Oligosaccharide Ligands of Galectin-4 and Its Subunits: Multivalency Scores Highly

Galectins are carbohydrate-binding lectins that modulate the proliferation, apoptosis, adhesion, or migration of cells by cross-linking glycans on cell membranes or extracellular matrix components. Galectin-4 (Gal-4) is a tandem-repeat-type galectin expressed mainly in the epithelial cells of the gastrointestinal tract. It consists of an N- and a C-terminal carbohydrate-binding domain (CRD), each with distinct binding affinities, interconnected with a peptide linker. Compared to other more abundant galectins, the knowledge of the pathophysiology of Gal-4 is sparse. Its altered expression in tumor tissue is associated with, for example, colon, colorectal, and liver cancers, and it increases in tumor progression, and metastasis. There is also very limited information on the preferences of Gal-4 for its carbohydrate ligands, particularly with respect to Gal-4 subunits. Similarly, there is virtually no information on the interaction of Gal-4 with multivalent ligands. This work shows the expression and purification of Gal-4 and its subunits and presents a structure–affinity relationship study with a library of oligosaccharide ligands. Furthermore, the influence of multivalency is demonstrated in the interaction with a model lactosyl-decorated synthetic glycoconjugate. The present data may be used in biomedical research for the design of efficient ligands of Gal-4 with diagnostic or therapeutic potential.


Introduction
Galectins (Gal-) form a small group of β-galactoside-binding lectins comprising fifteen members in humans. Their functions include the modulation of vital cellular processes, such as cell proliferation, apoptosis, adhesion, or migration by cross-linking glycans on cell membranes and/or extracellular matrix components [1]. Compared to Gal-1 and Gal-3, which have been widely shown to play significant roles especially in cancer progression, inflammation, fibrosis, heart disease, and stroke, as well as some metabolic disorders [2,3], there are few studies on the pathophysiology and the binding preferences of galectin-4 (Gal-4) [4]. Gal-4 is a tandem-repeat galectin consisting of two different carbohydraterecognition domains (CRDs) at the N-and C-terminus (Gal-4N, and Gal-4C, respectively), each with distinct binding specificities, which are covalently linked with a specific peptide [5]. The crystal structures of native Gal-4 and its individual CRDs show that both CRDs contain a concave binding site with five subsites (A-E) and preferentially bind lactose in the D/E subsites. These extended subsites can further accommodate various glycan epitopes, depending on subtle interactions with specific amino acids [6][7][8].

Expression and Purification of Gal-4 and Its Binding Domains
The Gal-4 construct carrying an N-terminal His 6 -tag cloned into the pET28a vector was expressed in Escherichia coli Rosetta (DE3) pLysS cells and purified to homogeneity by metal-ion-affinity chromatography ( Figure 1). Furthermore, the N-terminal and C-terminal subunits of Gal-4, designated as Gal-4NL (aa 1-160), and Gal-4CL (aa 169-323), respectively, were expressed and purified using analogous procedures. Both subunits carried a 10-amino-Molecules 2023, 28, 4039 3 of 15 acid linker at their respective ends, interconnecting these domains in the native protein. The presence of the linker was necessary to preserve the lectin activity of the subunits. Notably, while the whole Gal-4 remained stable and active at 4 • C for ca 3 weeks, the stability of its subunits was significantly lower, ca one week. After this time, there was a significant loss of binding activity. The typical yields of the purified forms of Gal-4 are listed in Table 1. The production yields of individual Gal-4 subunits, expressed as mg of protein gained from one gram of E. coli cells, were about one half of those obtained for the whole Gal-4 construct, which suggests that the molar yields of these proteins were very similar. The purity of the proteins was confirmed by SDS-PAGE ( Figure 1A); the presence of the His-tag was confirmed by Western blot, using detection with anti-His 6 -tag antibody ( Figure 1B). the subunits. Notably, while the whole Gal-4 remained stable and active at 4 °C for ca 3 weeks, the stability of its subunits was significantly lower, ca one week. After this time, there was a significant loss of binding activity. The typical yields of the purified forms of Gal-4 are listed in Table 1. The production yields of individual Gal-4 subunits, expressed as mg of protein gained from one gram of E. coli cells, were about one half of those obtained for the whole Gal-4 construct, which suggests that the molar yields of these proteins were very similar. The purity of the proteins was confirmed by SDS-PAGE ( Figure 1A); the presence of the His-tag was confirmed by Western blot, using detection with anti-His6tag antibody ( Figure 1B).

Binding Affinity of Gal-4 and Its Subunits to a Library of Carbohydrate Ligands
The affinities of purified His-tagged Gal-4 and its binding subunits Gal-4NL and Gal-4CL with a library of seven oligosaccharides (1-6; 9) and one defined multivalent lactosyl-decorated neo-glycoprotein (12) were investigated using a competitive enzymelinked immunosorbent assay (ELISA).
To design the ELISA method, we first examined the direct binding of the whole Gal-4, Gal-4NL, and Gal-4-CL to standard glycoprotein asialofetuin (ASF, MW 48.4 kDa), which carries up to nine LacNAc epitopes. The ASF was immobilized by hydrophobic interaction in microtiter-plate wells, and the binding of increasing concentrations of Gal-4 proteins was quantified by colorimetric immunodetection using horseradish peroxidase conjugated to an anti-His-tag antibody. The apparent dissociation constants (K D ) were calculated from the non-linear regression of the binding curves ( Figure 3). The total Gal-4 protein reached a low micromolar range of apparent K D with ASF (3.3 ± 1.1 µM), which was comparable to the values of Gal-1 and Gal-3 determined by the same method [32]. In contrast, individual Gal-4 subunits showed K D values that were about one order of magnitude higher (K D = 38 ± 3 µM and 19 ± 2 µM for Gal-4NL and Gal-4CL, respectively). These notable differences between the affinities of the subunits with ASF also resulted in slightly different setups for the competitive ELISA assays. While for the Gal-4 ELISA measurement we used the concentration of Gal-4 of 2.5 µM, for both subunits, it was 25 µM. Thus, we produced saturated inhibitory curves and acquired comparable values for the standard inhibitor, lactose, with all three protein constructs: IC 50 = 2.5 ± 0.2 mM for the whole Gal-4 ( Table 2); 2.9 ± 0.4 mM for Gal-4NL; and 8.6 ± 1.1 mM for Gal-4CL (Table 3). The potential of glycans 1-6, 9 and neo-glycoprotein 12 to inhibit the binding of the Gal-4 to the immobilized ASF was essentially analyzed as described previously [32,33]. The Gal-4 proteins were incubated with increasing concentrations of the respective inhibitors, and the concentration-dependent inhibition of the binding to the immobilized ASF was quantified using spectrophotometric colorimetric immunodetection (HRP-conjugated anti-His-tag  Tables 2 and 3.  Table 2. (C) The curves of dose-response inhibition of binding of the Gal-4NL subunit to immobilized ASF by monovalent inhibitors 1-6 and 9, as well as by multivalent neo-glycoprotein inhibitor 12. Respective values are in Table 2. (D) The curves of dose-response inhibition of binding of the Gal-4CL subunit to immobilized ASF by monovalent inhibitors 1-6 and 9, as well as by multivalent neo-glycoprotein inhibitor 12. Respective values are in Table 3.
As shown in Table 2, the inhibitory potential of the tested monovalent glycans toward the whole Gal-4, expressed as IC50, ranged over more than two orders of magnitude (2.5 mM to 50 µM), depending on the glycan structure. The best inhibitors, blood-group antigens A and B, offered improvements in the inhibitory potency of up to 48-fold compared with the lactose standard. For both subunits, the structure-affinity relationship was even more distinct-the best inhibitor, blood-group antigen A, reached 130-fold and 320fold increases in inhibitory potency with Gal-4NL and Gal-4CL, respectively, compared with the lactose. Blood-group antigen B was a considerably weaker inhibitor of the Gal-4 subunits, with 11-fold and 28-fold improvements over lactose for Gal-4NL and Gal-4CL, respectively. The IC50 values for the lacto-N-tetraose (3) were in the high micromolar range for both the whole Gal-4 and its subunits, Gal-4NL and Gal-4CL (cf. 0.43, 0.21 and 0.47 mM, respectively), closely followed by lacto-N-neotetraose (4) (cf. 0.6, 0.4, and 0.8 mM, respectively). Notably, the inhibitory potency of 2′-fucosyllactose (2) was much more distinct in the cases of both subunits (with up to 7.8-fold improvements in inhibitory potency compared with the lactose) than in the case of the whole Gal-4 (which was comparable to lactose). With all three proteins, the TF antigen motif (9) was a quite weak inhibitor, comparable to lactose.
This work demonstrates, for the first time, an exciting increase in inhibitory potency achieved with a synthetic multivalent ligand by the multivalent presentation of the relatively weak inhibitor, lactose. The multivalent neo-glycoprotein 12 broke the micromolar border with the whole Gal-4, reaching an IC50 of 190 nM (a 1400-fold-stronger affinity with one bound lactosyl than the free lactose). For both subunits, the multivalency effect was also considerable (IC50 = 900 nM for Gal-4NL and 1.7 µM for Gal-4CL). This clearly demon- The curves of dose-response inhibition of binding of the whole Gal-4 to immobilized ASF by monovalent inhibitors 1-6 and 9, and by multivalent neo-glycoprotein inhibitor 12. Respective values are in Table 2. (C) The curves of dose-response inhibition of binding of the Gal-4NL subunit to immobilized ASF by monovalent inhibitors 1-6 and 9, as well as by multivalent neo-glycoprotein inhibitor 12. Respective values are in Table 2. (D) The curves of dose-response inhibition of binding of the Gal-4CL subunit to immobilized ASF by monovalent inhibitors 1-6 and 9, as well as by multivalent neo-glycoprotein inhibitor 12. Respective values are in Table 3.  (9) 3.5 ± 0.2 b 5.8 ± 0.5 b 0.8 1.5 neo-glycoprotein 12 0.0009 ± 0.0001 0.0017 ± 0.0004 3200 (340) c 5100 (530) c a rp, relative potency (rp = IC 50 (lactose)/IC 50 (ligand); b the value is an estimate from two independent experiments. c The value in brackets expresses relative potency per lactosyl unit, i.e., rp/lactosyl = IC 50 (lactose)/IC 50 (ligand)/no. of lactosyls on the neo-glycoprotein, as determined by MALDI-TOF (9.6).
As shown in Table 2, the inhibitory potential of the tested monovalent glycans toward the whole Gal-4, expressed as IC 50 , ranged over more than two orders of magnitude (2.5 mM to 50 µM), depending on the glycan structure. The best inhibitors, blood-group antigens A and B, offered improvements in the inhibitory potency of up to 48-fold compared with the lactose standard. For both subunits, the structure-affinity relationship was even more distinct-the best inhibitor, blood-group antigen A, reached 130-fold and 320-fold increases in inhibitory potency with Gal-4NL and Gal-4CL, respectively, compared with the lactose. Blood-group antigen B was a considerably weaker inhibitor of the Gal-4 subunits, with 11-fold and 28-fold improvements over lactose for Gal-4NL and Gal-4CL, respectively. The IC 50 values for the lacto-N-tetraose (3) were in the high micromolar range for both the whole Gal-4 and its subunits, Gal-4NL and Gal-4CL (cf. 0.43, 0.21 and 0.47 mM, respectively), closely followed by lacto-N-neotetraose (4) (cf. 0.6, 0.4, and 0.8 mM, respectively). Notably, the inhibitory potency of 2 -fucosyllactose (2) was much more distinct in the cases of both subunits (with up to 7.8-fold improvements in inhibitory potency compared with the lactose) than in the case of the whole Gal-4 (which was comparable to lactose). With all three proteins, the TF antigen motif (9) was a quite weak inhibitor, comparable to lactose.
This work demonstrates, for the first time, an exciting increase in inhibitory potency achieved with a synthetic multivalent ligand by the multivalent presentation of the relatively weak inhibitor, lactose. The multivalent neo-glycoprotein 12 broke the micromolar border with the whole Gal-4, reaching an IC 50 of 190 nM (a 1400-fold-stronger affinity with one bound lactosyl than the free lactose). For both subunits, the multivalency effect was also considerable (IC 50 = 900 nM for Gal-4NL and 1.7 µM for Gal-4CL). This clearly demonstrates the strong beneficial effect of the multivalent presentation on Gal-4, as a representative of tandem-repeat galectins. To corroborate these results, an alternative affinity-determination method, biolayer interferometry (BLI), was used to assess the affinity of the whole Gal-4 and its both subunits with neo-glycoprotein 12 ( Figure 4). In contrast to competitive ELISA, BLI is a direct affinity measurement that was already proven to be very useful for assessing the kinetics of interactions between galectins and their multivalent ligands [32]. However, this is the first time it was employed with Gal-4. The His-tagged fusion proteins were attached to the Ni-NTA biosensors by nickel chelation. The acquired kinetic data were subjected to steady-state analysis, and the shift of the interference pattern was plotted against the ligand concentration. In accordance with the ELISA results, neoglycoprotein 12 exhibited the highest affinity for the whole Gal-4 (K D = 0.17 ± 0.02 µM), followed by Gal-4NL (K D = 1.0 ± 0.2 µM) and Gal-4CL (K D = 1.7 ± 0.1 µM). These submicromolar values of K D confirm the high potential of multivalency systems, such as neo-glycoprotein 12, to inhibit Gal-4. strates the strong beneficial effect of the multivalent presentation on Gal-4, as a representative of tandem-repeat galectins. To corroborate these results, an alternative affinitydetermination method, biolayer interferometry (BLI), was used to assess the affinity of the whole Gal-4 and its both subunits with neo-glycoprotein 12 ( Figure 4). In contrast to competitive ELISA, BLI is a direct affinity measurement that was already proven to be very useful for assessing the kinetics of interactions between galectins and their multivalent ligands [32]. However, this is the first time it was employed with Gal-4. The His-tagged fusion proteins were attached to the Ni-NTA biosensors by nickel chelation. The acquired kinetic data were subjected to steady-state analysis, and the shift of the interference pattern was plotted against the ligand concentration. In accordance with the ELISA results, neo-glycoprotein 12 exhibited the highest affinity for the whole Gal-4 (KD = 0.17 ± 0.02 µM), followed by Gal-4NL (KD = 1.0 ± 0.2 µM) and Gal-4CL (KD = 1.7 ± 0.1 µM). These submicromolar values of KD confirm the high potential of multivalency systems, such as neo-glycoprotein 12, to inhibit Gal-4. The affinity results (Tables 2 and 3) showed relatively minor differences between the whole Gal-4 and its subunits. Therefore, we decided to obtain more insights into the potential aggregation behavior of the Gal-4 subunits in solution, which, theoretically, might have contributed to the multivalency effect, even with the monovalent Gal-4 subunits. The hydrodynamic radii of the whole Gal-4 and its subunits in the concentrations used in the ELISA assay (25 µM) were assessed using dynamic light scattering (DLS). This method provided information about the size distribution of the particles in the samples (Table 4). Notably, the samples of the Gal-4 were quite polydisperse, and the autocorrelation function fits commonly yield multimodal intensity-weighed size distributions. Therefore, the larger particles seemed to be more abundant in these distribution diagrams because light scattering is proportional to the sixth power of the scattering-matter diameter. To avoid The affinity results (Tables 2 and 3) showed relatively minor differences between the whole Gal-4 and its subunits. Therefore, we decided to obtain more insights into the potential aggregation behavior of the Gal-4 subunits in solution, which, theoretically, might have contributed to the multivalency effect, even with the monovalent Gal-4 subunits. The hydrodynamic radii of the whole Gal-4 and its subunits in the concentrations used in the ELISA assay (25 µM) were assessed using dynamic light scattering (DLS). This method provided information about the size distribution of the particles in the samples (Table 4). Notably, the samples of the Gal-4 were quite polydisperse, and the autocorrelation function fits commonly yield multimodal intensity-weighed size distributions. Therefore, the larger particles seemed to be more abundant in these distribution diagrams because light scattering is proportional to the sixth power of the scattering-matter diameter. To avoid misinterpretation, we also present the volume-weighed size distributions in Table 4, which highlight the most abundant populations of particles. These values indicate that in the cases of the whole Gal-4 and Gal-4CL, the large aggregates at 1200 nm and 400 nm, respectively, can be neglected (the volume-weighted size distributions accounted for 9 and 7 nm, respectively). The whole Gal-4 formed the most abundant particles, of 11 nm, which was similar to Gal-4CL with 8 nm particles. In the case of Gal-4NL, the solution was more polydisperse, and two significant populations were observed. The first population, of 1.3 nm, probably represented the individual Gal-4NL subunits, whereas the slightly larger population of 16 nm belonged to the aggregated species. These data suggest that in 25 µM concentrations, the Gal-4CL subunit tended to aggregate, whereas the Gal-4NL subunits remained in equilibrium with a major population of monomers and a minor population of aggregates, which were similar to those found with the other two proteins.

Discussion
The present work provides a unique insight into the binding affinities/inhibitory potencies of a representative series of oligosaccharides (seven compounds) using an easily implementable and reproducible competitive ELISA method. Since our results with individual subunits of Gal-4 revealed a considerable difference in binding to the competitor ligand ASF (with more than 10-fold-higher apparent K D s compared with the total Gal-4), we reflected this fact in the optimized setup of the competitive ELISA assay. The structureaffinity relationship study allowed the evaluation of the selectivity and behavior of the scarcely studied but biomedically very relevant tandem-repeat galectin-Gal-4. Previous studies generally worked on the principle of relative affinities, which hardly allows any comparison with the results obtained by other research groups [20]. However, the trends found herein and the relative order of the inhibitors according to their potency (in particular, lactose > 2 -fucosyllactose > lacto-N-tetraose > lacto-N-neotetraose > blood group antigens) were quite well in line with the affinity information available in the literature [6,7]. In agreement with our data, the relative order of affinities shown by Vokhmyanina et al. also identified lacto-N-tetraose (3) as a superior ligand to lacto-N-neotetraose (4), using flow cytometry analysis [20]. To our knowledge, the most thorough study giving a numerical assessment of binding affinities is the paper by Quintana et al., presenting K D s determined by isothermal titration calorimetry (ITC) and by NMR [21]. The K D values reported therein for blood-group antigens A type 6 (5) and B type 6 (6) and Gal-4NL (other forms of Gal-4 were not analyzed) were in the micromolar range, as were our IC 50 values, which were acquired by ELISA (cf. Table 2 with K D = 86 µM for antigen A, and 51 µM for antigen B by ITC). However, in contrast to Quintana et al. [21], our results clearly identified blood-group antigen A as a superior inhibitor of Gal-4NL (a 12-fold stronger inhibitor than B). In our study, both the individual Gal-4NL and Gal-4CL subunits showed a significantly stronger affinity to the blood-group antigen A than to B ( Table 3). The preference for A over B was also apparent, albeit less distinctively, in the affinities of the whole Gal-4 ( Table 2). This discrepancy between our results and those of Quintana et al. [21] may have been caused by the use of completely different affinity-determination methods (in-solution vs. solid-phase assay). In sum, although all these comparisons are rather rough and relative (because the assessment methods used were different), they identify ELISA as a reliable method for assessing Gal-4 affinity.
Although size-related data for tandem-repeat galectins or their subunits (ca. 36 kDa and ca. 17 kDa, respectively) are currently lacking in the literature, the tendency of galectins to aggregate into dimers or oligomers was previously reported for other galectins, especially Gal-1 and Gal-3 [34,35]. Therefore, the generally relatively minor differences between the affinities found for the whole (bivalent) Gal-4 and its (monovalent) subunits might have partially contributed to the ability of the subunits to aggregate into larger clusters. However, the DLS analysis showed that this aggregation was relevant only for the Gal-4CL subunit, as the Gal-4NL subunit had an abundant population of monomers. Thus, the increase in the affinity of the Gal-4 subunits with the multivalent ligands was not primarily due to aggregation. This conclusion is neatly correlated with the results of the BLI measurements. Although aggregation cannot occur there because galectins are individually immobilized on the biosensor, the K D results acquired by BLI for neo-glycoprotein 12 compared well with the ELISA data. The phenomenon of aggregation, reported here for the first time with Gal-4, deserves more thorough exploration in the future.
In addition, the present work addresses a hitherto rather neglected aspect of the affinity of Gal-4 to a multivalent synthetic ligand. Due to the structure of Gal-4, a tandem-repeat galectin with two binding sites, the multivalency effect was extreme, with improvement in binding of more than three orders of magnitude (1400-fold) when one lactosyl bound to the multivalent neo-glycoprotein was compared with free lactose. There was no positive contribution of the thiourea linker in this case, as the deprotected lactosyl amine showed IC 50 = 2.8 mM (see also the legend in Table 2), which was practically the same value as that of the free lactose (2.5 mM). This was also in accordance with our previous results with other galectins and a variety of linkers and carriers [32,36,37]. Hence, the considerable avidity increase should be attributed to the multivalency effect, possibly based on statistical rebinding, which may result in stabilized ligand-lectin crosslinked complexes [38]. In sum, multivalent ligands, even with simple epitopes, such as the readily available lactose, are very promising as tools for biomedical research on Gal-4. The detailed mechanisms of multivalence and the avidity increase with multivalent ligands will be the subject of further studies.

Expression and Purification of Gal-4
The gene of human Gal-4 (GenBank: U82953.1; [42]) containing an N-terminal His 6tag cloned into the pET28a vector using the 5 -NdeI and 3 -XhoI restriction sites was obtained commercially (Generay, Shanghai, China). Gal-4 was expressed intracellularly in Escherichia coli Rosetta (DE3) pLysS cells (Merck, Darmstadt, Germany), first in an overnight preculture (60 mL, Luria-Bertani medium, 37 • C, 220 rpm), which was then transferred in TB (Terrific Broth, 600 mL in a 3-L flask) medium, both under pressure of kanamycin and chloramphenicol. When the culture reached an OD 600 of 0.6, the expression of Gal-4 was induced by 0.5 mM IPTG. After 24 h of cultivation at 37 • C, the cells were harvested by centrifugation and frozen at −20 • C overnight (frozen cells could be stored for several months). On the next day, the cells were resuspended in 20 mL of binding buffer (20 mM Na 2 HPO 4 /500 mM NaCl/20 mM imidazole, pH 7.4) with 200 µL PMSF and disrupted by sonication (6 × 1 min), followed by centrifugation to remove the cell debris. The collected supernatant was diluted to the final 50 mL volume with binding buffer and loaded onto an equilibrated 5 mL HisTrap column (Cytiva Life Sciences, Chicago, IL, USA) connected to the Äkta Purifier protein-chromatography system (Cytiva Life Sciences, Chicago, IL, USA). The proteins bound to the column were eluted by the gradient (10 mL) of the elution buffer (20 mM Na 2 HPO 4 /500 mM NaCl/500 mM imidazole, pH 7.4) and the fractions containing Gal-4 (as determined by SDS-PAGE) were pooled and dialyzed against 7 L of EPBS (50 mM Na 2 HPO 4 /150 mM NaCl/2 mM EDTA, pH 7.5) overnight, and then against 7 L of PBS (150 mM NaCl/50 mM Na 2 HPO 4 , pH 7.5) for additional 4 h to remove traces of imidazole. The concentration of the prepared Gal-4 was determined using Bradford assay (calibrated for IgG), and its purity was determined by SDS-PAGE. The purified Gal-4 was stored at 4 • C for ca 3 weeks without a significant loss of activity. The identity of the His-tagged galectin constructs was confirmed using Western blot. The gel was transferred onto a nitrocellulose membrane after SDS-PAGE, and then blocked with 10% skimmed milk and labeled with anti-His 6 antibody conjugated to HRP (His-probe, Santa Cruz Biotechnology, Dallas, TX, USA). The chemiluminescence signal was detected using G:box Chemi XRQ (Trigon Plus,Čestlice, Czech Republic) after substrate addition.

Expression and Purification of the N-and C-Terminal Subunits of Gal-4
The N-terminal subunit of Gal-4 (Gal-4NL) was identified as amino acid (aa) 1-150 in the original gene; the construct for expression contained additional 10 aa residues from the linker interconnecting both subunits at the C-terminus. The gene of Gal-4NL was prepared from the original plasmid containing the Gal-4 gene by PCR (T-Personal PCR cycler, Biometra, Göttingen, Germany) using Q5 Hot-Start High-Fidelity DNA polymerase (New England Biolabs, Ipswich, MA, USA) and the following primers: forward 5 -AGCTAGCTCATATGGCCTATGTCCCCGCACCGGGCT-3 and reverse 5 -TATACGATCTCGAGTCAGGGTCCCTGGGGCCGGAG-3 . The PCR product and the original plasmid were subjected to cleavage by the NdeI and XhoI restriction endonucleases (New England Biolabs, Ipswich, MA, USA), purified by the GeneJET PCR Purification Kit (Thermo Scientific, Vilnius, Lithuania) and ligated using T4 DNA Ligase (New England Biolabs, Ipswich, MA, USA) at 16 • C, overnight. The ligation mixture was transformed into Gold(DE3) cells, the plasmids were isolated from the obtained colonies using the High Pure Plasmid Isolation Mini Kit (Roche, Basel, Switzerland), and the sequence of the construct was verified by commercial Sanger sequencing (SeqMe, Dobříš, Czech Republic).
The C-terminal-binding domain of Gal-4 (Gal-4CL) was identified as aa 179-323 in the original gene; the construct for expression contained an additional 10 aa residues from the linker interconnecting the two domains at the N-terminus. The Gal-4CL construct for expression was prepared analogously to the Gal-4NL described above, with the following PCR primers: forward 5 -AGCCAGTGCATATGCCCGGACATTGCCATCAACAGCT-3 and reverse 5 -AGCACGATCTCGAGTCAGATCTGGACATAGGACAAGGTG-3 . The Gal-4NL and Gal-4CL subunits were expressed in E. coli Rosetta (DE3) pLysS and purified by the same procedure as described for the total Gal-4 in Section 4.3.
The apparent dissociation constant (K D ) of binding of the whole Gal-4 or its subunits to ASF was determined using direct enzyme-linked immunosorbent assay (ELISA), with washing steps as specified above. The microtiter plate was coated with immobilized ASF (0.1 µM) overnight and blocked with BSA (2 mg/mL, 250 µL/well) for 1 h. Increasing concentrations of Gal-4 or its subunits were added (50 µL/well) and incubated for 2 h. Residual galectins bound to the wells were labeled with anti-His-antibody conjugated with HRP, and evaluated as above.

Biolayer Interferometry (BLI)
The affinity and kinetics of neo-glycoprotein 12 with the whole Gal-4, Gal-4NL, and Gal-4CL were assessed by BLI under constant conditions (25 ± 0.1 • C, 800 rpm) using interferometry device Octet ® Red96e (FortéBio, Fremont, CA, USA). Galectins were diluted to a concentration of 2 µg/mL in PBS buffer containing 0.05% Tween-20 and immobilized on the Ni-NTA biosensor (Octet ® NTA Biosensors, Sartorius, Goettingen, Germany) via nickel chelation of N-terminal His-tags of the proteins. After the immobilization step (100 s), the interactions of the serially diluted (185-15 µM) neo-glycoprotein 12 with the immobilized proteins were monitored for 900 s during the association-and-dissociation step. No impairment of lectin activity due to immobilization and no non-specific interaction were observed. The acquired BLI data were investigated by Octet Analysis software (FortéBio, Fremont, CA, USA). The drift of the sensor itself, as obtained from the data with the reference sensor, was subtracted. The steady-state analysis was performed by plotting the shift of the interference pattern versus ligand concentration using Equation (1): where R eq refers to the shift of the interference pattern at equilibrium in each sensogram curve, R max refers to the maximal response at equilibrium, and c denotes the ligand concentration.

Dynamic Light Scattering (DLS)
The hydrodynamic diameter of the Gal-4 and its subunits (25 µM) was measured by dynamic light scattering (DLS) using Zetasizer Nano S90 (Malvern Instruments Ltd., Malvern, UK) at 25 • C. The light scattered at θ = 173 • from the incident light was fitted to an autocorrelation function using the method of cumulants (Malvern Instruments Ltd., Malvern, UK). The hydrodynamic diameters were determined from five independent repe-titions (10-50 runs) in Malvern disposable plastic cuvettes. The particle-size distribution was determined by analyzing the multimodal peak by intensity and volume.

Conclusions
This work presents a structure-affinity relationship study describing the affinities of the underappreciated Gal-4 protein with a series of carbohydrate ligands. It is the first study to numerically quantify the affinities of the entire Gal-4 protein and its two subunits with a variety of carbohydrate ligands. A robust and reliable ELISA design for assessing the affinities of this protein is presented. In addition, this work highlights the advantageous aspect of multivalency, which increased the avidity of a synthetic neo-glycoprotein for Gal-4 by more than three orders of magnitude. This result was validated by an alternative method of biolayer interferometry. In addition, the aggregation behavior of the whole Gal-4 and its subunits in solution was discussed, and its possible impact on the data obtained was outlined. These results represent a solid starting point for further biomedical and biological studies on the therapeutic or diagnostic inhibition/scavenging of Gal-4, such as in gastrointestinal cancer.