Dynamic Changes in Material Properties and Degradation of Poly

Sep 13, 2017 - Covalent adaptable hydrogels (CAHs) dynamically evolve when pushed out of equilibrium by force or change in environmental conditions. A...
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Dynamic Changes in Material Properties and Degradation of Poly(ethylene glycol)−Hydrazone Gels as a Function of pH Francisco Escobar, IV,† Kristi S. Anseth,‡ and Kelly M. Schultz*,† †

Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States Department of Chemical and Biological Engineering, the Biofrontiers Institute and Howard Hughes Medical Institute, University of Colorado at Boulder, Boulder, Colorado 80303, United States

‡

ABSTRACT: Covalent adaptable hydrogels (CAHs) dynamically evolve when pushed out of equilibrium by force or change in environmental conditions. Adapting these materials for advanced biological applications, including 3D cell culture and drug delivery platforms, requires in-depth knowledge of the evolution of scaffold microstructure and rheological properties. We use multiple particle tracking microrheology to measure the changes in a poly(ethylene glycol)−hydrazone CAH structure and properties when pushed out of equilibrium by a single change in pH. We determine the CAH degrades rapidly at acidic pH with multiple cycles of almost complete degradation and gelation. At pH 7.1, the scaffold degrades and re-forms cross-links over approximately 1.5 weeks with small oscillations between degradation and gelation. These degradation cycles are well described with first- and second-order reaction kinetics. MPT is sensitive enough to measure the phase transitions in these materials giving new insight into how CAHs evolve and their potential uses in biological applications.

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INTRODUCTION Covalent adaptable (CA) or dynamic covalent chemistries incorporated into hydrogel scaffolds have emerged as valuable cross-linking chemistries to recapitulate aspects of the native extracellular matrix in synthetic biomaterials.1−22 Covalent adaptable hydrogels (CAHs) are covalent networks at equilibrium; once pushed out of equilibrium the covalent bonds break, and when the material is allowed to relax they will re-form.1−7,15,21,23−26 This covalent adaptability enables the material to be remodeled without permanent mass loss or erosion. CA bonds are a result of several chemistries including Diels−Alder, oxime, and hydrazones.3,9,13,15,20,22,27−35 These unique materials have potential applications as platforms for 3D cell encapsulation,1,3−6,8,24,27,36−40 as drug delivery scaffolds,17−19,23 and as self-healing and environmentally adaptive materials.8,13,14,20,21,24,26,41−43As cell culture platforms, CAHs allow facile remodeling and degradation by encapsulated and invading cells during basic processes simply by cytoskeletal tension. As drug delivery platforms, CAHs can release active molecules and protect these molecules during remodeling and re-gelation. To use CAHs for these applications, changes in the structure and rheology of the material during dynamic evolution due to a push-out of equilibrium by their incubation environment must be well understood. Previous work by several groups that have developed CAHs has focused on measuring the change in bulk rheological properties during stress relaxation. In these experiments, the material is strained on a bulk rheometer, and the subsequent relaxation of the material is measured.3−6,8,10,16,21,22,42−44 The bulk evolution of CAHs has been well studied, but the changes © XXXX American Chemical Society

in the microstructure are still widely unknown. This microstructural evolution will greatly influence diffusion and release of active molecules out of this scaffold during drug delivery and cell−material interactions when used as an implantable scaffold. Several theories and simulations have begun to explain the microstructural evolution, but there have not been measurements.45,46 Our work uses multiple particle tracking microrheology (MPT) to characterize CAHs during phase transitions, focusing on the rheological and microstructural evolution as a result of a change in the material equilibrium. The CAH characterized in this work is a poly(ethylene glycol) (PEG)−hydrazone network. The scaffold consists of eight-arm PEG−hydrazine that self-assembles with eight-arm PEG−aldehyde to form covalent adaptable hydrazone bonds.3−5,12 This network is a stable covalent network at equilibrium, but when the equilibrium is shifted it breaks and re-forms hydrazone bonds. Equilibrium can be shifted by adding force, such as shear, to the scaffold, done by previous investigators.3−5,40 The equilibrium state can also be shifted by a change in the environmental conditions, such as a change in the incubation pH. In this work, we measure rheological properties and network structure of a PEG−hydrazone CAH using MPT after one change in the environmental pH. MPT is a passive microrheological technique that has several distinct advantages, making it ideal for measuring dynamically evolving CAHs. These advantages include measurement Received: June 12, 2017 Revised: August 22, 2017

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Macromolecules sensitivity in the low moduli range (10−3−4 Pa), rapid data acquisition enabling measurements of evolving materials at a quasi-steady state, and spatial visualization of the material microenvironment.47−55 This technique is passive relying only on thermal motion of embedded particles for each measurement, which is captured using video microscopy. Probe particle movement is related to rheological properties, such as creep compliance, by the Generalized Stokes−Einstein Relation (GSER). Using MPT, we determine the scaffold properties during phase transitions, including network structure and connectivity, as the CAH is pushed out of equilibrium quantifying the critical transitions in the scaffold. In this work, we use MPT to measure a PEG−hydrazone CAH when it is pushed out of equilibrium by a change in the incubation pH. Three different experimental procedures are explored: a CAH made at pH 4.3 and incubated at pH 4.3, a CAH made at pH 4.3 and incubated at pH 7.1, and a CAH made at pH 7.1 and incubated at pH 4.3. The incubation for all CAHs pushed the scaffold toward degradation or hydrolysis of the hydrazone bonds. All scaffolds incubated at pH 4.3, regardless of their pH when made, degraded over several hours. During this time, MPT measures cycles of degradation and regelation. These cycles include almost complete degradation of the scaffold with the material regelling after a new equilibrium state has been achieved on the stress relaxation time scale measured using bulk rheology. When incubated at pH 7.1, the scaffold degrades slowly with degradation and bond reformation occurring simultaneously throughout the entire degradation period of approximately 1.5 weeks. Each time bonds are re-formed in these scaffolds there is loss in scaffold connectivity. We use time-cure superposition to analyze MPT data pinpointing the critical relaxation exponent, n, which determines scaffold structure. When n is compared to MPT measurements, it also quantitatively determines the state of the scaffold, i.e., gel or sol. Additionally, MPT data are described using first- and second-order reaction kinetic models. The data are fit with these models, and the reaction kinetic constants agree well with previously published values.3−5 The results of this work describe the structure and rheological changes of a PEG−hydrazone CAH undergoing hydrazone hydrolysis due to a change in pH. These results will enable precise design of this scaffold for applications ranging from 3D cell culture to implantable sustained drug delivery platforms.

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Again 1H NMR determines the functionality of the PEG−aldehyde molecules.3−5 PEG−aldehyde and PEG−hydrazine self-assemble to form PEG− hydrazone hydrogel scaffolds. All hydrogels are made at a stoichiometric ratio of 1 aldehyde:1 hydrazine. 1 μm fluorescently labeled probe particles (2a = 1.0 ± 0.02 μm where a is particle radius, Polysciences, Inc.) are added to the gel precursor solution to enable multiple particle tracking microrheology measurements. These particles are washed three times by centrifugation and resuspension to remove any unreacted additives prior to addition to the gel precursor solution. The gel composition used for scaffold degradation experiments is 4.4 wt % PEG-aldehyde, 4.4 wt % PEG-hydrazine, and 0.04% solids/volume of probe particles. The buffered saline used to make CAHs is either acidic, pH 4.3, or physiological, pH 7.1. The acidic buffer consists of 70 mM acetic acid and 30 mM sodium acetate. The physiological buffer consists of 77 mM disodium phosphate and 23 mM hydrochloric acid. The pH of both buffers is checked using a pH meter and adjusted accordingly using hydrochloric acid or sodium hydroxide. Acidic CAHs will refer to scaffolds made with pH 4.3 buffer and physiological CAHs will refer to scaffold made with pH 7.1 buffer. Sample chamber are made out of glass-bottomed Petri dishes (D = 35 mm, no. 1.5 glass coverslip, MatTek Corp.). The sample chamber is made of a tube of cured polydimethylsiloxane (PDMS, Dow Corning, O.D. 10 mm and I.D. 6 mm). The PDMS is chemically attached to the glass using uncured PDMS and curing the entire chamber overnight at 60 °C. This chamber is essential for MPT measurements, since it limits the movement of the hydrogel, and therefore directed motion of probe particles, when it is incubated in buffer solution to cause degradation.56,57 Additionally, the coverslip on the bottom of the Petri dish is functionalized with 3-aminopropyltriethoxysilane (SigmaAldrich Co. LLC) to chemically attach the hydrogel to the glass surface further limiting movement of the CAH during degradation. Degradation of CAHs were done by incubation in buffer solution. A large sink of solution is used to ensure that the CAH is maintained at the degradation pH throughout the experiment. The CAH is 17 μL, and 4 mL of buffer is added for incubation. The time of diffusion of the new buffer solution into the CAH is calculated using the relation tD ∼ L2/D, where L is the height of the CAH (600 μm for our gels) and D is the diffusion of salt ions into the material.56,58 Estimating these values, we determine that the time for diffusion of ions into the scaffold would be on the order of hundredths of seconds and the time of CAH degradation ranges from hours to days. Therefore, when CAH degradation begins, the gel is at the pH of the buffer solution. Multiple Particle Tracking Microrheology. Data of CAH degradation are taken using multiple particle tracking microrheology (MPT). In MPT, probe particles are embedded into the material prior to gelation. Once the CAH is formed, these particles are suspended throughout the network. A low concentration of particles is used. At this concentration the formation of the CAH is not disrupted by the presence of the particles; this has been measured in other selfassembling gel systems.59−61 Additionally, the particle surface chemistry (carboxylated surface) ensures these particles do not interact with the polymers enabling measurement of particles undergoing purely Brownian motion.47−55 Data are collected on an inverted fluorescent microscope (Zeiss Observer Z1, Carl Zeiss AG) using video microscopy. 1 μm probe particles (2a = 1.0 ± 0.02 μm, carboxylated surface, Polysciences, Inc.) are magnified 63× using a low numerical aperture water immersion objective (N.A. 1.3, 1 × optovar, Carl Zeiss AG). Videos of embedded particle Brownian motion are captured at a frame rate of 30 frames/s and an exposure time of 1000 μs (Phantom Miro M120, 1024 × 1024 pixels, Vision Research Inc.) to minimize static and dynamic particle tracking errors.51 The brightness-weighted centroid of each particle is tracked, and positions are linked into trajectories using classical tracking algorithms.52−55,62 After tracking, the mean-squared displacement (MSD, ⟨Δr2(τ)⟩) of the probe particles is calculated using ⟨Δr2(τ)⟩ = ⟨Δx2(τ)⟩ + ⟨Δy2(τ)⟩, where τ is the lag time and x and y are coordinates in the 2D plane. Rheological properties, such as the creep compliance J(τ), can be

EXPERIMENTAL SECTION

Covalent Adaptable Hydrogel Scaffold and Sample Preparation. The covalent adaptable hydrogel scaffold consists of poly(ethylene glycol) molecules (8-arm, Mn 10 000 g mol−1) endfunctionalized with hydrazine and aldehyde. The materials were synthesized in the Anseth laboratory using previously published protocols.3−5 Briefly, the PEG−hydrazine is made by first activating tri-Boc-hydrazinoacetic acid with HATU and N-methylmorpholine. This activated molecule is reacted with PEG-amine overnight and then precipitated in cold diethyl ether. The solution is treated for 4 h in 50:50 dicholoromethane (DCM):trifluoroacetic acid and precipitated again in ether. The material is dissolved in deionized (DI) water and dialyzed for 24 h against DI water and lyophilized. Functionality of the molecule is determined by 1H NMR. The PEG−aldehyde molecules are functionalized using a Swern oxidation.3−5,31,32,34 Oxalyl chloride is dissolved in DCM and cooled. Dimethyl sulfoxide diluted 1:5 in anhydrous DCM is added and allowed to react. PEG−hydroxide (PEG-OH) is also dissolved in anhydrous DCM and added to the oxalyl chloride solution and reacted for 2 h. Triethlyamine is then added and reacted for 20 min. The solution is warmed to room temperature and precipitated and dialyzed as previously described. B

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tion.1,3−5,17,28−30,45,46 During degradation, both of these reactions are occurring, but the hydrazone hydrolysis reaction is the dominant reaction. To degrade this scaffold, previous work stressed the network, causing complete material degradation, and measured bond re-formation during stress relaxation.3−6,8,10,16,21,22,42−44 A parallel experiment is to change the environmental pH, which pushes the scaffold out of equilibrium, causing a reaction that is dominated by bond degradation but includes scaffold remodeling and bond reformation. Experiments where the pH is changed mimic the traditional stress relaxation experiments done on a bulk rheometer. The change in the pH is the “strain” applied to the network. A schematic of the change in the network due to imposed stress and change in incubation pH is shown in Figure 1. Figure 1 illustrates first the covalent network structure at equilibrium, the breakage of bonds during stress, and the bond re-formation after the material relaxes.

calculated from the MSD using the Generalized Stokes−Einstein Relation ⟨Δr 2(τ )⟩ =

kBT J(τ ) πa

(1)

where kBT is the thermal energy and a is the particle radius. Not only can rheological properties be calculated from the measured MSD, the state of the material can also be determined from the logarithmic slope of the MSD, α =

d log⟨r 2(τ )⟩ . d log τ

When α = 1, probe particles are

undergoing Brownian motion and the material is a fluid. α → 0 indicates that the particles are completely arrested in the gel network. 1 μm probe particles become arrested in the gel network at 1−4 Pa; therefore, to obtain equilibrium moduli data, bulk rheology is used to supplement microrheological measurements. Additionally, the gel−sol transition is determined using time-cure superposition, which will be discussed in-depth in the Results and Discussion section, and the resulting critical relaxation exponent n. Data of CAH degradation are collected through time. For degradation at acidic pH conditions, CAH degradation occurs over several hours. Data are collected every 2−3 min throughout degradation, starting when the incubation buffer is added to the CAH and ending approximately 30 min after complete degradation of the sample is measured. In these experiments, due to the short time scale of degradation, there is no buffer exchange. Samples are degraded in the initial incubation buffer added to start degradation. CAH degradation in physiological buffer occurs over approximately 1.5 weeks. Data are collected every several hours over the course of scaffold degradation. During these experiments samples are maintained at room temperature, and buffer is exchanged during the experimental time period. It should be noted that the exchange of buffer does not coincide with bond re-formation or degradation in the scaffold. Because of the time for complete degradation, at acidic pH several hours and physiological pH several days, the data collection window, 30 s, is assumed to be at a quasi-steady state. Care is taken to collect data spatially across the hydrogel scaffold. Data are collected in the middle and on each side of the scaffold to determine macroscopic homogeneity of degradation within the material. Because of the sensitivity of MPT and mechanism of hydrogel evolution, data collected during degradation are inherently noisier than gelation measurements. Additional noise is measured when particles are completely arrested in the matrix due to building vibrations that are not canceled by the vibration isolation table.

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RESULTS AND DISCUSSION CAH degradation is measured as a function of incubation buffer pH. In this work, we focus on changes in the scaffold rheological properties as it undergoes dynamic transitions from a gel to a sol. Because of the adaptability of the CAH crosslinks, the changes in the rheology are unique. MPT measurements characterize the scaffold during degradation in acidic pH buffer of an acidic CAH and a physiological CAH which occurs over several hours. Similarly, MPT experiments also measure the degradation in physiological buffer of an acidic CAH. These measurements characterize the rheological properties of the scaffold, capturing the degradation and reformation of bonds as the material is pushed out of equilibrium. Understanding the evolving structure and rheological properties is crucial in determining the suitability of the material for biological application, such as matrices for sustained drug delivery and 3D cell culture. CAH Degradation. Hydrazone formation is acid-catalyzed, but gelation of the CAH is rapid at any pH. CAHs form with a maximum rate of gelation at physiological pH.3−5 During hydrazone formation, a reversible second-order reaction occurs. This second-order reaction is the forward hydrazone formation reaction and the backward hydrazone hydrolysis reac-

Figure 1. Covalent adaptable hydrogel. Schematic of CAH at equilibrium (top), pushed out of equilibrium (middle) and after relaxation (bottom). The red box highlights bonds breaking and reforming with different functional ends.

Degradation data for acidic and physiological CAH scaffolds are shown in Figure 2a−c. Figures 2a and 2b are the measured mean-squared displacement and logarithmic slope of the MSD, α, for an acidic CAH degraded in an acidic pH buffer degrading through time. The degradation reaction in acidic pH buffer is independent of the gelation pH, with all samples having similar C

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network cluster is degraded several times prior to final hydrolytic degradation of the scaffold. Previous work by McKinnon et al. measured rapid rates of hydrazone hydrolysis in acidic buffers. The rapid hydrazone hydrolysis corresponds to an increase in stress relaxation in the scaffold.3−5 Our measurements agree with these findings, measuring faster degradation rates in acidic buffer. During our experiments, even though hydrazone hydrolysis is the dominant reaction there is always some bond re-formation. Once the network has broken the scaffold reaches a new equilibrium state and is able to relax the stress and re-form bonds, causing rapid gelation. The time scale of gelation in these experiments and stress relaxation in the previous work is the same3−5 (Table 1). Stress relaxation is reported to take Table 1. Bulk Rheological Data for CAH Degradation and Stress Relaxation from McKinnon et al.3−5 a incubation pH

k−1 (min−1)

trelax (s)

4.2 7.3

0.86* 0.02

300 190

a k−1 is the kinetic constant for hydrazone hydrolysis. The value for pH 4.2 is found using linear extrapolation and is not a measurement (indicated by ∗). trelax is the time for complete stress relaxation defined as the time for the modulus to completely recover during bulk rheological measurements of stress relaxation.

approximately 5 min at a pH of 4.2.3−5 Microrheological measurements of gelation indicate that the material goes through the sol−gel reaction on a similar time scale measured for stress relaxation, 5−10 min. Therefore, when the scaffold reaches a new equilibrium state, it can relax the stress due to the change in environmental pH and re-form hydrazone bonds and gel. Figure 2c is the logarithmic slopes of the MSD for an acidic gel degraded in a physiological buffer. It should be noted that this degradation reaction requires a change in pH; the scaffold made at pH 7.1 and incubated at pH 7.1 did not degrade. This degradation reaction has very different rheological properties and time scale. This scaffold undergoes complete degradation over approximately 1.5 weeks. The degradation reaction is characterized by an initial burst of cross-link degradation over ∼2 × 103 min (1.5 days). At this time point, the hydrazone bonds begin to break and re-form oscillating around the gel− sol transition at n = 0.66 ± 0.08 with α between 0.6 and 0.8. This indicates that this scaffold is changing between a sample spanning scaffold structure and large cross-linked polymer structures that do not form a network. During these oscillations, the minimum value of α does increase with time, indicative of fewer bonds re-forming after each degradation event. Finally, the PEG molecules undergo hydrolysis and the scaffold irreversibly degrades at 14.3 × 103 min (10 days). The rate of hydrolysis and stress relaxation is much slower at physiological pH according to McKinnon et al.3−5 This agrees with microrheological measurements that determine the transition from a gel to a sol first occurs at 50 h (3000 min). The push out of equilibrium for these gels takes an unstable gel made at an acidic pH and puts it in an environment where the hydrazone bonds become stable. Hydrazone hydrolysis and formation are occurring at this pH, with much smaller changes in scaffold connectivity as compared to degradation in acidic pH. The scaffold does not degrade far past the gel−sol transition and then re-forms bonds, as measured in acidic

Figure 2. MPT measurements of CAH. (a) Measured mean-squared displacement of CAH during acidic degradation. Color represents the time data are collected. Logarithmic slope of the MSD during (b) acidic and (c) physiological degradation. The gel−sol and sol−gel transitions are determined when these values are compared to the critical relaxation exponent, n, which is the dotted line.

time scales and rheological properties during degradation. This is due to the covalent adaptable scaffold reaction, which is a proton exchange reaction.3−5,30 With the excess of protons in the acidic buffer, the equilibrium is pushed toward the backward reaction with faster and more complete degradation occurring. α values change from a value of 0 to 0.8. These scaffolds undergo almost complete degradation before a new equilibrium state is achieved, and the forward reaction dominates, causing the material to re-gel. These cycles are repeated at least twice in each scaffold before complete degradation. Figure 2b shows three cycles of degradation and gelation before complete scaffold degradation. During the cyclic degradation reactions, the probe particles do not start to freely diffuse, α ≠ 1, which would indicate complete degradation of the material resulting in a solution of polymers in water. Instead, there is still a structure of cross-linked polymers, α < 1, but the sample spanning hydrogel network has been degraded. Additionally, in Figure 2b the critical relaxation exponent, n, is the dotted line. The value of n is determined using time-cure superposition and will be discussed in detail in the following section. n is the value where the material transitions from a viscoelastic fluid to a viscoelastic gel, defined as the first sample spanning network cluster. A value of α > n is a sol and α < n is a gel.49,57,60,63−71 For CAHs degraded in acidic buffer, the material critical relaxation exponent is n = 0.47 ± 0.06. In Figure 2b, the scaffold degrades with values of α above the critical relaxation exponent, indicating that the sample spanning D

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Macromolecules degradation. Instead, the scaffold breaks bonds through hydrolysis which are quickly re-formed once the forward react dominates. This change in equilibrium is much more subtle, indicating that the material is closer to chemical equilibrium at physiological pH. During degradation, the backward hydrolysis reaction does dominate, and after 50 h the material oscillates around the gel−sol transition until complete degradation. Time-Cure Superposition. Time-cure superposition (TCS) determines the critical values of the scaffold, which are properties unique to each degradation reaction. Most notably the critical relaxation exponent, n, is determined.49,60,63−71 As mentioned previously, this value quantitatively determines whether the material is in a gel or a sol. n also indicates how much elastic energy is stored or dissipated in the scaffold. If n > 0.5, the scaffold dissipates energy and has a loosely cross-linked network structure. If n < 0.5, the scaffold stores energy indicative of a tightly cross-linked hydrogel scaffold.49,57,60,63−71 Time-cure superposition is an analysis technique much like time−temperature superposition, but this technique superimposes viscoelastic functions at different extents of reaction.60,63−67 TCS is used to analyze data for acidic and physiological degradation (Figures 3 and 4). In this technique, gel and sol master curves are made by shifting on the time lag, τ, and mean-squared displacement, ⟨r2(τ)⟩, axes using shift factors a and b, respectively. This is illustrated for acidic degradation in Figure 3a. These shift factors diverge at the critical degradation time, tc, defined as the time when the last sample spanning network structure degrades (Figure 3b). This is the divergence of the elastic moduli in the gel and viscosity in the sol.60,63−68 Shifting on the time lag axis shifts the longest relaxation time, τL, of the polymers in the sol and network in the gel using the relation a ∼ τL−1 ∼

y

( ) , where t is time, |t − tc| tc

tc is the critical degradation time, and y is a scaling exponent. Shifting on the MSD axis is done by shifting the material dynamics related to the steady state creep compliance, Je, with the relation b ∼ Je−1 ∼ 49,57,60,63−71

( ), |t − tc| tc

Figure 3. TCS during acidic degradation. (a) Measured MSDs shifted into sol and gel master curves. (b) Shift factors diverge at the critical degradation time, tc. Critical scaling exponents (c) y and (d) z are used to determine the critical relaxation exponent, n.

z

where z is a scaling

exponent. Figures 3c and 3d determine the values of y and z for pre- and postgel shift factors for each cycle of degradation. The ratio of the scaling exponent is the critical z relaxation exponent, n = y . Values of n are reported with errors

degradation times are determined, tc,1 = 158 min, tc,2 = 350 min, and tc,3 = 494 min. Figures 3c and 3d determine y and z, resulting in five values of n. Generally, TCS would result in six values of each scaling exponent, a sol and gel value for each degradation. The final degradation of this material resulted in only one gel point inhibiting the determination of the scaling exponents and the critical relaxation exponent. The average critical relaxation exponent for this experiment is 0.47 ± 0.06. For all five CAHs degraded in acidic conditions navg = 0.48 ± 0.11 with a standard deviation of 0.14 with each scaffold undergoing at least two cycles of degradation. Degradation of an acidic CAH degraded in physiological buffer is also analyzed using TCS (Figures 4a−d). This degradation reaction only undergoes one cycle of degradation oscillating around the gel−sol transition during hydrazone hydrolysis. Gel and sol master curves (Figure 4b) are constructed from the MSD data in Figure 4a. The oscillations in scaffold connectivity are evident in the shift factors (Figure 4c). The critical degradation time and critical relaxation exponent for this scaffold degraded at physiological pH are tc = 4452 min and n = 0.66 ± 0.08. For all four scaffolds degraded

calculated from the propagation of error from fits of the logarithm of shift factors a and b versus the logarithm of the |t − tc| . The standard distance away from the critical gel time, tc

deviation is also reported to show the range of n values obtained from multiple experiments. Figures 3a−d are TCS of an acidic CAH degraded in acidic buffer. Physiological CAHs degraded in acidic buffer yield the same results. Therefore, the critical values determined for CAH degradation are dependent on the pH of the degradation buffer. When degraded in acidic buffer, the CAH undergoes cycles of degradation and gelation (Figure 2b), which are characterized by almost complete degradation of the scaffold and then network re-gelation. The longest relaxation times and creep compliances do not change between cycles, enabling the creation of one sol and one gel master curve for the entire degradation of the material. For the hydrogel in Figures 3a−d, there are three degradation reactions. In Figure 3b, three critical E

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important for determining whether these materials can be used for specific applications, such as scaffolds for wound healing and tissue regeneration. If implanted, cells from the surrounding tissue will encounter this structure when they invade the material to begin wound healing. Cells remodel their microenvironment and will constantly remodel this material by imposing tension on the scaffold during basic cellular processes. The cells will then degrade the scaffold to regrow native tissue. Kinetic Modeling of Degradation. The degradation of these scaffolds is modeled using first- and second-order kinetic models (Figure 5). These models describe the change in

Figure 5. First- and second-order kinetic models describe the change in modulus during degradation of CAH scaffolds at (a) pH 4.3 and (b) pH 7.1.

Figure 4. Time-cure superposition during physiological degradation. (a) Measured MSD are (b) shifted into sol and gel master curves. (c) Divergence of shift factors occurs at the critical degradation time, tc. (d) The critical scaling exponents y and z are determined. The ratio of these values determines the critical relaxation exponent, n.

modulus over time. Gelation of CAHs was previously modeled using second-order kinetics, accounting for the formation and rearrangement of hydrazone bonds.3−5 During degradation, the scaffold is pushed out of equilibrium, and the hydrazone hydrolysis generally dominates the change in scaffold material properties. To model these materials, we must first determine the change in the scaffold modulus, Ge. The modulus during degradation is determined from TCS using the relation b ∝ Je−1 ∝ Ge for the material in the gel state.63−69 For microrheological measurements, the shift factors are converted into equilibrium modulus because the upper limit of shifting (b = 1) is the same as the upper measurable limit of the moduli. The modulus of the material is directly related to the cross-link density, ρ, using Ge ∼ ρkBT. The modulus is a measure of the decrease in crosslink density through time. Degradation in the final cycle in acidic pH and physiological pH is modeled using first-order kinetics, dρ/dt = −k1ρ where t is time and k1 is the reaction rate constant.56,69,75,76 The resulting equation is ρ = ρ0e−k1t, where ρ0 is the initial cross-link density. This results in a final expression that describes scaffold degradation

at physiological pH the value of navg = 0.86 ± 0.04 with a standard deviation of 0.15. This value of n is much higher than the value for degradation in acidic pH. These n values are indicative of the structure of the material as it is degrading.49,57,60,63−71 The scaffold structure when degraded at acidic pH is a network that resembles a percolated network due to the value of n ≈ 0.5.60,63−68 In acidic pH, the scaffold degrades continuously due to the large push-out of equilibrium before gelation. This continuous degradation will follow a percolation path without much bond formation until a new equilibrium is reached and the scaffold re-gels. The rheological properties during degradation are similar to scaffolds that irreversibly degrade.56,69,72−74 In physiological pH buffer the scaffold has an open porous structure, n > 0.5. At physiological pH, the scaffold is closer to equilibrium, and degradation and bond formation are occurring simultaneously, with hydrazone hydrolysis dominating. Because of this, the scaffold can rearrange during degradation leading to a longer time to the phase transition and an open structure at the gel− sol transition. Understanding the structure of the CAH is F

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Macromolecules G(t ) = Ge,0e

−k1t

⎛ e−k1t − e−k1tc ⎞ z ⎟ ⎜ ⎝ 1 − e−k1tc ⎠

deviation of 9.0 × 10−5, indicating that hydrazone hydrolysis is the dominant reaction. In McKinnon et al., hydrazone hydrolysis is characterized by small molecule experiments that measure hydrazone formation by absorbance. They did not measure degradation at pH 4.3 but found a linear relationship between pH and log k−1. The extrapolated value for pH 4.3 is k−1 = 0.76 min−1 (Table 1).3−5 The value determined from this degradation using MPT is the same order of magnitude, k−1 = 0.16 ± 0.02 min−1, in agreement with the previous work. Since the experiments used to obtain these values are small molecule experiments, this is further confirmation that the change in pH is degrading bonds and changing the scaffold structure. MPT characterizes this structure and the rheological properties of the material as it undergoes dynamic transitions. Degradation in physiological pH buffer occurs over a much longer time scale and follows the weighted first-order reaction kinetics (eq 3) and shown in Figure 5b. Even though this reaction is slower, there is a similar shift of equilibrium toward degradation, with hysteresis in each bond formation event. The first points in Figure 5b are not fit with this model. These values are above the upper measurable limit of MPT and are not accurate measurements of the CAH equilibrium modulus. The reaction constants for gelation and degradation are k1 = 2.6 × 10−9 ± 9.3 × 10−8 min−1 with a standard deviation of 4.0 × 10−9 min−1 and k−1 = 0.003 ± 1.8 × 10−5 min−1 with a standard deviation of 0.003 min−1, respectively. The weight factor is x = 1.3 × 10−5 ± 5.1 × 10−12 with a standard deviation of 9.3 × 10−6. In comparison to values measured by McKinnon et al. of small molecule experiments at pH 7.1, the hydrazone degradation constant is k−1 = 0.03 min−1 (Table 1).3−5 There is an order of magnitude difference in these values, but this difference can be explained by the difference in the experiments. The values in Table 1 are absorbance measurements from small molecule experiments. The previous work measured the formation of hydrazone bonds between hydrazine and aliphatic aldehyde molecules. These functional groups were not measured when they were attached to polymers or as part of the hydrogel scaffold. McKinnon et al. also found disagreement between reaction constants measured with the small molecule experiments and bulk rheology.3−5 With microrheology, we find closer agreement between our reaction constants and those in Table 1 and believe the error is due to the difference in the molecules and structure of the materials being measured. In addition to our modeling work, dynamics of materials with reversible bonds have been explained using sticky reptation theory and molecular dynamic simulations.45,46 In sticky reptation theory, the polymers are functionalized with bonds that act as stickers, which are indistinguishable from reversible bonds. These stickers are at fixed positions on the polymers and can change between open (unbonded) or closed (bonded). Sticky reptation theory describes the change in modulus as a function of time as the scaffold degrades. The schematic representation of the change in modulus with time is modified from Leibler et al. and shown in Figure 6a. Figure 6b shows degradation of the CAH at physiological pH. In sticky reptation theory the modulus initially has a dramatic decrease with time, when the time is less than the Rouse time of an entanglement strand, τe. During this period, the relaxation is indistinguishable from the polymer relaxation without stickers.45,46 Next, a moduli plateau occurs, G1, between τe and the lifetime of a sticker, τ (Figure 6a). These changes in modulus are not captured with MPT measurements due to the upper

(2)

where tc and z are determined from TCS and the initial equilibrium modulus of the gel, Ge,0, has been previously measured by McKinnon et al.3−5,69 Additionally, during final CAH hydrolysis at acidic pH and hydrolysis at physiological pH, there is a 2-fold reaction of hydrazone hydrolysis and bond rearrangement. During this mechanism, the reaction equilibrium is strongly shifted toward hydrolysis but does have some bond formation during the initial degradation time. This is accounted for in the model by a weighted addition of the two reactions. The resulting equation is G(t ) = xGe,0e

−k1t

⎛ e−k1t − e−k1tc ⎞ z ⎟ + (1 − x)Ge,0e−k−1t ⎜ ⎝ 1 − e−k1tc ⎠

⎛ e−k−1t − e−k−1tc ⎞ z ⎟ ×⎜ ⎝ 1 − e−k−1tc ⎠

(3)

where x is the weighting factor, k1 is the bond formation reaction constant, and k−1 is the hydrolysis reaction constant. Values of k1, k−1, and x are reported with errors calculated from the propagation of error from model fits to the data. The standard deviation is also reported to show the range of k1, k−1, and x values obtained from multiple experiments. The second-order reaction best describes the first cycle of degradation for scaffolds undergoing acidic degradation. Here, the equilibrium is shifted toward degradation but not as strongly as during final hydrolysis, resulting in simultaneous bond degradation and formation. For the second-order reaction, the equation is dρ/dt = −k2ρ2, where k2 is the second-order rate constant. This equation results in an 1 1 expression for the cross-link density of ρ − ρ = −k 2t . The 0

model equation for this reaction is ⎛ 1 + G e−k 2t k t ⎞ z e,0 2c ⎜ ⎟ G (t ) = ⎜ ⎟ 1 + Ge,0k 2t ⎝ tc − t ⎠ Ge,0

(4)

This reaction has immediate bond degradation due to hydrolysis and as time continues the equilibrium shifts to both formation and degradation occurring on the same time scale, evident in the leveling off of the cross-link density. Degradation of CAHs in acidic pH buffer occurs over at least two cycles (Figure 5a). The first cycle has second-order kinetics as described by eq 4. These kinetics describe the simultaneous gelation and degradation of hydrazone bonds. This description is parallel to the gelation reaction described in previous work.3−5 The reaction constant for fitting several experiments is k2 = 0.08 ± 0.003 min−1 with a standard deviation of 0.09 min−1. The final degradation cycle at acidic conditions is well described by two weighted first-order reactions (eq 3). This equation describes the scaffold once it is pushed far out of equilibrium, with one reaction dominating. In this work, there is a small amount of cross-links forming, but the reaction equilibrium is pushed toward hydrazone hydrolysis. The reaction constant over several experiments for gelation is k1 = 8.0 × 10−4 ± 9.0 × 10−4 min−1 with a standard deviation of 0.002 min−1. For degradation, k−1 = 0.16 ± 0.02 min−1 with a standard deviation of 0.11 min−1. The weighting factor for these experiments is x = 6.8 × 10−5 ± 2.9 × 10−5 with a standard G

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cycle. During these cycles, there is hysteresis in the bond formation, leading to complete degradation of the scaffold over the period of 1.5 weeks. Using time-cure superposition, we determine that the critical relaxation exponent is dependent on the pH of the incubation buffer. At acidic pH the scaffold has a value of navg = 0.48 ± 0.11 with a standard deviation of 0.14, indicative of a tightly cross-linked material that stores energy. In contrast, during physiological degradation the scaffold has an navg value of 0.86 ± 0.04 with a standard deviation of 0.15, which indicates a loosely cross-linked network that dissipates energy. Because of the unique chemistry, the degradation mechanism of this scaffold is dependent on the incubation buffer pH, which determines how far the scaffold is pushed out of equilibrium. When the scaffold is pushed far out of equilibrium at pH 4.3, the material cannot easily rearrange, resulting in the scaffold remaining a tightly cross-linked network. At pH 7.1, the scaffold actively degrades and rearranges the network structure enabling a sample spanning network to remain with an open structure. To better understand the cycles of degradation, we derive simple models to explain the mechanism. In acidic degradation the first degradation cycle is modeled by second-order reaction kinetics. This describes simultaneous hydrolysis and gelation of the scaffold. For the final cycle, two weighted first-order reactions model the change in equilibrium modulus. This describes the scaffold pushed far out of equilibrium, toward degradation. The first-order reaction constant of hydrazone hydrolysis measured in this work agrees with previously reported values. Physiological degradation is also well described by two weighted first-order reactions. The hydrazone hydrolysis reaction constant is an order of magnitude smaller than previously measured due to the difference in molecules measured in these experiments. These microrheological measurements enable us to understand the mechanism and scaffold structure during degradation. In all, this CAH undergoes several degradation cycles due to one change in stimuli or push-out of equilibrium. Understanding and controlling these cycles of bond breakage and reformation will lead to the design and implementation of these materials in applications broadly ranging from cell culture platforms to sustained drug delivery. These novel, inherent mechanisms will lead to advances in sustained release and create unique environments that foster and manipulate basic cellular processes.

Figure 6. (a) Schematic of change in modulus versus time predicted by sticky reptation theory. Figure modified from Leibler et al.46 (b) CAH degraded at physiological conditions. The dotted and solid line are the weighted first-order model used to describe MPT data. The MPT data and model capture the change in modulus predicted by sticky reptation theory after the second moduli plateau, G2.

measurable moduli limit. In Figure 6a, a second moduli plateau occurs between τ and Td, the terminal relaxation time.45,46 The second modulus plateau, G2, is the modulus of the linear chain system without stickers. This plateau is measured by MPT for each cycle of degradation (Figure 6b). When time is greater than Td, the moduli goes to 0 and the gel−sol transition occurs.45,46 MPT measurements are well described by sticky reptation theory. Because of the measurable moduli limits, MPT measures the second moduli plateau and divergence of the moduli at the phase transition. Additionally, the weighted first-order reaction model agrees well with the change in moduli predicted by this theory after the second moduli plateau (t > τ). Therefore, MPT captures CAH degradation and scaffold relaxation of the weak incipient gel during the gel−sol transition.

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CONCLUSIONS The dynamic evolution of the microstructure and rheological properties of CAHs is complex. Building a comprehensive understanding of this process will enable design of these materials in biomedical applications ranging from 3D cell culture platforms to drug delivery materials. This information can enhance the design of well-defined scaffold architectures that manipulate and control cellular processes through environmental cues or sustainably release and protection of drugs within the scaffold. Using passive microrheological characterization, we measure the degradation of CAHs in acidic and physiological pH conditions. During degradation in acidic buffer, we measure cycles of degradation and gelation prior to complete degradation of the scaffold. Complete degradation occurs over a time period of several hours. Gelation occurs over 5−10 min, the same time measured in previous experiments for stress relaxation in this pH buffer. In physiological buffer, there are degradation and gelation events with a smaller extent of bond breakage and re-formation in each

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph (610) 758-2012; Fax (610) 758-5057. ORCID

Kelly M. Schultz: 0000-0001-9040-126X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding for this work was provided by the American Chemical Society Petroleum Research Fund (54462-DNI7, K.M.S.) and the National Science Foundation (CTS 1236662, K.S.A.). Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. The authors acknowledge helpful discussions H

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with Tobin Brown, Dr. Dylan Domaille, Dr. Eric M. Furst, Dr. Daniel D. McKinnon, and Benjamin Richardson.

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