Integrated Experimental and Modeling Study of Enzymatic

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Integrated Experimental and Modeling Study of Enzymatic Degradation Using Novel Autofluorescent BSA Microspheres Xiaoyu Ma,†,‡ Ji-Qin Li,§,‡ Christopher O’Connell,∥ Tai-Hsi Fan,*,§ and Yu Lei*,⊥ †

Department of Biomedical Engineering, University of Connecticut, Storrs, Connecticut 06269-3247, United States Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139, United States ∥ Biotechnology-Bioservices Center, University of Connecticut, Storrs, Connecticut 06269-3149, United States ⊥ Department of Chemical & Biomolecular Engineering, University of Connecticut, Storrs, Connecticut 06269-3222, United States §

ABSTRACT: Autofluorescent bovine serum albumin (BSA) hydrogel microspheres were prepared through the spraydrying of glutaraldehyde cross-linked BSA nanoparticles and then used for a proteinase K based degradation study in an aqueous solution. Experimental results and empirical models are presented to characterize the kinetics of BSA hydrogel microsphere degradation, as well as the accompanying release of synthesized fluorophore. The BSA gel degradation dynamics is primarily controlled by the concentration of proteinase K within the Tris buffer. The coupling of swelling dynamics and the transient distributions of fluorophore are traced by confocal microscopy. Models are developed based on the linear theory of elastic deformation coupled to enzyme and fluorophore transport. This study represents a fundamental investigation of the degradation and release kinetics of protein-based materials, which can potentially be applied for the dynamic and photostable tracking of relevant in vivo systems.

1. INTRODUCTION Biodegradability and biocompatibility are well-known significant functionalities of synthetic biomaterials.1,2 Controlled material degradation further allows for sustained release design for various biomedical applications. The advantages of controlled degradation are the avoidance of fast clearance and the availability of further access to biological response along a desired period of time. Specifically in tissue engineering, materials are often intended to degrade after serving as a temporary scaffold for cell therapy or tissue regeneration.2 Among all materials, natural polymers such as polysaccharides and many other proteins have attracted a great deal of attention because of their biocompatibility, in vivo affinity to tissues and scaffolds, and controllable degradation properties.3−7 More specifically, natural-polymer-based hydrogels have been widely explored in biomedical applications for drug delivery, medical diagnostics, biological tracking, and as personal care products.8−11 Hydrogels can absorb large amounts of water and exhibit three-dimensional structures. Protein-based hydrogels are important biodegradable and biocompatible materials, primarily because of their intrinsic high affinity to tissues and enzymatic degradation properties. Hydrogels made of bovine serum albumin (BSA) have been extensively studied, because of its low cost, good solubility and stability, and excellent ligandbinding accessibility and intrinsic fluorescence emission properties.12−15 Although several attempts to quantify the degradation of the synthesized materials using fluorescence imaging have been reported,16,17 physics-based modeling and quantification of the process are still lacking. Moreover, in our previous studies, we proposed the comparison of in vivo fluorescence © XXXX American Chemical Society

imaging and phenomenological models to systematically investigate protein-based hydrogels with different sizes.15,18,19 However, the dynamic degradation of the protein-based hydrogel matrix and the relevant transport mechanisms at the single-microsphere level are not well understood. In this study, spray-dried autofluorescent BSA microspheres were fabricated according to the method reported in our previous study15 and used for the further investigation of their enzymatic degradation and the release of the fluorophores. The use of autofluorescent microspheres has more advantages than the use of fluorescent microspheres with embedded chemical fluorophores. This is because autofluorescent materials can avoid photobleaching and leaking problems that exist in the majority of fluorescent materials. The diminishing of the fluorescence intensity can accurately reflect the degradation of the materials, which prevents complications from the decay of fluorescence intensity due to the leaking or photobleaching of chemical fluorophores. This advantage opens up many possibilities for using autofluorescent microspheres in investigations involving degradation kinetics. Figure 1 illustrates the problem at hand: a dynamic swelling and degrading autofluorescent hydrogel microsphere triggered by proteinase K in Tris buffer solution. The microspheres are about 2−4 μm and covalently immobilized on the surface of a cover glass. The enzymatic degradation of the BSA gel results in the swelling of the microspheres and the diminishing of the Received: August 30, 2017 Revised: November 10, 2017

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DOI: 10.1021/acs.langmuir.7b03057 Langmuir XXXX, XXX, XXX−XXX

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Figure 2. (A) SEM image of the spray-dried microspheres. (B,C) Confocal images of randomly deposited BSA hydrogel microspheres taken at the initial and end stages of the degradation process. water was added to the cover slides and allowed to stand overnight, enabling the microspheres to swell until reaching equilibrium. The proteinase K solution was diluted to different concentrations in Tris buffer at pH 7, with 10 mM Ca2+ in the solution. Upon the addition of 200 μL of the diluted proteinase K solution to the cover slides containing bound microspheres and 200 μL of DI water (giving a final Ca2+ concentration at 5 mM), enzymatic degradation of the BSA microspheres and release of the fluorophores were tracked with a Nikon A1R confocal laser scanning microscope. Transient fluorescence images on each sectional plane were acquired in a certain time period immediately after the addition of the enzyme solution. Figure 2B,C displays the confocal images obtained by scanning through the middle section of the spheres. Upon addition of proteinase K, the individual spheres, with radii ranging from 1 to 3 μm underwent a swelling and degradation process until the fluorescence signal diminished (Figure 2C). 2.3. Image Analysis. Image analysis was performed using ImageJ software. At each time point, the area values of single microspheres on each z plane were analyzed to identify the middle section. The circular regions of interest with different radii were selected, and then the transient local fluorescence intensities were collected.

Figure 1. Schematic of enzymatic degradation and the release of photostable fluorophores. Proteinase K is added to the Tris buffer solution to trigger the degradation process.

fluorescence intensity. Direct observation by confocal microscopy has shown that the swelling of a BSA gel is a continuous process, starting upon the addition of enzymes to the solution, involving continuous swelling, and then slowly degrading until the fluorescence signal diminishes. To characterize the swelling dynamics and simultaneous fluorophore release in detail, we present a side-by-side comparison of experimental results and diffusive-reactive species transport models. The transient fluorescence signals on each sectional plane of the hydrogel spheres were tracked intermittently using confocal laser scanning microscopy (CLSM). The enzyme and fluorophore transport equations are coupled with the empirical Tanaka− Hocker−Benedek (THB) hydrogel swelling model.20,21 The collective diffusivity represents a combined shear and bulk elasticity as well as the resistance coefficient for the relative motion between the solvent and the gel network. The overall process is likely controlled by three factors: the collective diffusivity for gel swelling, the self-diffusivity of enzyme molecules within the gel domain, and the apparent degradation rate constant of the fluorophores for the first-order irreversible reaction.

3. EMPIRICAL MODELS The following assumptions are made to simplify the analysis: Upon addition of proteinase K, the proteinase K diffuses immediately and is assumed to be uniformly distributed throughout the buffer solution. Plenty of proteinase K exists within the buffer, and thus, its depletion due to permeation into the hydrogel is negligible. The swelling of the gel is assumed to occur through a diffusive-like elastic deformation process and can be formulated by the THB model.21 The enzyme diffusivity within the hydrogel and the first-order reaction rate coefficient for BSA degradation are assumed to be constant throughout the whole process. Therefore, the enzyme and fluorophore transport equations are coupled to the swelling momentum equation through the gel configuration or local material displacement. The first approximation proposed here is applicable to the beginning stage of the degradation and is not applicable to the later stage when disintegration occurs. The modeling framework is described in detail next. 3.1. Swelling of BSA Hydrogel. The THB model that describes the swelling dynamics was developed from the linear elastic theory by assuming that gel swelling is under quasiequilibrium condition and that the friction due to the relative motion between the solvent and the gel network can be treated as a body force. The constitutive model for a linear elastic deformation can be defined as

2. EXPERIMENTS 2.1. Materials and Synthesis of BSA Microspheres. BSA, (3aminopropyl)trimethoxysilane (APTMS), sodium hydroxide, and Tris hydrochloride were purchased from Sigma. Glutaraldehyde, proteinase K solution (20 mg/mL, RNA grade, catalog no. 25530049), calcium chloride, and cover glass were purchased from Fisher Scientific. BSA microspheres were fabricated according to the method reported in our previous study.15 Briefly, BSA solution was first added rapidly to a glutaraldehyde cross-linking dispersion to form a dispersion of BSA nanoparticles, which was subjected to a spray-drying process, resulting in green and red autofluorescent microspheres. The scanning electron microscopy (SEM) image in Figure 2A shows the surface morphology of the as-synthesized microspheres. 2.2. Tracking Enzymatic Degradation of BSA Microspheres. Before the imaging experiments, the cover glass was treated with 1 M sodium hydroxide for 30 min, and then it was treated with APTMS vapor overnight, resulting in primary amine groups on the surface of the cover glass. This process enabled the covalent anchoring of the assynthesized BSA microspheres, as aldehyde groups on the surface of BSA microspheres, as indicated by the Fourier transform infrared (FTIR) results of our previous study.15 Next, 120 μL of spray-dried microsphere dispersion in deionized (DI) water at a concentration of 0.5 mg/mL was applied to the treated cover slides and allowed to stand for 1 h. Then, the cover slides were washed several times with DI water to remove unbound microspheres. After that, 200 μL of DI

σ = G(∇u + ∇u T) + λδ(∇·u)

(1)

where σ is the stress tensor; u is the displacement vector; G is the shear modulus; λ is Lame’s first parameter, which is associated with the bulk modulus of elasticity by K = λ + 2G/3; B


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Langmuir and δ is the Kronecker delta. The general momentum equation for the linear elastic deformation can thus be expressed as ρ

∂ 2u = G∇2 u + (λ + G)∇(∇·u) + Fb ∂t 2

moving boundary problem. First, we consider a simple Fickian diffusion equation with an assumed uniform diffusivity

∂E = De∇2 E ∂t

(2)

where E indicates the enzyme concentration and De is the apparent enzyme diffusivity within the swelling hydrogel. For a spherically symmetric case, the eq 9 can be simplified to

where ρ is the mass density; t is the time; and Fb is the body force assumed to be the resistance force proportional to the velocity of the relative motion between the solvent and the gel network, expressed as Fb = −f(∂u/∂t), where f is the apparent friction coefficient. The THB model20,21 is a quasi-steady-state approximation of the momentum equation, in which the outward osmotic force balances the inward resistance. As a result, the diffusive-like equation can be established as (K + G /3) ∂u G ≃ ∇2 u + ∇(∇·u) ∂t f f

⎛ ∂ 2E ∂E(r , t ) 2 ∂E ⎞ = De⎜ 2 + ⎟ r ∂r ⎠ ∂t ⎝ ∂r

R(t ) = R max − ur(R max , t )

E(r , 0) = 0 (4)

∂E /∂r = 0

where r is the radial variable, ur is the displacement in the radial direction, and Dswell = (K + 4G/3)/f is the apparent or collective diffusion coefficient for the swelling process. The initial condition is defined as the fully swollen state. The radial displacement ur at time t = 0 is obtained by assuming uniform osmotic stress within the hydrogel, σrr = π0, which leads to r ur(r , 0) = ΔR 0 R max (5)

E = Eb

⎛ ⎞ × exp⎜⎜ − Dswell βn2t ⎟⎟ ⎝ ⎠

⎪

⎪

∂u(r′, t ) ∂t

r = R (t )

(12)

(14)

where the interfacial moving velocity, Ṙ (τ) = Ṙ (t) = −∂u(Rmax,t)/∂t, is given by the analytical displacement function (eq 8). The corresponding initial and boundary conditions now become E(η , 0) = 0

(6)

∂E /∂η = 0 E = Eb

at

for at

0≤η≤1 η=0

η=1

(15)

With the given analytical solutions for R(t) and Ṙ (t) from the swelling dynamics, the transformed enzyme equation can be solved numerically by a standard finite-difference method with a fixed domain and mesh points. 3.3. Degradation of BSA Gel and Diminishing Fluorescence Intensity. The degradation of BSA hydrogel microspheres can be observed from the autofluorescent BSA and the released fluorophore through confocal microscopy. The diminishing fluorescence intensity implies that BSA degradation is caused by the diffusion of proteinase K into the matrix from the bulk solution. Assuming that the self-diffusivity and stressinduced diffusion of the BSA network are negligible during the swelling process, the concentration of the autofluorescent BSA is essentially affected by the gel expansion, swelling-induced advection, and first-order degradation reaction. The reaction is

(7)

The moving boundary is located at r(Rmax,t) = Rmax − ur(Rmax,t). The material moving velocity thus is v(r , t ) = −

r=0

⎛ 2D D ∂ 2E ηṘ ⎞ ∂E ∂E = e2 + ⎜ e2 + ⎟ 2 R ⎠ ∂η ∂τ R ∂η ⎝ ηR

where βn = nπ/Rmax represents the eigenvalues with n = 1, 2, ..., ∞. The prime symbol indicates the Lagrangian approach for the location of the tagged material element at t → ∞, and thus, the location of this tagged material within the swelling gel at time t can be defined as r ( r ′ , t ) = r ′ − u r (r ′ , t )

at

0 ≤ r ≤ R0

where τ ≥ 0 and 0 ≤ η ≤ 1. The transformed diffusion equation can be formulated as

⎞ ∞ ( − 1)n ⎧ cos β r ′ sin(βnr′) ⎫ (n ) ⎨ ⎬ − t ⎟⎟ = 6ΔR 0 ∑ 2 nπ ⎩ βnr′ (βnr′) ⎭ ⎠ n=1 ⎪

at

for

where Eb is the enzyme concentration in the bulk and r = R(t) is a moving boundary condition. The moving boundary problem can be solved by a coordinate transformation to immobilize the outer boundary. Consider the new temporal and spatial variables r τ = t and η = R (t ) (13)

where ΔR0 = π0Rmax/(3K), Rmax is the maximum radius of the gel at equilibrium, and ΔR0 is the total increase of the gel size. The initial size before swelling is R0 = Rmax − ΔR0. The corresponding boundary conditions are zero displacement at the center point and vanishing normal stress σrr at r = Rmax. The analytical solution of the eigenvalue problem given by Tanaka and co-workers20,21 therefore can be expressed in series form as ⎪

(11)

Assuming that the enzyme concentration in the buffer solution remains the same, the corresponding initial and boundary conditions for the enzyme transport are

Assuming that the hydrogel microspheres remain spherical during the swelling process, the above equation reduces to

⎛ ur ⎜⎜r′, ⎝

(10)

for the gel domain, 0 ≤ r ≤ R(t), and time t ≥ 0. The outer boundary of the BSA gel is defined by the time-dependent radius R(t), which can be formulated as

(3)

2 ∂ur ∂ ⎡ 1 ∂(r ur) ⎤ ⎥ = Dswell ⎢ 2 ∂t ∂r ⎣ r ∂r ⎦

(9)

(8)

which is used as the Eulerian velocity field in the transport equations given in sections 3.2 and 3.3. 3.2. Diffusion of Proteinase K. The diffusion of proteinase K from the buffer solution into the swelling BSA hydrogel is a C


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⎛ 2D D ∂ 2F ηṘ ⎞ ∂F ∂F = 2f + ⎜ 2f + + α E ( η R , t ) B (η R , t ) ⎟ 2 R ⎠ ∂η ∂τ R ∂η ⎝ ηR

assumed to be proportional to the concentrations of proteinase K and undegraded BSA. Meanwhile, the BSA degradation sets the combined fluorophore peptide free, so that the fluorophore can diffuse outward into the buffer. The apparent fluorescence intensity can be determined by superposing the concentrations of undegraded BSA and fluorophore, written as I (r , t ) = B (r , t ) + F (r , t )

(24)

for 0 ≤ η ≤ 1 and τ ≥ 0, and the equation is coupled with the gel swelling dynamics through the moving boundary and both enzyme and BSA concentrations. The corresponding initial and boundary conditions are

(16)

where I indicates the fluorescence intensity and B and F represent the concentrations of autofluorescent BSA and free fluorophore, respectively. The BSA transport can be phenomenologically simulated by the advection−reaction equation ∂B + ∇·(Bv) ≃ −α EB ∂t

F(η , 0) = Fb ∂F /∂η = 0 F = Fb

∂ur(r′, t ) ∂t

(18)

(19)

Numerically, the Lagrangian material location r′ can be found by computing the root of the following algebraic equation based on the field location r and time t r′(t ) − ur(r′, t ) − r(t ) = 0

(20)

The corresponding initial and boundary conditions for the traveling-wave-like equation are B(r , 0) = B0 B(r , 0) = 0 ∂B /∂r = 0

for

at

0 ≤ r ≤ R0 r > R0

for

r=0

η=0

η=1

(25)

4. RESULTS AND DISCUSSION Experimental tests were conducted based on two enzyme conditions: 0.5 and 0.05 mg/mL proteinase K in Tris buffer with 5 mM Ca2+. As reported, the Ca2+ concentration can significantly increase the activity and stability of proteinase K. Thus, calcium ion was added to enable degradation of the assynthesized microspheres within 1 h to facilitate the monitoring of degradation by confocal microscopy. The collective diffusivity, Dswell, is estimated from the slope of a plot of the radius squared versus time, R2(t)/t, which was tracked for each swelling BSA hydrogel microsphere. The estimated Dswell value almost remains the same throughout the swelling dynamics, which is phenomenologically approximated by a constant collective diffusivity near the initial stage of the swelling (without defragmentation). Figure 3 shows the experimental data extracted from the swelling and possibly softening microspheres as a result of enzymatic degradation. The uniform osmotic pressure is used as an initial condition, and the transient dynamics is controlled by the collective diffusivity, which represents the overall effect of the bulk modulus, shear

for 0 ≤ r ≤ R(t) and t ≥ 0. The Eulerian velocity field in the radial direction, vr, is the time derivative of the displacement function, expressed as vr(r , t ) = −

at

0≤η≤1

In summary, the three species transport equations along with the THB gel swelling model and the complementary initial and boundary conditions are proposed to resolve the enzyme reaction kinetics leading to the degradation of autofluorescent BSA hydrogel microspheres.

(17)

where v is the velocity field and α is the positive rate constant for the irreversible degradation reaction, which generally depends on the bulk concentrations of Ca2+ and proteinase K. For a spherical configuration, the eq 17 can be expressed as ∂B(r , t ) B ∂ 2 ∂B (r vr) − vr ≃− 2 − αEB ∂t ∂r r ∂r

at

for

(21)

Similarly to the diffusion of proteinase K, the diffusion of fluorophore from the hydrogel to the buffer solution can be computed with an additional source term due to the production of fluorophore from BSA degradation, written as ⎛ ∂ 2F ∂F(r , t ) 2 ∂F ⎞ = Df ⎜ 2 + ⎟ + αEB r ∂r ⎠ ∂t ⎝ ∂r

(22)

for the gel domain 0 ≤ r ≤ R(t) and time t ≥ 0, where Df represents the apparent fluorophore diffusivity within the hydrogel. The corresponding initial and boundary conditions for fluorophore transport are F(r , 0) = Fb ∂F /∂r = 0 F = Fb

at

for at

0 ≤ r ≤ R0 Figure 3. Square of the apparent radius versus time under low ([E] = 0.05 mg/mL) and high ([E] = 0.5 mg/mL) enzyme concentrations at a calcium concentration of [Ca2+] = 5.0 mM. M1, M2, and M3 and M1′, M2′, and M3′ are the selected microspheres under high- and lowenzyme conditions, respectively, and the lines of fitting 1 and fitting 2 indicate the mean values of Dswell, approximately 5.1 × 10−4 and 2.26 × 10−4 μm2/s, respectively.

r=0

r = R (t )

(23)

where Fb is the background fluorescence intensity observed from experiments. Similarly, through coordinate transformation (eq 13), the fluorophore diffusion equation reduces to D


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concentration gradient appears near the edge of the spheres (Figure 4B). The concentration gradient drives the removal or depletion of the fluorophores and decays as the gel progressively swells and degrades. Figure 5 shows the transient radii of the gels compared with the modeling results. The data points were obtained by tracking

modulus, and friction coefficient. Within the time range of interest, not far from the initial stage of degradation, Dswell is approximately a constant, and diffusive-type deformation well describes the dynamics as in the linear elastic regime. The collective diffusivity appears to double as the enzyme concentration is increased from 0.05 to 0.5 mg/mL. Here, we neglect the small variations in Dswell for various microspheres and select a mean value for the theoretical analysis. The modeling parameters include (i) BSA hydrogel, Dswell ≈ 5.1 × 10−4 μm2/s (high enzyme) and Dswell ≈ 2.26 × 10−4 μm2/s (low enzyme), extracted from Figure 3; (ii) for both proteinase K and fluorophore, both De and Df are assumed 100 times the values of Dswell for their corresponding high and low enzyme cases, and this guess is at least 3 orders of magnitude lower than the small molecules with similar size in an aqueous solution; and (iii) degradation rate constant α = 10−3 s−1 and 5 × 10−4 s−1 for the high and low enzyme cases, respectively, are adjusted numerically from sensitivity tests to match the observed fluorescence data as a best-effort approximation. Figure 4 shows a side-by-side comparison of sequential confocal images with the modeling results during the swelling

Figure 5. Two data sets corresponding to high (experimental 1 and model 1) and low (experimental 2 and model 2) enzyme conditions, respectively. The continuous curves are modeling results.

the material points initially located at the outer boundary of the gels. As the BSA hydrogel continuously degraded, the maximum radius Rmax at the almost fully swollen state was determined by setting the ImageJ circularity value at 0.3−1.0. Overall, the transient experimental results agree very well with the modeling results (continuous curves) using the input of the mean collective diffusivity. Because the dynamics is directly observed from the confocal experiment, it is reasonable to first extract Dswell from the configuration and then estimate the reaction constant and other diffusivities by matching the computational results with the distribution of fluorescence intensity. Figure 6 compares the scaled transient fluorescence intensities corresponding to relatively low (Figure 6A) and high (Figure 6B) enzyme concentration distributions. A uniform concentration and fluorescence intensity are assumed for the initial BSA content within the microspheres. The background intensity is set to Fb = 0.1 and remains the same throughout the process. The swelling dynamics and the moving boundary are obvious and qualitatively comparable with modeling results. The enzyme concentration in the BSA microsphere achieves its maximum within 10−50 s for all testing cases, which is much faster than the characteristic time scale for the gel swelling process. This implies that the BSA degradation is limited not by enzyme transport but by the degradation reaction kinetics. The diffusion of the fluorophore is also fast compared with swelling and degradation, and thus, the local fluorophore concentration remains quite uniform within the gel during the process. Therefore, the change in local fluorescence intensity is mainly due to the degradation of the BSA gel. Overall, the empirical model has captured the transient phenomena including gel swelling dynamics and BSA degradation in terms of the fluorescence intensity, except

Figure 4. (A) Sequential confocal images of the swelling BSA hydrogels taken at 0, 20, and 40 min for [E] = 0.05 mg/mL and [Ca2+] = 5 mM. (B) Corresponding modeling results, showing the deformation dynamics with velocity vectors and the scaled fluorophore concentration contours within the gel.

and degradation process. Each fluorescence intensity map was obtained from only the middle section of the selected microsphere (Figure 4A). The computed velocity field in each map represents the localized swelling dynamics at different material points, superposed by scaled fluorophore concentration contours (Figure 4B). The spherically symmetric model has successfully captured several important features of the dynamic process: (i) the diffusion-like elastic expansion of the hydrogel, (ii) the BSA degradation reaction kinetics, and (iii) the overall florescent intensity contributed by the remaining (undegraded) BSA and free fluorophore molecules. The overall expansion in terms of linear dimensions is limited to about 25% during the swelling process. Further degradation for both high and low enzyme concentrations causes fragmentation of the gels, which is not included in the theoretical model. A steeper E


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Furthermore, platforms made of protein-based microparticles exhibit excellent biocompatibility and biodegradability, allowing for advanced developments in multifunctional controlled release, monitoring, and regeneration therapy. In our study, a side-by-side comparison of experimental and modeling results is presented to characterize the enzymatic degradation and fluorophore release kinetics of autofluorecent BSA hydrogel microspheres. This investigation provides a better understanding of the protein-based hydrogel matrix and can potentially be employed for various biomedical applications such as fluorescence imaging and controlled drug delivery.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Yu Lei: 0000-0002-0184-0373 Author Contributions ‡

X.M. and J.-Q.L. contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially funded by the National Science Foundation.

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REFERENCES

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Figure 6. Transient local fluorescence intensity versus time for test cases with relatively (A) high and (B) low enzyme concentrations. Experimental data (symbols) are compared with the corresponding modeling results (solid lines).

near the center part of the hydrogel, where the significantly weakened intensity might be due to the crystallized salt content that is optically opaque. The salt content might come from the spray-dried process. In summary, during the process, the spray-dried BSA hydrogel microspheres are enzymatically degraded by proteinase K in aqueous solution, and the role of proteinase K has been quantified using the phenomenological transport model, which revealed the key features of the swelling dynamics and BSA degradation kinetics through the release of the fluorophore. This study can potentially be applied for dynamic and photostable tracking in many protein-based scaffolds and for studying the in vivo fate of enzymes upon degradation in cells or tissues.

5. CONCLUSIONS Fluorescent particles made of protein hydrogel are often applied as tracking and monitoring agents through noninvasive fluorescence imaging for many biomedical applications, such as long-term in vivo glucose monitoring, in situ monitoring of drug release, and fluorescence labeling for tissue regeneration. F


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Integrated Experimental and Modeling Study of Enzymatic

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