Catalytic Behaviors of Enzymes Attachedto Nanoparticles: The Effect ofParticle Mobility

Hongfei Jia, Guangyu Zhu, Ping Wang

Department of Chemical Engineering, The University of Akron, Akron,Ohio 44325-3906; telephone: 330-972-2096; e-mail: wangp@ukron.edu

Received 28 January 2003; accepted 18 June 2003

Published online 11 September 2003 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.10781

Abstract: Nanoparticles provide an ideal remedy to theusually contradictory issues encountered in the optimiza-tion of immobilized enzymes: minimum diffusional limita-tion, maximum surface area per unit mass, and higheffective enzyme loading. In addition to the promisingperformance features, the unique solution behaviors of thenanoparticles also point to a transitional region betweenthe heterogeneous (with immobilized enzymes) and homo-geneous (with soluble free enzymes) catalysis. The particlemobility, which is related to particle size and solutionviscosity through Stokes-Einstein equation, may impactthe reaction kinetics according to the collision theory. Themobility-activity relationship was examined through ex-perimental studies and theoretical modeling in the pre-sent work. Polystyrene particles with diameters rangingfrom 1101000 nm were prepared. A model enzyme,a-chymotrypsin, was covalently attached to the nano-particles up to 6.6 wt%. The collision theory model wasfound feasible in correlating the catalytic activities ofparticles to particle size and solution viscosity. Changesin the size of particles and the viscosity of reaction media,which all affect the mobility of the enzyme catalyst,evidently altered the intrinsic activity of the particle-attached enzyme. Compared to KM, kcat appeared to beless sensitive to particle size and viscosity. B 2003 WileyPeriodicals, Inc. Biotechnol Bioeng 84: 406414, 2003.Keywords: nanoparticle; nanotechnology; enzyme immo-bilization; collision theory; kinetics; viscosity

INTRODUCTION

Immobilized enzymes are preferred for most large-scaleapplications, largely because of the ease in catalystrecycling, continuous operation, and product purification.Often the catalytic efficiency limits the development oflarge-scale bioprocessing to compete with traditional chem-ical processes (Caruana, 1997; Demirjian et al., 1999). One

important approach to improve the efficiency of immobi-lized enzymes is to manipulate the structure of carriermaterials. Nonporous carrier materials, to which enzymesare attached at the surfaces, are subject to minimumdiffusional limitation (Horak et al., 1999; Kamei et al.,1987). However, enzyme loading per unit mass of support isusually considerably low. Alternatively, high enzymeloading can be achieved with porous materials (Cantarellaet al., 1988; Huang et al., 2001; Kajiwara et al., 1990;Martinek et al., 1977; Wang et al., 2001). Porous materials,however, suffer a much greater diffusional limitation. Forexample, the value of effectiveness factor (h) for a-chy-motrypsin was reported to bec 0.3 when it was entrapped inpolyacrylamide hydrogel (Martinek et al., 1977), below 0.1when incorporated into hydrophobic plastics (Wang et al.,1997), and less than 10!3 when cross-linked (Cerovsky andJakubke, 1994).To date, extensive R&D efforts have been conducted to

optimize the carrier materials structure to make more effi-cient biocatalysts (Balcao et al., 1996; Kennedy et al., 1990;Tischer and Wedekind, 1999; Wiseman, 1985). In this re-gard, nano-structured materials will provide the upper limitsin terms of balancing the contradictory issues includingsurface area, mass transfer resistance, and effective enzymeloading (Jia et al., 2002). Recently reported work in this areahas revealed the great potential for the use of nanoporous(Wang et al., 2001), nanofibrous (Jia et al., 2002), andnanoparticle (Caruso and Schuler, 2000; Daubresse et al.,1996; Liao and Chen, 2001; Martins et al., 1996) materialsas a new class of carriers for biocatalysts. The effectiveenzyme loading on nanomaterials can be very high (forexample, it can reach over 10 wt% with particles smallerthan 100 nm (Chen and Su, 2001)), and a large surface areaper unit mass is also provided to facilitate reaction kinetics.An interesting question arises considering the unique

physical behaviors of nanoparticles. Unlike large-size solidmaterials, nanoparticles dispersed in a solution are mobile inform of Brownian motion. In that sense, the enzymes

B 2003 Wiley Periodicals, Inc.

Correspondence to: Ping WangContract grant sponsor: National Science Foundation NER ProgramContract grant number: BES-0103232

attached to nanoparticles are not immobilized. On theother hand, according to the Stokes-Einstein equation, themobility or diffusivity of the nanoparticles has to be smallerthan those of native free enzymes due to their relativelylarger sizes. This mobility difference may point to atransitional region between the homogeneous catalysis withfree enzymes and the heterogeneous catalysis with immo-bilized enzymes. The question that follows that assumptionis Will the mobility of the nano-sized biocatalysts, inaddition to other factors such as structural stress, impact theintrinsic activities of the attached enzymes? In otherwords, does the size of the particles affect enzymesactivity? We address these questions in the current studythrough experimental observations and theoretical modelingof the catalytic behaviors of nanoparticles.

MATERIALS AND METHODS

Materials

a-Chymotrypsin (CT) from bovine pancreas, N, N-dime-thylformamide (DMF), dimethylsulfoxide (DMSO), divinyl-benzene (DVB), n-succinyl-ala-ala-pro-phe p-nitroanilide(SAAPPN), p-nitroaniline, and 4-methylumbelliferyl p-tri-methylammonium cinnamate chloride (MUTMAC) werepurchased from Sigma Chemical Co. (St. Louis, MO).Styrene, ethanol (HPLC grade), sodium hydroxide (NaOH)were obtained from EM (Gibbstown, NJ). 2,2V-Azobis [2-methyl-N-(2-hydroxyethyl) propionamide] (VA-086) waskindly provided as a gift from Wako Chemicals USA, Inc.(Richmond, VA). HPLC-grade methanol and toluene werepurchased from J.T. Baker (Phillipsburg, NJ). 2-Sulfoethylmethacrylate (2-SEM) was purchased from Monomer-Polymer & Dajac Labs, Inc. (Feasterville, PA). Epichlo-rohydrin (ECH), polyethylene glycol (PEG, MW 10 kDa),and polyvinylpyrrolidone (PVP, MW 29 kDa) were pur-chased from Aldrich (Milwaukee, WI). N-Acryloxysuccini-mide (NAS) was obtained from Acros Organics (Belgium).

Preparation of Nanoparticles

Nanoparticles were prepared via emulsion polymerization.Different recipes were used to prepare particles with sizeranging from 0.1 f1 Am. The stock solution of emulsifier,2-SEM, was prepared by dissolving 5 g of 2-SEM in 50 gDI water, and then diluting to 100 g using water while pH ofthe solution was adjusted to 3.5 by adding 10 wt% NaOHsolution (the pH of the 2-SEM solution from the supplierwas f 1). The emulsion solutions were prepared by dis-solving certain amount of NAS (ranging from 98196 mg)in the mixture of styrene (0.6 f 1.2 mL) and DVB (8.2f16.0 AL) in a 20-mL scintillation vial, followed by mixingwith the aqueous phase, which contains the initiator (VA-086, 2.5 mg/mL), stabilizer (PVP, up to 5.5 mg/mL), etha-nol (0.125 f0.50 mL/mL), and 2-SEM (25 f75 AL/mL).The phase ratio was controlled in the range of 1/30 to 1/15

(oil/aqueous). The vial was purged with nitrogen, sealed,and emulsified on a vortexer before the reaction. Polymer-ization was initiated by heating the system to 70jC in awater bath with stirring. The reaction was stopped after 10 hand the particles were washed with ethanol and DI water in astirred ultrafiltration cell (Milipore Corp., Bedford, MA)with a polyethersulfone membrane (cut-off MW: 300 kDa).Clean particles were stored in DI water at 4jC.Particle morphology was studied with both scanning

electronic microscopy (SEM) and transmission electronicmicroscopy (TEM). Particle size and distribution weredetermined by measuring at least 100 particles (from TEMimages) for each type of samples. Number-based meandiameter (Dn) and weight-based mean diameter (Dw) werecalculated by: Dn = S Di/N and Dw = S D i4/S D i3, where Nis the number of particles. Particles with sizes ranging from110 nm to 1000 nm were prepared, and the dispersity of theparticle size (defined as Dw/ Dn ) was < 1.05.

Enzyme Attachment

The enzyme was covalently attached onto polymericparticles via a coupling reaction between the succinimideester group of NAS and amino groups of enzyme (Chen andSu, 2001). Typically, the precleaned nanoparticles were firstdispersed into 0.1M pH 6.0 phosphate buffer at a concen-tration off50 mg/mL, and then 30 mg of CT was dissolvedin 2 mL of this particle-containing buffer in a 20-mL vial.The reaction mixture was stirred at 4jC for 10 h. pH 6 wasreported as the optimum condition for the enzyme attach-ment reaction and it was also inhibitory to the hydrolysisreaction of the functional group of NAS (Anjaneyulu andStaros, 1987; Chen and Su, 2001). The resulted enzyme-attached particles were purified using ultrafiltration (cut-offMw of 300 kDa): after each filtration, f45 mL of fresh pH7.8 buffer (0.05M phosphate) containing 0.2M NaCl wasadded into the filtration cell. The filtration cell was thensubject to 20-min sonication (using Branson 5510, Bran-don), followed by filtration under nitrogen. The particleswere washed at least 5 times till the filtrate solution showedno absorbance at 280 nm and no detectable SAAPPNhydrolysis activity. The final particles were rinsed with DIwater 3 times and stored at 4jC. Our tests showed that thesame rinsing procedure could effectively wash off theenzyme physically adsorbed to nonactive poly(styrene)particles (prepared without the use of NAS).The amount of active CT on particles was determined by

active site titration (Gabel, 1974). Typically, 100 AL ofsolution of particles (containing f 1 mg particles) wasadded to 3 mL MUTMAC solution (0.025 mg/mL, in pH7.5 borate buffer), and then the solution was shaken at roomtemperature (22jC) for 1 min, followed by removing theparticles with 0.02 Am syringe filters (Whatman Inc.,Clifton, NJ). The concentration of the reaction product wasmeasured using fluorescence (excitation at 360 nm,emission at 450 nm) on a luminescence spectrometer(Model LS50B, Perkin-Elmer Analytical Instruments).

JIA ET AL.: THE EFFECT OF PARTICLE MOBILITY ON ENZYMES ATTACHED TO NANOPARTICLES 407

Kinetic Studies

The hydrolytic activity of CT was measured using SAAPPNas substrate in 0.05M pH 7.8 phosphate buffers containing0.2M NaCl and 2 vol% DMSO. PEG was used as theviscogenic agent to control the viscosity of the reactionsolution (with concentrations up to 15 wt%). Viscosity wasmeasured with a falling ball viscometer (Barnat Company;Barrrington, IL) at room temperature.The hydrolysis of SAAPPN was monitored using a UV-

visible spectrophotometer (Shimadzu, Model UV-1601).For a typical measurement for native enzyme, 3 mL ofenzyme solution (c 8 nM) was mixed with 60 AL ofsubstrate stock solution in a 4-mL cuvette. The reactionrates were determined by monitoring the absorbance at410 nm (corresponding to the formation p-nitroaniline).Calibration curves were obtained separately for reactionsolutions containing different amounts of PEG to offsetpossible changes in extinction coefficient due to theaddition of PEG (Wells and DiCera, 1992). The activityof particle-attached enzyme was measured through thesame reaction. Typically, 14.7 mL buffer solution was firstmixed with 300 AL SAAPPN stock solution in a 20-mLvial. The reaction was then initiated by the addition ofparticles with stirring (dispersed in DI water). Aliquots of3 mL each were taken periodically for analyses of productconcentration using UV absorbance after filtration (0.02 Amsyringe filter). The absorbance at 410 nm of the reactionsolution after filtration remained constant for at leastseveral hours, indicating that the reaction was stoppedeffectively by the removal of the particles and that no freeenzyme leached off the particles. Michaelis-Menten kineticparameters, kcat and KM, were determined using the initialreaction rates measured with six different substrateconcentrations (15 f200 AM).

Enzyme Activity on Thin Film

To simulate the extreme situation where the particle sizeapproaches infinity, the activity of CT modified with poly-styrene (PS) and assembled as a thin film at the oil/waterinterface was measured. Polystyrene was first synthesizedvia free radical polymerization initiated by VA-086.Typically, 40 mL styrene was mixed with 160 mL toluenein a 500-mL reactor, followed by the addition of 20 mLVA-086 DMF solution (72 mg/mL). The reaction mixturewas incubated under nitrogen at 90jC with stirring for 8 hand finally stopped by washing the reaction mixture withmethanol. The molecular weight (Mw) of the PS used in thepresent work was 8000 Da, as determined by gel permeationchromatography (GPC). Polystyrene was activated byadding epichlorohydrin (1 mL) to a mixture of 2.5 mL of4% (w/v) NaOH solution, and 5 mL PS toluene solution(100 mg/mL). The reaction was carried out at roomtemperature for 8 h, followed by solvent evaporation. CTwas conjugated with activated PS through a biphasicreaction: 5 mL of a solution containing CT (15 mg/mL in

pH 6.1 citrate buffer) was mixed with 5 mL activated PStoluene solution (50 mg/mL) at 4jC for 24 h. The reactionmixture was then centrifuged and washed thoroughly withpure toluene and buffer to remove unreacted PS andenzyme, respectively. The amount of enzyme in the finalproduct was determined by active site titration (c 2.8 wt%).Interfacial reaction was carried out in a toluene/buffer

(10 mL/80 mL) biphasic system with the PS-enzymeconjugate partitioned at the interface and substratedissolved in buffer. Interfacial reaction rate was derivedfrom the product generation rate. Substrate concentrationused fro the study ranged from 2.08.8 mM.

THEORETICAL MODELS

Collision theory provides the upper limits of enzyme-catalyzed reactions (Blanch and Clark, 1997; Fersht, 1999).The reaction rate constant for a bimolecular reaction can beexpressed as:

kcoll Z # p # e!Eact=RT 1

where Z is the collision frequency, p a steric factor, and Eactthe activation energy. Taking the reagents (A and B) asspherical particles, Z (mol!1s!1) can be expressed as:

Z 4kNAvoDA DBrA rB1000

2

where NAvo is Avogadros number, while DA and DB arediffusion coefficients, rA and rB the radii of A and B, re-spectively. According to the Stokes-Einstein equation:

D kBT6kDr

3

where kB is Boltzmann constant, h the viscosity of themedium, the expression of Z can be further rearranged into:

Z 2RT3000D

rE rS2

rErS

" #4

where rE and rS are the radii of enzyme and substrate mole-cules, respectively.Although the Stokes-Einstein equation was originally

developed for small particles such as a single molecule, ithas been reported to be effective in predicting the mobilityof particles of sizes up to micrometer range (Bremmellet al., 2001; Crocker, 1997; Norris and Sinko, 1997).Assuming the validity of the Stokes-Einstein equation, theoverall collision frequency between the enzyme-attachedparticles and the substrate molecules can be expressed as:

Z0 2RT3000D

rPE rS2

rPErS

" #5

where rPE = rP + 2 rE corresponds to the radius of theparticles covered by monolayer of enzyme molecules. The

408 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 84, NO. 4, NOVEMBER 20, 2003

collision density (collisions per unit surface area) can becalculated as:

dcoll Z0

4krPE26

Taking the cross-section area of an enzyme molecule askrE2, the collision frequency between each enzymemolecule and the substrate can be expressed as:

Z RT6000D

rPE rS2r2ErPE 3rs

" #7

or

Z / rPE rS2r2E

DrPE 3rS: 8

For enzyme attached to spherical particles of the samematerial, size difference should not affect the steric factor( p) and activation energy (Eact). For a given nanoparticle-catalyst system, usually rP rS, Eq. (8) can be further sim-plified to

kcoll / Z / 1D # rPE

9

Should the collision theory be followed, Eq. (9) reflectsthe effect of particle size, and associated with that, theeffect of viscosity of reaction media on the reactionkinetics. On the other hand, kcoll can be related toMichaelis-Menten kinetic parameters for enzymatic reac-tions. For example, consider the hydrolysis of SAAPPNcatalyzed by a-chymotrypsin, which was generally taken as(Blanch and Clark, 1997; Fersht, 1985):

E S !k1

k1

ES(!k2 AE(!k3 E P2 P1 10

where ES and AE are reaction intermediates, P1 and P2hydrolytic products. Assuming Michaelis-Menten equationfor the apparent reaction rate (r),

r kcatE0(S(KM S(

, 11

where [E0] is the total enzyme concentration, kineticparameters, kcat (turnover number), KM (apparent dissoci-ation constant), and kcat/KM (apparent second-order rateconstant) can be defined as:

kcat k2k3

k2 k3; 12

KM k!1 k2

k1

k3k2 k3

; 13

and

kcatKM

k1k2k!1 k2

: 14

Three steps in the proposed reaction pathway may besubject to diffusional limitation: the association of enzymeand substrate (k1), dissociation of enzyme-substrate inter-mediate complex (k!1) and the release of products (k3).According to collision theory, these three rate constantsshould be affected by collision frequency, while the otherrate constant, k2, should be independent from the collisionfrequency and thus independent from solution viscosity (h)or catalyst size (rPE). The application of Eq. (9) to each ofk1, k!1, and k3 will then lead to the prediction for thedependency of kcat and KM on h and rPE. Specifically, as hor rPE increases, k3, k1, and k!1 should decrease, and kcatand kcat/KM decrease [see Eqs. (12) and (14)]. On the otherhand, KM has a bit more complicated response to changes inh or rPE. Equation (13) can be rearranged into:

KM k3k1

k!1=k2 1k3=k2 1

! ": 15

Noticing that in addition to k2, the ratio of k3/k1 doesnot change with viscosity and particle size either, KMwill decrease with h or rPE if k!1 > k3, or will increase ifk!1 < k3.The dependence of Michaelis-Menten kinetic parameters

of native enzymes on viscosity has been reported in sev-eral previous studies (Brouwer and Kirsch, 1982; Kawaiet al., 2000; Wells and Di Cera, 1992). In this work, theeffects of particle size and solution viscosity on the cata-lytic activity of particle-attached enzymes will be exam-ined by evaluating the above mathematical analysis usingexperimental data.

EXPERIMENTAL RESULTS AND DISCUSSIONS

Particle Preparation and Enzyme Attachment

Emulsion polymerization has been proven as an effectivemethod to prepare various polymeric particles withdiameters in the range of 5100 nm (Meier, 1999). Toexamine the effect of particle size on reaction kinetics,polystyrene particles of different size (1001000 nm indiameter) have been prepared by controling the amount ofemulsifer and the oil/water phase ratio. The polymerizableemulsifier (2-SEM) worked well in the preparation of smallparticles (f110 nm in diameter). Particles with diametersin the order of Am can be prepared without using anyemulsifier (Reese and Asher, 2002), but we experiencedcoagulation of the oil phase. Aqueous phase compositionprovides another tunable variable to control particle size.Generally, we observed that higher ethanol content led tolarger particles. Adding 50% (v/v) of ethanol into aqueousphase can usually increase the size of the particles bythreefold. However, the particle surface became roughwhen too much ethanol (> 70%) was used. Polyvinylpyrrol-idone (PVP), a stabilizer frequently used in dispersionpolymerization (Horak and Shapoval, 2000; Ma et al.,

JIA ET AL.: THE EFFECT OF PARTICLE MOBILITY ON ENZYMES ATTACHED TO NANOPARTICLES 409

2001), was applied to provide extra controling in particlesize and morphology. By manipulating the system com-position, monodispersed particles of four different sizeswere synthesized as the supports for the current study. Theimages of the smallest and the largest particles used in thecurrent study are shown in Figure 1, with number-basedaverage diameters of 110 and 1000 nm, respectively.a-Chymotrypsin was attached onto the particles via

covalent binding. The co-monomer (NAS) provided theactive succinimide group for direct enzyme attachment(Scheme 1). However, the hydrolysis of succinimide esterhappens in aqueous environment (Uludag et al., 2000),which competes with the immobilization reaction. Toaddress this issue, a high NAS content (9% mol) wasapplied in the preparation of nanoparticles, which offeredf10-fold functional groups needed to achieve monolayerenzyme coverage on the surface of nanoparticles. Inaddition, the acidic reaction conditions during bothpolymerization and immobilization were believed to beinhibitory to the hydrolysis of the succinimide ester group(Anjaneyulu and Staros, 1987; Chen and Su, 2001; Schnaarand Lee, 1975).Control experiments were conducted to confirm that the

enzyme was covalently attached to the particles. First, thevigorous washing procedure applied in the preparation ofthe particles was proven effective in washing off anyphysically adsorbed enzyme molecules. Second, the hydro-lytic reaction of SAAPPN catalyzed by the particles waseffectively stopped by the removal of the particles from the

reaction solutions via filtration (filter with pores size of0.02 Am), indicating that no free enzyme leached off theparticles during the reaction. The amount of enzymeattached to the particle surface was determined by activesite titration (Gabel, 1974). A theoretical enzyme loading,which varies with the diameter of the nanoparticles, can becalculated by assuming monolayer coverage of the outersurface of the particles. The experimental data for differentparticle sizes are shown along with theoretical calculationsin Figure 2. The loading for the 110 nm particles wasmeasured as 6.6 wt%, corresponding to a surface coverageof 83%. This is the amount of enzymes used for activitycalculation in the following discussions in this work. Theactual amount of total protein is expected to be higher thanthe loading determined through active site titration.

Figure 1. Polystyrene particles prepared by emulsion polymerization.(A): TEM image of particles of 110 nm in diameter; (B): SEM image ofparticles of 1.0 Am in diameter.

Figure 2. Enzyme Loading on Particles of Different Sizes. (.):Measured enzyme loading via active site titration. (): theoreticalenzyme loading corresponding to monolayer coverage (the molecularweight and diameter of a-chymotrypsin are taken as 25 kDa and 5.6 nm,respectively; the number of enzyme molecules corresponding to mono-layer coverage on the particles was determined by:

N 4krPE2

1:05krE 2

where rPE = rP + 2 rE; and rP and rE are the radius of CT molecules andparticles, respectively; the density of the particles is taken as 1.04 g/cm3).

Scheme 1. Chemical route for enzyme attachment.

410 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 84, NO. 4, NOVEMBER 20, 2003

The Effect of Particle Size

The hydrolysis of SAAPPN, catalyzed by CT attached topolystyrene particles with different sizes, was performed.The apparent Michaelis-Menten kinetic parameters deter-mined from experiment data are listed in Table I. It appearsthat kcat and kcat/KM decreased, while KM increased, withincrease in particle size. For example, when particlediameter increased from 110 to 1000 nm, KM doubledwhile kcat decreased by 25%. Interestingly, the kcat/KM ofsmall particles showed values higher than that of freeenzyme (Fig. 3). That is mostly due to the decrease in KMas compared to that of free CT. The theoretical mechanismsbehind this observation are not clear yet to the authors. It issuspected that the attachment of enzymes onto the surfacesof particles might improve the enzyme-substrate interactionby avoiding the potential aggregation of free enzymemolecules. Also, accountable are the complicated responsesof KM to changes in the mobility of the catalysts, asdiscussed below.While the experimental observation of kcat and kcat/KM

followed the trend predicted from collision theory, under-standing changes in KM requires more information about

k!1 and k3, which are to be evaluated through the followingstudy on the effect of viscosity.

The Effect of Viscosity

The dependence of kcat/KM on viscosity has been used as asimple steady-state method to determine individual reactionkinetic parameters for enzymatic reactions (Brouwer andKirsch, 1982; Loo and Erman, 1977; Nakatani andDunford, 1979). For a typical enzymatic reaction followingMichaelis-Menten kinetics, the dependence of rate con-stants on viscosity can be expressed as k = k0/hrel, wherehrel (= h/h

0) is the relative viscosity (Nakatani andDunford, 1979), and the superscript 0 denotes areference state. The apparent second-order rate constant,kcat/KM, can be related to hrel (Loo and Erman, 1977):

KMKcat

1k10

Drel 1

k10

k0!1k2

16

Plotting KM/kcat vs. hrel should give the association rateconstant (k1) from the slope and the partition ratio of the EScomplex, k!1

0/k2, from the intercept. The value of k!10/k2,

which is related to the value of (kcat/KM)/k1, also offers aparameter to determine whether the reaction system issubject to diffusional limitation. By rearranging Eq. (14)we can have:

kcat=KMk1

1k!1=k2 1

17

If k!1/k2 > 1, there is no diffusional limitation;if k!1/k2 is close to 1, the system is subject to light dif-fusional limitation.

Table I. Kinetic parameters for CT on particles with different sizes.

ParticleDiameter (nm) kcal (s

!1) KM (AM)kcal/KM

(106# M!1#s!1)

0a 17.8 (1.2) 47.8 (F2.9) 0.37 (F0.05)110b 20.0 (1.16) 31.7 (F2.7) 0.63 (F0.11)270b 18.6 (1.7) 40.9 (F3.2) 0.46 (F0.08)490b 19.4 (1.4) 66.4 (F4.5) 0.29 (F0.04)1000b 15.4 (1.3) 63.7 (F4.6) 0.24 (F0.04)lc 8.7 (0.4) 3300 (F200) 0.0026 (F0.001)

a Free CT.b Particle-attached CT.c Self-assembled CT thin film at the toluene/buffer interface.

Figure 3. The effect of particle size on kcat/KM. (n): reaction catalyzedby free CT; (5): reaction catalyzed by immobilized CT.

Figure 4. Determination of kinetic constants from the effect of visco-sity. Blank buffer (without PEG) was used as the reference state; (D):reaction catalyzed by free CT; (w , x): reaction catalyzed by CT immo-bilized on 1.0 Am particles in blank (hrel = 1) and PEG containing buffers.

JIA ET AL.: THE EFFECT OF PARTICLE MOBILITY ON ENZYMES ATTACHED TO NANOPARTICLES 411

The values of KM/kcat were plotted vs. hrel (relative toblank buffer) in Figure 4 with the data listed in Table II.Following Eq. (16), k1 and k!1/k2 for free CT (in blankbuffer) were calculated to be 6.6 ) 106M!1s!1 and 16.1,respectively. By following the same treatment, k1 and k!1/k2 for free CT in solutions of different viscosities werecalculated and are listed in Table III (Part A). In the case ofparticle-attached enzyme, the observations were morecomplicated. As shown in Figure 4, the KM/kcat in blankbuffer (hrel = 1) was off the general trend as indicated bydata for viscous solutions. It was suspected that the additionof PEG might complicate the interactions among substrate,enzyme, and the support. Values for k1 and k!1/k2 forparticle-attached CT were estimated by using data atelevated viscosities and were listed in Table III (Part B).Overall, experimental data indicated stronger diffusional

limitations with elevated viscosities. According to calcu-lated values for k!1/k2, free CT in blank buffer has littlediffusional limitation, and is subject to only slight diffu-sional limitations even in highly viscous solutions.Compared to free CT, particle-attached CT showed muchstronger diffusional limitation. This observation supportsthe kinetic data obtained for the effect of particle sizes inthat they both confirmed the applicability of the collisiontheory. Noticeably, the diffusional limitation (as indicatedby both the values of k!1/k2 and (kcat/KM)/k1) increasedlargely with increase in viscosity.As discussed above, the dependence of KM on h or rPE is

determined by the ratio between k!1 and k3. From thecalculations as listed in Table III, values of k!1/k2 forparticle-attached enzymes were generally low (c 1). Onthe other hand, it was demonstrated that k3 >> k2 (k3/k2 was103) (Kawai, 2000). Therefore, k!1 for the reactionconcerned here should be

(Table I). Since the activities associated with smallparticles did not show a dramatic difference from that offree CT (Table I), we can assume that the attachment of PSdid not change significantly the intrinsic activity of CT, andthat the conformational changes and other microenviron-mental interactions would not lead to the big loss of CTactivity observed with the thin film. The authors believethat the observed large gap between the activities of theenzyme attached to small particles and that immobilizedas a flat film is largely due to the effect of the mobility ofthe catalysts.

CONCLUSIONS

The present study demonstrated the validity of a simplemodel developed based on Stokes-Einstein equation andcollision theory for the prediction of catalytic behaviors ofnanoparticle biocatalysts. The model was proven feasiblein correlating the effects of particle size and viscosity onthe catalytic kinetics of the particle-attached enzyme.These observations suggest that the mobility of thecatalysts is an important factor in determining theiractivities, and thus providing an explanation, among otherconsiderations, for the high activities usually observed forenzymes attached to nanoparticles. It was also demon-strated that the loss of catalyst mobility, in addition toother factors such as protein conformational changes, alsocontribute to the loss of intrinsic activities of immobi-lized enzymes.

The authors thank Mr. Craig Hrobak for help in some experi-mental work. This work was supported by a grant from NationalScience Foundation (BES=0103232).

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