Measurements of kinetic parameters in a microfluidic reactor

Article abstract of DOI:10.1021/ac061189l

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 enz

Full text of DOI:10.1021/ac061189l

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 immobi-
lized 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-4-
methylumbelliferyl/phosphate to a fluorescent 6,8-dif-
luoro-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 mass-
transfer resistances, the Michaelis-Menten kinetic pa-
rameters 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 im-
mobilized 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 enzy-
matic 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 kinet-
ics, can superficially show a dependence on flow rate
conditions even in the absence of mass-transfer resis-
tances. High substrate conversions are shown to depend
on flow rate. A kinetic model based on known mecha-
nisms of the alkaline phosphatase enzyme reaction is
tested to predict the measurements for high substrate
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 phospho-
rylation, glycosylation, and lipidylation,8 combinatorial synthesis,9
and characterization of molecules or single cells. These applica-
tions 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 im-
mobilized 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.
10.1021/ac061189l CCC: $33.50 © 2006 American Chemical Society
Published on Web 11/14/2006
Analytical Chemistry, Vol. 78, No. 24, December 15, 2006 8273

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 reac-
tant 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-transfer-
limiting reaction rates.14
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-nitrophen-
ylphosphate 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 im-
mobilized 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.
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, streptavadin-
conjugated 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 â-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 consump-
tion 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
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 ob-
tained 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
(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), 303-
12.
(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), 718-
23.
(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.
8274 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

Table 1. Summary of Kinetic Parameters and Experimental Conditions in Select Previous Studies
solution
immobilized
phase
flow
mass
study
Km (µM)
Km (µM)
condition
comments
transfer, λ
Lilly et al. (1966)
3.5
2.5
Q large
ficin bound to cellulose, Km
decrease with Q
∼large
∼9.5 × 10-6
∼5 × 10-6
∼0.1
Seong et al. (2003)
1.51
363
12500/16200
1.55
380
14000
Q f 0
Q f 0
Q ) 0
horseradish peroxidase
â-galactosidase
Mao et al. (2002)
AP + MUP, no mass-transfer
effects discussed
Gleason and Carbeck (2005)
100 ( 50
49 ( 2
Q ) 4 mL/min
AP + MUP, pH 9, convection
diffusion model is used
AP + MUP, pH 10
∼0.75
2800 ( 400
570
2200 ( 500
3000
10500
251 ( 22
Q ) 4 mL/min
Q ) 5 - 20 µL/min
∼0.12
∼large
∼large
∼0.1
Koh and Pishko (2005)
AP+pNPP, pH 8.2
350
urease
DeLouise and Miller (2005)
1000 ( 300
Q ) 0
glutathione-S-transferase
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 con-
transforms to
Γ∞CsA
ΓA )
(3)
Km + CsA
where Km ) (R1 + â2)/â1 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
3k*(1 - ꢀ)Γ∞ CsA
v
maxCsA
Km + CsA Km + CsA
(1 - ꢀ)
4πR3/3
rv ) k*ΓA4πR2
)
)
centration gradient, {(CAb
-
CsA)}/{δ}, will be established across
R
a diffusion layer of thickness, δ. The diffusive flux of substrate
molecules will be balanced by the rate of reaction on the surface
as
(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
CbA - CsA
D
) k*ΓA
(1)
δ
Cs
1 - A ) λ
CAb
CAs
Km + CsA
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 Michaelis-
(5)
The dimensionless parameter λ ) (vmaxδR/3(1 - ꢀ)DCbA) quanti-
fies 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, CAs , in the fluid near the surface ap-
â1
â2
Menten mechanism A + E {\} AE 98 E + B + P for the
enzymatic reaction. Substrate ARb1inds 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 concentra-
tion of substrate molecules, which is proportional to the number
of unoccupied and occupied enzymatic sites, respectively. This
leads to
proaches the bulk concentration, CAb
.
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 cellulose-
ficin packed columns with high porosity of ꢀ ) 0.75 under fast
reaction conditions, where vmax was high. Insufficient data pre-
dΓA
dt
) â1(Γ∞ - ΓA)CsA - (R1 + â2)ΓA
(2)
where Γ∞ represents the total moles of substrate per unit area of
enzymatic sites on the bead surface. At steady state, eq 2
Analytical Chemistry, Vol. 78, No. 24, December 15, 2006 8275

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.
(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
At steady state, the mole balance in a differential packed bed
reactor yields
Materials. Calf intestinal alkaline phosphatase biotin (AP-
biotin) was obtained from Rockland Immunochemical (Gilberts-
ville, PA). Streptavidin-coated silica microspheres (5.06-µm diam-
eter) 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
dCb
A ) -
dz
v
maxCbA
Km + CbA
u
(6)
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-
Here, u is the superficial velocity in the bed. The Michaelis-
Menten mechanism is assumed in the derivation of this equation.
Equation 6 can be integrated over length, L, of the reactor to
obtain
CbAL
CbA0
v
maxVbed
Q
Km ln
+ CbAL - CbA0 ) -
(7)
where CbA0 and CAbL 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 phos-
phate (DiFMUp) to fluorescent 6,8-difluoro-4-methylumbelliferone
(23) Sun, W. C.; Gee, K. R.; Haugland, R. P. Bioorg. Med. Chem. Lett. 1998, 8
(22), 3107-10.
8276 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

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 meth-
ods 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.
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 AP-
biotin 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
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 down-
stream 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.
µ(1 - ꢀ)2L
dp ꢀ3A
∆p
Q
)
(8)
2
(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.
where µ is the viscosity of the solution, dp is the diameter of the
Analytical Chemistry, Vol. 78, No. 24, December 15, 2006 8277

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 deter-
mined 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 concentra-
tion.
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 bead-
bound 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 Michaelis-
Menten 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.
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.
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, mass-
transfer resistances played no role in altering the overall enzyme
kinetics. This condition resulted in constant values of Km for all
flow rates.
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.
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 prefunction-
High Substrate Conversion Results. Beyond kinetic mea-
surements, 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 concentra-
tion 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
8278 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

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
â2
A + E {Râ
\
1} AE
98 EP + B
EP {Râ
\
3} E + P
(9)
1
3
Here, A, B, and P represent DIFMUp, DIFMU, and PO42-
,
respectively. Again, adsorption and desorption of substrate mol-
ecules are proportional to the number of unoccupied and occupied
enzymatic sites, respectively. Equation 2 is now modified to
dΓA
dt
) â1(Γ∞ - ΓA - Γp)CbA - (R1 + â2)ΓA
(10)
where Γp are the moles per unit area of enzymatic sites occupied
by PO24-. Similarly, adsorption/desorption kinetics of PO24- sites
on enzyme can be described as
dΓp
dt
) â2ΓA + R3(Γ∞ - ΓA - Γp)Cbp - â3Γp
(11)
Using eqs 10 and 11, the rate of reaction per unit volume of bed
can again be calculated as
vmax CbA
rv )
(12)
Km + K1 + KmK2CbA0 + (1 - KmK2)CbA
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 micro-
channel flow rate at four input concentrations of DiFMUp. (b)
Production rate of DiFMU vs microchannel flow rate at four input
concentrations of DiFMUp.
CbAL
(Km + K1 + KmK2CbA0) ln
+ (1 - KmK2)(CbAL- CAb0) )
CbA0
v
maxVbed
Q
-
(13)
DiFMU as functions of flow rate for four input DiFMUp concen-
trations. 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 produc-
tion and conversion. Conversely, at high input substrate concen-
trations, the conversion percentage, (1 - CbAL)/CAb0, 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 concen-
trations.
The predictions of kinetic parameters of enzymes in micro-
fluidic reactors operating at high substrate conversions is quite
complex. Since the Michaelis-Menten mechanism fails to de-
scribe reaction at high conversions, predictions of kinetic con-
stants 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
where CbA0 and CAbL 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 Michae-
lis-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), 8737-
41.
(27) Coleman, J. E. Annu. Rev. Biophys. Biomol. Struct. 1992, 21, 441-83.
Analytical Chemistry, Vol. 78, No. 24, December 15, 2006 8279

reactor for both low and high substrate conversions. Solution-
phase 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 resis-
tances 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.
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.
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.
CONCLUSIONS
Received for review June 30, 2006. Accepted September
26, 2006.
The kinetic properties of immobilized alkaline phosphatase
catalyzing dephosphorylation of DiFMUp to fluorescent DiFMU
were measured in a continuous flow, microfluidic packed-bed
AC061189L
8280 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006