Measurements of Kinetic Parameters in a Microfluidic Reactor

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Anal. Chem. 2006, 78, 8273-8280

Measurements of Kinetic Parameters in a Microfluidic Reactor Matthew B. Kerby,‡ Robert S. Legge,† and Anubhav Tripathi*,†

Biochemical Engineering Laboratory, Division of Engineering, Brown University, Providence, Rhode Island 02912

Continuous flow microfluidic reactors that use immobilized components of enzymatic reactions present special challenges in interpretation of kinetic data. This study evaluates the difference between mass-transfer effects and reduced efficiencies of an enzyme reaction. The kinetic properties of immobilized alkaline phosphatase (AP) were measured by the dephosphorylation of 6,8-difluoro-4methylumbelliferyl/phosphate to a fluorescent 6,8-difluoro-4-methylumbelliferone. A glass microfluidic chip with an in-channel weir was created for the capture of solid silica microbeads functionalized with enzyme. The input substrate concentrations and flow rates across the bed were varied to probe the flow-dependent transport and kinetic properties of the reaction in the microreactor bed. Unlike previous reactors, substrate was titrated directly over the fixed enzyme bed by controlling the air pressure over the chip reservoirs. The reactor explored substrate conversions from near zero to 100%. The average bed porosity, residence time, and bed resistance were measured with dye pulses. A simple criterion was derived to evaluate the importance of flow-dependent mass-transfer resistances when using microreactors for calculating kinetic rate constants. In the absence of masstransfer resistances, the Michaelis-Menten kinetic parameters are shown to be flow independent and are appropriately predicted using low substrate conversion data. A comparison of the kinetic parameters with those obtained using solution-phase enzymatic reactions shows a significant decrease in enzyme activity in the immobilized conformation. The immobilized Km of AP is ∼6 times greater while the kcat is reduced by ∼28 times. Contradictions found in literature on the evaluation of Michaelis-Menten kinetic parameters for immobilized enzymes in microfluidic reactors are addressed. When product molecules occupy a significant number of enzymatic sites or modify the enzyme activity, the assumed Michaelis-Menten mechanism can no longer be valid. Under these conditions, the calculations of “apparent” kinetic rate constants, based on Michaelis-Menten kinetics, can superficially show a dependence on flow rate conditions even in the absence of mass-transfer resistances. High substrate conversions are shown to depend on flow rate. A kinetic model based on known mechanisms of the alkaline phosphatase enzyme reaction is tested to predict the measurements for high substrate 10.1021/ac061189l CCC: $33.50 Published on Web 11/14/2006

© 2006 American Chemical Society

conversion. The study provides a basis for appropriate use of mass-transfer and reaction arguments in successful application of enzymatic microreactors. Continuous flow microfluidic reactors provide a platform for studies of biomolecular and medically relevant reactions, where conservation of costly reagents and reproducibility are important. Immobilization of enzymes or substrate allows for sparing use of reagents or repeated enzyme use. Proteins, RNA, and DNA from investigative samples are commonly produced or available only in small quantities. Since purifications of large quantities of these substances from cells can be prohibitively expensive or labor intensive, a tool for rapid biomolecular detection, identification, and characterization of function from limited samples is desired. Microfluidic reactors offer the potential to screen hundreds or thousands of different combinations of enzymes, substrates, and solution conditions.1,2 The applications of microreactors include protein and peptide mapping,3-5 analysis of nucleic acids,6,7 determination of posttranslational modifications such as phosphorylation, glycosylation, and lipidylation,8 combinatorial synthesis,9 and characterization of molecules or single cells. These applications have importance in drug discovery, medical diagnostics, therapy, biosensors, and immunoassay development.2,10,11 Mass-transfer resistance and reduced enzyme activity both negatively impact microreactor yields. While the effects on operation are similar, solutions for each cause is very different. The fundamental characteristics of a continuous flow reactor can be quantified through kinetic measurements using either immobilized substrate or enzymes.12-14 However, conversion of existing enzyme assays to a microfluidic format is not trivial. * To whom correspondence should be addressed. E-mail: Anubhav_tripathi@ brown.edu. † Chemical and Biochemical Engineering. ‡ Biomedical Engineering. (1) Watts, P.; Haswell, S. J. Drug Discovery Today 2003, 8 (13), 586-93. (2) Krenkova, J.; Foret, F. 2004, 25 (21-22), 3550-63. (3) Palm, A. K.; Novotny, M. V. Rapid Commun. Mass Spectrom. 2004, 18 (12), 1374-82. (4) Wu, H.; et al. Lab Chip 2004, 4 (6), 588-97. (5) Gevaert, K.; Vandekerckhove, J. Electrophoresis 2000, 21 (6), 1145-54. (6) Hashimoto, M.; et al. Lab Chip 2004, 4 (6), 638-45. (7) Lagally, E. T.; Scherer, J. R.; Blazej, R. G.; Toriello, N.M.; Diep, B. A.; Ramchandani, M.; Sensabaugh, G. R.; Riley, L. W.; Mathies, R. A. Anal. Chem. 2004, 76 (11), 3162-70. (8) Nalivaeva, N. N.; Turner, A. J. Proteomics 2001, 1 (6), 735-47. (9) Watts, P.; Haswell, S. J. Comb. Chem. High Throughput Screening 2004, 7 (5), 397-405. (10) Urban, P. L.; Goodall, D. M.; Bruce, N. C. Biotechnol. Adv. 2006, 24 (1), 42-57. (11) Bilitewski, U.; et al. Anal. Bioanal. Chem. 2003, 377 (3), 556-69.

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Microfluidic assays often require adjustment of enzyme, substrate, and especially buffer composition to avoid adsorption to the surface of the chip channel, which will bias the results or cause the assay to fail.15 Large surface-to-volume ratios in the microfluidic device modify the adsorption-desorption characteristics of reactant and products, which alter the kinetics of the reaction. Intentional immobilization of enzymes often results in reduced enzymatic activity due to an altered protein conformation, steric hindrance of the catalytic site, or both.16 In addition, a diffusion layer around the immobilized support can lead to mass-transferlimiting reaction rates.14 Recently, a microfluidic reactor was used to evaluate the kinetic parameters in an immobilized enzymatic reaction. Mao et al.17 used multiple concentrations of substrate to determine the kinetics of alkaline phosphatase (AP) immobilized in a microchannel under zero flow conditions. On the wall of this device, streptavadinconjugated enzyme was bound to biotinylated phospholipid layers. The Michaelis constant, Km, and the maximum velocity of reaction, vmax, were obtained by using Lineweaver-Burk. The Km was found to be close to the value obtained in solution-phase conditions; however, the turnover rate kcat was found to be 6 times smaller than observed in bulk conditions. Imperfect immobilization chemistry, altered conformation of enzyme, and steric hindrance were presented as possible causes for the observed difference; however, the Km values were unaffected by above deficiencies. The mass-transfer limitations were not discussed in this study. Subsequently, Seong et al.18 studied immobilized horseradish peroxidase and immobilized β-galactopyranoside enzyme reactions in a continuous flow packed-bed microreactor. Data were analyzed using the Lilly-Hornby equation, which was originally derived19 by balancing convective transport of substrate with its consumption in a Michaelis-Menten-type reaction under steady-state conditions. The authors computed a Km value for the immobilized enzyme microreactor that was derived from data extrapolated to a zero flow condition. This immobilized Km was similar to the Km obtained during homogeneous catalysis in a solution-phase batch mode. The extrapolation step was supported by arguing that mass transfer plays a role in “masking the intrinsic enzyme kinetics”. The similarity in Km values is puzzling given that increases in flow rates reduce mass-transfer resistances by thinning the diffusion layer around solid substrates. In fact, the results obtained by Seong et al.18 contradict those obtained by Lilly et al.19 for hydrolysis of benzoylarginine ethyl ester in packed columns. Lilly et al. demonstrated a decrease in Km with an increasing flow rate of substrate through the reactor bed. Extrapolation of data to large flow rates, and therefore to low mass-transfer resistance, was argued to correspond to the intrinsic reactor rate conditions. It (12) Levenspiel, O., Ed. Chemical reaction engineering; 3rd ed.; J. Wiley: New York, 1999, (13) Schmidt, L. D. The engineering of chemical reactions, 2nd ed.; Oxford University Press: New York, 2005. (14) Fogler, H. S. Elements of Chemical Reaction Engineering. 3rd ed.; International Series in the Physical and Chemical Engineering Sciences; Prentice Hall: Upper Saddle River, NJ, 1999. (15) Wu, G.; et al. Comb. Chem. High Throughput Screening 2003, 6 (4), 30312. (16) DeLouise, L. A.; Miller, B. L. Anal. Chem. 2005, 77 (7), 1950-6. (17) Mao, H.; Yang, T.; Cremer, P. S. Anal. Chem. 2002, 74 (2), 379-85. (18) Seong, G. H.; Heo, J.; Crooks, R. M. Anal. Chem. 2003, 75 (13), 3161-7. (19) Lilly, M. D.; Hornby, W. E.; Crook, E. M. Biochem. J. 1966, 100 (3), 71823.

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will be shown in this work that the mass-transfer resistance cannot be the likely cause for the flow rate dependence of the Michaelis constant, Km, as observed by Seong et al. Recently, Gleason and Carbeck20 performed a steady-state kinetic analysis on a glass slide microreactor using an immobilized alkaline phosphatase enzyme. Conversion of nonfluorescent methylumbelliferyl phosphate (MUP) to the fluorescent product, 7-hydroxy-4-methylcoumarin was studied. The kinetic parameters were solved from equations describing transport and Michaelis-Menten reaction at a surface. The convective transport of reactant in the flow direction was balanced with its diffusive transport normal to the surface. The experiments were performed at a sufficiently high flow rate to create a thin diffusion boundary layer. Here the observed values of Km agreed fairly well with those obtained in solution-phase experiments, and the observed kcat values were found to be significantly lower than those obtained in solution phase. Imperfect immobilization chemistry, altered conformation of enzyme, and steric hindrance were again proposed as possible causes for the observed difference in kcat. More recently, Koh and Pishko21 performed experiments using alkaline phosphatase immobilized in a hydrogel structure in a microfluidic device. As p-nitrophenylphosphate was converted to phosphoric acid, the pH in the microenvironment decreased. The measured apparent Km values were 6 times lower than the referenced literature value obtained in solution phase. Mass-transfer resistance through the hydrogel was proposed to explain the disagreement between the immobilized and solution-phase Km. DeLouise and Miller studied glutathione-S-transferase on silicon where the immobilized Km was ∼4× greater and the kcat was ∼5× lower than the solution-phase enzyme.16 At equivalent concentrations, vmax for the immobilized enzyme was ∼20 times lower than in solution. Their results suggested that 25% of the bound enzyme was unavailable for reaction, either through hindered orientation or conformationally inactivation. Last, Liu et al.22performed kinetic analysis of the Michaelis-Menten equation using an electrochemically analyzed enzymatic reaction of glucose oxidase adsorbed on PET sheets. Under zero flow conditions, the observed value of Km was found 2 times lower than those obtained in solution-phase experiments. Table 1 summarizes the experimental conditions and kinetic parameters obtained in some of the studies discussed. The literature review in Table 1 clearly shows variability in data interpretation for computation of kinetic rate constants. Furthermore, the studies inherently assume the validity of a Michaelis-Menten mechanism for the immobilized enzymatic reaction in their operating range of conversions and input substrate concentrations. In this paper, we describe the reaction kinetics of immobilized alkaline phosphate using a short, or differential, length of packed beads in a microfluidic chip. The alkaline phosphatase enzyme was immobilized on the bead surface and reused for multiple reaction measurements. Kinetic reaction parameters were obtained experimentally at multiple flow rates for both low and high substrate conversion percentages. The relative importance of mass-transfer resistance was estimated by appropriately balancing the diffusional flux with the reaction on the bead surface. This study discusses some of these contradictions that impact data (20) Gleason, N. J.; Carbeck, J. D. Langmuir. 2004, 20 (15), 6374-81. (21) Koh, W. G.; Pishko, M. Sens. Actuators, B 2005, 106 (1), 335-42. (22) Liu, A. L.; et al. Lab Chip 2006, 6 (6), 811-8.

Table 1. Summary of Kinetic Parameters and Experimental Conditions in Select Previous Studies immobilized Km (µM)

study

solution phase Km (µM)

flow condition

Lilly et al. (1966)

3.5

2.5

Q large

Seong et al. (2003) Mao et al. (2002)

1.51 363 12500/16200

1.55 380 14000

Qf0 Qf0 Q)0

Gleason and Carbeck (2005)

100 ( 50

49 ( 2

Q ) 4 mL/min

Koh and Pishko (2005)

2800 ( 400 570 350 1000 ( 300

2200 ( 500 3000 10500 251 ( 22

Q ) 4 mL/min Q ) 5 - 20 µL/min

DeLouise and Miller (2005)

(1)

where D [(m2)/s] is the molecular diffusivity of the substrate molecules, k* [1/s] is the intrinsic reaction rate constant, and ΓA [mol/m2] are the moles per unit area of reactive sites occupied by substrate molecules. The reaction rate is assumed to be proportional to the number of molecules interacting with the immobilized enzyme on the surface. The substrate concentration on the surface, ΓA, can be estimated by assuming the Michaelisβ1

β2

Menten mechanism A + E {\ } AE 98 E + B + P for the R1 enzymatic reaction. Substrate A binds reversibly with the enzyme E to form an enzyme-substrate complex AE. AE also proceeds to product B and P to regenerate E. This mechanism is only valid if the number of sites occupied by molecules B or P is negligible. This classical assumption is valid only for low conversion of substrate. Adsorption and desorption rates govern the concentration of substrate molecules, which is proportional to the number of unoccupied and occupied enzymatic sites, respectively. This leads to

dΓA ) β1(Γ∞ - ΓA)CsA - (R1 + β2)ΓA dt

ficin bound to cellulose, Km decrease with Q horseradish peroxidase β-galactosidase AP + MUP, no mass-transfer effects discussed AP + MUP, pH 9, convection diffusion model is used AP + MUP, pH 10 AP+pNPP, pH 8.2 urease glutathione-S-transferase

Q)0

analysis in biochemical and microfluidics research. In the next section, we derive a simple criterion for estimating the importance of mass transfer on the kinetics of a continuous flow reaction through packed beads with surface-immobilized enzymes. Theoretical Details. The immobilized enzymatic reactions may be subject to mass-transfer limitations if fluid flow through the reactor is insufficient to resupply substrate to active enzymes that are immobilized on the bead surface. For rates of substrate transport that are lower than the rate of reactive consumption on the surface, the substrate concentration, CsA, at the surface is less than the bulk substrate concentration, CbA, in the fluid. A concentration gradient, {(CbA - CsA)}/{δ}, will be established across a diffusion layer of thickness, δ. The diffusive flux of substrate molecules will be balanced by the rate of reaction on the surface as

CbA - CsA D ) k*ΓA δ

comments

(2)

where Γ∞ represents the total moles of substrate per unit area of enzymatic sites on the bead surface. At steady state, eq 2

mass transfer, λ ∼large ∼9.5 × 10-6 ∼5 × 10-6 ∼0.1 ∼0.75 ∼0.12 ∼large ∼large ∼0.1

transforms to

ΓA )

Γ∞CsA Km + CsA

(3)

where Km ) (R1 + β2)/β1 is the Michaelis constant. For a packed bed of spheres of radius, R, and porosity, , the rate reaction per unit volume can be written as

vmaxCsA 3k*(1 - )Γ∞ CsA ) ) rv ) k*ΓA4πR R 4πR3/3 Km + CsA Km + CsA 2 (1

- )

(4) where vmax ) {3k*(1 - )Γ∞}/R is the maximum velocity (mol volume-1 s-1) of the reaction. Substituting this expression for vmax and the surface concentration from eq 3 into eq 1 results in

1-

CsA CbA

)λ

CsA Km + CsA

(5)

The dimensionless parameter λ ) (vmaxδR/3(1 - )DCbA) quantifies a ratio of reaction rate to mass-transfer rate. Large values of λ indicate the rate of reaction is large and mass-transfer effects limit the system. Small values indicate the mass-transfer rate is large, and the reaction limits the system. With increasing flow rate, the diffusion layer around the bead thins such that the substrate concentration, CsA, in the fluid near the surface approaches the bulk concentration, CbA. These examples from literature illustrate how mass-transfer and reaction effects can be quantitatively separated. Seong et al.18 performed their experiments using 15.5-µm-diameter closely packed beads. By assuming a diffusion layer thickness of δ ∼ 0.1R, a substrate diffusivity of D ≈ 10-9 m2/s, and porosity of  ) 0.33, the dimensionless parameter is approximately λ ) 9.5 × 10-6 for CbA ) 10 µM and vmax ) 1.90 µM/min. The small value of λ suggests that the mass-transfer resistances were not a likely cause for the observed flow rate dependence reported by Seong et al.18 In contrast, Lilly et al.19 performed experiments using celluloseficin packed columns with high porosity of  ) 0.75 under fast reaction conditions, where vmax was high. Insufficient data preAnalytical Chemistry, Vol. 78, No. 24, December 15, 2006

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Figure 1. (a) Schematic of the chip design, which shows a shallow weir between nodes N4 and N5. The bead bed, of user-defined length, occupies the microchannel between nodes N3 and N4. The flow is from left to right. The dimensions of channels are tabulated in Table 2. (b) Flowing from the right, the 5.06-µm spheres are trapped against the 4-µm-deep weir in a 15-µm microfluidic channel to create the packed bed.

vented precisely calculating a λ value; however, based on reaction data, these experiments were mass-transfer limited with large values of λ, which supports a flow rate dependence of the apparent kinetic parameters. The λ values for other studies are listed in Table 1. At steady state, the mole balance in a differential packed bed reactor yields

u

vmaxCbA dCbA )dz K + Cb m

(6)

A

Here, u is the superficial velocity in the bed. The MichaelisMenten mechanism is assumed in the derivation of this equation. Equation 6 can be integrated over length, L, of the reactor to obtain

CbAL

Km ln

CbA0

+ CbAL - CbA0 ) -

vmaxVbed Q

(7)

where CbA0 and CbAL are the inlet and outlet concentrations of substrate, Q is the flow rate in the packed reactor, and Vbed is the total volume of the reactor bed. Equation 7 has the same form derived by Lilly et al.19 Equation 7 can be used to evaluate Km and vmax in a reactor by curve fitting the input and output substrate concentrations assuming that a Michaelis-Menten mechanism accurately describes the enzymatic reaction on the surface. To validate this interpretation of the immobilized enzyme kinetics in a packed bed microfluidic reactor, we used AP to dephosphorylate quenched 6,8-difluoro-4-methylumbelliferyl phosphate (DiFMUp) to fluorescent 6,8-difluoro-4-methylumbelliferone 8276

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(DiFMU). The reactor was operated from a classical low substrate conversion percentage to full conversion to evaluate the role of flow-dependent, mass-transfer resistance. EXPERIMENTAL SECTION Materials. Calf intestinal alkaline phosphatase biotin (APbiotin) was obtained from Rockland Immunochemical (Gilbertsville, PA). Streptavidin-coated silica microspheres (5.06-µm diameter) were obtained from Bang’s Labs (Fischers, IN). DiFMUp (14 000 cm-1 M-1 at 320 nm) and fluorescent DiFMU (18 000 cm-1 M-1 at 358 nm)23 were purchased from Invitrogen (Carlsbad, CA). Both were freshly reconstituted, calibrated by UV absorbance (ND-1000, NanoDrop Wilmington, DE), and frozen as aliquots at -20 °C until needed. A priming buffer of 50 mM Tris pH8, 2% DMSO, 0.01% Tween 20, and 0.1% BSA was used to prevent nonspecific adhesion of AP-biotin to the channel walls. These reagents were obtained from Sigma-Aldrich (St. Louis, MO). All kinetic measurements were conducted in 50 mM Tris at pH8. Microreactor, Detection, and Flow Control. Figure 1a shows a schematic of a packed bead bed reactor, which was created in a borosilicate glass microfluidic chip by creating a 5-µm shallow weir within the 12-µm-deep main channel. The chip fabrication and design details are provided in the Supporting Information section. An inverted Nikon TE2000 microscope with a mercury lamp and UV-2E/C filter set (ex/em 372 nm/480 nm) attached to a PTI 814 and D-104 photomultiplier detector (Photon Technology International, Birmingham, NJ) recorded fluorescence in analog mode. The detector gain (1×) and integration time (50 ms) were selected to maximize accuracy, sensitivity, and signal(23) Sun, W. C.; Gee, K. R.; Haugland, R. P. Bioorg. Med. Chem. Lett. 1998, 8 (22), 3107-10.

Figure 2. Immobilized enzyme dephosphorolating nearly nonfluorescent DiFMUp (left side) into the fluorescent DiFMU (right side) as it flows through the bed.

to-noise ratio. Previous studies20,24,25 were performed using less sensitive and potentially nonlinear camera-based detection methods whereas the PMT “single pixel” is optimized for photon measurements. A PMT detection region over the chip channel was defined using manual shutters at the start of the experiment and not adjusted further. Transit Time Measurement. The hydrodynamic channel resistance of the double-depth chip with and without beads was calculated also from dye transit times. The pressure over reservoir 2 containing 10 µM DiFMU was increased stepwise at time zero while monitoring the fluorescence intensity immediately downstream of the shallow channel weir shown in Figure 1a as channel segment 7. The perturbation was considered arrived when the intensity reached 50% of the final intensity shift. These transit times were used in continuity and momentum equations to model flow in the chip. Analytical solution of these equations provides the pressures necessary to control precisely fluid flow in the chip. Microsphere Loading. Silica microspheres (SG ) 1.8) were loaded into the channel from well 2, shown in Figure 1b, using a 25% glycerol in Tris pH 8 bead loading buffer. While monitoring movement by microscope, a suspension of microspheres was pushed from well 2, down the main channel, until a bead bed of desired length accumulated against the shallow weir as shown in Figure 1b. Buffer from well 1 was used to clear the channels of extra beads while maintaining a firmly packed bead bed. The new channel flow resistance, which included the packed bead bed, was calculated by measuring transit times of step changes in dye concentration. The dilution control in packed-bed flow was performed using a standard procedure described in the Supporting Information. The packed beds were stable over durations of experimental runs. Bead Packing Density. Since the hydrodynamic resistance of the bead bed depends on packing, transit time measurements of DiFMU were used to determine the flow rate, Q, through the main channel experimentally. The step transit time was found by measuring the arrival time of a fluorescent pulse in Tris pH 8 across L ) 100-µm-long bed. After computing the flow rate through the packed bed, the bed porosity, , was calculated to be 0.355 using eq 8, which describes a packed bed of uniform spheres. 2 ∆p µ(1 - ) L ) 2 Q d 3A

(8)

p

where µ is the viscosity of the solution, dp is the diameter of the

beads, A is the cross sectional area of the channel, and ∆p is the applied pressure drop. For this bed with a cross sectional area of 1150 µm2 and a flow rate of 1.18 nL/s, a fluid element has a transit time across the bed of 34.5 ms. Enzyme Immobilization Procedure. Streptavidin-coated silica microspheres were loaded into the channel to measured bed lengths averaging 100 µm. The stock AP-biotin was diluted to 10 µg/mL with priming buffer and loaded into well 1, while well 2, where substrate is placed in later steps, was loaded only with priming buffer to prevent trace AP contamination. The APbiotin flowed at excess over the streptavidin bead at 0.5 nL/s for 30 min at 100% well 1 contribution. The wells were thoroughly cleaned, and fresh priming buffer was used to flush any remaining AP-biotin out of the channels and the bead bed. The beads adhered less to the channels when the enzyme was attached after bed formation. The immobilized enzyme dephosphorolates nearly nonfluorescent DiFMUp into the fluorescent DiFMU as it flows through the bed as shown in Figure 2. In control tests, where AP flowed through the chip without beads followed by DiFMUp, no conversion was detected, showing that enzyme was not adhering to the channels. Substrate Conversion Measurement. Calibrated DiFMU was serially diluted on the chip to make a standard curve. A 100% conversion equivalent was measured from the fluorescent signal of 1 µM DiFMU and 1 µM AP-converted DiFMUp following 3 h of incubation. The stock concentration of both compounds was calibrated by UV absorbance. The conversion percentage is calculated by dividing the reactor output fluorescence by the equivalent fluorescence from the calibrated 100% DiFMU standard curve. The weak fluorescence of DiFMUp was baseline subtracted from the fluorescent signal from partially converted reactor outflows based on a calibrated titration of DiFMUp. The highest concentration substrate was titrated in 10% increments to zero input concentration across the reactor bed. This PMT signal was normalized between zero and 1. The titration was repeated for lower substrate concentrations in the same 10% increments to generate finer steps. These data were normalized to the scale of the first set since the titrations were configured to include overlapping data sets at equivalent flow rates. For example, a 60 µM DiFMU titration included a 20 µM DiFMU step suitable for pairing with the 20 µM DiFMU titration and normalizing the signal over the entire range. The PMT voltage was adjusted to maximize the dynamic range of the signal in a given titration. As the (24) Mao, H. B.; Yang, T. L.; Cremer, P. S.Anal. Chem. 2002, 74 (2), 379-85. (25) Seong, G. H.; Heo, J.; Crooks, R. M. Anal. Chem. 2003, 75 (13), 3161-7.

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maximum substrate concentration was increased for each titration, the PMT voltage reduced. RESULTS AND DISCUSSIONS Solution-Phase Results. As a control, solution-phase kinetics were assayed at a fixed enzyme concentration of 33 pM (4.5 × 10-6 mg/mL) in eight serial dilutions of DiFMUp from 100 µM to 780 nM. Baseline fluorescence of DiFMUp substrate was measured in a 50-µL quartz cuvette (16.50F-Q-10/Z15, Starna cells, Atascadero, CA,) filled to 65 µL. The slopes, which determine the velocity, are plotted as functions of inverse substrate concentration (see Supporting Information). Lineweaver-Burke analysis determined the solution-phase AP-biotin properties of vmax ) 16 ( 0.018 nM/s and Km )8500 ( 58 nM. The turnover number kcat ) vmax/ [E]t ) 484.8/s was calculated using the initial enzyme concentration. Low Substrate Conversion Results. The accuracy and precision of control over the bead bed microchip was evaluated using a fluorogenic assay to calculate the apparent Km of beadbound alkaline phosphatase biotin at 22 °C. The experiments were first performed using high DiFMUp concentrations and high flow rates to achieve low conversion conditions satisfying MichaelisMenten assumptions. DiFMUp at concentrations of 540, 180m and 60 µM in well 2 were diluted stepwise on-chip with 50 mM Tris pH 8 buffer using the previously verified DiFMU pressure script. To ensure reproducibility, three trials were run for each DiFMUp concentration for 30 s and then averaged at steady state. The process was repeated for four flow rates. Figure 3a shows measured concentration of DiFMU for various concentrations of DiFMUp at the end of the packed bed at four microchannel flow rates. Figure 3b shows the fits of eq 7. The slopes of the fits were evaluated to yield a Km ) 51.75 ( 5.22 µM, which was independent of flow rate. The y-intercept of fits drawn in Figure 3b resulted in vmax )722 ( 144 µM/s. The total enzyme concentration available to the fluid volume in the bed can be evaluated using an estimated enzyme density on the bead surface of 2.2 × 10-8 mol/m3 and [E]t ) 48 µM. Hence, a turnover number kcat ) vmax/[E]t ) 17.67/s was observed. The flow independence of Km can be explained by evaluating the dimensionless parameter λ ) {(vmaxδR}/{3(1 - )DCbA)}, which describes the relative importance of mass-transfer rate to the reaction rate. By assuming a worst-case diffusion layer thickness δ ∼ 0.1R, substrate diffusivity of D ≈ 10-9 m2/s, and porosity  ) 0.33, the dimensionless parameter is approximately λ ) 2.6 × 10-3 for CbA ) 100 µM. This suggests that the conversion of DiFMUp by AP was “slow”, and therefore, masstransfer resistances played no role in altering the overall enzyme kinetics. This condition resulted in constant values of Km for all flow rates. The immobilized Km is 7 times higher than the solution-phase Km. The higher value can be attributed to altered enzymatic activity due to immobilization, through either steric hindrance of the catalytic site or deactivation. The experiments by Gleason and Carbeck20 for their flat plate reactor determined the immobilized Km doubled compared to the corresponding solution-phase value. The enzyme immobilized on the bead surfaces may be oriented in such a way that their active sites are not accessible to DiFMUp. Neighboring molecules may also contribute to steric inhibition. Since the solution-phase enzyme in our system was prefunction8278 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

Figure 3. (a) Plots of measured concentrations of DiFMU for various concentrations of input DiFMUp at four microchannel flow rates. The DiFMU signals were measured past the end of the packed bed. (b) Fits of eq 7 at low conversion of DiFMUp.

alized with biotin, further reductions in catalytic efficiency due to immobilization chemistry is not possible. The observed value of kcat was also found 27 times lower than the value observed in solution-phase reaction. This suggests that all the enzyme molecules on the bead surface may not be accessible to the reactant molecules. Furthermore, the enzyme density could be lower for our bead surface compared to their flat surface. Last, the immobilized alkaline phosphatase may be more efficient at higher pH and at catalyzing the reaction for the MUP substrate used by Gleason and Carbeck over DiFMUp. High Substrate Conversion Results. Beyond kinetic measurements, we evaluated the continuous flow microfluidic reactor at high conversions and product rates as would be needed in a synthesis reaction. DiFMUp at concentrations of 60, 20, 5, and 1 µM in well 2 were diluted stepwise in 50 mM Tris pH 8 buffer using the previously verified DiFMU pressure script. To ensure reproducibility, 2-3 trials were run for each DiFMUp concentration for 30 s and then averaged at steady state. The process was repeated for five flow rates. Panels a and b in Figure 4 show plots of measured DiFMUp conversion and the rate of production of

molecules can occupy a significant number of enzymatic sites. An appropriate model is needed to describe this behavior. The following mechanism for the free solution alkaline phosphatase enzymatic reaction has been proposed previously.26,27 β1

β2

A + E {\ } AE 98 EP + B R 1

β3

EP {\ }E+P R 3

(9)

Here, A, B, and P represent DIFMUp, DIFMU, and PO24 , respectively. Again, adsorption and desorption of substrate molecules are proportional to the number of unoccupied and occupied enzymatic sites, respectively. Equation 2 is now modified to

dΓA ) β1(Γ∞ - ΓA - Γp)CbA - (R1 + β2)ΓA dt

(10)

where Γp are the moles per unit area of enzymatic sites occupied 2by PO24 . Similarly, adsorption/desorption kinetics of PO4 sites on enzyme can be described as

dΓp ) β2ΓA + R3(Γ∞ - ΓA - Γp)Cbp - β3Γp dt

(11)

Using eqs 10 and 11, the rate of reaction per unit volume of bed can again be calculated as

rv )

vmax CbA b Km + K1 + KmK2CA0 + (1 - KmK2)CbA

(12)

where K1 and K2 are constants. At steady state, the mole balance in a differential packed-bed reactor can again be performed and integrated over length L of the reactor to obtain Figure 4. (a) Plots of measured conversion of DiFMUp vs microchannel flow rate at four input concentrations of DiFMUp. (b) Production rate of DiFMU vs microchannel flow rate at four input concentrations of DiFMUp.

CbAL + (1 - KmK2)(CbAL- CbA0) ) (Km + K1 + KmK2CbA0) ln CbA0 -

DiFMU as functions of flow rate for four input DiFMUp concentrations. For a 1 µM DiFMUp input, the conversion was greater than 95% over the entire range of flow rates while the production rate (mol/time) increased gradually with flow rates. At low input substrate concentrations, the highest flow rates maximize production and conversion. Conversely, at high input substrate concentrations, the conversion percentage, (1 - CbAL)/CbA0, drops and decreases rapidly with increasing flow rate. Production also increased rapidly with increasing flow rates. The microreactor should be run at lower flow rates for high conversions and moderate production when fed with high-input substrate concentrations. The predictions of kinetic parameters of enzymes in microfluidic reactors operating at high substrate conversions is quite complex. Since the Michaelis-Menten mechanism fails to describe reaction at high conversions, predictions of kinetic constants based on eq 7 would lead to unreasonable conclusions. Attempts to fit eq 7 into data in Figure 4 resulted into poor fits as well as a flow-dependent kinetic constant Km. In the enzymatic reaction at high conversions, increasing numbers of phosphate

vmaxVbed (13) Q

where CbA0 and CbAL are the inlet and outlet concentrations of substrate, Q is the flow rate in the packed reactor, and Vbed is the total volume of the reactor bed. Equation 13 is the modified form of the Michaelis-Menten mechanism, which is valid for conditions when PO24 occupies enzymatic active sites. Equation 13 clearly shows that the logarithm term is no longer a constant but rather a function of the initial substrate concentration, CbA0. Hence, the calculations of “apparent” kinetic rate constants, based on Michaelis-Menten kinetics, superficially show a dependence on flow rate conditions even in the absence of mass-transfer resistances. The source of the flow rate dependence clearly originates from the incorrect enzyme kinetics. To test the validity of the above model, experiments were performed for small step changes of DiFMUp. Concentrations ranging from 60 to 10 µM were titrated through the bed at Q ) (26) Labow, B. I.; Herschlag, D.; Jencks, W. P. Biochemistry 1993, 32 (34), 873741. (27) Coleman, J. E. Annu. Rev. Biophys. Biomol. Struct. 1992, 21, 441-83.

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Figure 5. Plot of measured concentrations of DiFMU as a function of DiFMUp concentrations at Q ) 1.126 nL/s. The curve fit is the kinetic model prediction described by eq 13.

1.126 nL/s by controlling the dilution ratio from the two channels feeding the packed bed. DiFMUp in well 2 was diluted in 50 mM Tris pH 8 buffer using the previously verified DiFMU pressure script. To ensure reproducibility, 2-3 trials were run for each DiFMUp concentration for 30 s and then averaged at steady state. Figure 5 shows the measured concentrations of DiFMU with inlet DiFMUp concentrations. Equation 13 can be fitted to this data using Km ) 51.75 ( 5.22 µM and Vmax ) 722 ( 144 µM/s while searching for best values of two parameters K1 and K2. Figure 5 shows a fair agreement with the model can be obtained using K1 ) 5.77 and K2 ) 20.86. Unfortunately, the model failed to describe the measured conversion accurately for other flow rates when the kinetic constants were held fixed. This suggests that the model indicated in eq 9 does not capture the exact reaction mechanism. This further validates our claim that the incorrect enzyme kinetics can lead to flow rate dependence of kinetic parameters. The use of a microreactor for kinetic measurements is best limited to conditions where a kinetic model, such as Michaelis-Menten, can accurately describe the enzymatic mechanism. CONCLUSIONS The kinetic properties of immobilized alkaline phosphatase catalyzing dephosphorylation of DiFMUp to fluorescent DiFMU were measured in a continuous flow, microfluidic packed-bed

8280 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

reactor for both low and high substrate conversions. Solutionphase reactions provided control results while permutations of flow rate and substrate concentration provided data used to characterize this microreactor. A criterion, λ, was developed to evaluate the importance of flow-dependent, mass-transfer resistances in predicting kinetic rate constants. We applied this parameter to differentiate between mass-transfer and reaction limitation effects in our enzymatic microreactor and select examples in the literature. In the absence of mass-transfer resistances, the Michaelis-Menten kinetic parameters are shown to be flow independent and are appropriately predicted using low substrate conversion percentage data. A comparison of kinetic parameters with those obtained from a solution-phase enzymatic reaction shows a significant decrease in enzyme activity in the immobilized conformation. The solution-phase biotinylated alkaline phosphatase had a Km ) 8.5 + 0.058 µM and a kcat ) vmax/[E]t ) 484.8/s. When immobilized on streptavidin beads, the kinetic properties changed to Km ) 51.75 ( 5.22 µM and kcat ) vmax/[E]t ) 17.67/s. This immobilized Km is ∼6× greater while the kcat is reduced by ∼28×, which was not caused by mass-transfer limitations. Contradictions found in the literature on the evaluation of Michaelis-Menten kinetic parameters for immobilized enzymes in microfluidic reactors were addressed. A kinetic model based on known mechanisms of alkaline phosphatase enzyme reaction was developed to predict the measurements for high substrate conversion. At high conversions, a significant number of enzymatic sites can be occupied by reaction product molecules, which invalidate the assumed Michaelis-Menten mechanism. An end goal of the model is to optimize the conversion and yield in a microreactor for biochemical assays through understanding of reaction and mass-transfer limitations. ACKNOWLEDGMENT We thank Professor Anuj Chauhan, Department of Chemical Engineering, University of Florida at Gainesville, for his extremely helpful suggestions and insightful perspective. A.T. acknowledges the financial support of the National Science Foundation (Grant BES- 0555874) for this research. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review June 30, 2006. Accepted September 26, 2006. AC061189L