Reliability of REMD simulations

To determine whether the temperatures were optimally distributed and the number of replicas was sufficient, the acceptance ratios of replica exchange were calculated. The acceptance ratios of the simulations of LFO 15 in the GB HCT model were almost constant around 28 %, implying a free random walk in the replica (temperature) space (Additional file 1: Figure S1a). Moreover, a free random walk both in the replica space (Additional file 1: Figure S1b) and the temperature space (Additional file 1: Figure S1c) were also confirmed. Furthermore, the canonical probability distribution of the total potential energy at each temperature had sufficient overlap with those of neighbors (Additional file 1: Figure S1d). The results of the REMD simulations of LFO 10 and LFO 5 in the GB HCT model were also similar, and their average acceptance ratios were almost constant around 37 and 50 % for LFO 10 and LFO 5 , respectively. For the systems simulated in the GB OBC1 model, the results of REMD simulations were also similar to those simulated in the GB HCT model, and their average acceptance ratios were almost constant around 28, 36 and 50 % for LFO 15 , LFO 10 and LFO 5 , respectively. These results indicate good reliability of the REMD simulations of all systems.

Sizes of LFOs

The sizes of LFOs were determined by measuring their radii of gyration. Figure 2 shows that the trends of the radii of gyration of LFOs simulated in the GB HCT model and those simulated in the GB OBC1 model are similar. The radii of gyration of LFOs tended to increase as their chain lengths increased from 5 to 15 residues. These results suggest the extension of the structures of LFOs as their chain lengths increase.

Fig. 2 The average radii of gyration calculated from the heavy atoms of LFOs simulated in GB HCT (square) and GB OBC1 (dot) models Full size image

Conformations of LFO 15 , LFO 10 and LFO 5

Figure 3 shows the free-energy maps of LFO 15 , LFO 10 and LFO 5 as simulated in GB HTC and GB OBC1 models as well as their major representative conformers and their population sizes from clustering analysis and centroid classification. For LFO 15 , four major conformations such as helix-like (a), partial helix (b), zig-zag (c) and random (d) structures were observed after clustering analysis and centroid classification (Fig. 3a, b and Additional file 1: Figure S2 and Figure S5), and they were characterized by their upper-middle and lower-middle torsions (χ 6-7 and χ 9-10 ). Helix-like structures were found with the highest population of 54.1 and 63.2 % for those simulated in GB HCT and GB OBC1 models, respectively. Helix-like structures took up conformations of left-handed 3-fold helices and tended to have their upper-middle and lower-middle torsions in the similar range of around 240–315°. The conformations with the second highest population were partial helix structures, and their population sizes were 33.9 and 22.3 % for systems simulated in GB HCT and GB OBC1 models, respectively. The other two conformations were zig-zag and random structures. Zig-zag structures were found with the population sizes of 2.8 and 6.7 % for systems simulated in GB HCT and GB OBC1 models, respectively. The population sizes of random structures simulated in GB HCT and GB OBC1 models were 9.2 and 7.8 %, respectively.

Fig. 3 The relative free energy (kcal/mol) maps of LFO 15 (a), LFO 10 (c) and LFO 5 (e) simulated in the GB HCT model as well as those of LFO 15 (b), LFO 10 (d) and LFO 5 (f) simulated in the GB OBC1 model. The groups a, b, c and d are helix-like, partial helix, zig-zag and random structures. Their major representative conformers and populations are also shown Full size image

Similar to the conformations of LFO 15 , four major conformations such as helix-like (a), partial helix (b), zig-zag (c) and random (d) structures were found for LFO 10 after clustering analysis and centroid classification (Fig. 3c, d and Additional file 1: Figure S3 and Figure S6). These conformations were characterized by their upper-middle and lower-middle torsions (χ 4-5 and χ 7-8 ). The conformation with the highest population sizes of 50.5 and 57.5 % was helix-like structures for those simulated in GB HCT and GB OBC1 models, respectively. Partial helix structures occurred with the second highest population sizes of 34.5 and 25.4 % for those simulated in GB HCT and GB OBC1 models, respectively. The population sizes of zig-zag structures were 6.8 and 8.7 % and those of random structures were 8.2 and 8.4 % for systems simulated in GB HCT and GB OBC1 models, respectively.

For LFO 5 , two major conformations such as partial helix (b) and random (d) structures were observed after clustering analysis and centroid classification, probably due to its shorter chain length as compared to those of LFO 10 and LFO 15 (Fig. 3e, f and Additional file 1: Figure S4 and Figure S7). These conformations were characterized by their molecular angles (θ a ) and middle torsion (χ 3-4 ). Partial helix structures were observed with the population sizes of 92.8 and 92.5 % for those simulated in GB HCT and GB OBC1 models, respectively. Random structures were also found with the population sizes of 7.2 and 7.5 % for those simulated in GB HCT and GB OBC1 models, respectively.

Table 1 shows the populations of major representative conformers of LFO 15 , LFO 10 and LFO 5 simulated in GB HCT and GB OBC1 models as determined from clustering analysis and centroid classification. As the chain length increased, the population of the helix-like structures tended to increase. These results may suggest that LFOs have tendencies to form helices as their chain lengths are extended.

Table 1 The populations of major representative conformers of LFO 15 , LFO 10 and LFO 5 simulated in GB HCT and GB OBC1 models as determined from clustering analysis and centroid classification Full size table

Hydrogen bonds important for the formation of helix-like structures

To elucidate the hydrogen bonds important for the formation of helix-like structures, the occurrence frequencies of hydrogen bonds in helix-like structures of LFO 15 and LFO 10 with the occurrence frequencies of at least 1 % were analyzed. For the systems simulated in the GB HCT model, the O6 (i) --H3O (i+1) hydrogen bonds (between residue i and i + 1) were found with the highest frequency, and their glycosidic oxygens acted as important hydrogen bond acceptors that interacted with the hydroxyl groups of C3 atoms of the furanose rings and probably helped stabilize the helix-like structures (Table 2 and Fig. 4). The hydrogen bonds with the second and third highest occurrence frequencies for both LFO 15 and LFO 10 were the O1 (i) --H3O (i) and O5 (i) --H1O (i) hydrogen bonds, which were the hydrogen bonds within the same residue (Table 2 and Fig. 4). The trends of the occurrence frequencies of the hydrogen bonds of LFO 15 and LFO 10 in the GB OBC1 model were also similar to those in the GB HCT model (Table 2). These three hydrogen bonds (O6 (i) --H3O (i+1), O1 (i) --H3O (i) and O5 (i) --H1O (i) hydrogen bonds), especially the O6 (i) --H3O (i+1) hydrogen bond that was found with the highest frequency, are probably important for the formation of helix-like structures of LFO 15 and LFO 10 as their occurrence frequencies are higher than other hydrogen bonds.

Table 2 Occurrence frequencies of hydrogen bonds found in helix-liked structures of LFO 15 and LFO 10 Full size table

Fig. 4 Hydrogen bonds important for the formation of helix-like structures (LFO 15 simulated in the GB HCT model is shown as an example). Middle; the O6 (i) --H3O (i+1) hydrogen bond (occurrence frequency = 65.0 %). Right; the O1 (i) --H3O (i) hydrogen bond. (occurrence frequency = 15.4 %). Left; the O5 (i) --H1O (i) hydrogen bond (occurrence frequency = 11.5 %). Hydrogen bonds are represented as dash lines. The LFO chain and fructosyl units are represented as ribbon and filled yellow color representations, respectively Full size image

Conformational flexibilities

To investigate the conformational flexibilities of LFO 15, LFO 10 and LFO 5 , the occurrence frequencies of ω, ψ and ɸ of all glycosidic bonds were measured. For the systems simulated in the GB HCT model, ψ and ɸ of all glycosidc linkages of all LFOs exhibited single major peaks around 173° and -63°, respectively (Fig. 5). However, ω was more flexible than ψ and ɸ as it exhibited one major peak and two minor peaks (Fig. 5). The results from the systems simulated in the GB OBC1 model were similar (Additional file 1: Figure S8); ω exhibited more peaks and was more flexible than ψ and ɸ. These results suggest that the flexibility of ω may be responsible for the conformational diversity of LFOs since this dihedral angle has more possibilities in rotating and changing the conformations of LFOs.