Tunable Mechanics of Peptide Nanofiber Gels

Oct 9, 2009 - The mechanical properties of self-assembled fibrillar networks are influenced by the specific intermolecular interactions that modulate ...
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Tunable Mechanics of Peptide Nanofiber Gels )

Megan A. Greenfield,† Jessica R. Hoffman,‡ Monica Olvera de la Cruz,†,‡, and Samuel I. Stupp*,‡, ,^,§ Department of Chemical and Biological Engineering, ‡Department of Materials Science and Engineering, and, Department of Chemistry, Northwestern University, Evanston, Illinois 60208, and, ^Feinberg School of Medicine and, and §Institute for BioNanotechnology in Medicine, Northwestern University, Chicago, Illinois 60611 )

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Received August 19, 2009 The mechanical properties of self-assembled fibrillar networks are influenced by the specific intermolecular interactions that modulate fiber entanglements. We investigate how changing these interactions influences the mechanics of self-assembled nanofiber gels composed of peptide amphiphile (PA) molecules. PAs developed in our laboratory self-assemble into gels of nanofibers after neutralization or salt-mediated screening of the charged residues in their peptide segment. We report here on the gelation, stiffness, and response to deformation of gels formed from a negatively charged PA and HCl or CaCl2. Scanning electron microscopy of these gels demonstrates a similar morphology, whereas the oscillatory rheological measurements indicate that the calcium-mediated ionic bridges in CaCl2-PA gels form stronger intra- and interfiber cross-links than the hydrogen bonds formed by the protonated carboxylic acid residues in HCl-PA gels. As a result, CaCl2-PA gels can withstand higher strains than HCl-PA gels. After exposure to a series of strain sweeps with increasing strain amplitude HCl- and CaCl2-PA gels both recover 42% of their original stiffness. In contrast, after sustained deformation at 100% strain, HCl-PA gels recover nearly 90% of their original stiffness after 10 min, while the CaCl2-PA gels only recover 35%. This result suggests that the hydrogen bonds formed by the protonated acids in the HCl-PA gels allow the gel to relax quickly to its initial state, while the strong calcium cross-links in the CaCl2-PA gels lock in the deformed structure and inhibit the gel’s ability to recover. We also show that the rheological scaling behaviors of HCl- and CaCl2-PA gels are consistent with that of uncross- and cross-linked semiflexible biopolymer networks, respectively. The ability to modify how self-assembled fibrillar networks respond to deformations is important in developing self-assembled gels that can resist and recover from the large deformations that these gels encounter while serving as synthetic cell scaffolds in vivo.

Introduction The design of synthetic scaffolds for cells is of great interest in biotechnology and regenerative medicine.1-3 Recent experiments suggest that the mechanical properties of scaffolds and substrates can affect cells in a variety of ways. The stiffness of cell substrates has been shown to be important in cell proliferation, differentiation, adhesion, and migration. Several experiments have shown that substrate stiffness affects a wide range of cells,4 from chondrocytes in collagen matrices5 to neurons in hydrogels,6 and can impact cell behavior, including cell motility,7 focal *Corresponding author. E-mail: [email protected]. (1) Langer, R.; Vacanti, J. P. Tissue Engineering. Science 1993, 260, (5110), 920-926. (2) Stupp, S. I.; Donners, J. J. J. M.; Li, L. S.; Mata, A. Expanding frontiers in biomaterials. MRS Bull. 2005, 30, (11), 864-873. (3) Stevens, M. M.; George, J. H. Exploring and Engineering the Cell Surface Interface. Science 2005, 310, (5751), 1135-1138. (4) Discher, D. E.; Janmey, P.; Wang, Y. L. Tissue cells feel and respond to the stiffness of their substrate. Science 2005, 310, (5751), 1139-1143. (5) Nehrer, S.; Breinan, H. A.; Ramappa, A.; Young, G.; Shortkroff, S.; Louie, L. K.; Sledge, C. B.; Yannas, I. V.; Spector, M. Matrix collagen type and pore size influence behaviour of seeded canine chondrocytes. Biomaterials 1997, 18, (11), 769-776. (6) Georges, P. C.; Miller, W. J.; Meaney, D. F.; Sawyer, E. S.; Janmey, P. A. Matrices with compliance comparable to that of brain tissue select neuronal over glial growth in mixed cortical cultures. Biophys. J. 2006, 90, (8), 3012-3018. (7) Pelham, R. J.; Wang, Y. L. Cell motility, cytoskeletal reorganization, and tyrosine phosphorylation are modulated by the mechanical properties of the adhesion substrate. Mol. Biol. Cell 1996, 7, 2429-2429. (8) Pelham, R. J.; Wang, Y. L. Cell locomotion and focal adhesions are regulated by substrate flexibility. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, (25), 13661-13665. (9) Georges, P. C.; Janmey, P. A. Cell type-specific response to growth on soft materials. J. Appl. Physiol. 2005, 98, (4), 1547-1553. (10) Wang, H. B.; Dembo, M.; Wang, Y. L. Substrate flexibility regulates growth and apoptosis of normal but not transformed cells. Am. J. Physiol. Cell Physiol. 2000, 279, (5), C1345-C1350.

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adhesions,8 growth,9 and apoptosis.10 Furthermore, microenvironment mechanical properties have been shown to influence mesenchymal stem cell differentiation11 and to affect the cell’s ability to uptake exogenous signaling molecules.12 Since the mechanical properties of the matrix surrounding cells can have a significant impact on cell behavior, the mechanical properties must be considered when developing artificial three-dimensional scaffolds for regenerative medicine. Our laboratory has developed bioactive scaffolds composed of peptide amphiphiles (PAs) that self-assemble into nanofiber networks.13-22 The PA molecules self-assemble into cylindrical nanofibers when the strong electrostatic repulsion between (11) Engler, A. J.; Sen, S.; Sweeney, H. L.; Discher, D. E. Matrix elasticity directs stem cell lineage specification. Cell 2006, 126, (4), 677-689. (12) Kong, H. J.; Liu, J. D.; Riddle, K.; Matsumoto, T.; Leach, K.; Mooney, D. J. Non-viral gene delivery regulated by stiffness of cell adhesion substrates. Nat. Mater. 2005, 4, (6), 460-464. (13) Hartgerink, J. D.; Beniash, E.; Stupp, S. I. Self-assembly and mineralization of peptide-amphiphile nanofibers. Science 2001, 294, (5547), 1684-1688. (14) Niece, K. L.; Hartgerink, J. D.; Donners, J. J. J. M.; Stupp, S. I. Selfassembly combining two bioactive peptide-amphiphile molecules into nanofibers by electrostatic attraction. J. Am. Chem. Soc. 2003, 125, (24), 7146-7147. (15) Silva, G. A.; Czeisler, C.; Niece, K. L.; Beniash, E.; Harrington, D. A.; Kessler, J. A.; Stupp, S. I. Selective differentiation of neural progenitor cells by high-epitope density nanofibers. Science 2004, 303, (5662), 1352-1355. (16) Beniash, E.; Hartgerink, J. D.; Storrie, H.; Stendahl, J. C.; Stupp, S. I. Selfassembling peptide amphiphile nanofiber matrices for cell entrapment. Acta Biomaterialia 2005, 1, (4), 387-397. (17) Behanna, H. A.; Donners, J. J. J. M.; Gordon, A. C.; Stupp, S. I. Coassembly of amphiphiles with opposite peptide polarities into nanofibers. J. Am. Chem. Soc. 2005, 127, (4), 1193-1200. (18) Bull, S. R.; Guler, M. O.; Bras, R. E.; Meade, T. J.; Stupp, S. I. Selfassembled peptide amphiphile nanofibers conjugated to MRI contrast agents. Nano Lett. 2005, 5, (1), 1-4. (19) Klok, H. A.; Hwang, J. J.; Hartgerink, J. D.; Stupp, S. I. Self-assembling biomaterials: L-lysine-dendron-substituted cholesteryl-(L-lactic acid)n. Macromolecules 2002, 35, (16), 6101-6111.

Published on Web 10/09/2009

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Figure 1. Molecular structure of the investigated peptide amphiphile. The molecule is composed of three segments, the alkyl tail, the β-sheet forming peptide sequence, and the charged peptide headgroup.

molecules is either neutralized by changing pH or screened by adding ions.23-25 At certain concentrations and in the presence of sufficient electrostatic screening, these PA molecules can form a three-dimensional network that is observed macroscopically as a self-supporting gel. The peptides that decorate the outer surface of the nanofibers can be designed to contain amino acids that serve as signals to the surrounding cells. PA fibers with bioactive epitopes have previously been used to promote bone growth,13 neural cell differentiation,15 and angiogenesis.26 Despite the nanofiber network common to most peptide amphiphile gels, the bulk mechanical properties of PA gels vary greatly and depend on a variety of parameters, including molecular structure, concentration of the PA, and concentration and type of gel-inducing ions in the sample. Although theoretical studies27-29 as well as mechanical measurements of PA gels have been performed previously, only a few experiments have systematically investigated the correlation between bulk elastic properties and experimental parameters.24,30,31 Here we investigate how the gelation kinetics, stiffness, and strain recovery of PA gels vary with the type of charge screening gelling agent, either HCl or CaCl2. The observed PA gel mechanics are discussed in comparison to other bioactive nanofiber networks, and semiflexible (20) Klok, H. A.; Hwang, J. J.; Iyer, S. N.; Stupp, S. I. Cholesteryl-(L-lactic acid)n building blocks for self-assembling biomaterials. Macromolecules 2002, 35, (3), 746-759. (21) Hwang, J. J.; Iyer, S. N.; Li, L. S.; Claussen, R.; Harrington, D. A.; Stupp, S. I. Self-assembling biomaterials: Liquid crystal phases of cholesteryl oligo(L-lactic acid) and their interactions with cells. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, (15), 9662-9667. (22) Guler, M. O.; Soukasene, S.; Hulvat, J. F.; Stupp, S. I. Presentation and recognition of biotin on nanofibers formed by branched peptide amphiphiles. Nano Lett. 2005, 5, (2), 249-252. (23) Hartgerink, J. D.; Beniash, E.; Stupp, S. I. Peptide-amphiphile nanofibers: A versatile scaffold for the preparation of self-assembling materials. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, (8), 5133-5138. (24) Stendahl, J. C.; Rao, M. S.; Guler, M. O.; Stupp, S. I. Intermolecular forces in the self-assembly of peptide amphiphile nanofibers. Adv. Funct. Mater. 2006, 16, (4), 499-508. (25) Tsonchev, S.; Niece, K. L.; Schatz, G. C.; Ratner, M. A.; Stupp, S. I. Phase diagram for assembly of biologically-active peptide amphiphiles. J. Phys. Chem. B 2008, 112, (2), 441-447. (26) Rajangam, K.; Behanna, H. A.; Hui, M. J.; Han, X. Q.; Hulvat, J. F.; Lomasney, J. W.; Stupp, S. I. Heparin binding nanostructures to promote growth of blood vessels. Nano Lett. 2006, 6, (9), 2086-2090. (27) Ha, B. Y.; Liu, A. J. Counterion-mediated, non-pairwise-additive attractions in bundles of like-charged rods. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. 1999, 60, (1), 803-813. (28) Solis, F. J.; de la Cruz, M. O. Attractive interactions between rodlike polyelectrolytes: Polarization, crystallization, and packing. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. 1999, 60, (4), 4496-4499. (29) Stevens, M. J. Bundle binding in polyelectrolyte solutions. Phys. Rev. Lett. 1999, 82, (1), 101-104. (30) Paramonov, S. E.; Jun, H. W.; Hartgerink, J. D. Self-assembly of peptideamphiphile nanofibers: The roles of hydrogen bonding and amphiphilic packing. J. Am. Chem. Soc. 2006, 128, (22), 7291-7298. (31) Niece, K. L.; Czeisler, C.; Sahni, V.; Tysseling-Mattiace, V.; Pashuck, E. T.; Kessler, J. A.; Stupp, S. I. Modification of gelation kinetics in bioactive peptide amphiphiles. Biomaterials 2008, 29, (34), 4501-4509.

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network theories are used to estimate the persistence length of PA nanofibers and the mesh size of PA gels. The PA molecules used here contain the peptide sequence V3A3E3 and a C16 alkyl tail at the peptide’s N-terminus, and their chemical structure is shown in Figure 1.

Materials and Methods Sample Preparation. The peptide amphiphile molecules were prepared as reported previously31 using standard fluorenylmethoxycarbonyl (Fmoc) chemistry on an Applied Biosystems 433A automated peptide synthesizer. Cleavage and deprotection of the PA was done with a 95:2.5:2.5 mixture of trifluoroacetic acid, water, and triisopropylsilane for 2 h at room temperature. The PA was then concentrated by rotary evaporation, precipitated with cold diethyl ether, and dried overnight. The PA was purified on an XBridge C18 reverse phase column (Waters Corporation, Milford, MA) using high-pressure liquid chromatography (HPLC) in a water/acetonitrile gradient. Following preparative HPLC, purity was assessed by analytical HPLC and was found to be 85.2% pure by amide content. To remove any excess salts, PAs were dialyzed against water in 500 molecular weight cutoff dialysis tubing (Spectrum Laboratories). The PA was characterized by electrospray ionization (ESI) and found to have the expected molecular weight. PA gels were formed by adding HCl or CaCl2 dropwise to the PA solutions in a gelling solution volume ratio of 5:1. The gelling agent concentration was determined by calculating the required number of charges needed to completely neutralize the charge of the PA molecules, assuming that all carboxylic acid groups in the PA molecules are deprotonated, and thus, the PA molecules have a charge of -4. Rheology. The mechanical properties of peptide amphiphile gels were characterized by small angle oscillatory rheology, which analyzes the sample’s response to shear flow. An oscillatory strain γ = γo sin ωt is applied, and the resulting shear stress τ is measured. The shear stress τ can be written as τðtÞ ¼ γo ½G0 sin ωt þ G00 cos ωt where γo is strain amplitude, ω is the angular frequency, G0 is the storage (or elastic) modulus, and G00 is the loss (or viscous) modulus. The storage and loss moduli can be related by tan δ ¼ G00 =G0 A value for δ approaching 90 or 0 indicates that the sample has a predominately viscous or elastic character, respectively. Time and frequency sweep measurements were collected with a Paar Physica modular compact rheometer 300 operating in a 25 mm parallel plate configuration with a 0.5 mm gap distance. A parallel plate configuration, rather than a cone and plate Langmuir 2010, 26(5), 3641–3647

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configuration, was used to minimize compression of the gel when the upper plate was lowered onto the sample. Lyophylized peptide amphiphiles were dissolved in Milli-Q water (pH ∼ 5), and loaded onto the rheometer, and then gelled with either HCl or CaCl2 before lowering the top plate. Each gel sample had a total volume of 300 μL and was formed from 250 μL of PA solution and 50 μL of an aqueous ion solution (HCl or CaCl2). The gelling solution was added dropwise onto the PA solution and was not mixed after the gelling solution was added. The gel was made directly on the plate to ensure good contact between the gel and the upper and lower plates. No homogenization process was used because the gels form almost immediately, and any homogenization process would alter the gel’s structure. All PA gels appeared to be uniform in composition, with no apparent phase separation. Gels of six different PA concentrations were studied. The final concentration of the PA and gelling solution in the HCl-PA gels were 1.5 mM PA with 5.8 mM HCl, 2.2 mM PA with 8.3 mM HCl, 2.9 mM PA with 11.2 mM HCl, 4.3 mM PA with 16.7 mM HCl, 6.5 mM PA with 25.0 mM HCl, 8.7 mM PA with 33.3 mM HCl, and 13 mM PA with 50 mM HCl. The final concentration of the PA and gelling solution in the CaCl2-PA gels were 1.5 mM PA with 2.9 mM CaCl2, 2.2 mM PA with 4.2 mM CaCl2, 2.9 mM PA with 5.6 mM CaCl2, 4.3 mM PA with 8.3 mM CaCl2, 6.5 mM PA with 12.5 mM CaCl2, 8.7 mM PA with 16.7 mM CaCl2, and 13 mM PA with 25 mM CaCl2. During all experiments, the stage temperature was maintained at 25 C by a Peltier heating system, and a chamber containing saturated tissues was placed around the gels to minimize evaporation. The wet tissues were not in contact with the sample or the upper plate but simply served as a water reservoir to increase the humidity in the semienclosed chamber surrounding the sample. Strain sweep experiments were performed to determine the linear viscoelastic regime, and all frequency and time sweep experiments were in performed in this regime. Time sweep measurements were performed at 10 rad/s and 0.5% strain. Frequency sweep measurements were performed at 0.5% strain from 100 to 1 rad/s. Before the frequency sweep measurements, the PA gels were allowed to gel for 30 min in the rheometer. For the cyclic strain sweep experiments, the strain was sequentially increased and decreased within the following strain ranges: 0.01-0.1, 0.01-0.5, 0.01-1.0, 0.01-2.0, 0.01-5.0, 0.01-20.0, 0.01-50.0, and 0.01-100.0%. In the high-strain test, the gels were exposed to 100% strain for 5 min and then monitored at 0.5% strain for 10 min. Scanning Electron Microscopy (SEM). The network structure of the PA gels was imaged by SEM after the gels were critically point dried. Critical-point drying is an established SEM sample preparation technique that allows delicate, hydrated samples to be dried without the structural damage associated with air drying. The gels formed for SEM analysis had a total volume of 36 μL and were made by combining 30 μL of PA solution with 6 μL of gelling solution. The final concentrations of the PA and gelling solution in the HCl-PA gels were 8.7 mM PA with 33.3 mM HCl, and the final concentrations of the PA and gelling solution in the CaCl2-PA gel were 8.7 mM PA with 16.7 mM CaCl2. After the gels were made, the water was slowly exchanged with a series of water-ethanol mixtures until the gel was in 100% ethanol. The ethanol exchange is done slowly to minimize the effect of changing the solvent on the gel structure. No macroscopic changes in the gel appearance were observed during the ethanol exchange process. The samples were then critically point dried in a Polaron E3000 critical point drying apparatus and were sputter coated with 3 nm of a gold palladium alloy in a Cressington 208 HR sputter coater. Samples were then imaged on a Hitachi S-4800 II SEM (Hitachi, Pleasanton, CA). Langmuir 2010, 26(5), 3641–3647

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Figure 2. SEM micrograph of: (a) HCl-PA gel formed with 8.7 mM PA and 33.3 mM HCl and (b) CaCl2-PA gel formed with 8.7 mM PA and 16.7 mM CaCl2.

Results and Discussion Nanoscale Morphology. The morphology of PA gels was characterized by SEM. The nanofiber network structure of PA gels formed with HCl and CaCl2, as observed by SEM, are shown in Figure 2a and b, respectively. No significant difference in nanofiber diameter or length is observed between the HCl- and CaCl2PA gels. Since a single PA nanofiber is expected to have a diameter on the order of 10 nm and most of the observed fibers are approximately 20-40 nm in diameter, it appears that the nanofibers formed by the specific molecule used in this study associate to form bundles that are micrometers in length. The fiber bundles likely form because of favorable interactions between nanofibers, such as hydrogen bonding, possibly mediated by water molecules and by ion bridging between the carboxylic acid groups on the glutamic residues of adjacent PA molecules. We can establish that the nanofiber bundles are semiflexible because they appear in the micrograph to be locally stiff. The nanofibers are not observed to form loops or knots, thus, seemingly not behaving as flexible chains. Rheological Properties of PA Hydrogels. The first rheological tests to be performed investigated the gelation, stiffness, and strain deformation of gels formed with either HCl or CaCl2. During these tests the storage modulus (G0 ) and loss modulus (G00 ) were recorded as a function of time, angular frequency, or strain amplitude. The results of the rheological experiments for gels formed with 8.7 mM PA and 33 mM HCl are shown in Figure 3. Figure 3a shows the dependence of G0 and G00 over a wide range of strain amplitudes. This strain sweep test allowed us to investigate DOI: 10.1021/la9030969

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Figure 3. Rheological properties of a HCl-PA gel formed with 8.7 mM PA and 33.3 mM HCl. (a) Strain sweep (10 rad/s), (b) time sweep (0.5% strain, 10 rad/s), and (c) frequency sweep (0.5% strain).

the transition from linear to nonlinear viscoelastic behavior. The transition between the linear and nonlinear regions is characterized by the limiting strain amplitude γL and can be identified by determining when G0 is no longer constant with increasing strain amplitude. From Figure 3a the limiting strain for HCl-PA gels was estimated to be 1%. Figure 3b shows how G0 and G00 evolved during the six hours following gelation. The storage modulus rapidly increased and then quickly leveled off at a plateau value of ∼4500 Pa. Figure 3c shows the results of the frequency sweep for the HCl-PA gel. The value of G0 for the HCl-PA gel was greater than G00 , indicating that these gels behaved as elastic solids. It is important to note that G0 and G00 were essentially independent of frequency, and no crossover of G0 and G00 at low frequencies was observed. This behavior is characteristic of cross-linked networks. The cross-linking can be covalent, as in rubbers,32 or noncovalent, as in biopolymers33 and (32) Macosko, C. W. Rheology: Principles, Measurements, and Applications. Wiley-VCH: New York, 1994. (33) Janmey, P. A.; Euteneuer, U.; Traub, P.; Schliwa, M. Viscoelastic Properties of Vimentin Compared with Other Filamentous Biopolymer Networks. J. Cell Biol. 1991, 113, (1), 155-160.

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Figure 4. Rheological properties of a CaCl2-PA gel formed with 8.7 mM PA and 16.7 mM CaCl2. (a) Strain sweep (10 rad/s), (b) time sweep (0.5% strain, 10 rad/s), and (c) frequency sweep (0.5% strain).

in other self-assembled gels.34 Since HCl does not covalently cross-link PA nanofibers, there must be other types of interactions among fibers, such as hydrogen bonds, that act as physical crosslinks, leading to the observed frequency sweep behavior. The rheological experimental results for gels formed with 8.7 mM PA and 17 mM CaCl2 are shown in Figure 4. Figure 4a shows the dependence of G0 and G00 on a wide range of strain amplitudes. At low-strain amplitudes, G0 and G00 were approximately constant and then both moduli decreased rapidly at highstrain amplitudes. The limiting strain, which can be calculated as described above, was estimated to be 5% for CaCl2-PA gels. The time sweep in Figure 4b shows that G0 and G00 increased gradually over six hours and that the plateau G0 value (∼7000 Pa) was not achieved until nearly six hours. This gelation behavior is in contrast to that of HCl-PA gels, which attain their final storage modulus within 30 min. The CaCl2-PA gel’s frequency sweep behavior (Figure 4c) was similar to that observed with the (34) Ozbas, B.; Rajagopal, K.; Schneider, J. P.; Pochan, D. J. Semiflexible chain networks formed via self-assembly of beta-hairpin molecules. Phys. Rev. Lett. 2004, 93, (26), -.

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HCl-PA gels. The storage modulus was always greater than the loss modulus, and both were insensitive to frequency. The strain sweep data showed that the storage and loss moduli of both the HCl- and CaCl2-PA gels were constant at low strains (linear viscoelastic regime), and they exhibited markedly different behavior at high-strain amplitudes (nonlinear regime). The limiting strain amplitude γL, which is the strain that marks the transition between the linear and nonlinear regimes, was about five times greater for CaCl2 gels than for HCl gels. This difference in γL indicates that CaCl2-PA gels can withstand much larger strains before plastic deformation. We can also compare the strain sweep behavior of PA gels to polymer solutions and gels. The strain behavior of polymer solutions are generally separated into four categories: (1) strain thinning, (2) strain hardening, (3) weak-strain overshoot, and (4) strongstrain overshoot.35 Figures 3a and 4a show that the storage modulus (G0 ) decreased with increasing strain amplitude, but that the loss modulus (G00 ) first increased with increasing strain before decreasing. This strain amplitude response can be classified as weak-strain overshoot.35 Weak-strain overshoot behavior is not as common as strain thinning, in which both G0 and G00 decrease with increasing strain amplitude, but it has been observed in other systems, including xanthan gum solutions,35 polyamide/clay nanocomposites,36 flour-water dough,37 and PEO/PBO diblock copolymer solutions.38 It has been hypothesized that solutions with weak strain overshoot behavior have complex structures that can resist strain deformation up to a certain point (until G00 reaches a maximum value). Increasing the strain amplitude past this point damages the complex structure and results in local alignment of the solution components with the flow field, resulting in a decrease of G00 . The PA gels may demonstrate this behavior because the entangled nanofiber network can resist the deformation until it is large enough to break interactions either between the nanofibers or the nanofibers themselves, allowing the nanofibers to align locally with the flow field. The strain studies indicate that the CaCl2-PA gels can resist strains up to five times larger than the HCl-PA gels before plastic deformation. The rheological results discussed above allowed us to systematically compare the mechanical properties of the HCl and CaCl2 gels. The time sweep measurements showed that both gels achieved a storage modulus of approximately 1 000 Pa in the time it took to prepare the sample and make the first measurement (approximately 2-3 min). This rapid increase of G0 indicates that the PA molecules are able to rapidly form networks with solid-like properties. The time sweep data also showed that CaCl2-PA gels formed more slowly than HCl PA gels. At early time points, HCl-PA gels had a higher G0 , while at longer time points, CaCl2-PA gels had a higher G0 . The gels had the same modulus approximately 1.5 h after they were initially formed. Unlike previous gelation studies, which correlate PA gelation kinetics with the number of nucleating aggregates in the solution before gelation,31 the difference observed here is only a result of the gelling agent (CaCl2 or HCl) because both gels are formed from the same PA solution. This difference in gelation kinetics may (35) Hyun, K.; Kim, S. H.; Ahn, K. H.; Lee, S. J. Large amplitude oscillatory shear as a way to classify the complex fluids. J. Non-Newtonian Fluid Mech. 2002, 107, (1-3), 51-65. (36) Wan, T.; Clifford, M. J.; Gao, F.; Bailey, A. S.; Gregory, D. H.; Somsunan, R. Strain amplitude response and the microstructure of PA/clay nanocomposites. Polymer 2005, 46, (17), 6429-6436. (37) Phan-Thien, N.; Safari-Ardi, M. Linear viscoelastic properties of flourwater doughs at different water concentrations. J. Non-Newtonian Fluid Mech. 1998, 74, (1-3), 137-150. (38) Daniel, C.; Hamley, I. W.; Wilhelm, M.; Mingvanish, W. Non-linear rheology of a face-centred cubic phase in a diblock copolymer gel. Rheol. Acta 2001, 40, (1), 39-48.

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Figure 5. Cyclic strain sweep of: (a) HCl-PA gel formed with

8.7 mM PA and 33.3 mM HCl and (b) CaCl2-PA gel formed with 8.7 mM PA and 16.7 mM CaCl2. The cycles are shown in the following colors, with the forward sweeps shown in full color and a solid circle and the reverse sweeps shown in lighter color and an open circle. Red (0.01 to 0.5 to 0.01%), orange (0.01 to 1 to 0.01%), yellow (0.01 to 2 to 0.01%), green (0.01 to 5 to 0.01%), blue (0.01 to 20 to 0.01%), purple (0.01 to 50 to 0.01%), and black (0.01 to 100 to 0.01%).

arise from the slower diffusion of the hydrated calcium ions through the nanofiber network. The frequency sweep tests show that both gels are predominately solid-like rather than liquid-like (G0 >G00 ). It is interesting that HCl- and CaCl2-PA gels have similar G0 values despite the different types of interactions the gelinducing ions provide, since the calcium ions are likely to form electrostatic bridges between molecules, whereas changing the pH neutralizes the charge on the acidic residues. Since our initial rheological experiments showed that HCland CaCl2-PA gels exhibit relatively uncommon weak-strain overshoot behavior, we decided to explore the mechanical properties of the gels in more depth by investigating how the gels deform under high strain. We were specifically interested in these qualities because many tissues, such as bone and cartilage, are regularly exposed to strain amplitudes higher than the γL for PA gels.4 Since the PA gel may be used as a synthetic cell scaffold to regenerate such tissues, it is important to understand how high strains affect their mechanical properties. Thus, we designed a rheological experiment to investigate how the material responded to a wide range of strains. To investigate these features, the gels were exposed to a series of strain sweeps, with each subsequent test achieving a higher maximum strain amplitude. We refer to this experiment as a “cyclic strain sweep.” Figure 5 shows cyclic strain sweep measurements of HCl- and CaCl2-PA gels. Each line indicates a forward strain amplitude path from 0.01 to N% strain or a reverse strain path from N to 0.01% strain. DOI: 10.1021/la9030969

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The cyclic strain sweeps show that before the HCl- and CaCl2-PA gels were exposed to high-strain amplitudes, the sweeps were superimposable and were similar to those shown in Figures 2a and 3a, respectively. However, both PA gels deformed significantly after γL was exceeded. The final storage moduli of the gels were both 42% of their initial values (see Supporting Information). Additionally, the final tan δ values were 9 and 40% higher than the initial tan δ values for the HCl- and CaCl2-PA gels, respectively (Figure 4b), indicating that both gels have increased viscous character after the experiment. Once the gels were exposed to 20% strain amplitude, both gels appeared to be irreversibly deformed. The subsequent strain sweeps did not have the same shape as the strain sweeps performed at low-strain amplitudes nor did they follow the strain sweep profiles presented in Figures 2a and 3a. Furthermore, γL decreased significantly for both gels after the gel had been exposed to strain amplitudes greater than the initial limiting strain. It appears that after γL was exceeded, the gel network was damaged and unable to recover. The observed abrupt change in gel mechanics observed after exceeding γL indicates that the network structure is damaged or destroyed after exposure to high-strain amplitudes. We hypothesize that reversible intra- and interfiber interactions are responsible for the HCl-PA gels’ ability to resist deformation by stiffening the PA fibers and by forming interactions between fibers. These interactions are most likely hydrogen bonds that could involve the acidic side chains in the PA molecules as well as water molecules. In the CaCl2-PA gel, the calcium ions may serve a similar role, by bridging the charged glutamic acid residues within and between PA fibers. At low-strain amplitudes, the physically cross-linked PA nanofiber bundles are able to resist the imposed strain, but once the gels are exposed to strains that exceed γL, the PA nanofiber bundles align locally with the flow field, resulting in a decrease in the storage modulus. However, since the cross-links between nanofibers are physical rather than covalent, these cross-links can rapidly reform between the partially aligned nanofiber bundles, enabling the gels to retain much of their original stiffness (G0 ). In a separate experiment, HCl- and CaCl2-PA gels were exposed to 100% strain for 5 min, and then the gel’s recovery was recorded over time (Figure 6). This experiment allows us to determine how the gels recover after sustained exposure to large deformations. The HCl-PA recovered nearly 90% of its original storage modus within 10 min, while the CaCl2-PA gel only recovered 35%. The recovery profiles have a similar shape to the gelation profiles (Figures 3a and 4a), with the G0 of the HCl-PA gel rapidly reaching a plateau modulus and the G0 of the CaCl2-PA gel slowly increasing with time. Interestingly, the ability of the HCl- and CaCl2-PA gels to recover after the cyclic strain sweep is very similar (see Supporting Information), but is markedly different after exposure to sustained 100% strain. We suggest that the HCl-PA gels recovered more after the 5 min of 100% strain than after the cyclic strain test because in the cyclic strain experiment the gel was repeatedly deformed with strains beyond γL, while in the 100% strain experiment the gel was only deformed once. Additionally, in the cyclic strain experiment most of the recovery is achieved under considerable strain, while the other test allows the gel to reform under very low strain, allowing the gel to relax quicker. Unlike the HCl-PA gel, the CaCl2-PA gel recovers less after the 5 min of 100% strain than after the cyclic strain sweep test. We hypothesize that during the cyclic strain sweep experiment the calcium ions do not have enough time to diffuse and fix the highly aligned structure present under high strain. Thus, the gel was able to recover much of its original storage modulus after the cyclic strain sweep. However, when the 3646 DOI: 10.1021/la9030969

Greenfield et al.

Figure 6. Recovery of the storage modulus of 8.7 mM HCl- and CaCl2-PA gels after being exposed to 100% strain for 5 min.

CaCl2-PA gel was under 100% strain for a prolonged period of time, the calcium ions have sufficient time to diffuse and fix the deformed structure, inhibiting the gel’s ability to recover. The slow diffusion of calcium ions in the PA gel is supported by the slow gelation of CaCl2-PA gel shown in Figure 4b. The strain experiments indicate that CaCl2-PA gels can withstand larger strains before plastic deformation, but are unable to recover as quickly as HCl-PA gels once plastic deformation has occurred. Scaling Analysis. As discussed above, gels formed with HCl and CaCl2 show significant differences in their rheological properties. The similarity in the nanoscale morphology of the two gels, shown in Figure 2, indicates that the differences in their properties arise from a difference in either intra- or interfiber interactions and not simply from a large change in morphology. Since the dependence of the network’s storage modulus (G0 ) on solute concentration is often used to compare the rheological behaviors of biopolymer networks, we decided to investigate this relationship for HCl- and CaCl2-PA gels. Figure 7a and b shows the concentration dependence of the storage modulus for HCl- and CaCl2-PA gels, respectively, after 30 min of gelation. By fitting the data to a power law, we find the scaling exponent to be ∼2.1 for CaCl2-PA gels and ∼1.5 for HCl-PA gels. Previous investigators have compared the power law dependence of G0 on concentration for a wide range of biopolymers, including actin,39,40 microtubules,33 fibrin,41 and vimentin.33 More recently, the scaling of synthetic networks has been investigated.34 Often the scaling behavior is compared with semiflexible network theories, which were first developed to explain the rheological behavior of stiff biopolymers, such as actin, and can be used to determine the characteristic mesh size ξ and the persistence length lp of the network. The scaling observed for the CaCl2-PA gels is similar to the theory of MacKintosh et al. for sterically entangled semiflexible networks.42 The theory predicts the storage modulus scales as G0 ∼ KðK=kB TÞ2=5 ðacÞ11=5 where κ is the semiflexible chain bending modulus, c is the concentration, a is the monomer size, kB is the Boltzmann constant, and T is the temperature. Since the bending modulus is related to the persistence length by κ ∼ lpkBT and the mesh size ξ ∼ (ac)-1/2, the MacKintosh scaling can be used to estimate the (39) Janmey, P. A.; Hvidt, S.; Peetermans, J.; Lamb, J.; Ferry, J. D.; Stossel, T. P. Viscoelasticity of F-Actin and F-Actin Gelsolin Complexes. Biochemistry 1988, 27, (21), 8218-8227. (40) Hvidt, S.; Janmey, P. A. Elasticity and Flow Properties of Actin Gels Makromol. Chem., Macromol. Symp. 1990, 39, 209-213. (41) Gerth, C.; Roberts, W. W.; Ferry, J. D. Rheology of Fibrin Clots 0.2. Linear Viscoelastic Behavior in Sheer Creep. Biophys. Chem. 1974, 2, (3), 208-217. (42) Mackintosh, F. C.; Kas, J.; Janmey, P. A. Elasticity of Semiflexible Biopolymer Networks. Phys. Rev. Lett. 1995, 75, (24), 4425-4428.

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mechanical properties of a variety of filamentous biopolymers have been studied and show a range of scaling behaviors. Fibrin clots, which play a key role in blood coagulation, are particularly interesting to compare to PA gels because they have similar power law dependencies. The power law exponent for unligated (noncross-linked) fibrin clots is ∼1.5 and for ligated (cross-linked) fibrin clots is ∼2.3.41 These exponents are similar to those observed with the HCl- and CaCl2-PA gels, respectively. The microstructure of unligated and ligated fibrin clots are similar, as verified by SEM,43 which is consistent with our observation of HCl- and CaCl2-PA gels. These results suggest that the covalent bonds formed during fibrin ligation have a dramatic effect on its mechanical properties without altering the overall morphology of the fibrin network. The difference in the power law scaling of HCl- and CaCl2-PA gels may be analogous to what has been observed between the unligated and ligated fibrin clots. We hypothesize that in the HCl-PA gels the protonated acidic groups form hydrogen bonds that serve as weak interfiber cross-links, while in the CaCl2-PA gels the calcium ions form very strong physical cross-links between PA fibers. The physical cross-links formed by the calcium ions in the PA gels may serve a similar role as the covalent cross-links do in the fibrin clots.

Conclusions

Figure 7. (a) Storage modulus (G0 ) versus concentration for HCl-PA gels formed with various concentration of PA. The dashed line represents a fit to the HCl-PA gel data points (equation of the line G0 = 144c1.51, R2 =0.986). (b) Storage modulus (G0 ) versus concentration for CaCl2-PA gels. The dashed line represents a fit to the CaCl2-PA gel data points (equation of the line G0 =35c2.14, R2 =0.984). Error bars represent the standard deviation between two runs.

persistence length and the mesh size of CaCl2-PA gels. For 8.7 mM PA, the storage modulus is approximately 5 000 Pa. Using a = 4.74 A˚, which corresponds to the spacing of chains connected by a β-sheet, lp is approximately 102 nm and ξ is approximately 20 nm. The mesh size is much smaller than the persistence length, as expected for networks composed of semiflexible chains. However, this estimated mesh size appears to be smaller than that observed by SEM in Figure 2. This difference could arise from the critical point drying processing required for SEM imaging, which tends to increase the mesh size, or from the inability of the MacKintosh model to accurately model the rheological behavior of PA gels. It is not clear why the HCl-PA gels have a higher stiffness than the CaCl2-PA gels at low PA concentrations, but it must reflect a difference in network structure that is not readily observed by microscopy. The HCl-PA gels may be composed of more flexible fiber bundles that can entangle more readily than the stiffer fibers present in the CaCl2-PA gels, resulting in a higher entanglement density in the HCl-PA gels. At low PA concentrations, the density of the fiber bundle entanglements may dominate the measured stiffness, while at higher PA concentrations the stiffness of the fiber bundles and the type of fiber entanglements may dictate the measured stiffness. It is instructive to compare the rheological properties of PA gels to other nanofiber networks. As mentioned previously, the

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The gelation, stiffness, and strain response of self-assembled fibrillar networks composed of peptide amphiphiles can be modified by changing the type of interactions between fibers. We find that the ionic bridges in CaCl2-PA gels form stronger intra- and interfiber cross-links than the hydrogen bonds in HCl-PA gels, so the CaCl2-PA gels can withstand higher strains than HCl-PA gels. However, after sustained deformation at 100% strain, hydrogen-bonded gels recover most of their stiffness, whereas ionically cross-linked networks, possibly hindered by calcium diffusion, are unable to recover. The ability to control how self-assembled nanofiber networks respond to deformation, without changing the molecules used, is a useful way to tailor their mechanics for biological response. Acknowledgment. This work was supported by the Department of Energy-Basic Energy Sciences (DE-FG02-00ER45810 and DE-FG02-08ER46539), the Northwestern University Materials Research Center (through the NSF MRSEC program DMR-0520513), and a Department of Homeland Security Fellowship (M.A.G.). This work made use of instruments in NUANCE (SEM), the Biological Imaging Facility (CPT Drying), the IMSERC (MS), and the Institute for BioNanotechnology in Medicine. The NUANCE Center is supported by NSF-NSEC, NSF-MRSEC, Keck Foundation, State of Illinois, and Northwestern University. We thank Prof. Wesley Burghardt and Dr. Liam Palmer for many helpful discussions. Supporting Information Available: Includes details on molecule purification, sample preparation, and supporting rheological and microscopy data. This material is available free of charge via the Internet at http://pubs.acs.org. (43) Ryan, E. A.; Mockros, L. F.; Weisel, J. W.; Lorand, L. Structural origins of fibrin clot rheology. Biophys. J. 1999, 77, (5), 2813-2826.

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