Rheology of Dispersions of High-Aspect-Ratio Nanofibers Assembled from Elastin-Like Double-Hydrophobic Polypeptides

Elastin-like polypeptides (ELPs) are promising candidates for fabricating tissue-engineering scaffolds that mimic the extracellular environment of elastic tissues. We have developed a “double-hydrophobic” block ELP, GPG, inspired by non-uniform distribution of two different hydrophobic domains in natural elastin. GPG has a block sequence of (VGGVG)5-(VPGXG)25-(VGGVG)5 that self-assembles to form nanofibers in water. Functional derivatives of GPG with appended amino acid motifs can also form nanofibers, a display of the block sequence’s robust self-assembling properties. However, how the block length affects fiber formation has never been clarified. This study focuses on the synthesis and characterization of a novel ELP, GPPG, in which the central sequence (VPGVG)25 is repeated twice by a short linker sequence. The self-assembly behavior and the resultant nanostructures of GPG and GPPG were when compared through circular dichroism spectroscopy, atomic force microscopy, and transmission electron microscopy. Dynamic rheology measurements revealed that the nanofiber dispersions of both GPG and GPPG at an extremely low concentration (0.034 wt%) exhibited solid-like behavior with storage modulus G′ > loss modulus G” over wide range of angular frequencies, which was most probably due to the high aspect ratio of the nanofibers that leads to the flocculation of nanofibers in the dispersion.


Introduction
Self-assembling peptides are promising candidates for the fabrication of tissue-engineering scaffolds, because their nanostructures resemble those of extracellular matrix (ECM) proteins, and their physicochemical and biological properties can be tailored by designing its amino acid sequences [1][2][3][4]. Elastin-like polypeptides (ELPs), which contain repetitive amino acid sequences that are found in elastin, an ECM protein abundant in elastic tissues, are among the self-assembling polypeptides that have been Differences in the self-assembled nanostructures of GPG and GPPG were examined through the analysis of the nanofiber formation while using circular dichroism (CD) spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM). The rheological characteristics of the fiber dispersions of these double-hydrophobic polypeptides were investigated for the first time, which revealed their solid-like behavior, even at extremely low concentrations (0.034 wt%). examined through the analysis of the nanofiber formation while using circular dichroism (CD) spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM). The rheological characteristics of the fiber dispersions of these double-hydrophobic polypeptides were investigated for the first time, which revealed their solid-like behavior, even at extremely low concentrations (0.034 wt%).

Synthesis of GPPG
The theoretical molecular weight of GPPG is 27,701 Da. A clear band that corresponded to GPPG was observed between 25 and 35 kDa during sodium dodecylsulfate polyacrylamide gel electrophoresis (SDS-PAGE, Figure 2a). There was another band at 25 kDa that was just below the band corresponding to GPPG. This was presumably attributed to SlyD (molecular weight: 20.8 kDa), a histidine-rich protein derived from E.coli [35]. Matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS) showed the presence of a peak at 27,732 Da ( Figure 2b). However, the peak originating from SlyD was not detected in the MS spectrum. These results indicated that GPPG was successfully expressed and purified as the main product. The successful synthesis of GPG was reported in our previous study [28].  Figure 3a,b show the CD spectra of GPG and GPPG (20 μM), respectively. It should be noted that the spectra of GPPG between 190-197 nm are inaccurate, because of the low signal-to-noise ratio due to relatively high weight fraction of GPPG (0.055 wt%). At 4 °C, an intense negative band at around 200 nm, with a negative shoulder at around 220 nm, was observed for both GPG and GPPG, which indicated that they adopted predominantly disordered structures that contained some β-turn structures. Soon after increasing the temperature to 37 °C, the intensity of a negative band at 200 nm decreased and the one at 220 nm increased, which showed the formation of more β-turn structures. The spectrum of GPG noticeably changed with time at 37 °C; the intensity of the negative band seen

Synthesis of GPPG
The theoretical molecular weight of GPPG is 27,701 Da. A clear band that corresponded to GPPG was observed between 25 and 35 kDa during sodium dodecylsulfate polyacrylamide gel electrophoresis (SDS-PAGE, Figure 2a). There was another band at 25 kDa that was just below the band corresponding to GPPG. This was presumably attributed to SlyD (molecular weight: 20.8 kDa), a histidine-rich protein derived from E.coli [35]. Matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS) showed the presence of a peak at 27,732 Da ( Figure 2b). However, the peak originating from SlyD was not detected in the MS spectrum. These results indicated that GPPG was successfully expressed and purified as the main product. The successful synthesis of GPG was reported in our previous study [28]. examined through the analysis of the nanofiber formation while using circular dichroism (CD) spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM). The rheological characteristics of the fiber dispersions of these double-hydrophobic polypeptides were investigated for the first time, which revealed their solid-like behavior, even at extremely low concentrations (0.034 wt%).

Synthesis of GPPG
The theoretical molecular weight of GPPG is 27,701 Da. A clear band that corresponded to GPPG was observed between 25 and 35 kDa during sodium dodecylsulfate polyacrylamide gel electrophoresis (SDS-PAGE, Figure 2a). There was another band at 25 kDa that was just below the band corresponding to GPPG. This was presumably attributed to SlyD (molecular weight: 20.8 kDa), a histidine-rich protein derived from E.coli [35]. Matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS) showed the presence of a peak at 27,732 Da ( Figure 2b). However, the peak originating from SlyD was not detected in the MS spectrum. These results indicated that GPPG was successfully expressed and purified as the main product. The successful synthesis of GPG was reported in our previous study [28].  Figure 3a,b show the CD spectra of GPG and GPPG (20 μM), respectively. It should be noted that the spectra of GPPG between 190-197 nm are inaccurate, because of the low signal-to-noise ratio due to relatively high weight fraction of GPPG (0.055 wt%). At 4 °C, an intense negative band at around 200 nm, with a negative shoulder at around 220 nm, was observed for both GPG and GPPG, which indicated that they adopted predominantly disordered structures that contained some β-turn structures. Soon after increasing the temperature to 37 °C, the intensity of a negative band at 200 nm decreased and the one at 220 nm increased, which showed the formation of more β-turn structures. The spectrum of GPG noticeably changed with time at 37 °C; the intensity of the negative band seen  Figure 3a,b show the CD spectra of GPG and GPPG (20 µM), respectively. It should be noted that the spectra of GPPG between 190-197 nm are inaccurate, because of the low signal-to-noise ratio due to relatively high weight fraction of GPPG (0.055 wt%). At 4 • C, an intense negative band at around 200 nm, with a negative shoulder at around 220 nm, was observed for both GPG and GPPG, which indicated that they adopted predominantly disordered structures that contained some β-turn structures. Soon after increasing the temperature to 37 • C, the intensity of a negative band at 200 nm decreased and the one at 220 nm increased, which showed the formation of more β-turn structures.

Self-Assembly of GPG and GPPG
The spectrum of GPG noticeably changed with time at 37 • C; the intensity of the negative band seen at around 220 nm continuously increased over the course of seven days with slight blue shifts [28,29]. In addition, the band observed at around 200 nm became positive after one day, and its intensity increased with time. A similar change in spectra was observed for GPPG, whereas the intensities of the negative bands seen at around 220 nm between one and seven days were smaller than those of GPG. The CD difference spectra (that compared samples at 15 min. and seven days at 37 • C) highlighted the nature of this transition; positive peaks observed at around 200 nm and negative peaks at 218 nm signaled the development of β-sheet structures with time [29]. The intensity of the molar residue ellipticity of GPG was higher than that of GPPG, which indicated that the β-sheet content per residue was higher for GPG. This result is compatible to the fact that the content of the β-sheet-forming VGGVG repeating units per molecule was higher in GPG than in GPPG. Int at around 220 nm continuously increased over the course of seven days with slight blue shifts [28,29]. In addition, the band observed at around 200 nm became positive after one day, and its intensity increased with time. A similar change in spectra was observed for GPPG, whereas the intensities of the negative bands seen at around 220 nm between one and seven days were smaller than those of GPG. The CD difference spectra (that compared samples at 15 min. and seven days at 37 °C) highlighted the nature of this transition; positive peaks observed at around 200 nm and negative peaks at 218 nm signaled the development of β-sheet structures with time [29]. The intensity of the molar residue ellipticity of GPG was higher than that of GPPG, which indicated that the β-sheet content per residue was higher for GPG. This result is compatible to the fact that the content of the β-sheet-forming VGGVG repeating units per molecule was higher in GPG than in GPPG. The data for GPG spectra at 37 °C in (a) and for the difference spectrum of GPG in (c) are adopted from our previous report with permission from ref. [29]. Copyright 2017, Wiley.
AFM was used to monitor the time-dependent morphological change in GPPG (20 μM, 0.055 wt%) (Figure 4a-c). GPPG followed a similar self-assembly pathway to that observed for GPG in our previous study [28]. Spherical particles of various sizes were observed 15 min. after the temperature was increased to 37 °C ( Figure 4a). The size of particles became more homogeneous after three days and then smaller after seven days, and they were organized as beaded nanofibers ( Figure 4c) with an average fiber diameter of 56 ± 16 nm, which was larger than that of GPG (42 ± 8 nm at 20 μM, 0.034 wt%) [29]. The nanofibers formed from 12 μM (0.034 wt%) GPPG were also observed ( Figure 4d) for comparison of the fiber morphology of GPG and GPPG at the same mass fraction. Beaded nanofibers with a diameter of 55 ± 11 nm were observed, which indicated that the concentration of GPPG (0.034 or 0.055 wt%) did not affect the morphology of the nanofibers. It should be noted that the diameter of nanofibers might be overestimated; the heights of nanofibers were measured to be around 10 nm in the AFM images. This is because of the relatively low lateral resolution due to the tip-sample convolution effect and/or deformation of nanofibers on the substrate.  (c) CD difference spectra of GPG and GPPG obtained by subtracting the spectra acquired at 37 • C, 15 min. from those acquired at 37 • C, 7 days in (a) and (b). The data for GPG spectra at 37 • C in (a) and for the difference spectrum of GPG in (c) are adopted from our previous report with permission from ref. [29]. Copyright 2017, Wiley.
AFM was used to monitor the time-dependent morphological change in GPPG (20 µM, 0.055 wt%) (Figure 4a-c). GPPG followed a similar self-assembly pathway to that observed for GPG in our previous study [28]. Spherical particles of various sizes were observed 15 min. after the temperature was increased to 37 • C ( Figure 4a). The size of particles became more homogeneous after three days and then smaller after seven days, and they were organized as beaded nanofibers ( Figure 4c) with an average fiber diameter of 56 ± 16 nm, which was larger than that of GPG (42 ± 8 nm at 20 µM, 0.034 wt%) [29]. The nanofibers formed from 12 µM (0.034 wt%) GPPG were also observed ( Figure 4d) for comparison of the fiber morphology of GPG and GPPG at the same mass fraction. Beaded nanofibers with a diameter of 55 ± 11 nm were observed, which indicated that the concentration of GPPG (0.034 or 0.055 wt%) did not affect the morphology of the nanofibers. It should be noted that the diameter of nanofibers might be overestimated; the heights of nanofibers were measured to be around 10 nm in the AFM images. This is because of the relatively low lateral resolution due to the tip-sample convolution effect and/or deformation of nanofibers on the substrate.
comparison of the fiber morphology of GPG and GPPG at the same mass fraction. Beaded nanofibers with a diameter of 55 ± 11 nm were observed, which indicated that the concentration of GPPG (0.034 or 0.055 wt%) did not affect the morphology of the nanofibers. It should be noted that the diameter of nanofibers might be overestimated; the heights of nanofibers were measured to be around 10 nm in the AFM images. This is because of the relatively low lateral resolution due to the tip-sample convolution effect and/or deformation of nanofibers on the substrate.  The nanofibers of GPG and GPPG (0.034 wt%) were observed with TEM to obtain higher-resolution images ( Figure 5). GPG formed branched nanofibers ca. 5-30 nm in diameter (Figure 5a). Some nanofibers laterally assembled to form bundles. The beaded nanostructure of the nanofibers was not observed probably because of progressive dehydration under vacuum conditions, in contrast to the results from the AFM observation in our previous study [29]. On the other hand, more homogeneous, less branched nanofibers ca. < 10 nm in diameter were observed from GPPG ( Figure 5b). It was difficult to estimate the length of both nanofibers, because they were long enough to protrude from the field of view in the TEM images. A lower magnification image of GPPG showed that the fiber length was at least 5 µm ( Figure S1). The nanofibers of GPG and GPPG (0.034 wt%) were observed with TEM to obtain higherresolution images ( Figure 5). GPG formed branched nanofibers ca. 5-30 nm in diameter (Figure 5a). Some nanofibers laterally assembled to form bundles. The beaded nanostructure of the nanofibers was not observed probably because of progressive dehydration under vacuum conditions, in contrast to the results from the AFM observation in our previous study [29]. On the other hand, more homogeneous, less branched nanofibers ca. < 10 nm in diameter were observed from GPPG ( Figure  5b). It was difficult to estimate the length of both nanofibers, because they were long enough to protrude from the field of view in the TEM images. A lower magnification image of GPPG showed that the fiber length was at least 5 μm ( Figure S1).

Rheology of Nanofiber Dispersions
The nanofibers of GPG and GPPG were obtained as optically clear dispersions with no precipitates (Figure 6a,b), which prompted us to evaluate the rheology of these fiber dispersions. Figure 6c-f show the dynamic rheological characteristics of the nanofiber dispersions at 0.034 wt%. The sample was collected twice from a nanofiber dispersion and, in both cases, readings were conducted independently to confirm reproducibility. The rheological behavior observed for GPG and GPPG fiber dispersions was similar. Both moduli were shown to decrease at above 2% strain, even though strain sweep measurements revealed that the storage modulus (G′) and the loss modulus (G") were relatively constant (between 0.1% and 2% strains) (Figure 6c,d). This was indicative of a transition from a linear to non-linear viscoelastic regime. Frequency sweep measurements showed that G′ was greater than G" over a wide range of frequencies, highlighting the solid-like behavior of these dispersions (Figure 6e,f). Fluctuations between the samples were observed for GPG, and there was an anomalous drop for G′ above 30 rad s −1 only for the first fraction.

Rheology of Nanofiber Dispersions
The nanofibers of GPG and GPPG were obtained as optically clear dispersions with no precipitates (Figure 6a,b), which prompted us to evaluate the rheology of these fiber dispersions. Figure 6c-f show the dynamic rheological characteristics of the nanofiber dispersions at 0.034 wt%. The sample was collected twice from a nanofiber dispersion and, in both cases, readings were conducted independently to confirm reproducibility. The rheological behavior observed for GPG and GPPG fiber dispersions was similar. Both moduli were shown to decrease at above 2% strain, even though strain sweep measurements revealed that the storage modulus (G ) and the loss modulus (G") were relatively constant (between 0.1% and 2% strains) (Figure 6c,d). This was indicative of a transition from a linear to non-linear viscoelastic regime. Frequency sweep measurements showed that G was greater than G" over a wide range of frequencies, highlighting the solid-like behavior of these dispersions (Figure 6e,f).
Fluctuations between the samples were observed for GPG, and there was an anomalous drop for G above 30 rad s −1 only for the first fraction.

Discussion
In this study, a new double-hydrophobic ELP derivative, GPPG, was successfully constructed. GPPG had a proline-rich sequence (VPGXG)25, which was double the length of GPG and with a short linker sequence as the middle block. GPPG dissolved in 4 °C water to form the disordered structures that were seen in the CD spectrum (Figure 3b). In general, the increase in molecular weight of (VPGXG)n resulted in a decrease in Tt [13,14]. Thus, the Tt of GPPG (20 μM) was estimated to be between 4 and 16 °C, which was the reported Tt of 20 μM GPG.
GPPG underwent a self-assembling pathway that was similar to that of GPG via the formation of the nanoparticles above the Tt followed by maturation into nanofibers through the subsequent formation of β-sheet structures. The structural differences that were found in the resultant GPG and GPPG nanofibers were related to the content of the β-sheet structures and the diameter of the nanofibers. The β-sheet content per residue was GPG > GPPG (Figure 3c), which was expected from the sequences in which the content of β-sheet forming VGGVG repeating units per molecule was

Discussion
In this study, a new double-hydrophobic ELP derivative, GPPG, was successfully constructed. GPPG had a proline-rich sequence (VPGXG) 25 , which was double the length of GPG and with a short linker sequence as the middle block. GPPG dissolved in 4 • C water to form the disordered structures that were seen in the CD spectrum (Figure 3b). In general, the increase in molecular weight of (VPGXG) n resulted in a decrease in T t [13,14]. Thus, the T t of GPPG (20 µM) was estimated to be between 4 and 16 • C, which was the reported T t of 20 µM GPG.
GPPG underwent a self-assembling pathway that was similar to that of GPG via the formation of the nanoparticles above the T t followed by maturation into nanofibers through the subsequent formation of β-sheet structures. The structural differences that were found in the resultant GPG and GPPG nanofibers were related to the content of the β-sheet structures and the diameter of the nanofibers. The β-sheet content per residue was GPG > GPPG (Figure 3c), which was expected from the sequences in which the content of β-sheet forming VGGVG repeating units per molecule was higher for GPG. The average diameters of the nanofibers, as determined via AFM, were 55 ± 11 nm (GPPG) > 42 ± 8 nm (GPG) at 0.034 wt%. A structural model for the nanofibers of GPG was proposed in our previous work (Figure 7a), in which the GPG molecules were shown to align with each other to form nanoparticles that were connected by interdigitated β-sheet structures [28]. We have proposed this model based on (1) the beaded morphology of nanofibers, (2) no spectrum change of Congo red and thioflavin T (dyes sensitive to cross-β structures) in the presence of the nanofibers [32], and (3) the presence of oligohistidine tag (His tag); the hydrophilic His tags should induce the adjacent (VGGVG) 5 segments to locate near the surface of the particle [28]. Given that the proline-rich (VPGXG) 25 segment formed ideal β-spiral structures, as previously proposed by Urry et al. [13], the length of the segment was estimated to be ca. 8.3 nm due to the β-spiral structure, which possessed a spiral pitch of 1 nm, contained three VPGXG pentapeptide units per turn. However, recent molecular dynamics simulation showed that the β-spiral model was too ideal and that an ELP, in this case (VPGXG) n , contained predominantly random coil structures in which each repeat was independently capable of transiently sampling β-turn and polyproline type II (PPII) structures [36,37]. Taking these into account, it is understandable that the length of (VPGXG) 25 segment, in fact, should be longer than the 8.3 nm expected from the β-spiral model. Figure 7b shows a plausible structure for GPPG where the same model as GPG was applied. The particle size increased because of the doubling in size of the central segments when compared to that of GPG. This model could be used to account for the larger fiber diameter (13 nm larger than that of GPG) of GPPG while assuming that the fiber diameter was roughly same as the particle diameter. Another difference that was found in the TEM observations was the branching and lateral associations between the GPG nanofibers, whereas no branching or association was observed for the GPPG nanofibers ( Figure 5). The association between GPG nanofibers could be a result of smaller fiber diameter. The intrinsically hydrophobic nature of these nanofibers meant that they showed a predilection for assembly in order to reduce the interfacial area between the nanofiber and the water molecules. The formation of branchless nanofibers from GPPG was unexpected, since there is greater freedom in the molecular configuration of GPPG due to the presence of a flexible linker sequence KLGSG between the VPGXG repeating units, which could rather cause branching of nanofibers. Nevertheless, branchless nanofibers were formed from GPPG, because there might be the π-π stacking interactions between the aromatic rings from F guest residues in VPGXG repeating unit, which facilitate the alignment of (VPGXG) 25 segments. In addition, molecular exchange kinetics between nanofibers should be much smaller for GPPG due to its longer chain length [38], which reduces a frequency of dissociation of GPPG molecules from the nanofibers that triggers fiber branching. higher for GPG. The average diameters of the nanofibers, as determined via AFM, were 55 ± 11 nm (GPPG) > 42 ± 8 nm (GPG) at 0.034 wt%. A structural model for the nanofibers of GPG was proposed in our previous work (Figure 7a), in which the GPG molecules were shown to align with each other to form nanoparticles that were connected by interdigitated β-sheet structures [28]. We have proposed this model based on (1) the beaded morphology of nanofibers, (2) no spectrum change of Congo red and thioflavin T (dyes sensitive to cross-β structures) in the presence of the nanofibers [32], and (3) the presence of oligohistidine tag (His tag); the hydrophilic His tags should induce the adjacent (VGGVG)5 segments to locate near the surface of the particle [28]. Given that the prolinerich (VPGXG)25 segment formed ideal β-spiral structures, as previously proposed by Urry et al. [13], the length of the segment was estimated to be ca. 8.3 nm due to the β-spiral structure, which possessed a spiral pitch of 1 nm, contained three VPGXG pentapeptide units per turn. However, recent molecular dynamics simulation showed that the β-spiral model was too ideal and that an ELP, in this case (VPGXG)n, contained predominantly random coil structures in which each repeat was independently capable of transiently sampling β-turn and polyproline type II (PPII) structures [36,37]. Taking these into account, it is understandable that the length of (VPGXG)25 segment, in fact, should be longer than the 8.3 nm expected from the β-spiral model. Figure 7b shows a plausible structure for GPPG where the same model as GPG was applied. The particle size increased because of the doubling in size of the central segments when compared to that of GPG. This model could be used to account for the larger fiber diameter (13 nm larger than that of GPG) of GPPG while assuming that the fiber diameter was roughly same as the particle diameter. Another difference that was found in the TEM observations was the branching and lateral associations between the GPG nanofibers, whereas no branching or association was observed for the GPPG nanofibers ( Figure 5). The association between GPG nanofibers could be a result of smaller fiber diameter. The intrinsically hydrophobic nature of these nanofibers meant that they showed a predilection for assembly in order to reduce the interfacial area between the nanofiber and the water molecules. The formation of branchless nanofibers from GPPG was unexpected, since there is greater freedom in the molecular configuration of GPPG due to the presence of a flexible linker sequence KLGSG between the VPGXG repeating units, which could rather cause branching of nanofibers. Nevertheless, branchless nanofibers were formed from GPPG, because there might be the π-π stacking interactions between the aromatic rings from F guest residues in VPGXG repeating unit, which facilitate the alignment of (VPGXG)25 segments. In addition, molecular exchange kinetics between nanofibers should be much smaller for GPPG due to its longer chain length [38], which reduces a frequency of dissociation of GPPG molecules from the nanofibers that triggers fiber branching. Despite the aforementioned differences in nanofiber structures, GPG and GPPG behaved similarly in rheological experiments except for the poor reproducibility in frequency sweep measurements for GPG ( Figure 6). The steep drop in G' that was seen at higher frequencies, which was most probably due to a change in the nanostructure of the dispersion, was detected in other nanofiber dispersion systems [39]. GPG nanofibers may be locally aggregated in a dispersion, as suggested by the TEM observation (Figure 5a), which causes a slight sample-to-sample variation in the rheological readings. Despite the aforementioned differences in nanofiber structures, GPG and GPPG behaved similarly in rheological experiments except for the poor reproducibility in frequency sweep measurements for GPG ( Figure 6). The steep drop in G' that was seen at higher frequencies, which was most probably due to a change in the nanostructure of the dispersion, was detected in other nanofiber dispersion systems [39]. GPG nanofibers may be locally aggregated in a dispersion, as suggested by the TEM observation (Figure 5a), which causes a slight sample-to-sample variation in the rheological readings.
The self-assembly system of the current double-hydrophobic polypeptides has some similarities with that of EP20-24-24 [24] and the ELP with silk-like sequences [26,27], in terms of the initial hydrophobic association followed by maturation into the nanofibers through β-sheet formation. Nevertheless, the solid-like behavior of the dispersion at this extremely low concentration (0.034 wt%) has never been reported for any ELP-based polymer. The viscoelastic properties that were presented in this paper were also uncommon among other fiber dispersion systems to the best of our knowledge. For example, Hsiao, Söderberg, and coworkers reported on the mechanistic behavior of charged cellulose nanofibers (CNF) in aqueous systems [39]. The dispersion behaved solid-like (G' > G") at 0.1 wt% nanofiber concentration with G' of ca. 1 Pa, while it behaved liquid-like (G' < G") at 0.03 wt% with G' of ca. 0.02 Pa. On the other hand, our data show that dispersions of double-hydrophobic ELPs were solid-like at 0.034 wt% with G' of ca. 10 Pa.
The rheological properties of fiber dispersions have been described based on the concept of fiber flocculation [40]. Flocculation takes place above a certain concentration threshold, where the fibers initiate continuous contact in a network structure. Whereas, the number of contact points, the stiffness of the fibers, and the friction between fibers controls the mechanistic character of the dispersion dictated by fiber flocculation, the primary controlling mechanism is the number of contact points [39,41]. To characterize this, Kerekes and Schell defined a crowding factor, N, which represented the number of fibers within the rotational sphere of influence of a single fiber [41]. The values for N were calculated from the volume fraction of fibers, φ; fiber length, L; and, fiber diameter, D, while using the following equation: Continuous interfiber contact is expected when N > 60. Hsiao et al. found that the N value was closely correlated with the dynamic moduli of the dispersions of charged CNF [39,42]. The dispersion exhibited a fluid behavior (G" > G') when N < 16, a soft gel behavior (G" ≈ G') when 16 < N < 60, and a hard gel behavior (G' > G") when N > 60. For example, N was calculated to be < 16 for the liquid-like dispersion of charged CNF (0.03 wt%), the aspect ratio (L/D) of which was ca. 100 [39]. The lengths of nanofibers (L) of GPG and GPPG were calculated at N = 16 and 60, respectively, by using the relationships between N and the nanofiber aspect ratio ( Table 1). The L can be estimated to be > 22 µm and > 28 µm for GPG and GPPG, respectively, because N values are expected to be > 60 because G' > G" for GPG and GPPG dispersions at 0.034 wt%. In the present findings, the rheological characteristics are similar between GPG and GPPG, regardless of their structural differences in terms of β-sheet content and the degree of fiber branching, which should affect the stiffness of the fibers and the friction between fibers. Nevertheless, these structural differences between GPG and GPPG were not reflected in the rheological characteristics. This fact also supports the formation of sufficiently long nanofibers with high aspect ratio as the primary mechanism that governs the rheological behavior. In conclusion, this study showed the sequence-structure-property relationships of elastin-like, double-hydrophobic polypeptides, GPG and GPPG. GPG has a block sequence of (VGGVG) 5 -(VPGXG) 25 -(VGGVG) 5 , whereas the central sequence (VPGVG) 25 is repeated twice in GPPG. Polypeptides both self-assembled to form nanofibers in water at 37 • C. GPPG gave thicker nanofibers with smaller β-sheet content compared to GPG. The dispersions of both polypeptides showed similar dynamic viscoelastic properties and exhibited solid-like behavior at extremely low polypeptide concentration (0.034 wt%) with storage modulus G' > loss modulus G" over a wide range of angular frequencies. This is most probably due to the formation of sufficiently high-aspect-ratio nanofibers from these polypeptides that leads to the flocculation of nanofibers in the dispersion. The formation of self-supportive hydrogels are expected at higher polypeptide concentrations, although the present polypeptide dispersions could not support their macroscopic structures in tilted vials due to a G' value of ca. 10 Pa [43]. The findings revealed in this study will provide useful insights in the design of polypeptide-based scaffold and artificial ECMs in the future.

Plasmid Construction
The plasmid pET22b(+)-GPG encoding GPG polypeptide was previously constructed [28]. A gene fragment encoding for the proline-rich sequence [(VPGVG) 2 VPGFG(VPGVG) 2 ] 5 (P) was amplified via polymerase chain reaction (PCR) while using pET22b(+)-GPG as the template. PCR amplification modified the 3' end of the P gene by introducing a BamHI restriction site. The PCR product was isolated via BamHI digestion and inserted into pET22b(+)-GPG at the BamHI site to give pET22b(+)-GPPG. Restriction mapping and DNA sequencing analysis verified the gene sequence.

Polypeptide Expression and Purification
Plasmids pET22b(+)-GPG and pET22b(+)-GPPG were each transformed into the E.coli BLR (DE3) strain. The polypeptides were expressed, as previously reported [29], and they were purified using Ni-NTA affinity chromatography since both contained His tags at their C-termini. The purity of the polypeptides was confirmed via SDS-PAGE and MALDI-TOF-MS while using an AXIMA-CFR Plus spectrometer (Shimadzu, Kyoto, Japan). The polypeptides were stored as lyophilized powder at −20 • C prior to use.

Sample Preparation
The polypeptide powders were dissolved in cool water and then agitated at 4 • C overnight. Concentrations of the polypeptides were determined by measuring the absorbance at 280 nm while using a Nanodrop 2000 UV-visible spectrometer (Thermo Fisher Scientific, Wilmington, DE, USA). Adequate amounts of milliQ water were added to adjust their concentrations to 20 µM (0.034 wt% for GPG and 0.055 wt% for GPPG) or 12 µM (0.034 wt% for GPPG). The sample solutions were kept on ice to prevent any undesired aggregation prior to performing the experiments.

Characterization of Nanofiber Structures
The CD spectra were obtained with a J-820 spectrometer (Jasco, Tokyo, Japan). The readings were collected from 190 to 260 nm. The final spectra were acquired by subtracting the spectrum of the blank solvent. The data are expressed, as follows: ellipticity/[path length (cm) × concentration (mol/L) × number of residues × 10].
AFM was carried out while using an MFP-3D Origin TM AFM, Oxford Instruments plc, U.K., via the tapping mode in air at room temperature. Scans were performed with a Si cantilever (OMCL-AC240TS, Olympus, Japan) at a rate of 1.0 Hz. The samples were each cast on a freshly cleaved mica substrate and allowed to dry at 37 • C. Fiber diameters were quantified by measuring widths of nanofibers by randomly picking 100 fibers in the AFM images using ImageJ. TEM was carried out using JEOL JEM-2100plus at an accelerating voltage of 200 kV. The samples were applied to a carbon-coated grid (Cu 100 mesh), stained with phosphotungstic acid, and the excess solution was wiped away using blotting paper.

Rheological Measurements
The rheological measurements were carried out using an Anton Paar MCR302 rheometer with a 1 • cone-and-plate configuration (25 mm diameter). The experiments were performed at a constant temperature of 37 • C, which was controlled using an integrated Peltier system. A solvent trap cover was used to keep the sample hydrated. The sample was transferred to the stage while using a micropipette.