Gelation Kinetics and Mechanical Properties of Thiol-Tetrazole Methylsulfone Hydrogels Designed for Cell Encapsulation

Hydrogel precursors that crosslink within minutes are essential for the development of cell encapsulation matrices and their implementation in automated systems. Such timescales allow sufficient mixing of cells and hydrogel precursors under low shear forces and the achievement of homogeneous networks and cell distributions in the 3D cell culture. The previous work showed that the thiol-tetrazole methylsulfone (TzMS) reaction crosslinks star-poly(ethylene glycol) (PEG) hydrogels within minutes at around physiological pH and can be accelerated or slowed down with small pH changes. The resulting hydrogels are cytocompatible and stable in cell culture conditions. Here, the gelation kinetics and mechanical properties of PEG-based hydrogels formed by thiol-TzMS crosslinking as a function of buffer, crosslinker structure and degree of TzMS functionality are reported. Crosslinkers of different architecture, length and chemical nature (PEG versus peptide) are tested, and degree of TzMS functionality is modified by inclusion of RGD cell-adhesive ligand, all at concentration ranges typically used in cell culture. These studies corroborate that thiol/PEG-4TzMS hydrogels show gelation times and stiffnesses that are suitable for 3D cell encapsulation and tunable through changes in hydrogel composition. The results of this study guide formulation of encapsulating hydrogels for manual and automated 3D cell culture.     

New neutral and ionic poly(ethylene oxide) networks by radical polymerization

New opportunities resulting from a turn to radical polymerization in the synthesis of poly(ethylene oxide) (PEO) networks are discussed and exemplified. Several series of such networks have been prepared by radical homo‐ and copolymerization in aqueous media of “macromonomers”, i.e. partly methacrylated poly(ethylene glycol) (PEG) of varied molecular weight (MW ≅ 2000‐12000) and functionality (f_n ≅ 1.25‐1.8). This family of gels as a whole has the volume swelling degree Q in the range of 10 to 200 ml/ml. The hydrogels are characterized by means of Q, elastic modulus, swelling pressure, and with the use of some probes. The swelling behaviour of neutral hydrogels of this kind is briefly resumed. The multifunctional junctions formed in the propagation reaction of methacrylate end groups determine their main peculiarity. Anomalous elastic behaviour of the swollen networks prepared at high concentration of polymer has been observed and attributed to the network chains stretching of the same nature as in polymer stars or brushes. The junctions' functionality (F ≈ 20‐300) is evaluated from these data as well as from MW of the soluble models of network junctions. The PEO networks with charged units in junctions have been obtained by copolymerization of macromonomers with some ionic (meth)acrylic monomers. These gels display all the polyelectrolyte features, e.g. enhanced Q values in water (up to 50‐70) and, contrary to neutral PEO gels, the strong dependence on salt content. However, the osmotic contribution of mobile ions into swelling is shown to be low due to localization of charges in the junctions. The hydrogels that combine PEO and polymethacrylic acid chains capable of interpolymer complexation have been prepared and studied. They show much higher swelling in pure water (Q up to 200), strong deswelling by NaCl, and very sharp drop in swelling (ca. two order in Q) at pH ≈ 4.5‐5.5 due to complexation.     

Effect of the functionality of junctions on the elasticity of polymacromonomer networks: Computer simulation

The elastic properties of polymer networks formed via the radical polymerization of macromonomers with two polymerizable end groups are studied via computer simulation. It is shown that variation in the average functionality of network junctions, f _avg, in a wide range (∼5–55) leads to a significant change in the shear modulus of the network. According to experiments with real networks (gels of poly(ethylene oxide) macromonomers), the shear modulus increases as f _avg increases. This effect is not due only to a decrease in the fluctuations of positions of network junctions. The main cause of the increase in the modulus is that the modulus component due to interaction between polymer chains (entanglements) increases as the functionality of junctions in the investigated networks increases. The conclusion is made that these networks gain entanglements during the formation of network junctions with high functionality rather than inherit them from the solution of macromonomer chains.     

Preparation of interpenetrating polymer network composed of poly(ethylene glycol) and poly(acrylamide) hydrogels as a support of enzyme immobilization

Poly(ethylene glycol)(PEG)‐based interpenetrating polymeric network (IPN) hydrogels were prepared for the application of enzyme immobilization. Poly(acrylamide)(PAAm) was chosen as the other network of IPN hydrogel and different concentration of PAAm networks were incorporated inside the PEG hydrogel to improve the mechanical strength and provide functional groups that covalently bind the enzyme. Formation of IPN hydrogels was confirmed by observing the weight per cent gain of hydrogel after incorporation of PAAm network and by attenuated total reflectance/Fourier transform infrared (ATR/FTIR) analysis. Synthesis of IPN hydrogels with higher PAAm content produced more crosslinked hydrogels with lower water content (WC), smaller M_c and mesh size, which resulted in enhanced mechanical properties compared to the PEG hydrogel. The IPN hydrogels exhibited tensile strength between 0.2 and 1.2 MPa while retaining high levels of hydration (70–81% water). For enzyme immobilization, glucose oxidase (GOX) was immobilized to PEG and IPN hydrogel beads. Enzyme activity studies revealed that although all the hydrogels initially had similar enzymatic activity, enzyme‐immobilizing PEG hydrogels lost most of the enzymatic activity within 2 days due to enzyme leaching while IPN hydrogels maintained a maximum 80% of the initial enzymatic activity over a week due to the covalent linkage between the enzyme and amine groups of PAAm. Copyright © 2008 John Wiley & Sons, Ltd.     

大孔PAMPS/PVA半互穿网络型水凝胶的制备及其性能研究

以PEG6000为成孔剂, 合成了大孔聚(2-丙烯酰胺-2-甲基丙磺酸)/聚乙烯醇半互穿网络型(s-IPN)水凝胶. 红外分析表明, PVA与PAMPS之间形成了较强的氢键, 使得PVA分子上的C—O伸缩振动吸收峰移向了低波数处. X射线衍射分析发现, 当PVA用量较高时, 由于部分的PVA结晶, 使得凝胶的半互穿网络结构不均匀. 电镜分析结果表明, 没有使用成孔剂的凝胶表面成褶皱形, 不存在任何孔洞结构; 而以PEG6000为成孔剂的凝胶表面存在相互贯穿的大孔结构. 研究了该水凝胶的溶胀性能, 结果表明, 该水凝胶的平衡溶胀度在116至320之间; 而成孔剂PEG6000的加入能较大幅度提高凝胶的溶胀速率, 凝胶在240 min之内就能达到溶胀平衡. 对凝胶抗压缩性能的研究表明, 当PVA用量为9.1% (w)时, 凝胶的抗压缩强度最大, 可达12.0 MPa; 而成孔剂的加入会在一定程度削弱凝胶的抗压缩强度. 该凝胶具有较好的电场敏感性, 研究发现, 将吸去离子水达到溶胀平衡的凝胶放入施加有电场的0.2 mol•L－1 NaCl溶液中时, 凝胶迅速偏向阳极. 而PVA和成孔剂PGE6000的用量均对凝胶的偏转速度以及最大偏转角存在较大的影响.     

A non-Gaussian model for the chemo-mechanical coupling behavior of largely deformed hydrogels

A non-Gaussian model is developed to precisely describe the chemo-mechanical coupled large deformation of responsive hydrogels. In this model, the free-energy density is composed of two parts, including the elastic energy due to stretching of cross-linked polymer networks described by Gent hyperelastic model, and the mixture energy of polymer network and described by Flory–Huggins theory. The effects of junction functionality and chain entanglements are investigated by analyzing free swelling of a cubic hydrogel and constrained swelling of a blanket layer of the gel. The present model is found to exhibit obvious hardening characteristic during large deformation of the hydrogel, and the considerations of functionality of junctions and chain entanglements are essential in the coupled chemo-mechanical deformation analysis of hydrogels.     

Injectable supramolecular hybrid hydrogels formed by MWNT‐grafted‐poly(ethylene glycol) and α‐cyclodextrin

Poly(ethylene glycol)‐grafted‐multiwalled carbon nanotube (MWNT‐g‐PEG) was synthesized by a coupling reaction and formed inclusion complexes (ICs) after selective threading of the PEG segment of the MWNT‐g‐PEG through the cavities of α‐cyclodextrins (α‐CDs) units. The polypseudorotaxane structures of the as‐obtained hydrogels were confirmed by ¹H NMR, X‐ray diffraction and DSC analyses. The complexation of the PEG segments with α‐CDs and the hydrophobic interaction between the MWNT resulted in the formation of supramolecular hybrid hydrogels with a strong network. Thermal analysis showed that the thermal stability of the hydrogel was substantially improved by up to 100 °C higher than that of native hydrogel. The resultant hybrid hydrogels were found to be thixotropic and reversible, and could be applied as a promising injectable drug delivery system. The mechanical strength of the hybrid hydrogels was greatly improved in comparison with that of the corresponding native hydrogels. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3145–3151, 2010     

Hydrogels of chemically cross-linked and organ-metallic complexed interpenetrating PEG networks

The aim of the present work was to prepare a well-defined hydrogel of chemically cross-linked and organ-metallic complexed interpenetrating PEG networks. The hydrogel was synthesized via the reaction of copper(I)- catalyzed 1,3-dipolar azide-alkyne cycloaddition(CuA AC) with poly(ethylene glycol)-dopamine(PEG-DA)("Click Chemistry") followed by complexation with Fe~(3+) ions to crosslink the polymeric network. The chemical composition and morphology of the resulting hydrogels were characterized by Fourier transform infrared spectroscopy(FTIR), ~1H-NMR and scanning electron microscopy(SEM). Swelling ratio, mechanical strength, conductivity, and degradation behaviors of the hydrogels were also studied. The effect of the polymer chain length on properties of hydrogels was explored. The compressive strength of hydrogels could reach as high as 13.1 MPa with a conductivity of 2.2 × 10~(-5) S·cm~(-1). The hydrogels also exhibited excellent thermal stability even at a temperature of 300 °C, whereas degradation of the hydrogel after 7 weeks was observed under a physiological condition. In addition, the hydrogel exhibited a good biocompatibility based on its in vivo performance through an in vivo subcutaneous implantation model. No inflammation and no obvious abnormality of the surrounding tissue were observed when the hydrogel was subcutaneously implanted for 2 weeks. This work is a step towards creating a new pathway to synthesize hydrogels of interpenetrating networks which could be of important applications in the future research.     

New aspects in chemistry and characterization of poly(ethylene oxide) hydrogels

To extend the variability of poly(ethylene oxide) (PEO) hydrogels in their swelling behaviour, ability to bind various subjects, and possible applications, some new synthetic approaches have been elaborated recently: (i) PEO networks with ionic and reactive groups were prepared by the reaction of P-OH groups of poly(oligoethylene glycol phosphate)s with diepoxide. The swelling degree of these hydrogels is strongly affected by salts, what is typical of polyelectrolyte networks. The structure parameters of the network evaluated from the swelling data are discussed. (ii) A series of hydrogels with controlled structure was obtained by radical polymerization of methacrylate PEO macromonomers of various molecular weights and average functionality (0.99–1.85) in aqueous media. The networks prepared are characterized by means of elastic modulus and swelling pressure measurements as well as with the help of microparticles of liquid-crystalline dispersion of DNA as probes highly sensitive to the network structure and state.     

Investigation of swelling and network parameters of poly(ethylene glycol)-crosslinked poly(methyl vinyl ether-co-maleic acid) hydrogels

The influence of poly(ethylene glycol) (PEG) plasticiser content and molecular weight on the physicochemical properties of films cast from aqueous blends of poly(methyl vinyl ether-co-maleic acid) was investigated using thermal analysis, swelling studies, scanning electron microscopy (SEM) and attenuated total reflectance (ATR)-Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy revealed a shift of the CO peak from 1708 to 1731 cm⁻¹, indicating that an esterification reaction had occurred upon heating, thus producing crosslinked films. Higher molecular weight PEGs (10,000 and 1000 Da, respectively), having greater chain length, producing hydrogel networks with lower crosslink densities and higher average molecular weight between two consecutive crosslinks. Accordingly, such materials exhibited higher swelling rates. Hydrogels crosslinked with a low molecular weight PEG (PEG 200) showed rigid networks with high crosslink densities and, therefore, lower swelling rates. Polymer:plasticizer ratio alteration did not yield any discernable patterns, regardless of the method of analysis. The polymer-water interaction parameter (χ) increased with increases in the crosslink density. SEM studies showed that porosity of the crosslinked films increased with increasing PEG MW, confirming what had been observed with swelling studies and thermal analysis, that the crosslink density must be decreased as the M_w of the crosslinker is increased. Hydrogels containing PMVE/MA/PEG 10,000 could be used for rapid delivery of drug, due to their low crosslink density. Moderately crosslinked PMVE/MA/PEG 1000 hydrogels or highly crosslinked PMVE/MA/PEG 200 systems could then be used in controlling the drug delivery rates. We are currently evaluating these systems, both alone and in combination, for use in sustained release drug delivery devices.     

One‐pot fabrication of robust interpenetrating hydrogels via orthogonal click reactions

Interpenetrating polymer network (IPN) hydrogels have been fabricated through a facile one‐pot approach from tetra/bifunctional telechelic macromonomers with epoxy, amine, azide, and alkyne groups by orthogonal double click reactions: epoxy‐amine reaction and copper‐catalyzed azide‐alkyne cycloaddition. Both the crosslinked networks are simultaneously constructed in water from the biocompatible poly (ethylene glycol)‐based macromonomers. The crosslinking density of each network was finely tuned by the macromonomer structure, permitting control of network molecular weights between crosslinks of the final gels. Compared to corresponding single network gels, the IPN gels containing both tightly and loosely crosslinked networks exhibited superior mechanical properties with shear moduli above 15 kPa and fracture stresses over 40 MPa. The synthetic versatility of this one‐pot approach will further establish design principles for the next generation of robust hydrogel materials. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1459–1467     

A thermoresponsive hydrogel based on telechelic PEG end-capped with hydrophobic dipeptides

The self-assembly in aqueous solution of PEG (1500 Da) telechelically end-capped with hydrophobic dipeptides has been investigated using spectroscopic, microscopic, scattering, and rheological methods. A self-assembled β-sheet fibril-based hydrogel has been identified (containing dityrosine end groups), which exhibits a gel-sol transition near body temperature. This thermo-responsive PEG-based biofunctional hydrogel is expected to have diverse potential uses in delivery or diagnostics for biomedical applications.     

Synthesis of well-defined hydrogel networks using click chemistry

New PEG-based hydrogel materials have been synthesized by Click chemistry and shown to result in well-defined networks having significantly improved mechanical properties; the selectivity of the azide/acetylene coupling reaction also allows for the incorporation of various additives and functional groups leading to chemical tailoring of the hydrogels.     

Fabrication of poly(ethylene glycol)‐based hydrogels entrapping enzyme‐immobilized silica nanoparticles

In this study, we immobilized enzymes by combining covalent surface immobilization and hydrogel entrapment. A model enzyme, glucose oxidase (GOX), was first covalently immobilized on the surface of silica nanoparticles (SNPs) via 3‐aminopropyltriethoxysilane (APTES), and the resultant SNP‐immobilized enzyme was physically entrapped within photopolymerized hydrogels prepared from two different molecular weights (MWs) (575 and 8000 Da) of poly(ethylene glycol)(PEG). The hydrogel entrapment resulted in a decrease in reaction rate and an increase in apparent K_m of SNP‐immobilized GOX, but these negative effects could be minimized by using hydrogel with a higher MW PEG, which provides higher water content and larger mesh size. The catalytic rate of the PEG 8000 hydrogel was about ten times faster than that of the PEG 575 hydrogel because of enhanced mass transfer. Long‐term stability test demonstrated that SNP‐immobilized GOX entrapped within hydrogel maintained more than 60% of its initial activity after a week, whereas non‐entrapped SNP‐immobilized GOX and entrapped GOX without SNP immobilization maintained less than 20% of their initial activity. Incorporation of SNPs into hydrogel enhanced the mechanical strength of the hydrogel six‐fold relative to bare hydrogels. Finally, a hydrogel microarray entrapping SNP‐immobilized GOX was fabricated using photolithography and successfully used for quantitative glucose detection. Copyright © 2009 John Wiley & Sons, Ltd.     

Optically transparent, amphiphilic networks based on blends of perfluoropolyethers and poly(ethylene glycol)

Amphiphilic networks of perfluoropolyethers (PFPE) and poly(ethylene glycol) (PEG) have been achieved to yield optically transparent, mechanically robust films over a wide range of compositions. Telechelic diols of these oligomers were transformed to a photocurable dimethacryloxy form (DMA) and free radically cured at various composition weight ratios to yield free-standing films. Clear and colorless amphiphilic networks could be achieved when low molar mass versions of both the PFPE-DMA (1 kg/mol) and the PEG-DMA (550 g/mol) were used. The bulk morphologies of the samples were extensively characterized by a variety of techniques including ultraviolet-visible spectroscopy, differential scanning calorimetry, dynamic mechanic thermal analysis, small-angle X-ray scattering, atomic force microscopy, X-ray photoelectron spectroscopy, and optical microscopy, which strongly suggest that nanoscopic to macroscopic phase-separated materials could be achieved. By incorporating a threshold amount of PFPEs into PEG-based hydrogel networks, water swelling could be significantly reduced, which may offer a new strategy for a number of medical device applications. Along these lines, strong inhibition of nonspecific protein adsorption could be achieved with these amphiphilic network materials compared with an oligo(ethylene glycol)-based self-assembled monolayer coated surface.     

Surfactant Mediated Cationic and Anionic Suspension Polymerization of PEG-Based Resins in Silicon Oil: Beaded SPOCC 1500 and POEPOP 1500

A novel surfactant has been synthesized for use in cationic and anionic ring-opening suspension polymerization of PEG-based macromonomers in silicon oil. A polymer of acrylate esters containing pentamethyldisiloxane and PEG was prepared by radical polymerization. The surfactant can stabilize an emulsion of PEG-based macromonomers, initiator, and solvent in silicon oil such that polymer beads are obtained by ring-opening polymerization, initiated either by a Lewis acid (cationic ring opening) or potassium tert-butoxide (anionic ring opening). The average bead size could be controlled by varying the stirring rate and the amount of surfactant and solvent. The surfactant does not interfere with the polymerization and can be removed together with residual silicon oil by a simple washing procedure.     

Supramolecular hydrogel formation based on inclusion complexation between poly(ethylene glycol)-modified chitosan and alpha-cyclodextrin

Supramolecular hydrogels have been prepared on the basis of polymer inclusion complex (PIC) formation between poly(ethylene glycol) (PEG)-modified chitosans and alpha-cyclodextrin (alpha-CD). A series of PEG-modified chitosans were synthesized by coupling reactions between chitosan and monocarboxylated PEG using water-soluble carbodiimide (EDC) as coupling agent. With simple mixing, the resultant supramolecular assembly of the polymers and alpha-CD molecules led to hydrogel formation in aqueous media. The supramolecular structure of the PIC hydrogels was confirmed by differential scanning calorimetry (DSC), X-ray diffraction, and (13)C cross-polarized/magic-angle spinning (CP/MAS) NMR characterization. The PEG side-chains on the chitosan backbones were found to form inclusion complexes (ICs) with alpha-CD molecules, resulting in the formation of channel-type crystalline micro-domains. The IC domains play an important role in holding together hydrated chitosan chains as physical junctions. The gelation property was affected by several factors including the PEG content in the polymers, the solution concentration, the mixing ratio of host and guest molecules, temperature, pH, etc. All the hydrogels in acidic conditions exhibited thermo-reversible gel-sol transitions under appropriate conditions of mixing ratio and PEG content in the mixing process. The transitions were induced by supramolecular association and dissociation. These supramolecular hydrogels were found to have phase-separated structures that consist of hydrophobic crystalline PIC domains, which were formed by the host-guest interaction between alpha-CD and PEG, and hydrated chitosan matrices below the pK(a).The formation of inclusion complexes between alpha-cyclodextrin and PEG-modified chitosan leads to the formation of hydrogels that can undergo thermo-reversible supramolecular dissociation.     

The influence of diffusion time on the properties of sequential interpenetrating PEG hydrogels

Four sets comprising a total of 16 sequential interpenetrating network (SeqIPN) hydrogels were efficiently fabricated via UV initiated thiol‐ene coupling chemistry and from 2 kDa or 8 kDa primary poly(ethylene glycol) (PEG) networks (S2 and S8). Each primary system delivered four different SeqIPNs constructed after 2, 4, 20, and 44 h diffusion of secondary network PEG precursors, 2 kDa and 8 kDa. This allowed the assessment of both mechanical and swelling properties for a wide range of novel hydrogels ranging from loosely crosslinked SeqIPN 8‐8 to densely crosslinked SeqIPN 2‐2 systems. All gel fractions of secondary networks were above 83% and 44 h of diffusion was found sufficient to fully saturate the primary networks. Disperse red functionalized PEGs (2 kDa and 8 kDa) were further used as probes to investigate the diffusion mechanisms. The impact of diffusion time on loosely crosslinked S8 network with a swelling degree of 970% and tensile modulus of 175 kPa displayed a significant change in the final properties. For instance, a 2 h diffusion of 2 kDa PEG precursors generated a SeqIPN 8‐2:2 comprising a secondary network solid content of 34% with a water swelling degree 580% and a tensile modulus of 365 kPa. On saturation, that is, 44 h of diffusion, SeqIPN 2‐8:44 exhibited 64% of secondary network solid content, a swelling capacity of 380% and over fourfold of tensile modulus (758 kPa) when compared with the primary network S8. SeqIPN hydrogel with the highest tensile modulus and lowest degree of water swelling was obtained after 44 h diffusion of 2 kDa PEG precursors within the densely crosslinked S2 primary network. In this case, SeqIPN 2‐2:44 noted a water swelling capability of 280% and a tensile modulus over 1 MPa. The latter was twofold when compared with S2 with a tensile modulus of 555 kPa. Consequently, the diffusion time of secondary network is a promising parameter to control and that enables the fabrication of PEG hydrogels with a wider window of mechanical and swelling properties. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Micropatterns of double-layered nanofiber scaffolds with dual functions of cell patterning and metabolite detection

This paper describes the development of multi-functional nanofiber scaffolds consisting of multiple layers of nanofiber scaffolds and nanofiber-incorporated poly(ethylene glycol) (PEG) hydrogels. As a proof-of-concept demonstration, we fabricated micropatterned polymeric nanofiber scaffolds that were capable of simultaneously generating cellular micropatterns within a biomimetic environment and detecting cellular metabolic products within well-defined microdomains. To achieve this goal, we designed nanofiber scaffolds with both vertical and lateral microdomains. Vertically heterogeneous structures that were responsible for multi-functionality were realized by preparing double-layered nanofiber scaffolds consisting of an antibody-immobilized bottom layer of nanofibers and an upper layer of bare polystyrene (PS) nanofibers by a two-step sequential electrospinning process. Photopatterning of poly(ethylene glycol) (PEG) hydrogel on the electrospun nanofibers produced laterally heterogeneous micropatterned nanofiber scaffolds made of hydrogel microwells filled with a nanofibrous region, which is capable of generating cell and protein micropatterns due to the different interactions that cells and proteins have with PEG hydrogels and nanofibers. When HepG2 cells were seeded into resultant nanofiber scaffolds, cells selectively adhered within the 200 μm × 200 μm PS fiber microdomain and formed 180.2 ± 6.7 μm spheroids after 5 days of culture in the upper layer. Furthermore, immobilized anti-albumin in the bottom layer detected albumin secreted by micropatterned HepG2 cells with higher sensitivity than flat PS substrates, demonstrating successful accomplishment of dual functions using micropatterned double-layered nanofiber scaffolds.     

Dependence of Self-Assembled Peptide Hydrogel Network Structure on Local Fibril Nanostructure

Physically cross-linked, fibrillar hydrogel networks are formed by the self-assembly of β-hairpin peptide molecules with varying degrees of strand asymmetry. The peptide registry in the self-assembled state can be used as a design element to generate fibrils with twisting, nontwisting, or laminated morphology. The mass density of the networks varies significantly, and can be directly related to the local fibrillar morphology as evidenced by small angle neutron scattering (SANS) and in situ substantiation using cryogenic transmission electron microscopy (cryo-TEM) under identical concentrations and conditions. Similarly, the density of the network is dependent on changes in the peptide concentration. Bulk rheological properties of the hydrogels can be correlated to the fibrillar nanostructure, with the stiffer, laminated fibrils forming networks with a higher G' as compared to the flexible, singular fibrillar networks.