David Teze

Franck Daligault

Vincent Ferrières

Yves-Henri Sanejouand

Charles Tellier
email: charles.tellier@univ-nantes.fr

Semi-rational approach for converting a GH36 αglycosidase into an α-transglycosidase

Semi-rational approach for converting a GH36

α-glycosidase into an α-transglycosidase.

INTRODUCTION

Carbohydrates play major roles in most biological processes such as inflammation reactions, cell death, cellular interactions, stabilization of proteins, adhesion of pathogenic microorganisms and binding of toxins [START_REF] Hart | Essay glycomics hits the big time[END_REF][START_REF] Lichtenstein | Glycobiology of cell death: when glycans and lectins govern cell fate[END_REF][START_REF] Ghazarian | A glycobiology review: carbohydrates, lectins and implications in cancer therapeutics[END_REF]. In particular, most naturally-occurring human antibodies recognize a carbohydrate, the α-gal epitope [START_REF] Macher | The Galα1,3Galβ1,4GlcNAc-R (α-Gal) epitope: a carbohydrate of unique evolution and clinical relevance[END_REF], and α-galactosyl residues are present in glycan antigens targeted by carbohydrate vaccines against various pathogens such as Neisseria meningitidis, Shigella dysenteriae and Leishmania spp. [START_REF] Astronomo | Carbohydrate vaccines: developing sweet solutions to sticky situations?[END_REF]. Furthermore, α-1,6 linked galactooligosaccharides have been recognized for their prebiotic properties [START_REF] Andersen | Transcriptional analysis of oligosaccharide utilization by Bifidobacterium lactis Bl-04[END_REF][START_REF] Cervera-Tison | Functional analysis of family GH36 αgalactosidases from Ruminococcus gnavus E1: insights into the metabolism of a plant oligosaccharide by a human gut symbiont[END_REF][START_REF] Hachem | Raffinose family oligosaccharide utilisation by probiotic bacteria: insight into substrate recognition, molecular architecture and diversity of GH36 αgalactosidases[END_REF][START_REF] Nakai | Aspergillus nidulans α-galactosidase of glycoside hydrolase family 36 catalyses the formation of α-galacto-oligosaccharides by transglycosylation[END_REF][START_REF] Wang | A New αgalactosidase from Thermoacidophilic alicyclobacillus sp. A4 with wide acceptor specificity for transglycosylation[END_REF]). However, their use is hindered by their poor availability: unlike for proteins and nucleic acids, there is no general synthetic route for oligosaccharides and, despite the considerable development of efficient methods in this field [START_REF] Wang | Regioselective onepot protection of carbohydrates[END_REF]Zhu and Schmidt 2009), the assembly of oligosaccharides remains a substantial challenge. Consequently, alternative synthetic strategies have been explored, particularly those based on enzymatic processes.

The enzymatic synthesis of glycosidic bonds can be performed by glycosyltransferases or transglycosidases. The former can catalyze the formation of glycosidic bonds with both high yield and selectivity, but their use is limited in the large-scale production of oligosaccharides by the difficulty in accessing activated sugar donors (sugar nucleotides for Leloir-type transferases or phosphate sugars for non-Leloir types) [START_REF] Lairson | Glycosyltransferases: structures, functions, and mechanisms[END_REF], even though a recent approach seems promising [START_REF] Gantt | Broadening the scope of glycosyltransferase-catalyzed sugar nucleotide synthesis[END_REF][START_REF] Zhang | Exploiting the reversibility of natural product glycosyltransferase-catalysed reactions[END_REF]. As an alternative, engineered retaining glycosidases have provided an efficient approach for the synthesis of oligosaccharides. A first methodology was based on the substitution of the catalytic nucleophile by a neutral amino acid and the use of activated donors with an anomeric configuration opposite to that of the original substrate (such as α-glycosyl fluorides), which yielded new enzymes called glycosynthases [START_REF] Wang | Changing enzymatic reaction mechanisms by mutagenesis: converting a retaining glucosidase to an inverting enzyme[END_REF][START_REF] Mackenzie | Glycosynthases: mutant glycosidases for oligosaccharide synthesis[END_REF][START_REF] Malet | From Β-glucanase to β-glucansynthase: Glycosyl transfer to αglycosyl fluorides catalyzed by a mutant endoglucanase lacking its catalytic nucleophile[END_REF][START_REF] Cobucci-Ponzano | Thermophilic glycosynthases for oligosaccharides synthesis[END_REF]. However, although these glycosynthases have been very efficient for the synthesis of β-glycosidic bonds, the results are disappointing when they are applied to α-galactosidases, despite recent advances [START_REF] Cobucci-Ponzano | A Novel α-D-galactosynthase from Thermotoga Maritima converts β-D-galactopyranosyl azide to α-galacto-oligosaccharides[END_REF]. A second methodology based on the Hehre-resynthesis hydrolysis properties of inverting glycosidases [START_REF] Hehre | Scope and mechanism of carbohydrase action. Hydrolytic and nonhydrolytic actions of beta-amylase on alpha-and beta-maltosyl fluoride[END_REF]) has been proposed. Mutating residues involved in the hydrolysis reaction but not in the Hehre-resynthesis reaction yield variants that efficiently catalyze the synthesis β-linkages [START_REF] Honda | The first glycosynthase derived from an inverting glycoside hydrolase[END_REF][START_REF] Honda | Alternative strategy for converting an inverting glycoside hydrolase into a glycosynthase[END_REF]. This methodology was also extended to the synthesis of α-linkages [START_REF] Wada | 1,2-alpha-L-Fucosynthase: a glycosynthase derived from an inverting alpha-glycosidase with an unusual reaction mechanism[END_REF]), but with less efficiency.

As an alternative, natural α-transglucosidases, such as amylosucrase and dextransucrase, have been identified in CAZy [START_REF] Cantarel | The Carbohydrate-Active EnZymes Database (CAZy): an expert resource for glycogenomics[END_REF]) families GH13 and GH70 that can efficiently catalyze the formation of α-glucosidic bonds using sucrose as a natural activated donor [START_REF] Irague | NMR-based structural glycomics for highthroughput screening of carbohydrate-active enzyme specificity[END_REF][START_REF] Champion | Design of α-transglucosidases of controlled specificity for programmed chemoenzymatic synthesis of antigenic oligosaccharides[END_REF][START_REF] Pizzut-Serin | Characterisation of a novel amylosucrase from Deinococcus radiodurans[END_REF]Plou, Segura, and Ballesteros 2007). These examples of natural transglycosidases suggested that directed evolution of glycosidases into transglycosidases could be possible and this strategy was validated in our laboratory on both αand β-glycosidases [START_REF] Feng | Converting a β-glycosidase into a β-transglycosidase by Directed Evolution[END_REF][START_REF] Osanjo | Directed evolution of the alpha-L-fucosidase from Thermotoga maritima into an α-Ltransfucosidase[END_REF][START_REF] Koné | Digital screening methodology for the directed evolution of transglycosidases[END_REF]. Although molecular modeling and structural analysis were tentatively applied to explain why these evolved mutants present improved transglycosidase activities [START_REF] Teze | Semi-rational approach for converting a GH1 β-glycosidase into a βtransglycosidase[END_REF][START_REF] Osanjo | Directed evolution of the alpha-L-fucosidase from Thermotoga maritima into an α-Ltransfucosidase[END_REF][START_REF] Feng | Converting a β-glycosidase into a β-transglycosidase by Directed Evolution[END_REF]Teze et al. 2013b), the molecular events leading to an improved transglycosylation over hydrolysis ratio have not yet been determined precisely, even for natural transglycosidases such as cyclodextrin glycosyltransferases [START_REF] Leemhuis | Mutations converting cyclodextrin glycosyltransferase from a transglycosylase into a starch hydrolase[END_REF][START_REF] Kelly | Elimination of competing hydrolysis and coupling side reactions of a cyclodextrin glucanotransferase by directed evolution[END_REF]). However, the data led us to propose the working hypothesis that mutating conserved residues within the donor subsite of Thermus thermophilus β-glycosidase would enable the creation of transglycosidases and indeed four new β-transglycosidases were obtained [START_REF] Teze | Semi-rational approach for converting a GH1 β-glycosidase into a βtransglycosidase[END_REF].

Therefore, the aim of this study was to investigate whether this approach could also enable the rapid creation of efficient α-transgalactosidases. AgaB was chosen as a model system as this enzyme, which belongs to the CAZy family 36 [START_REF] Lombard | The Carbohydrateactive enzymes database (CAZy) in 2013[END_REF]), subgroup I (Fredslund et al. 2011;[START_REF] Hachem | Raffinose family oligosaccharide utilisation by probiotic bacteria: insight into substrate recognition, molecular architecture and diversity of GH36 αgalactosidases[END_REF], has shown interesting transgalactosylation properties. It was shown to catalyze the synthesis of 4-nitrophenyl α-Dgalactopyranosyl-(1,6)-α-D-galactopyranoside (GalGal-pNP) with yields up to 53% when high substrate concentration were used (100 mM) [START_REF] Spangenberg | Comparative study of new α-galactosidases in transglycosylation reactions[END_REF]. Higher yields of this disaccharide (74% with 40 mM of substrate) have been obtained with the α-galactosidase from Aspergillus nidulans, which belongs to the same subgroup and shares 39% identity with AgaB [START_REF] Nakai | Aspergillus nidulans α-galactosidase of glycoside hydrolase family 36 catalyses the formation of α-galacto-oligosaccharides by transglycosylation[END_REF]. We also previously showed that the regioselectivity of the enzyme could be modulated by mutagenesis (Dion et al. 2001a, b). In addition, its crystallographic structure has recently been published [START_REF] Merceron | The Molecular mechanism of thermostable α-galactosidases AgaA and AgaB explained by X-ray crystallography and mutational studies[END_REF]. Recently, the first reported αgalactosynthase was created from a GH36 enzyme, the Thermotoga maritima α-galactosidase (TmαGal, subgroup III) [START_REF] Cobucci-Ponzano | A Novel α-D-galactosynthase from Thermotoga Maritima converts β-D-galactopyranosyl azide to α-galacto-oligosaccharides[END_REF]) and moderate improvement of the transglycosylation catalyzed by the same enzyme has been reported [START_REF] Bobrov | Improvement of the efficiency of transglycosylation catalyzed by α galactosidase from Thermotoga maritima by protein engineering[END_REF].

Interestingly, the GH36 family also contains pure transgalactosidases, such as stachyose and verbascose synthases, which are important for carbon storage in seeds (Peterbaueret al. 2002a, b;[START_REF] Peterbauer | Enzymatic control of the accumulation of verbascose in pea seeds[END_REF]. However, these plant enzymes, which belong to the GH36 subgroup II [START_REF] Fredslund | Crystal structure of α-galactosidase from Lactobacillus acidophilus NCFM Insight into tetramer formation and substrate binding[END_REF], are difficult to produce and their structure is not known.

Their sequences present less than 15% identity with AgaB, preventing reliable sequence alignments, not to mention homology modeling. Nevertheless, their existence suggests that glycoside hydrolases from this family could be evolved to pure transglycosidases, with little or no hydrolysis activity, while keeping their original double-displacement mechanism.

The present work describes a semi-rational approach to convert the Geobacillus stearothermophilus α-galactosidase (AgaB) into transglycosidases by mutating highly conserved residues located around the -1 donor subsite. An initial Ala scanning allowed identifying critical positions that affect the hydrolysis/tranglycosylation ratio, and the most effective positions were then mutated into a more conservative amino acid. We found that 50% of the mutated positions led to an improvement of the transglycosidase activity, suggesting that targeting the -1 site of glycosidases could significantly decrease the screening effort to evolve glycosidases into tranglycosidases.

RESULTS

Amino acid conservation within the GH36 family

To study the effect of mutations on conserved residues within the donor subsite of the enzyme, the conservation of all AgaB amino acids was investigated. Thus, using the AgaB sequence as the query, 205 sequences from the GH36 subgroup I were obtained that shared between 25 and 95% of sequence identity between all pairs of sequences and between 25 and 66% with the query sequence. The average conservation was 54.4%, with 5.2% of amino acids (38 AAs) at least 99.5% conserved (Fig. 1A). Given the AgaB structure (PDB code 4FNQ) and the very homologous AgaA structure (97% identity) in complex with stachyose (PDB code 4FNU) [START_REF] Merceron | The Molecular mechanism of thermostable α-galactosidases AgaA and AgaB explained by X-ray crystallography and mutational studies[END_REF], an α-Gal residue was added to the AgaB structure by superimposition (RMSD=0.5 Å). The minimal distance between one of the non-hydrogen atoms of the aforementioned conserved residues and one of the glycosyl non-hydrogen atoms was measured (Fig. 1B). It is particularly interesting to note that 10 residues have a minimal distance less than 3.5 Å from the glycosyl, and that no other residues have a minimal distance less than 4.5 Å. These 10 residues constitute the first shell, directly involved in catalytic activity (D478 and D548) or in substrate binding (D366, D367, W411, K476, N480, C526, G529 and W545; Fig. 2A). Six of these highly conserved residues are located from 4.5 to 6.1 Å away from the glycosyl, interacting with first-shell residues and thus constituting the conserved residues of the second interaction shell (N334, W336, R373, E413, R443 and S547; Fig. 2B). These 16 residues located at less than 6.1 Å from the glycosyl are likely to be involved in the enzyme function and their impact on the transglycosylation is worth exploring. Then, the next conserved residue is the G368 at 7 Å, which might be involved in protein folding.

Ala-scanning

Among the 16 conserved AAs close to the donor subsite, two are the catalytic residues (D478 and D548) and the remaining 14 were individually mutated into alanine to assess if these residues have an influence on the transglycosylation yields. The resulting mutants were produced and their kinetic parameters k cat /K M as well as their ability to catalyze GalGal-pNP synthesis are summarized in Table I.

Most of the mutants, except for the E413A and W411A variants, display a non-Michaelian behavior as they do not present any saturation at high substrate concentration, thus catalytic constants, K M and k cat , could not be individually determined and only the apparent secondorder rate constant k cat /K M ("catalytic efficiency") is presented (Table I). The WT enzyme and the G529A showed a slight substrate inhibition. Examples of these non-classical behaviors are presented in Figures S16 andS17 (Supplementary data).

Of the 14 mutants produced, only 6 displayed sufficient activity to measure their yield of GalGal-pNP synthesis when used with α-Gal-pNP 10 mM as a substrate (Table I). This Alascanning was successful for rapidly obtaining transglycosidases, with three variants presenting transglycosylation yields in the range of 31 to 38% against 22% with the WT. However, the kinetic parameter k cat /K M of these six mutants dropped dramatically by two to three orders of magnitude. It should be noted that in three (G529A, C526A and S547A) of these six variants, Ala mutation resulted in low steric change and that two of these three presented the highest activities among all variants. While Ala-scanning was performed to analyze the effect of each conserved residue substitution in a similar fashion, it appeared that minimizing the steric difference between the variant and the native enzyme was needed in order to avoid drastic loss of activity. Thus, a second round of mutagenesis featuring "conservative mutations", i.e. mutations closest in structure to the wild-type enzyme, was performed.

Conservative mutations

Of the 14 chosen positions, 10 were selected for a second round of mutagenesis in which the novel amino acid replaced the original one in a more isosteric way. G529, C526 and S547 were excluded as Ala is already a good replacement choice and mutating R373 was excluded as it seemed to engender a strong deleterious effect on the transglycosylation yield, with a drastic drop from 22 to 2% (Table I). As the N334A mutant was the best variant selected by Ala-scanning, more substitutions on this specific position were added. The kinetic parameters k cat /K M as well as GalGal-pNP synthesis yields of the resulting mutants are summarized in Table II.

In the set of variants obtained by "conservative mutations", only three mutants were inactive: R443Q, D366N, E413Q, and a 10-to 75-fold increase in k cat /K M was observed on four positions with regard to Ala mutants as well as a 15-to 100-fold decrease in the amount of enzyme needed to reach reaction completion. Consequently, 8 out of 9 variants were active enough to assay GalGal-pNP synthesis and showed improved yields compared to the native enzyme (from 26 to 45% against 22% with the WT). Interestingly, none of the newly created variants displayed yields lower than the corresponding Ala variant, which suggest that starting directly with a round of conservative mutations is most probably the best approach to create new transglycosidases.

As the resulting mutants after this second round of mutagenesis kept high levels of activity, combinations of the most successful mutations were performed.

Mutant recombination

After two rounds of mutagenesis, the variants obtained by mutating conserved residues of 7 out of 14 positions showed an increase in transglycosylation yields, therefore 21 recombination mutants, resulting from the combination of mutations S547A, N334T, W336F, D267N, W411F, K476Q and W545F, were created. The W545F-N334S double mutant was added to this set. Kinetic parameters k cat /K M as well as GalGal-pNP synthesis yield of the resulting mutants are summarized in Table III.

Among the 22 newly created double mutants, only 6 were active enough to allow quantification of GalGal-pNP synthesis (Table III), and these 6 mutants always contained W545F and/or N334T mutations, which are the least deleterious to the k cat /K M parameter among those used for recombination (Tables I andII). It can be concluded from these 15 inactive or low active mutants that there is a strong additivity of the decrease in catalytic efficiency, while the beneficial effect on transglycosylation shows a less additive effect: only the double mutant N334T-W545F displayed a higher yield than the single mutant N334T or W545F, with a 57% yield (against 45% for N334T, 35% for W545F and 22% for the WT).

For the best variants (N334T, W545F and N334T-W545F), the kinetics of GalGal-pNP synthesis were compared with that of the WT (Fig. 3). One of the drawbacks of the use of glycosidases for oligosaccharide synthesis is often the secondary hydrolysis of the formed products. However, thanks to the use of an activated donor for which AgaB presents a much higher specificity than for natural substrates (the k cat /K M towards α-Gal-pNP is 500 times greater than towards raffinose [START_REF] Merceron | The Molecular mechanism of thermostable α-galactosidases AgaA and AgaB explained by X-ray crystallography and mutational studies[END_REF])), small amounts of enzyme were used and the transglycosylation product was barely hydrolyzed and maximum yields of product formation remained for a long time (Fig. 3). Only the N334T variant exhibited a slight secondary hydrolysis compared to the other mutants and the native enzyme.

After these three rounds of mutagenesis, AgaB variants with a strong improvement in their synthetic activity towards GalGal-pNP synthesis were obtained. However, as 4-nitrophenyl groups are hard to remove without breaking the glycosidic bond, this disaccharide is of little interest. Thus, a study of transglycosylation towards an acceptor bearing a thiophenyl group instead was undertaken, as this protecting group has proved successful in chemo-enzymatic synthesis (D' Almeida et al. 2009;[START_REF] Marton | Engineering of glucoside acceptors for the regioselective synthesis of β-(1-->3)-disaccharides with glycosynthases[END_REF].

Effect of changes in donors and acceptors on synthetic yields of transglycosylation with AgaB variants

The closest analogue of α-Gal-pNP containing a thiophenyl group is phenyl 1-thio-α-Dgalactopyranoside. However, given the low availability of this compound, the more affordable phenyl 1-thio-β-D-galactopyranoside (Gal-S-Ph) was used. Moreover, this compound made it possible to assess whether the N334T variant could use acceptors with a β-configuration as well as with an α-configuration. The N334T variant was chosen over the N334T-W545F double mutant for the sake of enzyme consumption, as it gives the best transglycosylation yield after the N334T-W545F variant, but needs 35-fold less enzyme to reach reaction completion (Table 4). Transglycosylation yields of phenyl α-D-galactopyranosyl-(1,6)-1-thioβ-D-galactopyranoside (GalGal-S-Ph) synthesis are given in Table IV. Both native AgaB and the N334T variant were able to catalyze the synthesis of GalGal-S-Ph, with a net increase from 14 to 33% with the latter, which demonstrates that newly created variants keep the promiscuity of the native enzyme towards acceptors. A comparative study with the αgalactosynthase approach (Cobucci-Ponzano et al. 2010) has been also performed: the D478G AgaB variant (equivalent to the D327G TmαGal glycosynthase variant) was produced and tested with β-Gal-N 3 as donor. It showed an interesting increase in synthetic yields compared to the native enzyme (from 14 to 23%, Table IV). Nevertheless, the α-transgalactosidase N334T variant displayed higher yields (33 against 23%), while consuming 42-fold less enzyme. When using Gal-S-Ph instead of α-Gal-pNP as an acceptor, a drop of one-third in synthetic yields with both N334T and the native enzyme was observed. This decrease is mainly due to competition with the GalGal-pNP synthesis. This competition could be turned towards synthesis by adding α-Gal-pNP gradually, which resulted in an increase from 33 to 54% of GalGal-S-Ph synthesis yield when the N334T variant was used. In order to go further in avoiding competition with the GalGal-pNP synthesis, α-Gal-F was used as donor instead of α-Gal-pNP [START_REF] Andre | In Situ 19 F NMR spectroscopy study of enzymatic transglycosylation reactions using α-D-aldohexopyranosyl fluorides as donors and acceptors[END_REF]. This resulted in a drastic increase in transglycosylation yields from 14 to 37% with the native enzyme and from 33 to 62% with the N334T variant (Table IV).

DISCUSSION

With the best N334T AgaB variant, one-step glycosidic bond formation with high yields (from 45 to 62%) with unprotected sugars and moderate enzyme consumption was achieved, which makes this variant suitable for bioconversion uses. It also competes favorably with the glycosynthase D478G variant as it provides higher transglycosylation yields (62 against 23%), while using 151-fold less enzyme (Table IV). Thus, this approach, which targets highly conserved amino acids around the active site of AgaB, is very efficient for obtaining transglycosidase mutants rapidly and avoiding the tedious screening procedures imposed by random evolution approaches [START_REF] Koné | Digital screening methodology for the directed evolution of transglycosidases[END_REF]. Furthermore, the initial approach [START_REF] Teze | Semi-rational approach for converting a GH1 β-glycosidase into a βtransglycosidase[END_REF]) has been improved, as we demonstrate in this work that one round of conservative mutations allowed a fast access to new transglycosidases while avoiding drastic drops in activity. It is particularly interesting to note that the best variant, N334T, was obtained by mutating a second-shell residue, showing that very slight modifications may provoke strong effects on the balance of transglycosylation over hydrolysis. The addition of a second mutation induced a strong deleterious effect on the activity of all the 22 double mutants produced (Table III). On the other hand, the effect on transglycosylation yields seems less predictable: among the six double mutants that exhibited an activity high enough to study the transglycosylation yields, two displayed an interesting increase compared to the single mutants (N334T-W545F (+12%) and W411F-W545F (+9%)), two showed slight yield modifications (N334S-W545F (+1%) and N334T-W411F (-1%)) and two presented a drastic drop in yields (N334T-K476Q (-7%) and W336F-W545F (-9%)) (Table III).

Mutants were screened for the best transglycosidase activity by following the GalGal-pNP synthesis. As this product is of limited interest as an intermediate in oligosaccharide synthesis, we also demonstrated that by switching to other acceptors, mutants kept their improved transglycosylation properties since mutations did not affect the +1 and +2 acceptor sites. Moreover, by using alternative donors such as α-Gal-F, the transglycosylation yields improved due to the absence of the competing GalGal-pNP synthesis. As the α-Gal-F is a more activated donor than the α-Gal-pNP, the enzyme consumption was decreased by 3.6 to 5-fold, which also contribute to the transglycosylation yields increase due to the reduction of secondary hydrolysis.

The spatial arrangement of the mutated residues can be seen in the published structure of AgaB [START_REF] Merceron | The Molecular mechanism of thermostable α-galactosidases AgaA and AgaB explained by X-ray crystallography and mutational studies[END_REF]) (Fig. 2). The N480 residue is located in the neighborhood of the acceptor subsite, which may explain the drop in transglycosylation yields obtained with the variant N480D as some interactions with an acceptor moiety could be missing. However, all the most beneficial mutations for transglycosidase activity are located farther from the catalytic residues, at the bottom of the -1 site cavity (mutations on residues S547, N334, W545 and K476 (Fig. 2)). Thus, structural information does not give any clues for understanding the effect of mutation on the transglycosylation/hydrolysis ratio. To date, a possible explanation is that highly conserved amino acids in the strict vicinity of the glycosyl subsite are involved in stabilizing the transition states of the catalyzed reactions, i.e. glycosylation, hydrolysis and transglycosylation. Thus, mutating these residues might decrease the transition state stabilization of these three reactions (resulting in a drop in kinetic parameters), but their contributions to the stabilization of each of these three transition states is most probably not identical. Thus, the finely tuned equilibrium between these three reactions would be disturbed and it is likely that variants presenting a balance slightly shifted towards transglycosylation would be obtained (as well as those with a balance shifted towards hydrolysis). Indeed, on 14 mutated positions, the substitution of 4 of them led to variants with a decreased synthetic ability, 7 led to an increased ability and 3 gave no quantifiable yields.

As the rationalization of the results proved unsuccessful, it seems to be essentially impossible to identify by rational design the key positions to mutate. However, the methodology proposed in this work to create improved transglycosidases is much more rapid and efficient than directed evolution, which requires screening procedures on a large library of mutants. As it has been proved efficient for creating both α-(this work) and βtransglycosidases [START_REF] Teze | Semi-rational approach for converting a GH1 β-glycosidase into a βtransglycosidase[END_REF], it may be a general route to obtain transglycosidases rapidly.

MATERIALS AND METHODS

α-Gal-pNP and β-Gal-S-Ph were purchased from Carbosynth, oligonucleotides from Eurofins, and enzymes from Fermentas. Other laboratory reagents were purchased from Sigma-Aldrich unless otherwise indicated and used without further purification.

Site-directed mutagenesis

The QuikChange site-directed mutagenesis kit from Stratagene was used to make point mutations without any modifications: during PCR, Pfu polymerase extends the primers and generates a nicked plasmid with the desired mutation incorporated. Then the product is treated with Dpn I endonuclease, which digests the parental DNA. The nicked plasmid can then be transformed into XL-1 Blue competent cells. The 1.3-kb DNA fragments encoding the mutant AgaB enzymes were sequenced in both forward and reverse directions. Primers used for the site-directed mutagenesis are listed in Supplementary Data (Tables TS1,TS2).

Protein expression and purification

Recombinant strains expressing AgaB genes were grown in 1 L of LB medium at 37°C overnight, centrifuged and resuspended in 35 mL of lysis buffer (0.1 M phosphate, pH 8, 0.5 M NaCl, 10 mM imidazole, 10 µg.mL -1 DNAse I). After sonication and centrifugation, 6xHistagged proteins were purified by immobilized ion metal-affinity chromatography (IMAC): 250 µL of Ni-NTA Superflow (Qiagen) was added to the supernatant and stirred for 1 h at 4°C, then loaded onto a 10 mL column. The column was washed using 25 mL of washing buffer (0.1 M phosphate, pH 8, 0.5 M NaCl, 25 mM imidazole), then 5 mL of elution buffer was added (0.1 M phosphate, pH 8, 0.5 M NaCl, 250 mM imidazole). Purity of the final product was checked by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Enzyme concentrations were determined by UV absorbance at 280 nm (Abs 0.1% = 2.18 and 2.07 for the W mutants) using NanoDrop 1000 (Thermo Scientific)

Bioinformatic analysis

GH36 sequences were retrieved from the Uniprot database [START_REF] Apweiler | UniProt: the universal protein knowledgebase[END_REF]) and multiple sequence alignment (MSA) was performed with CLUSTALW [START_REF] Chenna | Multiple sequence alignment with the Clustal series of programs[END_REF].

To assess the degree of amino acid residue conservation, 205 different sequences more than 30% identical to AgaB after the MSA were considered. Hereafter, amino acid residues found conserved in more than 99.5% of these sequences are termed "highly conserved".

Kinetic studies

All kinetic studies were performed with a TECAN Infinite M1000 spectrophotometer at 30°C in phosphate buffer 0.1 M, pH 7. Initial reaction rates were calculated from the slope of the first-order plot of product concentration (pNP) against reaction time, then initial reaction rates were plotted against substrate concentration and the resulting curves were fitted to the hyperbolic equation v=Vmax * [S] * [E]/(K M +[S]) using Origin 7.0 (OriginLab) to obtain k cat and K M parameters. For most mutants hyperbolic curves were not observed since the kinetic of pNP release was the result of both glycosylation, hydrolytic and transglycosylation reactions.

The k cat /K m parameter was evaluated at low substrate concentrations, when kinetic can be approximate to the equation: v=k cat /K M* [E] * [S]. k cat /K M is then an apparent second order rate constant (referred as the "catalytic efficiency"), which is determined by the initial slope of the curve V/[E] = f([S]). All measurements were made in triplicate with at least 12 different substrate concentrations ranging from 9.8 µM to 20 mM.

Transglysosylation studies

Screening of the transglycosylation efficiency of AgaB variants was achieved by following GalGal-pNP synthesis [START_REF] Spangenberg | Comparative study of new α-galactosidases in transglycosylation reactions[END_REF]. Synthetic yields with 10 mM α-Gal-pNP were determined by capillary electrophoresis (Beckman P/ACE System 5000 with an uncoated fused silica capillary, 47 cm) as previously described (Teze et al. 2013a;[START_REF] Teze | Semi-rational approach for converting a GH1 β-glycosidase into a βtransglycosidase[END_REF]. 200 µL of media containing 10 mM imidazole (used as an internal standard), 10 mM α-Gal-pNP and the enzyme (enzyme concentrations are indicated in Tables II, III, and IV) was incubated at 30°C in phosphate buffer 0.1 M, pH 7, within the capillary electrophoresis apparatus and analyzed every 24 min for 2.8 h then each hour for the remaining 7 h. If specified, α-galactosyl-fluoride (α-Gal-F) 10 mM or β-galactosyl-azide (β-Gal-N 3 ) 10 mM was used as a donor instead of α-Gal-pNP. If specified, 1-thio-β-D-galactopyranoside (Gal-S-Ph) 10 mM was used as an acceptor, in which case the given transglycosylation yields refer to the synthesis of phenyl-(α-D-galactopyranosyl)-(1,6)-1-thio-β-D-galactopyranoside (GalGal-S-Ph). Separations were performed at 17 kV with 50 mM Borax, pH 9.5, as running buffer. Int. Ed. 48: 1900-1934. a Enzyme concentration necessary to reach the maximum yield of GalGal-pNP formation within 4 hours. b W411A (k cat = (1.9 ± 0.02) x 10 -2 s -1 ; K M =1.5 ± 0.07 mM) and E413A (k cat = (3.0 ± 0.1) x 10 - 2 s -1 ; K M =2.4 ± 0.2 mM) display a classic Michaelis-Menten behavior. c Not Determined. Activities of these enzymes were too low to measure GalGal-pNP formation. d W336A and R443A presented a detectable activity, but too low to be measured. b WT, N334T and W545F were included as a reminder of the effect of single mutations.

Table IV. Yields of GalGal-S-Ph synthesis using AgaB variants with Gal-S-Ph (10 mM) as acceptor and various donors (each at 10 mM).

Enzyme

  ABBREVIATIONS

Fig. 1 .

 1 Fig. 1. Amino acid conservation within the GH36 family. (A) Histogram of the population of

Fig. 2 .

 2 Fig. 2. Localization of highly conserved amino acids within the AgaB active site (PDB code

Fig. 3 .

 3 Fig. 3. Time course of GalGal-pNP synthesis in the presence of α-Gal-pNP 10 mM as

a

  Enzyme concentration necessary to reach the maximum amount of GalGal-pNP within 4 hours.

a

  Yields of GalGal-pNP synthesis, measured at the time of the maximum yield of the transglycosylation product. b Enzyme concentration necessary to reach the maximum transglycosylation yield within 4 hours. c Instead of having 10 mM of donor at the beginning of the reaction, the same amount of donor was reached by 5 additions during the time course of the reaction.

Table I .

 I Kinetics and yields of GalGal-pNP synthesis of the AgaB variants obtained by Ala-

	scanning.
			GalGal-pNP	Enzyme concentration
	Enzyme	k cat /K M (s -1 .mM -1 )	(%)	(µg.mL -1 ) a
	WT	200 ± 4	22	1.0
	G529A	3.06 ± 0.03	21	5.5
	W545A	(6 ± 0.3) x 10 -2	34	790
	C526A	0.33 ± 0.02	19	34
	S547A	0.70 ± 0.05	31	29
	N334A	0.57 ± 0.02	38	170
	R373A	0.67 ± 0.04	2	11
	W411A b	(1.3 ± 0.1) x 10 -2	ND c	ND c
	E413A b	(1.2 ± 0.1) x 10 -2	ND c	ND c
	K476A	(3.1 ± 0.1) x 10 -3	ND c	ND c
	W336A; R443A	ND d	ND c	ND c
	N480A; D366A; D367A	NDA e	ND c	ND c

Table II .

 II Kinetics and yields of GalGal-pNP synthesis of AgaB variants presenting "conservative mutations". Enzyme concentration necessary to reach the maximum amount of GalGal-pNP within 4 hours. b These AgaB variants present a slight substrate inhibition. c No Detectable Activity.

				Enzyme
		k cat /K M	GalGal-pNP
	Enzyme			concentration
		(s -1 .mM -1 )	(%)
				(µg.mL -1 ) a
	WT b	200 ± 4	22	1.0
	N334D	6.6 ± 0.2	44	3.0
	N334S	2.4 ± 0.02	39	11.5
	N334T	5.4 ± 0.03	45	10.5
	W336F	0.38 ± 0.005	27	205
	D367N b	0.23 ± 0.005	26	55
	W411F b	0.75 ± 0.02	27	23
	K476Q	(6.7 ± 0.4) x 10 -2	36	115
	N480D	(7.3 ± 0.3) x 10 -2	14	140
	W545F b	2.7 ± 0.02	35	7.5
	R443Q; D366N; E413Q	NDA c	NDA	NDA

a

Table III .

 III Kinetic parameters and yields of GalGal-pNP synthesis of the double mutants obtained by recombination.

behaviors of mutants W411F and D367N are presented in FigureS17. (Supplementary Data).

FUNDING

This work was supported by the Pays de la Loire and Bretagne regions (Glyconet Network) and the French Agence Nationale de la Recherche [ANR-10-BLAN-0718].

ACKNOWLEDGMENT

The authors are grateful to Genadi Chikov, Corentin Léger, Amina Fateh and Claude Solleux for their help and technical support.

SUPPORTING INFORMATION AVAILABLE

Primers used for site-directed mutagenesis are listed in Tables TS1 andTS2


Benoît Lelandais

Fréderic Ducongé

DECONVOLUTION REGULARIZED USING FUZZY C-MEANS ALGORITHM FOR BIOMEDICAL IMAGE DEBLURRING AND SEGMENTATION

Keywords: Deconvolution, segmentation, deblurring, regularization, Fuzzy C-Means, heterogeneity, quantification, molecular imaging

We address deconvolution and segmentation of blurry images. We propose to use Fuzzy C-Means (FCM) for regularizing Maximum Likelihood Expectation Maximization deconvolution approach. Regularization is performed by focusing the intensity of voxels around cluster centroids during deconvolution process. It is used to deconvolve extremely blurry images. It allows us retrieving sharp edges without impacting small structures. Thanks to FCM, by specifying the desired number of clusters, heterogeneities are taken into account and segmentation can be performed. Our method is evaluated on both simulated and Fluorescence Diffuse Optical Tomography biomedical blurry images. Results show our method is well designed for segmenting extremely blurry images, and outperforms the Total Variation regularization approach. Moreover, we demonstrate it is well suited for image quantification.

INTRODUCTION

In biomedical imaging, the blurring of images is often a problem for the segmentation and the quantification of the signal. To solve this problem, deconvolution is used [START_REF] Pankajakshan | Deconvolution and denoising for confocal microscopy[END_REF]. Because deconvolution is an ill-posed problem, there is no consensus on this issue. In fluorescence imaging, the well-known Maximum Likelihood Expectation Maximization (MLEM) deconvolution method, is often used because it has the advantage to ensure non-negativity [START_REF] Sarder | Deconvolution methods for 3-D fluorescence microscopy images[END_REF]. However, this iterative process has the drawback to converge to noise producing ringing artifacts. Convergence is ensured if regularization is implemented [START_REF] Pankajakshan | Deconvolution and denoising for confocal microscopy[END_REF]. In biomedical imaging, Wavelet

To appear in Proc. ISBI2015, April 1619, 2015 c 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. [START_REF] Chaux | Waveletbased restoration methods: application to 3d confocal microscopy images[END_REF][START_REF] Boussion | Incorporation of wavelet-based denoising in iterative deconvolution for partial volume correction in whole-body PET imaging[END_REF] and Total Variation [START_REF] Dey | Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution[END_REF][START_REF] Laasmaa | Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images[END_REF][START_REF] Temerinac-Ott | Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (otf)[END_REF] are widely used for regularization. Multiscale wavelet-based approach reduces the noise in the residual using Bayeshrink filtering. Because of the multiscale approach, small structures can be preserved. However, contours are not sharp [START_REF] Boussion | Incorporation of wavelet-based denoising in iterative deconvolution for partial volume correction in whole-body PET imaging[END_REF]. Total Variation enforces smoothness in the convolved data by adding a term based on spatial context (L1 or L2 norm) [START_REF] Dey | Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution[END_REF]. Using L1 norm, the advantage is that contours are sharp. The disadvantage is that small structures can be removed.

The Fuzzy C-Means (FCM) [START_REF] Bezdek | Pattern Recognition with Fuzzy Objective Function Algorithms[END_REF] clustering method is widely used for biomedical image segmentation. Derived from fuzzy logic [START_REF] Zadeh | Fuzzy sets[END_REF], FCM is used to model imprecision by affecting to each voxel membership degrees according to multiple clusters. In [START_REF] Ahmed | A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data[END_REF], the authors propose to use FCM for dealing with heterogeneity in magnetic resonance images. In [START_REF] Belhassen | A novel fuzzy C-means algorithm for unsupervised heterogeneous tumor quantification in PET[END_REF], a wavelet based approach is incorporated to the FCM algorithm in order to model heterogeneity using a multiscale approach in positron emission tomography images. In these two approaches, a spatial constraint is also added for noisy data regularization. Using FCM in imaging, incorporating neighborhood information is needed to improve voxel labeling. Although it can be easy to use neighborhood to remove noise, it is more difficult to remove blur corresponding to a lack of knowledge.

Methods combining both restoration and segmentation have been proposed. In [START_REF] Ayasso | Joint NDT image restoration and segmentation using Gauss-Markov-Potts prior models and variational Bayesian computation[END_REF], a bayesian framework is used for dealing with both noise and blurry information. In [START_REF] Bar | Mumford and shah model and its applications to image segmentation and image restoration[END_REF], the Mumford and shah model is presented. The method consists of the minimization of a sum of criterions whose aim is to perform image restoration with homogeneous regions and thin boundaries.

Here, we propose a new regularization approach for MLEM deconvolution using FCM. The idea is to focus the intensity of voxels around cluster centroids during deconvolution process. Instead of using neighborhood information, regularization is performed according to a specified number of clusters that is given by the experimenter. The advantage is that small structures are preserved and sharp edges are retrieved. Moreover the image is segmented.

The paper is organized as follow. First, some background about deconvolution and FCM are given. It is followed by our proposed method which is then evaluated on simulated im-ages and on images acquired from fluorescence Diffuse Optical Tomography in vivo molecular imaging system.

BACKGROUND

Deconvolution

The general framework in deconvolution is based on the following model:

i(x) = (o ⊗ p)(x) + n(x), (1)
where

p(i|o) = x (p ⊗ o)(x) i(x) • exp (-(p ⊗ o)(x)) i(x)! (2)
or minimizes the negative log-likelihood function given by:

J ML = x -i(x)ln(p ⊗ o)(x) + (p ⊗ o)(x) + ln(i(x)!) (3)
Assuming that x p(x) = 1, finding the null derivative of (3) according to o(x) leads to the following updating:

o t+1 (x) = o t (x) i(x) (p ⊗ o t )(x) ⊗ p(-x) (4)
where p(-x) corresponds to the mirrored PSF function. As mentioned in introduction, this update scheme has the drawback to amplify noise, that is why regularization is needed [START_REF] Pankajakshan | Deconvolution and denoising for confocal microscopy[END_REF].

Regularization can be performed using L1 norm Total Variation (TV1) denoising approach [START_REF] Dey | Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution[END_REF]. The functional becomes:

J ML T V1 = J ML + λ T V1 x |∇o(x)| (5)
where ∇ is the gradient operator, and λ T V1 is a parameter controlling the regularization term. It leads to the updating:

o t+1 (x) = o t (x) i(x) (p⊗o t )(x) ⊗ p(-x) 1 -λ T V1 div ∇o(x) |∇o(x)| (6)
where div is the divergence operator.

Fuzzy C-Means (FCM)

FCM [START_REF] Bezdek | Pattern Recognition with Fuzzy Objective Function Algorithms[END_REF] is a clustering method allowing us to assign an object to two or more clusters with different membership degrees. Let j = {1, . . . , C}, where C is the number of cluster, FCM is based on the minimization of the objective function:

J FCM = x C j µ m j (x)||i(x) -c j || 2 (7)
with the constraint j µ j = 1, where µ j (x) is the membership degree of i(x) according to cluster j, and where ||i(x)c j || is the norm expressing the similarity between i(x) and the the cluster centroid c j . m > 1 is a parameter controlling the fuzziness of the data (m = 2 by default). A large m value results in fuzzy clusters, whereas a value close to 1 results in crisp clusters. Finding the null derivative of (7) according to c j and µ j (x) leads to the following alternately updating:

c j = x µ m j (x)i(x) x µ m j (x) ∀ j = {1, . . . , C} (8)
µ j (x) = 1 k ||i(x)-c j || ||i(x)-c k || 2 m-1 ∀ j = {1, . . . , C} (9)
Derived from fuzzy logic [START_REF] Zadeh | Fuzzy sets[END_REF], FCM can be used to model heterogeneity in biomedical imaging [START_REF] Ahmed | A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data[END_REF][START_REF] Belhassen | A novel fuzzy C-means algorithm for unsupervised heterogeneous tumor quantification in PET[END_REF].

PROPOSED METHOD

We propose to use FCM for regularizing the MLEM deconvolution. It is performed by minimizing both the MLEM and the FCM objective functions. The resulting functional is:

J ML FCM = J ML + λ FCM C j µ m j (x)||o(x) -c j || 2 (10)
subject to j µ j = 1, where λ FCM controls the regularization term. By finding the null derivation of (10) according to c j , µ j (x) and o(x), we adopt the following alternately updating:

c j = x µ m j (x)o t (x) x µ m j (x) ∀ j = {1, . . . , C} (11)
µ j (x) = 1 k ||o t (x)-c j || ||o t (x)-c k || 2 m-1 ∀ j = {1, . . . , C} (12)
o t+1 (x) = o t (x) i(x) (p⊗o t )(x) ⊗ p(-x) 1 + λ FCM 2 C j µ m j (x) o t (x) -c j (13)
Because the intensities of voxels are brought close to the cluster centroid they belong to, noise is not amplified during the deconvolution process. As in FCM algorithm, m controls the fuzziness of the data. Furthermore, because the membership degrees are in the power of m in equation ( 13), a large value of m results in a low regularization for data whose intensity is far from cluster centroids. We set m to its default value m = 2. As using TV1 approach, the regularization is controlled by a parameter λ FCM . Because the regularization term in equation 13 is according to o t (x)c j that depends on image content, we suggest to normalize λ FCM according to the maximum image intensity: λ FCM = Λ FCM max x (i(x)) . Our proposed method performs simultaneously the segmentation by specifying the number of clusters, and the deconvolution with a regularization approach focusing the intensity of voxels around clusters.

Simulated image

To evaluate the behavior of our deconvolution method, a simulated image given in Figure 1(a) was used. It consists in three gray scales (0.2, 0.63 and 1) and three regions: one thin, one heterogeneous and one contaminating another. The image is blurred using a Gaussian PSF whose standard deviation is 1.6 pixels (see Figure 1(b)). The same PSF is used for deconvolution. Three deconvolution methods were compared, the MLEM method (ML), the MLEM regularized using TV1 (ML TV1 ) and our proposed method using two and three classes (respectively ML FCM2 and ML FCM3 ). Iterations are perform until the normalized sum of image differences between two iterations is lower than 10E -5 . For our method, centroids are initialized using C-Means algorithm, and o(x) 0 is set to i(x). Regularization parameter values were determined empirically, by applying the deconvolutions with different parameter values and by selecting those minimizing the criterions (equations ( 5) and ( 7)). We obtained λ T V1 = 0.001 and Λ FCM = 0.001. Root-Mean-Square Deviations (RMSD) between the deconvolution results and the simulated image (Figure 1(a)) are used for evaluation. The deconvolution results are given in Figure 1. The best result is obtained with ML FCM3 presenting the lower RMSD. The contours are sharp, the small region is retrieved and the contamination is well corrected. By maximizing the membership value of each pixel according to the three classes, a segmented image can be obtained. We observed that only 2 pixels were not well classified with ML FCM3 : in the thin and the white regions. With ML, the contours are still blurry and the signal vary slightly inside homogeneous regions. Using ML TV1 , the contours are sharp and noise is not amplified. However the small region is not well retrieved and the pixel values between the two contaminated regions is higher than in simulated image (∼ 0.25 instead of 0.2). Concerning ML FCM2 , we observe that two classes of pixels (black and gray) have been regularized, whereas the contours of the third class (White pixels) are still blurry as using ML. This result is interesting because it shows that our method can be applied in the case of heterogeneous regions, affecting to the voxels different membership degrees according to the clusters. In conclusion, as long as the number of classes is known, the best deconvolution is obtained using our method. In biomedical cases, this number if often known by the experimenter thanks to its expertise in a pathology. Furthermore, the estimation of this number is still possible, using for example Bayesian Information Criterion as proposed in [START_REF] Belhassen | A novel fuzzy C-means algorithm for unsupervised heterogeneous tumor quantification in PET[END_REF].

fluorescence Diffuse Optical Tomography (fDOT) images

In order to validate our method on biomedical images, we used images provided by fDOT in a mouse. It is a new imaging technique used to follow in 3-Dimensions (3D) a fluorescent probe in tissues [START_REF] Koenig | Fluorescence diffuse optical tomographic system for arbitrary shaped small animals[END_REF]. Reconstructed images are extremely blurry, leading to imprecision that corresponds to a lack of knowledge [START_REF] Garofalakis | In vivo validation of free-space fluorescence tomography using nuclear imaging[END_REF]. It is the case at the contour of objects, and especially in the presence of small structures. In medical applications as oncology, a precise segmentation is necessary in order to quantify the quantity of probes in tumors. Due to imprecision, fDOT image segmentation is difficult to achieve and measurements can not reflect the actual probe quantity in tissues.

The images are obtained as follow. First, a transparent capillary filled with 4 µL of fluorescent probes was inserted under the skin of a mouse (see Figure 2(a)). Then, a transillumination 685 nm-laser scan was performed at the region of interest (see Figure 2(a)), and 3D reconstruction was performed [START_REF] Koenig | Fluorescence diffuse optical tomographic system for arbitrary shaped small animals[END_REF]. Figure 2(c) gives an example of reconstructed image. Voxels after reconstruction are 0.6 × 0.6 × 1 mm 3 . By changing the quantity of probes in the capillary, five quantities with the same volume were imaged: 2.6, 10.6, 21.2, 42.4 and 84.8 pMol. Assuming the autofluorescence of the mouse is null compared to the probes, the images give information about the total quantity of fluorescent signal in probes. Four segmentation methods are compared: a thresholding with a 0 threshold that allows us to measure the total signal quantity (Thresh), the FCM using 2 classes (FCM2), the ML TV1 deconvolution followed by FCM2 (ML TV1 ) and our proposed method with two classes (ML FCM2 ). λ T V1 and Λ FCM was set to 0.1, allowing us to obtain sharp contours without noise amplification. Moreover, increasing these parameter values increases the size of the fluorescent region. Concerning ML FCM2 the value was chosen in order to obtain fluorescent volumes around 12µL. This volume corresponds to only 27 voxels. A Gaussian PSF is used whose 3D standard deviation is ∼ 1 mm. This value was approximated using a reconstructed image of a capillary filled with a probe of 0.5 µL, which is close to the volume of a voxel (0.44 µL). Finally, using FCM, segmentation results are obtained by choosing the class having the highest membership degree.

Figure 2 gives the segmentation results according to the four compared methods. Thresh allows retrieving the total quantity of signal. However, the volume of capillaries is about 108.2 ± 23.1 µL that is extremely large compared to the actual filled volume. Using FCM segmentation method, the volume is also large (41.2 ± 2.7 µL). Moreover, as we can see in Figure 2(b), the measured quantity corresponds to an under-estimation of the total quantity given by Thresh. The large measured volumes using Thresh and FCM2 are due to blurry signal in fDOT images. ML TV1 and ML FCM2 deconvolution methods give the best volume estimation (respectively 11.6 ± 1.5 µL and 12.2 ± 1.2 µL). Moreover, the deconvolved image using ML FCM2 is sharper than using ML TV1 (see Figure 2(e) vs. (f)). Thanks to our proposed regularization using FCM, intensity of voxels is close to the centroid of the cluster it belongs to, resulting in sharp contours. Furthermore, we observe that the measured quantity is under-estimated using ML TV1 , but is well estimated using ML FCM2 (see Figure 2(b)). In conclusion, our method gives the best volume estimation without under-estimation of the quantity of probes in the segmented region.

CONCLUSION

Dedicated to blurry image segmentation, we propose to use FCM for regularization of MLEM deconvolution method. Regularization is achieved focusing the intensity of voxels close to the centroid of the cluster it belongs to. Furthermore, it allows us to deal with heterogeneity by affecting to each voxel membership degrees according to the different clusters. Applied on simulated and fDOT images, the results show our method is well designed for segmenting extremely blurry images, and outperforms the TV1 regularization approach.

Our method removes blurry information corresponding to imprecision thanks to the knowledge about the number of clusters. It can be applied on blurry biomedical images. For dealing with both imprecision and uncertainty due to noise, our method could also integrate TV1 regularization.

In future works, the PSF of fDOT images will be estimated more accurately. The noise will also be estimated and the robustness to our method toward this noise will be evaluated. The automatic determination of the cluster number in each region to segment will also be studied.

3 Fig. 1 .

 31 Fig. 1. Deconvolution results on a simulated blurry image using MLEM with and without regularization approaches (TV1 and FCM). The RMSD are given below each figure.

Fig. 2 .

 2 Fig. 2. Segmentation of a fDOT image using four methods. (a) is a white planar image of a capillary inserted in a mouse. The fluorescent scanned region is represented by a rectangle. (b) is a comparison of the measured quantity of fluorescence with each method according to each capillary. (c), (d), (e) and (f) correspond to fluorescence segmentation results on one slice according to the four compared methods.

  i denotes the recored image, o denotes the real object, p is the Point Spread Function (PSF), n is an additive noise and ⊗ is the convolution operator. MLEM deconvolution consists in reconstructing o by finding o = arg max o {p(i|o)}. Because of the quantum nature of light, photon noise is Poisson distributed. Thus, o maximizes the likelihood function: