DielsâAlder Hydrogels for Controlled Antibody Release: Correlation

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Diels-Alder hydrogels for controlled antibody release: Correlation between mesh size and release rate Susanne Kirchhof, Michela Abrami, Viktoria Messmann, Nadine Hammer, Achim M. Goepferich, Mario Grassi, and Ferdinand P. Brandl Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/acs.molpharmaceut.5b00375 • Publication Date (Web): 12 Aug 2015 Downloaded from http://pubs.acs.org on August 18, 2015

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Molecular Pharmaceutics

Diels-Alder hydrogels for controlled antibody release: Correlation between mesh size and release rate

Susanne Kirchhof1, Michela Abrami2, Viktoria Messmann1, Nadine Hammer1, Achim M.

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Goepferich1, Mario Grassi3, and Ferdinand P. Brandl1,*

1

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Department of Pharmaceutical Technology, Faculty of Chemistry and Pharmacy, University

of Regensburg, 93040 Regensburg, Germany 2

Department of Life Sciences, University of Trieste, Cattinara Hospital, Strada di Fiume 447,

34127 Trieste, Italy 3

Department of Engineering and Architecture, University of Trieste, Piazzale Europa 1,

34127 Trieste, Italy 15

Submitted to: Molecular Pharmaceutics

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* Corresponding author. Phone: +49 941 943-4920; fax: +49 941 943-4807. E-mail address: [email protected] (Ferdinand P. Brandl)

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Abstract Eight-armed PEG, molecular mass 10 kDa was functionalized with furyl and maleimide groups, respectively; the obtained macromonomers were cross-linked via Diels-Alder chemistry. The mesh size (ξ) of the prepared hydrogels was determined by swelling studies, 5

rheology and low field NMR spectroscopy. The in vitro release of fluorescein isothiocyanate labeled dextrans (FDs) and bevacizumab was investigated. The average mesh size (ξavg) increased from 5.8 ± 0.1 nm to 56 ± 13 nm during degradation, as determined by swelling studies. The result of the rheological measurements (8.0 nm) matched the initial value of ξavg. Low field NMR spectroscopy enabled the determination of the mesh size distribution; the

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most abundant mesh size was found to be 9.2 nm. In combination with the hydrodynamic radius of the molecule (Rh), the time-dependent increase of ξavg was used to predict the release profiles of incorporated FDs applying an obstruction-scaling model. The predicted release profiles matched the experimentally determined release profiles when Rh < ξavg. However, significant deviations from the theoretical predictions were observed when Rh ≥ ξavg, most

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likely due to the statistical distribution of ξ in real polymer networks. The release profile of bevacizumab differed from those of equivalently sized FDs. The delayed release of bevacizumab was most likely a result of the globular structure and rigidity of the protein. The observed correlation between ξ and the release rate could facilitate the design of controlled release systems for antibodies.

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Keywords: Diels-Alder; hydrogel; mesh size; controlled release; antibody



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Introduction Controlled release technology has the potential to improve the safety and efficacy of antibody-based therapies. For example, controlled release systems can improve the local bioavailability of antibodies, maintain effective antibody concentrations over extended periods 5

of time, lower the required antibody dose, and reduce systemic side effects.1 Compared to other dosage forms, such as implants or microspheres, hydrogels may offer several advantages. For example, the high water content of hydrogels is extremely suitable to accommodate high loads of hydrophilic antibodies. Furthermore, hydrogels are capable of preserving the bioactivity of antibodies, since protein denaturing conditions (i.e., the use of organic solvents

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and/or high shear forces) are usually avoided during the fabrication process. The mobility of physically entrapped antibodies is limited by the polymer network; the hydrogel forms a reservoir from which the antibody is released in a controlled manner. Depending on the size of the incorporated antibody and the cross-linking density of the hydrogel, the release will be controlled by diffusion, swelling, degradation, or a combination of these mechanisms.2,3

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An important parameter that characterizes the permeability of hydrogels is the mesh size or correlation length, ξ. The mesh size depends on the polymer concentration and is defined as “the average distance between consecutive cross-links”;4 it indicates the maximum size of solutes that can pass through the gel network. Besides the diffusivity of solutes, the mesh size determines the mechanical strength and degradability of hydrogels. In combination with the

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size of the entrapped molecule, knowledge of ξ allows to estimate the rate of drug release from hydrogels. Based on Flory’s theory of rubber elasticity, information about the average mesh size of swollen, cross-linked hydrogels can be derived from the elastic modulus or the equilibrium polymer volume fraction.4,5 While ideal networks are adequately described by the average mesh size, most real hydrogels are characterized by a broad range of mesh sizes that

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affect the release rate of entrapped drugs. The morphology and network density of hydrogels can be visualized by optical methods such as cryogenic transmission electron microscopy; 4 Environment ACS Paragon Plus

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however, care must be taken during sample preparation to avoid artifacts.6,7 Other methods that allow the evaluation of the mesh size include confocal laser scanning microscopy,8,9 small angle neutron scattering,10,11 small-angle X-ray scattering,12 and pulsed field gradient NMR spectroscopy.13 Moreover, the mesh size distribution can be determined by differential 5

scanning calorimetry14-16 and low field NMR spectroscopy.16,17 In this manuscript, we focus on the correlation between the mesh size of degradable, poly(ethylene glycol) (PEG) based hydrogels and the release rate of macromolecules. In particular, we aim at establishing a theoretical framework that may facilitate the rational design of controlled release systems for antibodies. To this end, eight-armed PEG, molecular

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weight 10 kDa (8armPEG10k) was functionalized with furyl and maleimide groups, respectively; the obtained macromonomers were cross-linked via Diels-Alder (DA) reaction. As previously reported, the hydrogels degraded under physiological conditions by retro-DA reaction and subsequent ring-opening hydrolysis of the generated maleimide groups.18,19 The mesh size of 8armPEG10k-hydrogels was determined using swelling studies, rheology and

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low field NMR spectroscopy. The calculated values of ξ allowed us to estimate the release rate of fluorescein isothiocyanate-labeled dextran (FD); four different molecular masses (4 kDa, 20 kDa, 150 kDa and 500 kDa) were studied. To verify the validity of the model, the predicted release profiles were compared to the results of in vitro release experiments. Finally, the hydrogels were loaded with bevacizumab, which served as a model compound.

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Bevacizumab is a monoclonal antibody that inhibits angiogenesis by neutralizing vascular endothelial growth factor (VEGF). It is approved for the treatment of various types of cancer; furthermore, it is used off label in the treatment of neovascular age-related macular degeneration (AMD).20,21 Since the bioavailability of antibodies in the posterior segment of the eye is generally low, bevacizumab is administered every four to six weeks by intravitreal

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injection. However, these injections are associated with significant discomfort and rare but severe complications.22 To reduce the injection frequency and improve the compliance, the 5 Environment ACS Paragon Plus


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use of controlled release systems for bevacizumab seems obvious. Therefore, the in vitro release of bevacizumab from 8armPEG10k-hydrogels was studied and compared with the release profiles of dextran molecules of equivalent size.

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Experimental section Materials Eight-armed PEG (10 kDa molecular mass, hexaglycerol core) was purchased from JenKem Technology (Allen, TX, USA) and functionalized with furyl (8armPEG10k-furan) and maleimide groups (8armPEG10k-maleimide) as previously described.18 The degree of

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functionalization with furyl and maleimide groups was 67% and 68%, respectively, as determined by 1H-NMR spectroscopy. Fluorescein isothiocyanate-labeled dextrans with molecular masses of 4 kDa, 20 kDa, 150 kDa and 500 kDa (FD4, FD20, FD150 and FD500) were obtained from Sigma-Aldrich (Taufkirchen, Germany). Bevacizumab (Avastin®, 25 mg mL-1, Roche, Basel, Switzerland) was kindly provided by the hospital pharmacy,

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University of Regensburg, Germany. Ultrapure water was freshly prepared every day using a Milli-Q water purification system (Merck Millipore, Darmstadt, Germany).

Swelling studies For the preparation of hydrogels, equal molar amounts of 8armPEG10k-furan (19.0 mg) and 20

8armPEG10k-maleimide (18.5 mg) were dissolved in 375 µL of water, cast into cylindrical glass molds (7 mm inner diameter), and allowed to gel over night at 37 °C. The gel cylinders were weighed in air and hexane using a density determination kit (Mettler-Toledo, Gießen, Germany), and the gel volume after cross-linking (Vgc) was calculated. The volume of the dry polymer (Vp) was calculated from the mass of the polymer in the hydrogel (mp) and the

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density of PEG (taken as 1.12 g mL-1).23 To study the swelling behavior, the gel cylinders were immersed in 10 mL of 50 mM phosphate buffer, pH 7.4 and incubated at 37 °C. The gel 6 Environment ACS Paragon Plus

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volume in the swollen state (Vgs) was determined at regular time points as described above. From these data, the polymer fraction of the gel after cross-linking, υ2c = Vp / Vgc, and after swelling, υ2s = Vp / Vgs, was calculated. The number of moles of elastically effective chains in the gel network, νe, was calculated using the Peppas–Merrill equation, which is a modified 5

form of the Flory–Rehner equation for highly swollen hydrogels cross-linked in solution:24-26

(1) where V1 is the molar volume of the swelling agent (taken as 18 mL mol-1), and χ1 is the Flory-Huggins interaction parameter for PEG in water. The value of χ1 was found to be nearly independent of the polymer fraction (υ2 ranging from 0.04 to 0.2); therefore, the average 10

value (0.43) was used in all calculations.27 The branching factor of the macromonomers, f, was taken as 8, assuming 100% functionalization with furyl and maleimide groups, respectively, and 100% reaction during cross-linking. The average mesh size (ξavg) was then calculated according to eqn. (2):4

(2) 15

where l is the average bond length along the PEG backbone (taken as 0.146 nm),27,28 Mr is the molecular mass of the PEG repeating unit (taken as 44 g mol-1), and Cn is the Flory characteristic ratio (taken as 4 for PEG).27,28

Rheological characterization 20

Oscillatory shear experiments were performed on a TA Instruments AR 2000 rheometer (TA Instruments, Eschborn, Germany) with parallel plate geometry (40 mm diameter). For the measurements, equal molar amounts of 8armPEG10k-furan (38.0 mg) and 8armPEG10kmaleimide (37.0 mg) were dissolved in 750 µL of water, and cast onto the lower plate of the



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rheometer. The upper plate was immediately lowered to a gap size of 500 µm, and the sample was allowed to gel over night at 37 °C. A solvent trap was used to minimize the evaporation of water. After full gelation, a stress sweep experiment was run at 1 Hz oscillatory frequency to determine the linear viscoelastic region of the sample. Afterwards, a frequency sweep 5

experiment was run at 1000 µNm torque (equivalent to a stress of 79.5 Pa and within the linear viscoelastic region, see results and discussion) following the same procedure.

Low field NMR measurements Equal molar amounts of 8armPEG10k-furan (51.0 mg) and 8armPEG-maleimide (49.0 mg) 10

were dissolved in 1000 µL of water and transferred into an NMR tube. Low field NMR measurements were performed at 37 °C using a Bruker Minispec mq20 (Bruker Italy, Milan, Italy). A Carr-Purcell-Meiboom-Gill pulse sequence with a 90°–180° pulse separation time of 0.25 ms was used to measure the transverse relaxation time, T2 (4 scans, 5 s delay). To determine the discrete distribution of T2, the signal intensity, Is, related to the decay of the

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transverse component of the magnetization vector was fitted by:

(3) where t is the time, Ai are the dimensionless pre-exponential factors proportional to the number of protons with the relaxation time T2i, and ⟨1/T2⟩ is the average value of the inverse relaxation time. Based on a statistical procedure, m was determined by minimizing the 20

product χ2 · 2m, where χ2 is the sum of the squared errors and 2m represents the number of fitting parameters of eqn. (3). The determined T2i value represents the transverse relaxation time of protons of water molecules entrapped in polymer meshes of size ξi. To evaluate the mesh size distribution, the continuous distribution of T2 was considered. To this end, although another approach can be followed,29,30 eqn. (4) was fitted to the decay of the signal (Is):


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(4) where a(T2) is the unknown amplitude of the spectral component at relaxation time T2, e–t/T2 represents the decay term, and T2min – T2max indicates the range of the T2 distribution (here

T2min = 40 ms, T2max = 4000 ms and N = 200). The initial values of all unknowns (Ai) were set to 5

zero and a constrained fitting was performed imposing that Ai ≥ 0 (negative values would be physically meaningless). The fitting parameters, Ai and ai = Ai / (T2i+1 – T2i), were determined by minimizing the smoothed sum of the squared error (χs2):

(5) where σi is the standard deviation of the noise, and µ is the weight of smoothing term.31,32 The 10

optimal value of µ was determined as described by Wang and Ni32 (here µ = 200). The average value of the inverse relaxation time, ⟨1/T2⟩, was then calculated by eqn. (6):

(6) To study the mobility of water molecules inside the gel network, pulsed gradient spin-echo (PGSE) measurements were performed at 37 °C. A Carr-Purcell-Meiboom-Gill sequence with 15

two equal gradient pulses (δ = 1 ms) occurring at x1 = 1 ms and x2 = 1 ms after the 90° and 180° pulses, respectively, was applied. The interval between the gradient pulses, indicated by ∆ (≈ τ – x1 – δ + x2), is related to the diffusion time of the water molecules (td) according to

td ≈ ∆ – δ / 3. The self-diffusion coefficient of the water molecules was determined by fitting eqn. (7) to the experimental data:

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(7) 9 Environment ACS Paragon Plus


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where At and A0 are the measured amplitudes of the echo with and without the gradient applied, γ is the gyromagnetic ratio of the protons, g is the known magnetic field gradient, and

A0i are the fractions of water molecules characterized by a self-diffusion coefficient Di. In case of homogenous systems, the summation is limited to the first term (p = 1), as all water 5

molecules are characterized by the same self-diffusion coefficient. In case of heterogeneous systems, however, p > 1 occurs. In this case, p was determined by minimizing the product χ2 · 2p, where χ2 is the sum of the squared errors and 2p represents the number of fitting parameters (A0i and Di) of eqn. (7).

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In vitro release of fluorescein isothiocyanate-labeled dextran Hydrogels were loaded with fluorescein isothiocyanate-labeled dextran (FD); different molecular masses (4 kDa, 20 kDa, 150 kDa and 500 kDa) were investigated. For the preparation of hydrogels, equal molar amounts of 8armPEG10k-furan (61.0 mg) and 8armPEG10k-maleimide (59.0 mg) were dissolved in 1080 µL of water; 120 µL of an FD

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stock solution (c = 10 mg mL-1) were added. Directly after mixing, 375 µL of the prepared solution were cast into cylindrical glass molds (7 mm inner diameter) and allowed to gel over night at 37 °C. The gel cylinders were carefully removed from the glass molds, immersed in 5 mL of 50 mM phosphate buffer, pH 7.4, and incubated at 37 °C in a shaking water bath. Samples of 1000 µL were withdrawn at regular time points and replaced with fresh buffer.

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The samples were stored at 4 °C until completion of the release experiment. The amount of released FD (λex = 485 nm and λem = 510 nm) was determined on a fluorescence microplate reader (BMG LABTECH, Ortenberg, Germany) using standard calibration curves.

In vitro release of bevacizumab 25

For the preparation of bevacizumab-loaded hydrogels, equal molar amounts of 8armPEG10kfuran (38.0 mg) and 8armPEG10k-maleimide (37.0 mg) were dissolved in 600 µL of water; 10 Environment ACS Paragon Plus

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150 µL of a bevacizumab stock solution (c = 25 mg mL-1) were added. Directly after mixing, 250 µL of the prepared solution were cast into cylindrical glass molds (7 mm inner diameter) and allowed to gel over night at 37 °C. The gel cylinders were carefully removed from the glass molds, covered with 5 mL of 50 mM phosphate buffer, pH 7.4, and incubated at 37 °C 5

in a shaking water bath. Samples of 300 µL were withdrawn at regular rime points and replaced with fresh buffer. The samples were stored at 4 °C until completion of the release experiment. The amount of released bevacizumab (λex = 280 nm and λem = 335 nm) was determined on a PerkinElmer LS 55 Fluorescence spectrometer (Perkin Elmer, Wiesbaden, Germany) using a standard calibration curve.

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Results and discussion Determination of the network mesh size In order to determine the time-curve of ξavg, DA hydrogels consisting of 10% (w/v) 8armPEG10k were incubated in 50 mM phosphate buffer, pH 7.4 at 37 °C. The volumetric 15

swelling ratio, Q = Vgs / Vp, was determined at regular time points until complete degradation of the hydrogel (Figure 1A); ξavg was calculated according to eqn. (1) and (2), and the results are shown in Figure 1B. After 1 day of swelling, an initial ξavg value of 5.8 ± 0.1 nm was determined. During degradation, the number of elastically effective chains in the gel network is decreasing; as a consequence, both Q and ξavg were increasing during the incubation period.

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The high standard deviations of the last two data points indicate the beginning dissolution of the hydrogel; the maximum ξavg value (56 ± 13 nm) was determined at day 35. Since the swelling of DA hydrogels was observed to increase exponentially during the first 30 days, Q can be described by the exponential function: (8)



where Q0 is the initial volumetric swelling ratio (here Q0 = 11), and kQ is the rate constant of the process (here kQ = 0.040 d-1). In the same way, ξavg can be described during the first 30 days by the exponential function: (9) 5

where ξ0 is the average mesh size at time t = 0 (here ξ0 = 5.7 nm), and kξ is the rate constant of the process (here kξ = 0.054 d-1). Thus, Q and ξavg can be calculated throughout the degradation time. A

B

80

80

ξavg (t) = 5.7exp 0.054t

Q (t) = 11exp 0.040t R2 = 0.99 60

R2 = 0.99 60

Experiment Best fit ξ (nm)

Q

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40

20

Experiment Best fit

40

20

0

0 0

10

20

30

40

0

10

Time (days)

10

15

20

30

40

Time (days)

Figure 1: Volumetric swelling ratio (A) and average mesh size (B) of 10% (w/v) 8armPEG10k hydrogels in 50 mM phosphate buffer, pH 7.4 at 37 °C. The high standard deviations of the last two data points indicate the beginning dissolution of the hydrogel. To describe the increase of Q and ξ over time, exponential equations were fitted to the experimental data by minimizing the sum of the squared errors. Data is expressed as mean ± standard deviation based on the results of n = 3 samples. The error bars are smaller than the symbols, except for the last two data points.

Rheological experiments were performed to validate the result of the swelling studies. The stress sweep shown in Figure 2A indicates a broad linear viscoelastic region of 10% (w/v) 8armPEG10k-hydrogels. The absolute value of the complex shear modulus (|G*|) was 20

independent from the applied oscillatory stress (σ) between 1 Pa and 200 Pa. The subsequent frequency sweep experiments (σ = 79.5 Pa) were run within the linear viscoelastic region of 12 Environment ACS Paragon Plus

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the hydrogels. As shown in Figure 2B, 10% (w/v) 8armPEG10k-hydrogels are strong, fully elastic hydrogels. The storage modulus (G’), which represents the elastic portion of the hydrogel, was two orders of magnitude higher that the loss modulus (G”), which represents the viscous portion of the hydrogel. Moreover, both G’ and G” were virtually independent 5

from the angular frequency (ω), which is characteristic for covalently cross-linked, permanent hydrogels. To determine ξavg, the generalized Maxwell model was fitted to the experimental data of G’ and G”:16,17

(10)

(11) 10

where n is the number of considered Maxwell elements; Gi, ηi and λi represent the spring constant, the viscosity of the dashpot component and the relaxation time of the ith Maxwell element, respectively, while Ge is the spring constant of the last Maxwell element, which is supposed to be purely elastic. The simultaneous fitting of eqn. (10) and (11) to the experimental data of G’ and G” was performed assuming that the relaxation times (λi) are

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scaled by a factor of 10. Hence, the parameters of the model are Gi, Ge and λ1. Based on a statistical procedure, n was selected in order to minimize the product χ2 · (n + 2), where χ2 is the sum of the squared errors. In this way, the shear modulus (G) can be calculated from the sum of all elastic contributions by G = Ge + ΣGi. According to Flory’s theory of rubber elasticity, the cross-link density (defined as the number of moles of cross-links per volume),

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ρx, can be calculated from G: (12) where R is the universal gas constant, and T is the temperature. The “equivalent network” approach allows calculating ξavg according to eqn. (13):33



(13) where NA is the Avogadro constant, and 1 / (ρx · NA) is the spherical volume competing with each cross-link. In the case of 10% (w/v) 8armPEG10k-hydrogels, n = 4 Maxwell elements were necessary to describe the mechanical spectrum. On the basis of eqn. (10) through (12), 5

the values of λ1 (0.03 s), G (15,988 Pa) and ρx (6.21·10-6 mol cm-3) were calculated. Using eqn. (13), a ξavg value of 8.0 nm was calculated, which is in good agreement with the value derived from swelling studies. A

B

105

105

G' and G" (Pa)

104

|G*| (Pa)

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104

103

102

101

103 10-1

100

101

102

103

104

100 10-2

σ (Pa)

10

15

G' Best fit G' G" Best fit G" 10-1

100 ω

101

102

(rad s-1)

Figure 2: (A) Absolute value of the complex shear modulus vs. oscillatory stress for 10% (w/v) 8armPEG10k hydrogels. (B) Storage and loss modulus vs. oscillatory frequency for 10% (w/v) 8armPEG10k hydrogels. The filled and open symbols represent G’ and G”, respectively; The solid line represents the best fit of eqn. (10) and (11) to the experimental data. The result of the frequency sweep represents the mean of n = 3 samples.

To estimate the statistical distribution of ξ, low field NMR measurements were performed. The transverse relaxation time (T2) of the water protons was measured over 24 h, starting from the time point of gel preparation; however, no significant changes in T2 were recorded. Thus, it is conceivable that a physical gel is formed initially, which is then reinforced by chemical cross-links. The discrete distribution of T2 was determined by fitting eqn. (3) to the


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relaxation data. Two different relaxation times were identified, with T21 being the longest and most abundant one, and T22 being the shortest and least abundant one. The determined T2i values and their relative weights, Ai, are reported in Table 1.

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Table 1: Transverse relaxation times (T2i) of protons of water molecules entrapped in polymer meshes of size ξi; Ai represent the relative weights of T2i and ξi, respectively. The reported T2i values represent the average of all measurements performed during 24 h.

T2i (ms)

i=2

2567.6 ± 95.6

603.1 ± 109.3

a

Ai (%)

90.8 ± 1.6

9.2 ± 1.6

ξi (nm)

11.1 ± 2.1

1.0 ± 0.3

a

10

i=1

Calculated by A1% = A1·100% / (A1 + A2) and A2% = A2·100% / (A1 + A2)

Since the transverse relaxation time of protons of water molecules near the surface of polymer chains is shorter than the transverse relaxation time of protons of bulk water, T2H2O,34,35 ξi can be estimated from T2i. The mesh size of an ideal network, ξideal, can be calculated on the basis of the Scherer theory by eqn. (14):36,37

(14) 15

where φ is the polymer volume fraction of the hydrogel (taken as 0.082), and Rf is the radius of the polymer chain (taken as 0.51 nm).38 According to the “fiber cell” theory, the average of the inverse relaxation time of the water protons entrapped within the polymer network, ⟨1/T2⟩, is given by eqn. (15):35

(15) 20

where ⟨ℳ ⟩ (length / time) is an empirical parameter (relaxation sink strength) accounting for the effect of the polymer chain surface on proton relaxation. As ⟨1/T2⟩, T2H2O and ξideal are 15 Environment ACS Paragon Plus


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known, eqn. (15) allows the determination of ⟨ℳ ⟩. Furthermore, by knowing T2i and ⟨ℳ ⟩, ξi can be calculated for each class of network meshes by eqn. (16):

(16) Using this strategy, the ξi values of 10% (w/v) 8armPEG10k-hydrogels were estimated. The 5

value of ξ1, which represents about 91% of all network meshes, was found to be 11.1 ± 2.1 nm; the value of ξ2, which represents the remaining 9% of all network meshes, was 1.0 ± 0.3 nm (Table 1). The weighted average mesh size, ξavg = 100% / (A1% / ξ1 + A2% / ξ2), was calculated to be 5.4 nm, which is close to the value derived from the swelling experiments (5.8 nm, Table 2).

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Table 2: Mesh size of 10% (w/v) 8armPEG10k hydrogels as determined by swelling studies, rheological experiments and low field NMR measurements. Type of mesh size

Method

Determined value

Average size (ξavg)

Swelling studies

5.8 ± 0.1 nmb


Rheological experiments

8.0 nm

Most abundant size (ξ1)

Low field NMR (discrete)

11.1 ± 2.1 nm

Least abundant size (ξ2)


1.0 ± 0.3 nm



5.4 nmc

Most abundant size (ξ)

Low field NMR (continuous) 9.2 nm

b c

Determined after 24 h of swelling Calculated by ξavg = 100% / (A1% / ξ1 + A2% / ξ2)

15 To evaluate the continuous distribution of the mesh size, the relaxation time distribution,

a (T2), was determined by fitting eqn. (4) to the relaxation data. The result reveals the presence of two peaks occurring at relaxation times similar to T21 and T22, respectively (Figure 3A). Once a (T2) or A (T2) are known, ⟨ℳ ⟩ can be derived from eqn. (14) and (15), with the only 20

difference that ⟨1/T2⟩ is calculated according to eqn. (6). Using eqn. (16), A (T2) is converted 16 Environment ACS Paragon Plus

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into the mesh size distribution, A (ξ), where Ai (ξ) = Ai (T2). To allow the comparison of mesh size distributions of different systems, Ai is normalized according to:

(17) As shown in Figure 3B, A (ξ) spanned over three orders of magnitude; meshes as large as 5

300 nm were observed, even if this probability, Ai, is very low. Two distinct peaks were identified: a small peak at around 1 nm and a larger one at around 10 nm. Interestingly, the proportion between the two peaks matched the result found in the discrete approach (about 9% smaller meshes and 91% larger meshes, Table 1); however, the continuous distribution provided more information than the discrete one. The most abundant mesh size (Ai = 5.2%) was

10

found to be 9.2 nm, which is in good agreement with the value derived from the discrete approach (11.1 ± 2.1 nm, Table 2). A

B 80

0.08

6%

Is (t) Best fit

60

0.06

a (T2)

40

0.04

20

0.02

A (ξ)

4% a (T2)

Is (t) and I (t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2%

0 0

2000

4000

6000

0.00 8000

0% 0.01

t (ms) or T2 (ms)

15

0.1

1

10

100

1000

ξ (nm)

Figure 3: (A) Signal intensity, related to the decay of the transverse component of the magnetization vector, vs. time. The open symbols represent the relaxation data, and the dashed line represents the best fit of eqn. (4). The solid line represents the continuous distribution of the relaxation time, a (T2). (B) Continuous distribution of the mesh size, A (ξ), of 10% (w/v) 8armPEG10k hydrogels. The results represent the average of all measurements performed during 24 h.



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These conclusions are supported by the measurements of the water self-diffusion coefficient. PGSE studies revealed that two exponential terms in eqn. (7) are required to properly describe the experimentally determined ratio of At / A0 to q2 for every td considered (7.6 ms < td < 44 ms). Figure 4 shows the existence of two species of water molecules with different mobility. The 5

fastest species is characterized by a self-diffusion coefficient of D1 ≈ 2.7·10-9 m2 s-1, which is close to the self-diffusion coefficient of free water at 37 °C (3.04·10-9 m2 s-1),39 and represents about 94% of all water molecules. The slowest species is characterized by a self-diffusion coefficient of D2 ≈ 5.4·10-10 m2 s-1 and represents the remaining 6% of water molecules. While

D1 is connected to the existence of wide network meshes (with respect to the size of the water 10

molecule), D2 is most likely due to the presence of narrow meshes that significantly hinder the diffusion of water molecules. Interestingly, these findings match the results of the T2 measurements (about 91% larger meshes and 9% smaller meshes, Table 1). Moreover, it is worth mentioning that, as D1 and D2 are essentially independent from td, both wide and narrow meshes are interconnected.40 In conclusion, all three methods (i.e., swelling studies, rheological

15

experiments and NMR spectroscopy) give similar estimates of ξavg. Low field NMR measurements might be the preferred method when the mesh size distribution is important; on the other hand, swelling studied might be most appropriate to determine the mesh size during degradation or drug release.


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A

B

10-8

120%

D1 D2

100%

A1 A2

80%

10-9

Ai

Di (m2 s-1)

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60%

40%

20% 10-10 0.05

0.10

0.15 td

5

0.5

0.20

0.25

0% 0.05

0.10

0.5

(s )

0.15 td

0.5

0.20

0.25

0.5

(s )

Figure 4: (A) High (D1) and low (D2) self-diffusion coefficients of water molecules versus the square root of the diffusion time, td. The self-diffusion coefficient of free water at 37 °C is 3.04·10-9 m2 s-1.39 (B) A1% and A2% represent the relative abundance of the fast and slow diffusing species, respectively.

In vitro release of fluorescein isothiocyanate labeled dextran To correlate the determined mesh sizes with release profiles, the in vitro release of macromolecules from DA hydrogels was investigated. Fluorescein isothiocyanate-labeled 10

dextrans (FDs) were used as model compounds; four different molecular masses (4 kDa, 20 kDa, 150 kDa and 500 kDa) were studied. The hydrodynamic radius (Rh) of FDs can be estimated according to eqn. (18):41 (18) where Mr is the relative molecular mass of the FD. The hydrodynamic radii and the diffusion

15

coefficients in water (D0), calculated from the Stokes-Einstein equation:

(19) are listed in Table 3. In eqn. (19), k is the Boltzmann constant, T is the temperature (310.16 K), and η is the viscosity of water (0.69 mPa s).



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Table 3: Relative molecular mass (Mr), hydrodynamic radius (Rh) and diffusion coefficient in water (D0) of the studied fluorescein isothiocyanate-labeled dextrans (FDs). The values of Rh were estimated according to eqn. (18); the values of D0 were calculated from eqn. (19). Mr (Da)d

Rh (nm)

D0 (cm2 s-1)

FD4

4,000

1.8

1.8·10-6

FD20

20,000

3.7

8.9·10-7

FD150

150,000

8.9

3.7·10-7

FD500

500,000

15.1

2.2·10-7

d

Average molecular mass. Data from the manufacturer.

5 The mobility of solutes in homogenous hydrogels can be described by the obstruction-scaling model developed by Amsden:42

(20) where Dg is the diffusion coefficient of the solute in the hydrogel. Based on the results of the 10

performed swelling studies and eqn. (9), eqn. (20) can be used to estimate the mobility of FDs within DA hydrogels during the release period (Figure 5A). Since Rh is much smaller than ξavg, the diffusivity of FD4 should be high in the non-swollen (t = 0) and swollen state (t > 0). The mobility of FD20 should be restricted in the beginning; however, the diffusivity of entrapped FD20 should increase with increasing degree of swelling. In contrast to this, the Rh values of

15

FD150 and FD500 are much greater than the initial ξavg value. Thus, both dextrans will not be free to move through the hydrogel network in a spherical conformation. Eqn. (20) predicts an extremely low diffusivity at low degrees of swelling; however, the diffusivity of FD150 and FD500 should increase during swelling once a critical ξavg value is exceeded. Since the Dg values can be calculated from eqn. (19) and (20), the release of entrapped FDs from hydrogel

20

cylinders can be described according to eqn. (21):43

(21) 20 Environment ACS Paragon Plus

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where Mt and M∞ represent the absolute cumulative amounts of FD released at time t and infinity, respectively; qn are the roots of the Bessel function of the first kind of zero order, and

r and h denote the radius and height of the gel cylinder. The increase in r and h due to swelling is taken into account, and the predicted release profiles are shown in Figure 5B. As it 5

is expected from the Dg values, the release of FD4 and FD20 from DA hydrogels should be extremely fast; the release should be completed after 1 day and 2 days, respectively. Compared to FD4 or FD20, the release of FD150 should be considerably slower; the maximum release should be reached after 15 days. In contrast to this, a sigmoidal release profile is predicted for FD500. Since the mobility of FD500 is extremely low during the first 10 days of release,

10

eqn. (21) predicts a lag time of approximately 5 days; the release of FD500 should be completed after 25 days. A

B 1.0

1.0

0.8

0.8

M t / M∞

D g / D0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

0.4

0.6

FD4

0.4

FD20 0.2

0.2

0.0

0.0

FD150 FD500

0

10

20

30

0

Time (days)

15

10

20

30

Time (days)

Figure 5: (A) Diffusion quotients (Dg/D0) of fluorescein isothiocyanate-labeled dextrans (FDs) vs. time. The values of Dg/D0 were calculated from eqn. (20). (B) Predicted release of FDs from 10% (w/v) 8armPEG10k hydrogels. The predictions are based on eqn. (21).

To verify the validity of the applied model, the release of FDs from DA hydrogels was experimentally determined (Figure 6). The release of FD4 from DA hydrogels was extremely fast; the incorporated dextran was completely released after 2 days (Figure 6A). In comparison



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to FD4, the release of FD20 was slightly slower; the maximum release was reached after 5 days (Figure 6B). The release of FD150 from DA hydrogels was considerably slower than the release of FD4 or FD20; 90% of the incorporated dextran was released after 30 days (Figure 6C). In contrast to FD4, FD20 and FD150, the release profile of FD500 had a 5

sigmoidal shape. Approximately 10% of the incorporated FD500 was released during the first day; this was followed by a phase of slow release, with approximately 30% of the incorporated dextran being release at day 15. Following this, the release rate considerably increased; 90% of the incorporated FD500 was released after 30 days (Figure 6D).


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A

B

FD4

FD20

100%

Released amount

Released amount

100%

50%

50%

Experiment Prediction

Experiment Prediction

0%

0%

0

10

20

30

0

10

C

20

D

FD150

FD500

100%

Released amount

100%

50%

50%

Experiment

Experiment

Prediction

Prediction

0%

0%

0

10

20

30

0

Time (days)

5

30

Time (days)

Time (days)

Released amount

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

20

30

Time (days)

Figure 6: Release of fluorescein isothiocyanate-labeled dextrans (FDs) from 10% (w/v) 8armPEG10k hydrogels. The symbols represent the experimental data, and the solid lines represent the predictions based on eqn. (21). The theoretical predictions match the release profiles of FD4 (A) and FD20 (B) very well; however, significant differences between the theoretical predictions and the experimental data are observed for FD150 (C) and FD500 (D). Data is expressed as mean ± standard deviation based on the results of n = 3 samples.

The theoretical predictions for the release behavior are shown by the lines in Figure 6. In case 10

of FD4 and FD20, the predicted release profiles match the experimentally determined release profiles very well. However, marked differences between the theoretical predictions and the experimental data are observed for FD150 and FD500. On the one hand, the applied model 23 Environment ACS Paragon Plus


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underestimates the initial “burst” release; on the other hand, it overestimates the release rate in the terminal phase of release. These deviations are explained by the statistical distribution of ξ in real polymer networks. As shown in Figure 3B, A (ξ) spans over three decades (from 0.3 nm to 300 nm), while eqn. (20) only considers ξavg (5.8 nm at t = 0). This simplification 5

may be acceptable when Rh is smaller than ξavg and the dextran is free to diffuse throughout the gel network; however, deviations from the experimental results occur when Rh is similar to or greater than ξavg. The existence of larger meshes (ξ > Rh) can explain the initial “burst” release, while the continued existence of smaller meshes (ξ < Rh) may delay the terminal phase of release. Furthermore, the values of Rh were estimated from the average molecular

10

mass of the FDs, assuming that these molecules were monodisperse. In fact, however, FDs are polydisperse, which may also contribute to the observed deviations. In addition, eqn. (20) assumes that the solutes behave as hard spheres; however, dextran is flexible polymer of Dglucopyranose that behaves like a random coil.41 When Rh is similar to ξ, the dextran may get “trapped” in the larger meshes, where the molecule can extend and maximize its

15

conformational entropy (“entropic trapping”).44 On the other hand, when Rh is greater than ξ, the dextran can migrate through the network in a wormlike fashion (“reptation”).45 However, both entropic trapping and reptation are not considered by eqn. (20). And last but not least, it is possible that cross-linking in the presence of FD150 or FD500 affects ξavg, given the large

Rh of these molecules. The FD molecules could be physically entangled with the PEG 20

molecules before cross-linking, which would influence the mesh size distribution.

In vitro release of bevacizumab In the final experiment, the release profiles of bevacizumab and FD were compared. With an hydrodynamic radius of 6.5 nm,46 the release of bevacizumab from 10% (w/v) 8armPEG10k25

hydrogels should be comparatively fast; the release profile of bevacizumab should fall between those of FD20 (Rh = 3.7 nm) and FD150 (Rh = 8.9 nm). However, the experimentally 24 Environment ACS Paragon Plus

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determined release profile differed significantly from those of FD20 and FD150. As shown in Figure 7, a sigmoidal release profile was observed for bevacizumab. Approximately 10% of the incorporated bevacizumab was released after 24 h; this is attributed to non-entrapped protein molecules located at the surface of the gel cylinders. No bevacizumab release 5

occurred during the following 16 days, indicating that the protein molecules were entrapped within the hydrogel meshes. However, since ξ is increasing during the degradation process, the incorporated bevacizumab was completely released between day 17 and 22 after a critical ξ value had been exceeded. No further release was observed after day 22.

100%

80% Released amount

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


60%

40%

20%

0% 0

5

10

15

20

25

30

Time (days)

10

Figure 7: Release of bevacizumab from 10% (w/v) 8armPEG10k hydrogels. The amount of drug loading was 1.25 mg of bevacizumab per hydrogel. Data is expressed as mean ± standard deviation of n = 3 samples.

The discrepancy in the release profiles can be explained by the different molecular 15

configuration (i.e., size, charge, shape and deformability) of proteins and dextran molecules. Dextran is a linear, rather flexible polymer of D-glucopyranose; proteins, on the other hand, are globular, rather rigid molecules. As a consequence, dextran molecules are able to pass through pores smaller than the molecule itself. For example, it has been shown that the glomerular sieving coefficient of dextran is approximately sevenfold higher than that of a



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globular protein of equivalent size.41 Thus, the delayed release of bevacizumab is the result of the globular structure and rigidity of the protein. Furthermore, it has been shown that 20–30% of the incorporated protein is immobilized within the hydrogel by Michael-type addition reaction to 8armPEG10k-maleimide and not released until the hydrogels dissolves.47 This 5

portion of the protein is not released until the hydrogel dissolves. Depending on the number of PEG molecules remaining attached, the antigen binding activity of these PEGylated antibodies can be slightly decreased or completely lost.48 Although most controlled release systems for proteins are designed to provide sustained release, the delayed release of bevacizumab from DA hydrogels could prove to be beneficial

10

for the treatment of AMD. There is increasing evidence that chronic blocking of VEGF signaling might have detrimental long-term effects such as the development of geographic atrophy, which is accompanied by a massive loss of photoreceptors.49-51 For that reason, the treatment with VEGF inhibiting antibodies should be intermittent to allow the damaged choriocapillaris to recover during drug-free intervals. DA hydrogels could provide such

15

intermittent drug release. The first dose would be administered together with the hydrogel, while the second dose would be released from the gel four to six weeks after injection.

Conclusion Hydrogels were prepared by cross-linking 8armPEG10k-furan and 8armPEG10k-maleimide 20

via DA reaction. The mesh size of the formed hydrogels was determined using swelling studies, rheology and low field NMR spectroscopy. The in vitro release of incorporated FDs and bevacizumab was investigated. In principle, all three methods (i.e., swelling studies, rheology and NMR spectroscopy) give similar estimates of ξavg; however, low field NMR measurements are the preferred method when the mesh size distribution is important. On the

25

other hand, swelling studies are most appropriate to determine the time-dependent increase of ξavg during hydrogel degradation or drug release. Combined with the hydrodynamic radius of 26 Environment ACS Paragon Plus

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the drug molecule, the determined values of ξavg can be used to predict drug release over time. When Rh is smaller than ξavg, the predicted release profiles match the experimentally determined release profiles very well. However, deviations from the theoretical predictions are observed when Rh is similar to or greater than ξavg. These deviations are most likely due to 5

the statistical distribution of ξ in real polymer networks. Nevertheless, the applied model correctly predicts the expected sigmoidal shape of the release profile. Furthermore, the structure and rigidity of the drug molecule must be taken into account. In contrast to globular proteins (e.g., bevacizumab), FDs are able to pass through pores smaller than the molecule itself in a wormlike fashion (“reptation”). Altogether, we believe that the established

10

correlation between ξ and the release rate may facilitate a more rational design of controlled release systems for antibodies. In the future, the model could be further refined by evaluating the mesh size distribution, A (ξ), instead of ξavg.

Acknowledgements 15

Financial support from the German Research Foundation (DFG), grant number GO 565/16-1, and the Italian Ministry of Education, grant number PRIN 2010-11 (20109PLMH2), is gratefully acknowledged.

Supporting information 20

Additional figures showing the chemical structures of 8armPEG10k-furan, 8armPEG10kmaleimide and the cross-linked hydrogel are included. The molecular mass distribution of the FDs and the resulting variation of the predictions are given in the supporting information. This information is available free of charge via the Internet at http://pubs.acs.org/.

25

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89x36mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Volumetric swelling ratio (A) and average mesh size (B) of 10% (w/v) 8armPEG10k hydrogels in 50 mM phosphate buffer, pH 7.4 at 37 °C. The high standard deviations of the last two data points indicate the beginning dissolution of the hydrogel. To describe the increase of Q and ξ over time, exponential equations were fitted to the experimental data by minimizing the sum of the squared errors. Data is expressed as mean ± standard deviation based on the results of n = 3 samples. The error bars are smaller than the symbols, except for the last two data points. 80x40mm (300 x 300 DPI)


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(A) Absolute value of the complex shear modulus vs. oscillatory stress for 10% (w/v) 8armPEG10k hydrogels. (B) Storage and loss modulus vs. oscillatory frequency for 10% (w/v) 8armPEG10k hydrogels. The filled and open symbols represent G’ and G”, respectively; The solid line represents the best fit of eqn. (10) and (11) to the experimental data. The result of the frequency sweep represents the mean of n = 3 samples. 80x40mm (300 x 300 DPI)



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(A) Signal intensity, related to the decay of the transverse component of the magnetization vector, vs. time. The open symbols represent the relaxation data, and the dashed line represents the best fit of eqn. (4). The solid line represents the continuous distribution of the relaxation time, a (T2). (B) Continuous distribution of the mesh size, A (ξ), of 10% (w/v) 8armPEG10k hydrogels. The results represent the average of all measurements performed during 24 h. 76x35mm (300 x 300 DPI)


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(A) High (D1) and low (D2) self-diffusion coefficients of water molecules versus the square root of the diffusion time, td. The self-diffusion coefficient of free water at 37 °C is 3.04·10-9 m2 s-1. (B) A1% and A2% represent the relative abundance of the fast and slow diffusing species, respectively. 81x40mm (300 x 300 DPI)



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(A) Diffusion quotients (Dg/D0) of fluorescein isothiocyanate-labeled dextrans (FDs) vs. time. The values of Dg/D0 were calculated from eqn. (20). (B) Predicted release of FDs from 10% (w/v) 8armPEG10k hydrogels. The predictions are based on eqn. (21). 80x40mm (300 x 300 DPI)


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Release of fluorescein isothiocyanate-labeled dextrans (FDs) from 10% (w/v) 8armPEG10k hydrogels. The symbols represent the experimental data, and the solid lines represent the predictions based on eqn. (21). The theoretical predictions match the release profiles of FD4 (A) and FD20 (B) very well; however, significant differences between the theoretical predictions and the experimental data are observed for FD150 (C) and FD500 (D). Data is expressed as mean ± standard deviation based on the results of n = 3 samples. 170x178mm (300 x 300 DPI)



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Release of bevacizumab from 10% (w/v) 8armPEG10k hydrogels. The amount of drug loading was 1.25 mg of bevacizumab per hydrogel. Data is expressed as mean ± standard deviation of n = 3 samples. 80x58mm (300 x 300 DPI)


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DielsâAlder Hydrogels for Controlled Antibody Release: Correlation

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