Influence of nanoparticle diameter on conjugated enzyme activity

food and bioproducts processing 9 1 ( 2 0 1 3 ) 693–699

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Influence of nanoparticle diameter on conjugated enzyme activity Joey N. Talbert ∗ , Julie M. Goddard Department of Food Science, University of Massachusetts, 102 Holdsworth Way, Amherst, MA 01003, USA

a b s t r a c t Lactase conjugated to nanomaterials represents an area of significant potential to the food processing as a means to produce novel value-added products, reduce waste, and enable diagnostics. While it is recognized that, in general, matter exhibits unique properties when manipulated at the nanoscale, little is known about how reducing the size of the carrier to the nanoscale effects attached lactase. The purpose of this work is to investigate the influence of particle size on activity retention of lactase (Aspergillus oryzae) covalently conjugated to magnetic nanoparticles of varying sizes. Lactase was attached to carboxylic acid functionalized magnetic nanoparticles 18 nm, 50 nm, and 200 nm in diameter using carbodiimide chemistry. After attachment, activity retention was 73%, 39%, and 14% compared to the free enzyme for the 18 nm, 50 nm, and 200 nm conjugates, respectively. The apparent Km was not significantly different as a function of particle size while the apparent kcat decreased with increasing particle size. Reducing the particle size of magnetic nanoparticles can increase the activity retention of conjugated lactase. This work provides improved understanding of enzyme-nanoparticles systems and allows for enhanced design of lactase-conjugated materials. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Galactosidase; Lactase; Nanoparticle; Nanomaterial; Bioprocessing; Immobilized enzyme

1.

Introduction

Nanomaterials are of interest to the food industry as a means to increase the safety, quality, and value of food products by leveraging the unique properties often exhibited by materials when manipulated at the nanoscale. Nanoparticles, nanofibers, and nanoemulsions have been used to protect additives, deliver active ingredients, and as components in biosensors and active packaging (de Azeredo, 2009; Kriegel et al., 2010; Li et al., 2012; Mita et al., 2007; Rao and McClements, 2011; Sessa et al., 2011; Tan et al., 2011; Troncoso et al., 2012; Wang et al., 2011; Yang et al., 2011; Zhou et al., 2011; Zhu et al., 2012). Nanomaterials have been shown to be useful for enzyme conjugation due to increased protein loading per volume of support, enhanced enzyme-substrate interactions that occur from reduced diffusional restrictions of the substrate as well as catalytic mobility that is more akin to the free enzyme than a traditional immobilized enzyme, reduced gravitational sedimentation, and reduced detrimental

∗

lateral protein-protein or surface-protein interactions that occur from an increasing radius of curvature with decreasing particle size (Kim et al., 2006, 2008; Rana et al., 2010; Wang, 2006; Asuri et al., 2006b; Shang et al., 2007, 2009; Talbert and Goddard, 2013). Magnetic nanoparticles are of special interest due to the ability of these materials to be separated from the reaction stream without the need for centrifugation, which requires high speeds or materials with a high density compared to the reaction solution (Yiu and Keane, 2012). Likewise magnetic particles do not require filtration units that may, due to the size of nanoparticles, limit product flux. Though knowledge of enzyme interactions with nanomaterials is increasing, there is a gap in the understanding and utilization of enzyme-nanomaterial conjugates for food applications. The purpose of this study is to aid in bridging that gap by evaluating the influence of material size on the retained enzymatic activity of lactase covalently immobilized to carboxylic acid functionalized magnetic nanoparticles. Lactase (␤-galactosidase; EC 3.2.1.23) is an enzyme commercially

Corresponding author. Tel.: +1 413 577 0466; fax: +1 413 545 1262. E-mail address: [email protected] (J.N. Talbert). Received 1 July 2013; Received in revised form 8 August 2013; Accepted 12 August 2013 0960-3085/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fbp.2013.08.006

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derived from Kluyveromyces lactis and Aspergillus oryzae that is used in the food processing to reduce lactose in whey and fluid milk, as a component in the analysis of lactose, and for production of oligosaccharide prebiotics. Immobilization of the enzyme to material supports has been employed to reduce cost and provide a means to separate the enzyme from the product (Ansari and Husain, 2010; Conzuelo et al., 2010; Goddard et al., 2007; Guidini et al., 2011; Husain et al., 2011; Kosseva et al., 2009; Neri et al., 2009, 2011a,b; Panesar et al., 2006; Park and Oh, 2010; Talbert and Goddard, 2012). Recent studies suggest that immobilization of ␤-galactosidase enzymes to nanomaterials yields conjugates with high activity retention (Talbert and Goddard, 2013; Husain et al., 2011; Dwevedi et al., 2009; Pan et al., 2009). While it is recognized that, in general, matter exhibits unique properties when manipulated at the nanoscale, little is known about the effect of material properties on activity retention. This work investigates the influence of particles size on the activity retention of lactase covalently conjugated to carboxylic acid functionalized, magnetic nanoparticles for the purpose of advancing understanding of enzyme-nanoparticles systems and enhanced design of lactase-conjugated materials for use in food systems.

2.

Fig. 1 – Carbodiimide-mediated conjugation of lactase to nanoparticles. Separator). The extent of nanoparticle recovery was assessed by measuring the absorbance of the recovered nanoparticle solution at 400 nm and comparing to a standard curve developed through serial dilution of a known concentration of nanoparticles.

Materials and methods 2.4.

2.1.

Nanoparticle characterization

Materials

Magnetic nanoparticles with iron oxide cores and surface carboxylic acid groups derived from oleic acid with reported hydrodynamic diameters of 18 nm (Ocean Nanotech; Springdale, Arkansas, USA), 50 nm (Chemicell; Berlin, Germany), and 200 nm (Chemicell; Berlin, Germany) were purchased from the manufacturers. 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) was purchased from ProteoChem (Denver, CO, USA). 2-nitrophenol (99%) was purchased from Acros Organics (Geel, Antwerp, Belgium). O-nitrophenol␤-d-galactopyranoside (ONPG), sulfo-N-hydroxysuccinimide (Sulfo-NHS), bicinchoninic acid (BCA) assay reagents, and bovine serum albumin were purchased from Thermo Scientific (Rockford, IL, USA). Amicon Ultra centrifugal filter devices (50 K MWCO) were purchased from Millipore Ireland (Carrigtwohill, Co. Cork, Ireland). Syringe filters (0.22 ␮m) were purchased from Fisher (Fairlawn, NJ, USA). Dried lactase preparation from A. oryzae was kindly donated by Enzyme Development Corporation (New York, NY, USA) and purified as described below. All other chemicals and reagents were purchased from Fisher Scientific (Fairlawn, NJ, USA) and used as received.

The number of available carboxylic groups on the surface of the nanoparticles was confirmed using a modification of the Toluidine Blue dye assay (Kang et al., 1996). Nanoparticles (25 ␮l) were suspended in 1 ml of 5 × 10−4 M Toluidine Blue O in deionized water adjusted to pH 10.0 by NaOH. All experiments were performed at room temperature (ca. 20 ◦ C) unless otherwise stated. Following three hours of rotational mixing, nanoparticles were magnetically separated for 24 h. After separation, the solution was removed and the nanoparticles were rinsed twice in distilled water adjusted to pH 10.0 to remove non-complexed dye, suspended in 1 ml pH 10.0 water and magnetically separated for 24 h at room temperature. After separation the solution was removed and the particles were suspended in 1 ml 50% v/v acetic acid for 15 min at room temperature to desorb the complexed dye and then magnetically separated for 24 h at room temperature. Following separation, the desorbed dye was removed and diluted in acetic acid as needed. The absorbance of the desorbed dye was read at 633 nm and the concentration of surface carboxyl groups were determined by comparison with a standard curve of dye in 50% v/v acetic acid.

2.2.

2.5.

Lactase preparation

Commercial lactase was purified by preparing a solution in phosphate buffer (10 mM; pH 7.0) that was syringe filtered through a 0.22 ␮m filter, followed by centrifugal filtration in 50 kDa MW centrifugal filter units (5000 × g; 22 ◦ C). The lactase solution was recovered in phosphate buffer (10 mM; pH 7.0) and stored at 4 ◦ C until use. Protein concentration of the purified lactase preparation was determined using the BCA assay as described elsewhere (Smith et al., 1985).

2.3.

Nanoparticle separation

Nanoparticles were removed from reaction solutions using a high gradient magnetic separator (Ocean Nanotech: SuperMag

Nanoparticle activation

Nanoparticles were activated using a two-step EDC/NHS reaction. The scheme of the overall nanoparticle activation and enzyme conjugation pathway is illustrated in Fig. 1. All experiments were performed at room temperature (ca. 20 ◦ C) unless otherwise stated. Carboxylic acid groups on the surface of the nanoparticles were activated by addition of a volume of particles to achieve an available surface area of 1.7 × 1016 nm2 /ml of the appropriate buffer. Preliminary experiments determined that the appropriate conjugation buffer for 15 and 50 nm diameter nanoparticles was 0.1 M borate buffer pH 5.5 while the 200 nm diameter nanoparticles needed 10 mM MES buffer pH 5.5 as a conjugation buffer to prevent aggregation during activation. EDC was added to a final concentration of 4 × 10−4 M

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and sulfo-N-hydroxysuccimide (sulfo-NHS) was added to a concentration of 4 × 10−3 M. Sulfo-NHS was employed rather than N-hydroxysuccinmide (NHS) to maintain a negative charge on the activated nanoparticles. Activation in this manner limits particle aggregation and precipitation of the intermediate. The reaction was allowed to proceed for 30 min to yield an activated succinimidyl ester on the surface of the nanoparticles. At the completion of the reaction time, 2mercaptoethanol was added to a concentration of 9 × 10−4 M and allowed to react for 10 min to quench unreacted EDC (Hermanson, 1996). Mercaptoethanol was added to the reaction to quench excess EDC to prevent enzyme crosslinking (Carraway and Triplett, 1970). The second step of the reaction results in a covalent attachment of lactase to the surface of the nanoparticles through a zero-length attachment between free amines on the enzyme and activated carboxylic acids on the particle, allowing for study of direct interaction with the carrier surface.

2.6.

Enzyme conjugation to nanoparticles

Purified lactase was added to a solution of activated nanoparticles in conjugation buffer to a concentration of 0.27 mg/ml and allowed to react for two hours under rotation. All experiments were performed at room temperature (ca. 20 ◦ C) unless otherwise stated. At the completion of the reaction time, samples were magnetically separated from the reaction buffer for 1 h, 3 h, and 17 h for 200 nm, 50 nm, and 18 nm particles, respectively. After completion of the separation time, the reaction buffer was removed and the particles were washed two additional times with the storage buffer (10 mM phosphate buffer; pH 5.5) prior to final dilution in the storage buffer. For lower protein loading experiments, one-half of the experimental maximum quantity of protein that could be loaded per support was added in the conjugation buffer to the same concentration of nanoparticles.

2.7.

Protein loading on nanoparticles

The protein concentration of soluble and immobilized enzyme was determined using an enhanced bicinchoninic acid (BCA) assay (Smith et al., 1985; Plant et al., 1991). After completion of the BCA reaction period, the solution was passed through a 0.22 ␮m syringe filter to exclude aggregated particles. The absorbance of the filtered solution was read at 562 nm and compared to a bovine serum albumin (BSA) standard curve. The standard curve was spiked with an equivalent amount of protein-free nanoparticles and subjected to identical conditions to account for the influence of nanoparticles on spectrophotometric readings.

2.8.

Enzyme activity

The activity of lactase was determined based on the Food Chemicals Codex method for the determination of acid lactase units (Anonymous, 2003). An amount of the native or immobilized enzyme consisting of 1 ␮g of protein was added to 2.5 ml of a buffer solution containing 9.6 mM solution of orthonitrophenyl-␤-galactopyranoside (ONPG), and allowed to react under shaking for 15 min at 50 ◦ C and pH 5.0 (0.1 M acetate buffer). At the completion of the time period, 2.5 ml of 10% sodium carbonate was added to stop the reaction. The solution was diluted to 25 ml with deionized water, absorbance read at 420 nm, and activity calculated from the extinction

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coefficient of ortho-nitrophenol (ONP) compared to a control containing no enzyme and spiked with an equivalent amount of protein-free nanoparticles subjected to identical reaction conditions to account for the influence of nanoparticles on spectrophotometric readings. Activity retention was expressed as percentage activity relative to the native enzyme at 50 ◦ C and pH 5.0.

2.9.

Enzyme kinetics

The Michaelis–Menten kinetics of native lactase and apparent kineticsof immobilized lactase were determined by a method described by Cavaille (Cavaille and Combes, 1995). An 8 mM solution of ONPG in 0.1 M acetate buffer (pH 5.0) was serially diluted to establish a substrate range from 0 to 8 mM. Lactase (1 ␮g enzyme as free or immobilized enzyme-nanoparticle conjugate) was added to individual tubes containing 2.5 ml of the ONPG solutions. The reaction was allowed to proceed for four minutes at 50 ◦ C with representative tubes stopped every 30 s by removing 150 ␮l of the solution and adding to 150 ␮l of 10% sodium carbonate. The absorbance was measured at 420 nm and the velocity of product conversion was determined using the initial rate of the reactions and the extinction coefficient of ONPG. The Michaelis constant (Km ) and Vmax were extrapolated from nonlinear regression of a plot of velocity versus substrate concentration using Michaelis–Menten enzyme kinetics (v. 5.04, Graphpad Software, Inc., La Jolla, CA, USA). The turnover number (kcat ) was determined by dividing the Vmax by the initial enzyme concentration assuming a molecular weight of 105,000 Da for the enzyme (Tanaka et al., 1975). Apparent kinetics are designated by the prime symbol ( ).

2.10.

Statistical analysis

Statistical analysis was conducted using Graphpad Prism software (v. 5.04, Graphpad Software, Inc., La Jolla, CA, USA). One-way analysis of variance (ANOVA) was conducted followed by Tukey’s pairwise comparison to determine statistical difference at a significance level of 0.05.

3.

Results and discussion

3.1.

Nanoparticle characterization

For enzyme-conjugated nanoparticles to be useful, the catalyst must be able to be separated from the product. Magnetic nanoparticles offer the potential to recover the enzyme catalyst through the application of an external field that allows for recovery of the enzyme without non-specific separation of components in the product matrix (Yiu and Keane, 2012). The magnetic nanoparticles used in this study contained an iron oxide core that permitted the carrier to be directed toward a magnetic support. The separation time was inversely proportional to the diameter of the beads. While the magnetic nanoparticles tested were able to be recovered, it is important to note that the rate was slow with 17 h being required to obtain ≥50% recovery of nanoparticles with an 18 nm core size when using a high gradient magnet (Table 1). Prior to adoption for food applications, further research is warranted on improving the separation efficiency of magnetic nanoparticles to improve commercial utilization. Surface charge density (i.e. the surface area per carboxylic acid) was assessed by determining the carboxylic acid density

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Table 1 – Characterization of nanoparticles used for conjugation of lactase. Particle size (nm)

Surface charge density (Å2 /Carboxylic acid group)

Protein loading (mg/m2 )

89.3 ± 1.2 74.2 ± 2.3 15.2 ± 0.9

18 50 200

3.8 ± 0.6 1.1 ± 0.2 1.2 ± 0.2

Enzymes/particle (#)

Separation time (h)

22 ± 4 50 ± 9 865 ± 144

17 3 1

Values represent mean ± standard deviation (n = 3).

of nanoparticles through the use of dye binding. As seen in Table 1, the carboxylic acid density for the nanoparticles was inversely proportional to size, with the largest nanoparticle presenting the smallest surface area per carboxylic acid, and the smallest nanoparticle presenting the largest. However, the difference among nanoparticles was less than one order of magnitude. Most importantly for our study, all nanoparticle sizes had multiple carboxylic acid functional groups were available for surface activation and subsequent enzyme attachment.

Protein loading was determined to be 3.8 mg/m2 , 1.1 mg/m2 , and 1.2 mg/m2 on the 18 nm, 50 nm, and 200 nm supports, respectively (Table 1). As expected, surface loading of the enzyme per volume increased with decreasing particle size. These numbers indicate that protein loading on the surface of the support is approaching that of a monolayer when considering the size of lactase from A. oryzae to be between 6.8 nm and 12 nm (Talbert and Goddard, 2013; Yang et al., 1994).

followed by 38% and 14% activity retention after conjugation to 50 nm and 200 nm particles, respectively. With each increase in particle size, a significant decrease (p < 0.05) was seen in activity retention of the conjugated enzyme. These results indicate that activity retention is a function of particle size, and smaller carriers can yield recoverable conjugates with specific activity approaching that of the free enzyme. These results are in agreement with other published work. Indeed, the increase in activity retention with decreasing size of carrier has been documented for enzymes adsorbed to the surface of the materials including nanoparticles and nanotubes. Enhanced activity retention with decreasing material size has been attributed to reduced interactions between protein molecules on the surface of the material, reduced collision rates between the conjugated enzyme and the substrate, diminished boundary layers for substrate diffusion, and fewer interactions between the enzyme and the surface of the carrier (Shang et al., 2009; Asuri et al., 2006a; Bailey and Cho, 1983; Illanes et al., 2010; Jia et al., 2003). The importance of each of these influences was evaluated to elucidate the mechanisms for the observed activity retention as a function of particle size.

3.3.

3.4.

3.2.

Protein loading on nanoparticles

Enzyme activity

Activity retention of lactase was evaluated after conjugation to nanoparticles of the described sizes, and compared to the specific activity of the soluble enzyme. After covalent conjugation, enzymatic activity was retained on all particles (Fig. 2). It was observed that activity retention under evaluated conditions (50 ◦ C; pH 5.0) was inversely proportional to particle size. Relative to the free enzyme, the highest activity retention (73%) was seen after conjugation of lactase to 18 nm particles

Fig. 2 – Activity retention of lactase in the free form and conjugated to nanoparticles of 18 nm, 50 nm, and 200 nm. Values represent means ± 95% confidence intervals (n = 5).

Effect of protein loading on enzyme activity

Lateral protein–protein interactions on the surface of carrier can lead to a decrease in activity retention due to associations between adjacent enzyme molecules on the surface of the carrier (Asuri et al., 2006a). By decreasing the size of a particle, the curvature of the particle increases and lateral interactions are reduced. To determine if lateral protein–protein interactions were responsible for decreased activity retention as a function of particle size, the amount of enzyme offered for conjugation on the nanoparticles was reduced to onehalf the maximum protein loading obtained when offering excess enzyme to the nanoparticles (Fig. 3). Reducing the enzyme loading on the nanoparticles is expected to yield reduced interactions between adjacent protein molecules on the surface of the carrier. If lateral protein–protein interactions are responsible for loss of enzymatic activity, an increase in activity should be observed with decreasing protein loading. We were able to successfully reduce the amount of enzyme loaded onto the nanoparticle surfaces by controlling the concentration of enzyme in the conjugation buffer. With reduced protein loading, no significant difference in retained enzyme activity was observed for 18 nm and 200 nm particles, and a significant decrease in retained activity (p < 0.05) was observed for the 50 nm particles at loadings of 1.0 mg/m2 , 0.48 mg/m2 , and 0.41 mg/m2 for 18 nm, 50 nm, and 200 nm particles, respectively (Fig. 4). The decrease in activity for the 50 nm particle may be due to enhanced surface interactions between the protein and carrier that increase when the enzyme-material interactions are not restricted by neighboring enzyme molecules under high loading conditions (Cruz et al., 2010a,b; Bosley and Peilow, 1997). These interactions

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Fig. 3 – The influence of protein loading on lateral protein-protein interactions on nanoparticles. (a) Maximum protein loading. (b) One-half maximum protein loading. may be minimal on the 18 nm particles, regardless of loading, due to surface curvature of the particle. Likewise, neighboring molecules may have little influence on restricting enzymematerial interactions when the enzyme is conjugated to large particles (i.e. 200 nm particles) or planar surfaces. These results suggest that lateral protein–protein interactions are not the primary cause of loss of enzyme activity retention as a function of particle size.

3.5.

Effect of particle size on enzyme kinetics

For enzymatic product conversion, a substrate needs to interact with an enzyme. Reducing the size of a carrier can enhance substrate interactions with a conjugated enzyme by increasing the mobility of enzyme–carrier conjugate. Likewise, decreasing the particle size can yield a reduction in the effective boundary layer that limits the mass transfer of a substrate to the surface of the catalysis (Jia et al., 2003; Oh and Kim, 2000). These effects become especially interesting when enzymes are immobilized onto nanomaterials. Attachment of enzymes to nanoparticles results in conjugates that are able to diffuse and collide with substrates in a manner than is more akin to a free enzyme than an “immobilized” enzyme that is stationary on a macro-scale carrier (e.g. film, microparticle) in the reaction medium. Reducing the size of the particle increases the mobility of the enzyme-conjugate and increases the rate of collision as described by the Stokes-Einstein equation (Jia et al., 2003). Additionally, thin films around the surface of a carrier can limit the substrate diffusion to the carrierattached enzyme. These boundary layers decrease with the size of the particle, and can cause the rate of substrate diffusion to limit product conversion rather than the intrinsic rate

of enzymatic conversion of the substrate (Shuler and Kargi, 2002). When substrate diffusion limits product conversion, activity retention may appear to decrease. Under the assumption that no denaturation of the enzyme occurs after conjugation, and the rate constant for disassociation of the enzyme–substrate complex as well as the turnover number (kcat ) remain unchanged, an increase in the apparent Km would suggest that reduced collisions caused by a decrease in molecular diffusivity with increasing particle size limits the apparent activity of the attached enzyme. However, after conjugating the enzyme to the nanoparticles, no significant change in Km  was seen as a function of carrier size (Table 2). This result indicates that molecular collisions caused by decreased diffusion of the enzyme conjugate with increasing carrier size does not account for the loss of activity retention. With increasing particle size, a reduction in apparent catalytic efficiency (kcat  /Km  ) was observed. This reduction correlated with a decrease in apparent turnover number (kcat  ). Because kcat  is calculated from the Vmax  and protein concentration of a reaction and assumes that all protein in the solution is enzymatically active, the observed reduction in kcat  as well as catalytic efficiency may be due to denaturation or reorientation of the enzyme on the surface of the carrier. The presence of inactive enzyme on the carriers would appear as artificially low turnover numbers and catalytic efficiency when calculated. This result indicates that the loss of activity retention may be due increased carrier-protein interactions at the interface, which can decrease with particle size due to increased curvature of the carrier. Boundary layers can appear to reduce enzyme activity retention due to a lowering of substrate diffusion (Shuler and Kargi, 2002). With increasing particle size, the thickness of the effective boundary layer becomes greater which can in turn limit activity of enzymes immobilized to flat carriers (Oh and Kim, 2000; Kamal et al., 2008; Kheirolomoom et al., 2002). To determine if boundary layers pose a problem for the enzyme–nanoparticle conjugate systems studied herein, the liquid mass transfer coefficient (kL ) was calculated using Eq. (1) and the Damköhler number (Da) was calculated according to Eq. (2) (Shuler and Kargi, 2002): kL =

Da = Fig. 4 – Influence of protein loading on the activity retention of lactase conjugated to nanoparticles of 18 nm, 50 nm, and 200 nm. Values represent means ± 95% confidence intervals (n = 5).

Ds ı  Vmax kL [SB ]

(1)

(2)

When the rate of diffusion is low compared to the enzymatic reaction rate, product formation is limited by substrate diffusion as indicated by a Da of >1. However, when

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Table 2 – Kinetics of free lactase and enzyme-conjugated nanoparticles. Particle size (nm)

Km (mM)

Native Lactase 18 50 200

0.97 0.84 0.87 0.70

± ± ± ±

0.05 0.15 0.11 0.32

kcat (s−1 ) 258 199 146 44

± ± ± ±

13 43 67 9

kcat /Km (M−1 s−1 ) 2.66 × 105 2.40 × 105 1.67 × 105 0.71 × 105

± ± ± ±

0.01 × 105 0.47 × 105 0.73 × 105 0.28 × 105

Values represent mean ± standard deviation (n = 3).

the Da is <1, the system is limited by reaction kinetics. Given the molecular diffusion (Ds ) of the ONPG substrate (6.5 × 10−10 m2 /s) and the effective boundary layer of the nanoparticle, which is approximately equal to the diameter of nanoparticle (i.e. < 200 nm), the liquid mass transfer (kL ) for the enzyme conjugated nanoparticles was calculated to be >0.32 cm/s (Galli, 2006; Swarts et al., 2010). The maximum reaction rate per unit surface (Vmax  ) for the tested enzyme was calculated to be 3 × 10−10 mol/s cm2 , and the bulk substrate concentration [SB ] was assumed to be in excess of Km for the entirety of the activity reaction. When using these values and Eq. (2), the dimensionless Damköhler number (Da) is determined to be 9 × 10−9 , which is «1, and indicates that the boundary layer can be assumed to be negligible as product conversion is reaction limited rather than limited by substrate diffusion (Shuler and Kargi, 2002).

4.

Conclusions

These results, in combination with the data presented above, indicate that reducing the particle size of magnetic nanoparticles can increase the activity retention of conjugated lactase. Lateral protein-protein interactions and mobility of the carrier are not responsible for the loss of enzymatic activity, and suggests that the primary mechanism for increasing retained activity with decreasing nanoparticle size may be due to interactions of the enzyme with the surface of the particle, which are reduced with increasing curvature (i.e. decreasing particle size). This work provides improved understanding of the interactions between enzymes and material surfaces, and allows for enhanced systematic design of lactase-conjugated materials for use in food and agricultural applications.

Acknowledgements This work was supported in part by Dairy Management Inc. as managed by Dairy Research Institute (Rosemont, IL) and in part by the UMass Amherst Center for Hierarchical Manufacturing, a nanoscience shared facility funded by the National Science Foundation under NSF Grant no. CMMI-1025020.

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