating a relationship between predicted methylation status and gene expression. Moreover, the availability of C. gigas methylome has exemplified the importance of methylation during the molluscan embryo development and in their adaptability to environmental fluctuations (Gavery and Roberts, 2010;Rivière et al., 2013;Rivière, 2014). All these evidences support a conservative role of methylation in invertebrates, presenting a plastic response to environmental changes and allowing the integration of these signals in the genome, as it happens in vertebrates. In fact, previous studies in O. vulgaris have highlighted the important role of DNA methylation during the paralarvae period, when major morphological changes take place (Díaz-Freije et al., 2014).
Under the premise that the paralarvae stage should be sensitive to the environment (including rearing conditions and nutritional aspects), monitoring the methylation status of O. vulgaris during this life stage will help assessing the impact of the rearing conditions on their development and, ideally, will predict the later outcome of the culture.
In this sense, we focused our attention on DNA methylation in O. vulgaris paralarvae fed two different diets commonly used during the rearing of this life stage. First, the global methylation level in paralarvae was examined using an Enzymelinked immunosorbent assay (ELISA) and then, methylation status changes, associated with early stages of development and diets, were quantified by means of methylation-sensitive amplified polymorphism (MSAP).

Experimental Design and Diets
Adult octopuses were captured using artisanal traps in Tenerife coastal waters (Canary Islands, Spain) and maintained as a breeding stock in the facilities of the Oceanographic Centre of the Canary Islands (Spanish Institute of Oceanography). Individuals were kept in 1,000 L tanks (with a maximum density of 10 kg/tank) with water renovation (5 L/min), under dissolved oxygen 100% saturation conditions and low light intensity (400 lx on average). Broodstock were fed ad libitum with 50% of frozen crab (Portunus validus) and 50% of squid (Loligo opalescens) every day. PVC shelters were provided as refuges to enrich the environment and induce natural spawning.
Hatchlings were obtained from spontaneous spawning of one adult octopus female (2 kg) kept in captivity. The female was mature at the moment of the capture and after 2 months was paired with only one male (2.4 kg) which was the main contributor to the offspring. A total of 30,000 paralarvae, 6 replicates of 5,000 paralarvae per tank (10 paralarvae/L) were reared during 28 days in 500 L black fiberglass cylinder-conical tanks. Two fluorescent lights (OSRAM Dulux superstar 36 W/840) were placed above each tank to attain 700 lx focused in the middle of the tank surface with a 12L:12D photoperiod (8:00-20:00). A flow-through seawater system equipped with 20, 5, and 1 µm filter cartridges and UV lamps were used. A water flow per tank of 1 L/min (which promoted over 1.5 renewals/day) was applied from 18:00 to 8:00, removing the excess of Artemia sp. through a 500 µm outflow mesh located in the middle of the tank. Two moderated flux aeration stones were placed in front each other in the edges of the tanks. The green-water technique was applied, using 5·10 5 cell/mL of Nannochloropsis sp. (Phytobloom Green Formula R , Olhão, Portugal) that was added to the tanks before turn on light. Temperature and oxygen were daily checked, while nitrite, ammonium and salinity were verified once a week.
Paralarvae were fed with either Artemia sp. (Sep-Art BF, INVE Aquaculture, Dendermonde, Belgium) enriched with microalgae Isochrysis galbana (T-Iso) and Nannochloropsis sp. (control diet from now onwards) or Artemia sp. enriched with Marine Lecithin LC 60 R (PhosphoTech Laboratoires, Saint Herblain, France) (enriched diet from now onwards). In order to adapt prey size along the experimental period, three Artemia sp. sizes (on-growing at different ages) were used along the experimental period: nauplii from 0 to 3 days post-hatching (dph) paralarvae, 4 days old metanauplii from 4 to 11 dph and 8 days old metanauplii from day 12 to 28 dph. The enrichments and on-growing of the Artemia sp. was carried out according to Garrido et al. (2017).

Paralarvae Sampling and DNA Isolation
Paralarvae growth was assessed at 0, 10, 20, and 28 dph. Dry weight (DW) measurements were individually determined as described by Fuentes et al. (2011). Briefly, paralarvae were euthanized in chilled seawater (−1 • C), washed in distilled water, oven dried (110 • C, 20 h) and weighted. The specific growth rate (SGR, %DW/day) was expressed as: , where DW f and DW i are the DW at final time (t f ) and initial time (t i ), respectively following Garrido et al. (2017) protocol. Dorsal mantle length (DML) measurements were done for each individual with a stereomicroscope (Nikon SMZ-10A. Nikon, Tokyo, Japan) following Villanueva (1995). Survival (S%) was assessed at the end of the experiment as: , where X f is the number of alive individuals at the end of experiment, X i is the initial number of individuals and X s is the number of sacrificed individuals during the experiment. To detect significant changes in terms of these growth parameters an unpaired T-test was performed using the software R.
For DNA methylation analysis, 10 paralarvae were sampled at 0, 10, 20, and 28 dph for each of the two tanks conditions. Larvae were euthanized in chilled seawater (−1 • C) and stored in ethanol 100% at −20 • C until their analysis. Genomic DNA was individually purified from entire paralarvae using an NZY Tissue gDNA Isolation kit (NZYtech). Subsequently DNA quality and concentration were checked with a Nanodrop-1000 spectrophotometer. DNA extracted samples were adjusted to a final concentration of 100 ng/µL and frozen until use.
All animal experiments were performed in compliance with the Spanish law 65/2013 within the framework of European Union directive on animal welfare (Directive 2010/63/EU) for the protection of animals employed for scientific purposes, following the Guidelines for the care and welfare of cephalopods proposed by Fiorito et al. (2015), and approved by the Ethic Committee of the National Competent Authority.

Global 5-Methylcytosine Levels
A global 5-methylcytosine (ELISA) y (5-mC DNA ELISA Kit, ZYMO) was used as a first attempt to measure in an easy and fast way the patterns of the global DNA methylation levels in octopus paralarvae. DNA from three individuals at two different developmental stages including starting developmental point (0 dph) and also 20 dph for both diets were analyzed. Measurements were tested in duplicates, according to the manufacturer instructions. The optical density at 415 nm was determined after 45 min using an iMark TM Microplate Absorbance Reader, (Bio-Rad). The global DNA methylation levels were expressed in percentages as the mean of the two technical replicates and further analyzed using paired T-tests in the software R.

Methylation Sensitive Amplification Polymorphism (MSAP)
A MSAP protocol, adapted from Reyna-López et al. (1997) was applied to 10 paralarvae per sampling point (0, 10, 20, and 28 dph). Briefly, each DNA sample was digested in parallel reactions with either EcoRI/HpaII or EcoRI/MspI endonucleases. The obtained DNA fragments were ligated with specific adapters and subjected to two consecutive PCR amplification rounds: a first pre-selective PCR, using an HpaII/MspI+T and EcoRI+A primer pair was followed by a second selective PCR with 6-FAM labeled HpaII/MspI+TAG and HpaII/MspI+TCC primers. All reactions were run in a GeneAmp PCR system 9,700 (Applied Biosystems). A detailed protocol of the entire procedure is given in Morán and Pérez-Figueroa (2011). Following AFLP reading on an ABI Prism 310 Genetic Analyzer (Applied Biosystems) restriction profiles were scored using the GeneMapper v.3.7 software (Applied Biosystems).
Methylation Sensitive Amplification Polymorphism (MSAP) profiles were assessed from the resulting absence/presence matrix with the R package MSAP (Pérez-Figueroa, 2013). Loci were categorized as non-methylated (NMT) on specimens amplifying bands for both HpaII and MspI digestions, internal cytosine methylated (ICM), or hemimethylated (HMM) if bands were, respectively present only on either MspI or HpaII, or hypermethylated (HPM) whenever both bands were not present for a given specimen. Loci below a 5% error rate threshold and showing < 2 occurrences of each state were systematically excluded from the analysis. Differences among experimental groups were assessed with a multivariate Principal Coordinates Analysis (PCoA) and Analysis of Molecular Variance (AMOVA).
To further assess whether locus-specific methylation on the paralarvae is dependent on diet and/or age, Fisher's exact tests were used to detect candidate loci among the methyl sensitive loci (MSL). After statistical adjustment of the resulting P-values according to Benjamini and Hochberg false discovery rate (FDR), only loci showing P < 0.05 were selected. Estimates of relationships among selected loci were computed by Gower's Coefficient of Similarity and expressed as Euclidean distances. The resulting matrix was clustered by the average linkage method (UPGMA) and visualized as a heatmap matrix with the R "ComplexHeatmap" package (Gu et al., 2016).

Culture Data: Growth and Survival
A total of 30 individual paralarvae were measured at four different sampling points (0, 10, 20, and 28 dph) for each of the two tested diets. Table 1 shows the DW, DML, SGR, and survival ratio parameters of paralarvae fed with control and enriched diet. The individuals at the starting point (0 dph), showed a DW of 0.23 ± 0.03 mg. This DW increased at 10 dph when the paralarvae were fed with the enriched diet, showing a DW significant higher than the control diet. However, at 28 dph the differences in terms of DW were not significant between the tested feeds. The DML increased from 2.15 ± 0.08 mm at hatching to 2.48 ± 0.35 mm at 28 dph in the control diet group. Concerning the enriched diet group, the DML at 28 dph increased reaching 2.71 ± 0.25 mm. The control diet group showed a survival ratio of 1.47 ± 1.28% at the end of the experiment. For enriched diet the survival ratio increased up to reach 11.7 ± 3.41%.

Global 5 MeC Levels
The 5-mC (ELISA) performed showed that the methylation level of cytosines ranged from 1.21% (minimum values) to 1.24% (maximum value). The methylated cytosine mean level was 1.22 ± 0.07% at the initial stage (0 dph). At 20 dph methylated cytosine mean level was slightly inferior (1.19 ± 0.19%) for larvae fed with the control diet and it slightly increased (1.24 ± 0.25%) for larvae fed with the enriched diet. No differences were found between groups.

MSAP Analyses
The MSAP analyses yielded a total of 297 polymorphic loci when all data from the 70 individuals under study were included (7 groups: 0, 10, 20, and 28 dph for control and enriched diets; 10 individuals per group). Of these, 269 loci were identified as MSL, whereas the remaining 28 ones were non-methyl sensitive (NML). A 100% (28 loci) of the NML were classified as polymorphic whilst the proportion of polymorphic loci reached 70% (188 loci) of the MSL.
The analysis of different methylation states over the time revealed a global demethylation phenomena occurring along O. vulgaris early development and directly driven by the age of the paralarvae. A gradual decline in methylated categories (HMM, ICM, HPM) parallel to a progressive gain in NMT loci toward the later sampling points was verified regardless of the diet provided (see Figure 1). In fact, the NMT state, representing a 26.12 ± 2.45% of the total at hatching (0 dph), reached maximum values at 28 dph: 37.93 ± 4.08% for the control diet and was even slightly higher, 39.84 The PCoA performed with the MSL revealed a grouping of the samples according to this age-driven demethylation process (Figure 2). The first principal component, explaining a 19.4% of the observed variation, clearly discriminates between early (0 dph and 10 dph) and late (28 dph) time-points, with samples from the same period clustering together into relatively compact groups. Nevertheless, a differential behavior between diets was observed at 20 dph. At this age, paralarvae subjected to an enriched feeding diet grouped closer to the later samples (28 dph) than to their equivalents for the control diet. A larger intragroup variability was observed at 20 dph in control paralarvae with regards to their LC-PUFA enriched equivalents. This may be interpreted in terms of a slower and/or random loss of epigenetic marks in the absence of enriched diet supply during Differences between control and enriched diet groups at same age were analyzed with an unpaired T-test. DW, Dry weight; SGR, specific growth rate; DML, dorsal mantle length. Data reported with standard deviation. *Indicate significant differences between treatments at the same age (P < 0.05).
Frontiers in Physiology | www.frontiersin.org  this period. More specifically, pairwise comparisons between adjacent sampling times ( Table 2) revealed significant differences in DNA methylation profiles only at diet groups the 10-20 dph (Control diet: ST = 0.1411, P < 0.0001; Enriched diet: ST = 0.3365, P < 0.0001) and 20-28 dph comparisons for both diet groups. Overall, these MSAP results were consistent with a preprogrammed gradual loss of methylation throughout the early development of O. vulgaris, having a diet-sensitive period around 20 dph. The statistical analysis of the different loci by the Fisher Exact test allowed the identification of a total of 51 statistically significant loci (Adjusted P < 0.05) among experimental groups. These loci presented a differential distribution of its methylation Pairwise AMOVA between adjacent ages was analyzing separately for control and enriched diets. Identification of specific loci by Fisher's test and False Discovery Ratio adjust (P < 0.05 and FDR < 0.05).
**Indicate significant differences between treatments at the same age (P < 0.01). ***Indicate significant differences between treatments at the same age (P < 0.001).
ST Analysis of molecular variance ST genetic differentiation (Excoffier et al., 1992). # Number of. status mainly between diets at the 10-20 dph comparison ( Table 2). The result indicates that 15 loci exceeded the FDR cut-off established in the enriched diet compared with the only 2 loci for the same comparison in the control diet. These 2 loci detected in 10-20 dph control diet were also present in the enriched diet group so they were diet independent and correspond to development driven changes. The rest of the loci were identified in the enriched diet group and highlight a specific dietary effect.
The representation of these 51 statistically relevant loci in a heatmap split the samples into two major clusters, discriminating between early (0 and 10 dph) and late (28 dph) developmental stages (Figure 3). In a similar way to the previous PCoA on the MSL, samples of 20 dph showed a distinct behavior between diets, with all enriched diet samples grouping with 28 dph paralarvae whilst most control diet samples (9/10) clustered together with 0 and 10 dph samples. More in detail, the clustering analysis shows that these 51 loci are grouped in 5 clusters (see Figure 3). The first four clusters, ordered from left to right, are characterized by losing methylation with the paralarvae development. In the first one, loci showed mainly transitions from HPM to HMM or NMT from the early developmental paralarvae group to the later one. Loci undergoing complete demethylation from ICM in 0 and 10 dph cluster to 28 dph, but also in 20 dph control samples were found on the second cluster, confirming its intermediate status between early and advanced culturing times are found on the second cluster. The third cluster presents a less clear patterning, although it could group those loci losing its HPM status from 0 dph onwards. There was a fourth cluster of loci which change from HMM status at 0 and 10 dph samples to NMT status on later days. Finally, and despite the loss of methylation is associated with development, the fifth and last cluster of the heatmap contained some loci suffering de novo methylation. The latter showed that, even though there is a general pattern of loss of methylation over this developmental period, there is room for certain positions to undergo de novo methylation, although such events can be considered rare.

DISCUSSION
Nowadays the only commercial available prey for O. vulgaris paralarvae is Artemia sp. However, nutrient enrichments are necessary to improve their nutritional quality. In this regard, LC-PUFA and phospholipid enriched supplements are particularly promising, since they boost the paralarvae viability (Guinot et al., 2013b;Garrido et al., 2016a). Our results show a significant improvement of the survival ratio at 28 dph for the Artemia sp. enriched with LC-PUFA and phospholipids respect to control diet. Nonetheless, no significant effect was detected in terms of size and DW at 28 dph between both diets despite the higher values found in the DW of LC-PUFA enriched diet. These results appear to be contrary to the positive effect of LC-PUFA described by Garrido et al. (2016a) in the same species, but it must be considered that the last study was a meta-analysis, which found differences integrating many independent experiments whose results were not often significant. In fact, the variability among studies has been also highlighted by the same authors (Garrido et al., 2017). However, a statistically significant increment of the DW was detected at 10 dph in the enriched diet group (see Table 1) suggesting a critical sensitive window where diet could have major effects.
In fish culture, special attention has been taken on lipid and fatty acid requirements due to their essentiality for a correct development and the link between fatty acids and gene expression has already been shown (Tocher, 2010;Xu et al., 2014). However, in O. vulgaris, little is known about the molecular basis of the effects of the lipids requirements (Monroig et al., 2013;Reis et al., 2014). For this reason, a better knowledge of octopus genomic regulation mechanisms will be valuable to diet formulation, managing welfare conditions related to culture facilities and to identifying the best conditions to improve breeding programs. To our knowledge, the present research is the first attempt to link diet and methylation in the context of the O. vulgaris aquaculture.
The methylation levels herein described for O. vulgaris paralarvae using 5-mC (ELISA) (on average 1.2%) are low but in line with those of other mollusks (for example Biomphalaria glabrate and C. gigas), around 2% (Fneich et al., 2013;Gavery and Roberts, 2013). In contrast to vertebrates, invertebrates present an exceptional variability of how DNA methylation is distributed in their genomes and its function is yet to be completely elucidated. Species of invertebrates like Caenorhabditis elegans or dipteran insects like Drosophila melanogaster (two model organisms), present an apparent absence of cytosine methylation on their genomes, illustrating that changes in gene expression are independent to DNA methylation (Schübeler, 2015). Nevertheless, DNA methylation in mollusks, such as the oyster C. gigas, is likely to vary among life history stages, playing an important role during the embryogenesis of this species and progressively decreasing its levels toward the adult stages, when it no longer exerts a relevant function in the control of gene expression (Rivière, 2014). In fact, previous results on O. vulgaris have remarked for an important role of methylation during the earlier development stages (at 1 dph) and having no effect in adults (Díaz-Freije et al., 2014). Our results extend the range of knowledge for this species and demonstrate a pre-established demethylation program during its early development. As methylation levels are low, the 5-mC (ELISA) failed to detect methylation changes in paralarvae either related to age or to diet. However, in this work, the potential of MSAP to analyze methylation patterns in paralarvae have been proved to be highly informative, revealing significant changes in methylation levels, from more methylated DNA of the larvae at hatching to less methylated DNA larvae after 28 days.
Far from being a stochastic phenomenon, our results demonstrate that this loss of methylation follows a well-defined pattern involving a 20% of the MSAP loci, that highlights how some genomic regions are specifically demethylated. Previous research has demonstrated for a pre-defined pattern of active and directed demethylation throughout the early development of vertebrates (Razin and Shemer, 1995;Paranjpe and Veenstra, 2015). The enzymatic machinery behind the methylation process and the changes produced in gene expression are known in detail in vertebrates. Unscheduled alterations provoked by either environmental agents or artificially induced with drugs, such as AZA-5 (5-aza-2 ′ -deoxycytidine) during this period leads to developmental arrest and/or disorders at the adulthood (Rivière et al., 2013). Up to date, octopus DNA methyltransferases have not been described but the presence of cytosine methylation cannot be possible without the enzymatic machinery. In bivalves, these methylation changes correlate with alterations in the expression of DNMT orthologue genes, as shown for C. gigas and the scallop Chlamys farreri Lian et al., 2015). In both cases this agedriven demethylation process correlates to low expression levels of the maintenance methyltransferase DNMT1 and, apparently, undetectable de novo methyltransferases (DNMT3). Consequently, this loss of methylation might occur in a passive way, yet preferentially directed toward certain genomic regions.
Although the pattern of methylation loss in octopus paralarvae is mainly age-driven, our results also demonstrate a certain diet influence on the methylation profiles. Indeed, LC-PUFA fed paralarvae showed a premature transition into 28 dph methylation profiles. These results have been demonstrated for a diet-sensitive period in the paralarvae of O. vulgaris at around 20 dph and for an effect of LC-PUFA supplementation over the methylation profiles. Despite there are no previous studies correlating this type of dietary supplementation with changes in methylation in invertebrates, the addition of LC-PUFA has shown a global effect over the levels of DNA methylation (Boddicker et al., 2016) and an impact over regulator regions of specific genes (Ma et al., 2016) in vertebrates (wellknown in Mus musculus, Rattus norvegicus and Sus scrofa). The implication of fatty acids on the methylome landmark is well-known but the mechanism behind this effect and their targets are still under study (see Burdge and Lillycrop, 2014 for review). Recent studies have started to elucidate this mechanism, correlating the addition of PUFA and changes over the DNA methyltransferase expression patterns (Huang et al., 2016). Thus, in some cases the dietary input of fatty acids finally acts, trough methylation mechanism, over the regulator regions of clue genes in the metabolic homeostasis. The final consequence is a change in the lipid metabolism. The results obtained by (Xu et al., 2014) have special interest since they show how the dietary input of LC-PUFA induce DNA methylation changes which directly affect the main pathway of biosynthesis of these LC-PUFA. These fatty acids are an essential nutritional requirement during O. vulgaris early development (Monroig et al., 2013;Reis et al., 2014). In view of the effect of the diet at 20 dph some similar mechanisms may be running in the octopus paralarvae, which could be sensitive to small alterations in nutritional but also environmental conditions during the paralarvae stage, including the digestive tract functionality, and immune system competence, and thus have a great impact on its health, growth and survival.
In vertebrates, the effect over DNA methylation of a diet rich in LC-PUFA and the impact of that over gene expression modulation have been demonstrated. Also, the knowledge of that kind of mechanisms of regulation has promising uses in aquaculture in terms of improve welfare and performance trough diet design. Nevertheless, it remains unknown if this also applies to invertebrates. For other dietary elements and environmental factors, a plastic response during sensitive periods on the early development has been proposed. This mechanism would act as an adaptation mechanism (Saint-Carlier and Rivière, 2015). For instance, in the honeybee, larvae differentiation into either workers or queens is directly dependent on the diet via global methylation changes (Lyko et al., 2011). In the case of O. vulgaris paralarvae our results show a dietary effect at 10-20 dph with no changes on loci methylation at 28 dph between control and enrichment diet. Previous studies have shown that differences in lipid composition between cultured paralarvae and their wild equivalents start to be appreciated at around 10 dph (Navarro and Villanueva, 2003;Garrido et al., 2016b). Such differentiation could be due to alterations in the expression of genes regulating lipid metabolism, mediated, among other mechanisms, by DNA methylation as it has been shown for fishes (Xu et al., 2014).
In summary, we have described the existence of an agedriven predetermined demethylation process during the early development of O. vulgaris, with a sensitive period to a LC-PUFA supplemented diet at around 20 dph. Enriched diet paralarvae accelerate its transition into latter developmental methylation profiles and show better survival than those verified in the control diet individuals. Nevertheless, more exhaustive studies have to be performed to check the effect of these changes over gene expression patterns with special interest on those genes involved in fatty acid metabolism.

AUTHOR CONTRIBUTIONS
PG performed laboratory experiments, statistical analysis and wrote the manuscript. DG collaborated in laboratory experiments, statistical analysis and manuscript writing. EA performed paralarvae culture and sampling. PM supervised DNA methylation analysis and statistical analysis. CG conceived and designed the study and collaborated in the manuscript writing. All authors helped with the draft of the manuscript and approved the final document.

ACKNOWLEDGMENTS
We wish to thank Diego Garrido for his technical assistance in paralarvae culture and sampling, and Antonio Sykes for critical reading and polishing the English of the manuscript. We acknowledge support of the publication fee by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI). This work is a contribution to the COST (European COoperation on Science and Technology) Action FA1301 "A network for improvement of cephalopod welfare and husbandry in research, aquaculture and fisheries (CephsInAction)."


extfieldsofstudy:
Chemistry
Medicine
Computer Science

text:
A master equation approach to actin polymerization applied to endocytosis in yeast

We present a Master Equation approach to calculating polymerization dynamics and force generation by branched actin networks at membranes. The method treats the time evolution of the F-actin distribution in three dimensions, with branching included as a directional spreading term. It is validated by comparison with stochastic simulations of force generation by actin polymerization at obstacles coated with actin “nucleation promoting factors” (NPFs). The method is then used to treat the dynamics of actin polymerization and force generation during endocytosis in yeast, using a model in which NPFs form a ring around the endocytic site, centered by a spot of molecules attaching the actin network strongly to the membrane. We find that a spontaneous actin filament nucleation mechanism is required for adequate forces to drive the process, that partial inhibition of branching and polymerization lead to different characteristic responses, and that a limited range of polymerization-rate values provide effective invagination and obtain correct predictions for the effects of mutations in the active regions of the NPFs.

where is the radius of the ith subunit at each given height that branches through (r, y, t), and is the ith mesh angle. To check that n ✓ is large enough, we performed some calculations with n ✓ = 16, which gave changes of much less than 1% in the F-actin count.
In three dimensions, Eq. S1 becomes wherer = r/ r, and nowk nuc = k nuc r 3 . 3. Rule for updating y-positions of outer Las17 ring and central Sla2 cap. The positions of the Las17 and Sla2 regions on the membrane are determined by the mechanical equilibrium between the actin force and the membrane force. We use the following algorithm to find this equilibrium, where y L (t) is the position of the Las17 ring at t, f net (t) is the net force on the Las17 ring, consisting of the contribution from the actin network and the membrane force, with the latter obtained from the membrane model in Ref. [1].
The time evolution of the Sla2 cap y-position depends on whether or not there is enough F-actin present to bend the membrane by exerting pulling forces. We assume that the pulling force "kicks in" when the F-actin count reaches a minimum value F min . The y-positions y S and y L of the Sla2 cap and the Las17 ring are taken relative to the actin network. When F < F min , the Sla2 cap moves with the Las17 ring, and there is no bending. When F > F min , the Sla2 cap stays put relative to the actin network. Thus where t is the time step. Initially the actin network pushes the Las17 ring to move along the y direction, and the Sla2 cap follows because there is no force to bend the membrane. Later, when F > F min , the Sla2 cap is anchored to the stationary actin network and thus remains fixed, but the Las17 ring is still pushed by the actin network to move in the y direction. A separation between the Sla1 and Las17 is then created. The F-actin may thus be considered to be a molecular clutch for creating bending by moving the Sla2 cap relative to the Las17 ring.
4. Calculation of membrane deformation profile from invagination length y I . Given y I (t) = y L (t) y S (t), we calculate the deformation profile and the corresponding force using the method of Ref. [1]. First, we solve the Euler-Lagrange equations [1], based on the general analysis of Ref. [2].
The equations are made dimensionless as in Ref. [1]. We use a turgor pressure value ⇧ = 0.2 MP a recently obtained [3] by a high-speed indentation method that avoids some potential pitfalls of slower methods. Then a spatial scale R ⇧ = 15nm corresponding to the observed invagination shapes is used to determine a bending modulus  = 2⇧R 3 ⇧ = 328k B T , which is the unit of energy. This value is comparable to the value of 285 ± 30k B T measured for clathrin-coated vesicles [4]. The corresponding force scale is f ⇧ = 2⇧/R ⇧ = 565pN . The turgor pressure ⇧ = 0.2MP a. Then the pressure scale is 2⇧, so the dimensionless pressure is ⇧ = 0.5. The dimensionless spontaneous curvature, as in Ref. [1], is We take the membrane tension to be = 0 because it is mechanically insignificant [1]. In the actin network calculations, R ⇧ is multiplied by a factor ( p 2/a) to make it compatible with the actin coordinates, giving a final value ofR ⇧ = 7.85.
Then the Euler-Lagrange equations are: where the geometrical variables are illustrated in Fig. S2, while ⌫ and ⌘ are Lagrange multipliers. Here f in is a point force that acts at the peak of the invagination, but which affects the Lagrange equations of motion at all values of s. A "shooting" method is used to solve them, starting with six boundary conditions at an outer boundary chosen where the membrane is flat (right side in Fig. S2), where we define s = 0: We have taken ⌘ = 0, which holds when the z-coordinate of one of the endpoints is not fixed (see Ref. [2]). The boundary conditions for˙ and ⌫ are taken from the Supplemental Material of Ref. [1]. Then, for a given value of y I , r i m and f in , as well as the total arc length s tot from s = 0 to the top of the invagination, are varied, until Eqs. (S8-S12) satisfy the following boundary conditions at the highest point in Fig S2: r m (s = s tot ) = 0, (S19) The shape function is then defined from s = 0 to s tot as Each shape function has a uniquely associated actin force value [1]. Thus, the inward pulling force required to bend the membrane to form the shape described by Eq. (S22) is defined as the membrane force function, For computational convenience, we pre-calculated a set of shapes with discrete invagination lengths of y pre 5. Molecular force clutch. To treat the initiation of deformation, we use a different approach to calculate the membrane force for y I < 0.1R ⇧ . We assume, as above, that a minimum F-actin count F min is required to transmit pulling forces through the actin network, and thus use a broadened transition of the following form: where A = 0.005.
6. Mechanical equilibration procedure. We balance the pushing force on the Las17 region from the actin network, calculated using a linear approximation, with the pulling force f in on the Sla2 region resulting from membrane bending. (a) Start with y S (t) = y L (t) = 0 (see Fig. S2). (b) Calculate ⇢(r, y, t) using 2. The forces enter ⇢(r, y, t) through the filament length as described in subsection 7 below.
(c) Calculate y L (t) and y S (t) based on the force balance. i. Calculate the linear pushing force with a spring constant k hmc exerted by the actin network based on the configuration of the F-actin below the Las17 ring as following ii. Update y L (t) using Eq S6. iii. Update y S (t) using Eq S7. iv. Repeat i), ii) and iii) until To reduce the computational load, we choose a relatively large 1/ so that f net converges quickly. In some cases, this value is too large and f net does not converge. In these cases we reduce 1/ by 90% and keep repeating i), ii) and iii). If convergence still fails, then we scan over an interval of y L to find the force-balancing y L value. (d) Repeat b) and c) to calculate the actin network and the membrane force for the next time step.
7. Calculation of filament length. First, a Brownian ratchet factor [5] is defined as where a = 2.7 nm is the length of the actin monomer, k B is Boltzmann's constant, T is the temperature, and In the first case the last subunit of the new branch is above the membrane, while in the second case the last subunit of the new branch impinges the membrane. Thus part of the new branch is affected by the Brownian ratchet factor, reducing the length. For example, the case of a filament growing into the membrane, with its base at y L , corresponds to y L (t) y = l (y, t). In this case one readily shows that l (y, t) = l max B, as expected from the Brownian-ratchet analysis. After normalization by r and discretization, where bxc = max {n 2 Z|n 6 x} is the floor function andl max = l max /(a/ p 2) is the number of subunits in a filament grown in the absence of force.
8. Spatial distribution of spontaneous filament nucleation. First, we find r m as the inverse function of Eq. S22: Then, we define the spontaneous-nucleation layer as the set of points satisfying the following condition: Thus the spontaneous-nucleation region extends from the membrane by a distance r nuc in the r direction and a distance y nuc in the y-direction, as shown in 4. Within the spontaneous-nucleation layer, where the values of y nuc , r nuc , and are given in Table S1. Also, branching is absent in the forbidden zone in 4, which is defined by 9. Stochastic simulations for validation of the ME method. The procedure is the same as that described in the Supplemental Material of Ref. [6], except that we replace explicit polymerization with instantaneous branching using the length function in Eq. S29. The NPF ring in the validation system has an inner radius of 80a and an outer radius of 120a, chosen to be in line with typical dimensions of systems that might be studied by the method, and the simulations contain enough subunits that the overall behavior (for example constant F-actin count vs. oscillations) can be straightforwardly determined. To enable the most direct comparison of the ME method with stochastic calculations, we do not include the negative-feedback term that is present in our application to endocytosis. In the absence of this term, smaller systems have large fluctuations that render the comparison of the ME with stochastic simulations difficult.
10. Choice of parameter values. The value of the parameters in Table S1 not referenced or discussed above are estimated as follows: The value F min = 500, about 10% of F max , is chosen to be large enough to avoid excessively large forces on individual filaments, and small enough that pulling and pushing forces are exerted over most of the polymerization time course.
For k hmc = 0.5pN/a, we find that values larger than this cause the actin network to be pushed away from the membrane so much that the number of attached filaments is reduced, resulting in excessive forces per filament. If the value is too small, the actin network penetrates unphysically far into the membrane.
The value 1/ = 1.0pN 1 ⇥ a is a choice of computational convenience. Since it does not represent physical dynamics, we simply choose its value to quickly find the invagination length required for achieving equilibrium at each time step.
The parameters r nuc and y nuc are chosen to limit spontaneous nucleation to the spatial region near the membrane.

The parameter
br is chosen so that the branching region, after being modified by the Gaussian function, provides a number of branching spots similar to that in Ref. [6].
The decay parameter nuc is chosen so that spontaneous nucleation is mainly confined to the center of the protein patch.
The sources or justifications for the remaining parameter values are given in Table  S1.