Diffusion based kinetic selectivity modulation of enzymatic proteolysis in a microfluidic reactor: Experimental analysis and stochastic modeling

Article abstract of DOI:10.1039/c3ra46005c

Microreactors enable new experimental ways for enzyme engineering. In this context, we show that the liquid-liquid parallel laminar flows in microchannels cause a kinetic selectivity modification of proteolytic enzymatic reaction involving hemoglobin and pepsin, reaction that generates numerous bioactive peptides at different advancement state. Here we show that this diffusion based kinetic modulation induces an altered peptides appearance kinetics for a part of the initial substrate population. Indeed, microfluidic and conventional batch experiments performed in the same reaction conditions lead to strong differences in the resulting peptidic profiles obtained by reversed-phase high-performance liquid chromatography. Such differences are explained by the laminar flow diffusive conditions inside microchannels and are supported by a stochastic algorithm based on the Michaelis-Menten equation. Several bioactive peptides are identified by mass spectrometry and show the potential of such methodology in peptides screening from a complex proteolysis but also for selective peptides preparation by microfluidics.

Full text of DOI:10.1039/c3ra46005c

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Diffusion based kinetic selectivity modulation of
enzymatic proteolysis in a microfluidic reactor:
experimental analysis and stochastic modeling
Cite this: RSC Adv., 2014, 4, 3873
Adil Elagli,ab Simon Laurette,b Anthony Treizebre,b Bertrand Bocquetb
a
*
and Renato Froidevaux
Microreactors enable new experimental ways for enzyme engineering. In this context, we show that the
liquid–liquid parallel laminar flows in microchannels cause a kinetic selectivity modification of proteolytic
enzymatic reaction involving hemoglobin and pepsin, reaction that generates numerous bioactive
peptides at different advancement state. Here we show that this diffusion based kinetic modulation
induces an altered peptides appearance kinetics for a part of the initial substrate population. Indeed,
microfluidic and conventional batch experiments performed in the same reaction conditions lead to
strong differences in the resulting peptidic profiles obtained by reversed-phase high-performance liquid
chromatography. Such differences are explained by the laminar flow diffusive conditions inside
microchannels and are supported by a stochastic algorithm based on the Michaelis–Menten equation.
Several bioactive peptides are identified by mass spectrometry and show the potential of such
Received 21st October 2013
Accepted 24th October 2013
DOI: 10.1039/c3ra46005c
methodology in peptides screening from
a complex proteolysis but also for selective peptides
www.rsc.org/advances
preparation by microfluidics.
modication, facilitate the conduction of chemical processes in
nanoliter and sub-nanoliter volumes. Following the fast evolu-
tion of micro- and nanotechnologies, the possibility to design
advanced tools is highly attractive for various applications
including high-throughput screening,11 studies on single
cell,11,12 but also for the rapid search of specic chemical data
such as enzyme kinetic constants.13–16 Today, bio-processing
takes advantage of microuidics and technological innova-
tions in order to design specic devices. They benet to enzyme
engineering in particular trough the use of specic micro-
reactors.14–18 Microreaction technology constitutes an interdis-
ciplinary area of sciences and engineering and has led to the
development of various microreactors. Enzymes are organic
catalysts used for the production of useful substances in an
environmentally friendly way and have high potential in
analytical science and industry.19 Innovation in process engi-
neering and microreaction devices can serve as efficient tools
for the development of enzyme processes. As reaction condi-
tions associated with specic enzymatic reactions are a crucial
factor for enzyme activity, many studies focus on conditions
which can affect an enzyme reaction. Continuous-ow micro-
uidic reaction approach provides a good tool to evaluate the
impact of reactor miniaturization on enzyme kinetic behavior.
Micro and nanoliters of reactants are a real advantage in
performing rapid reactions or analyses by the fact that mass and
heat transfer are highly efficient compared to batch systems.20–22
Performing reactions in microreactors can be a real advantage
due to the large surface to volume ratio. A good example is the
1. Introduction
Microtechnology development has led to the design of new tools
for biology and chemistry. With microuidic systems, congu-
rations for uid handling are changed and offer new experi-
mental ways to study biomaterial interactions.1 Reaction
chamber size reductions affect uid transport properties
because of diffusion-effect enhancing.2 Thermal evacuation is
also increased and enables a better temperature control,
compared to batch reactions.3 Multifunctional microdevices
such as pumping devices,4 thermal devices,5 microlters,6
micromixers,7 or physical probes can be co-integrated with
microchannels and can serve as efficient tools, particularly for
modern catalytic research or to study interactions in real-time
conditions.8,9 Microstructured devices can also deal with
biology complexity by parallelization or statistical studies.10
More generally microuidic conguration reduces reagents
consumption due to small microchannel volumes.
Microchannel reaction systems, prepared by micro-
fabrication techniques or by microcapillaries assembly or
a
´ ´
´
Laboratoire des Procedes Biologiques, Genie Enzymatique et Microbien (ProBioGEM)
´
´
– EA 1026, Universite Lille Nord de France – Sciences et Technologies, Universite Lille 1
´
– Cite Scientique, Polytech’Lille, Avenue Paul Langevin, 59655 Villeneuve d’Ascq
cedex, France. E-mail: renato.froidevaux@univ-lille1.fr; Fax: +33 328 76 73 56; Tel:
+33 328 76 73 90
b
´
Institut d’Electronique, de Microelectronique et de Nanotechnologie (IEMN) – UMR
´
CNRS 8520, Universite Lille 1 – Sciences et Technologies, Villeneuve d’Ascq, France
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case of liquid–liquid heterogeneous reactions like phase inuence the hydrolysis by the same way. Thus, our goal was to
transfer catalysis.23 Nevertheless, the major challenge remain to modulate the kinetics of the reaction in order to obtain a new
realize efficient mixing under laminar ow between two kinetic behavior leading to an altered peptides appearance
miscible uids to rapidly create a homogeneous mixture at the kinetics. Herein, we present thus a new approach of enzymatic
beginning of a reaction, i.e. at a position in space where the proteolysis kinetic selectivity modulating by laminar ow
reagents start to be in contact through an interface. In the case regime specic to microuidic systems. In the same reaction
of fast reactions in which reagents are initially present in time and acidic pH conditions, strong kinetic selectivity
separate streams, reaction rarely occurs uniformly in the whole differences between batch and microuidic modes appear
volume.21 Consequently, the rate of continuous laminar ow during denatured hemoglobin hydrolysis by pepsin.
reaction is no longer dened by inherent kinetics but is limited
or favored by diffusional rates, depending on the reaction
2. Materials and methods
2.1. Reactor microfabrication
microchannel wide and on reactants molecular weights.22,24
However, diverse microuidic systems promoting rapid mixing
of uids have been proposed,16,25 classied either as active or
passive micromixers.21,26 In this study, rapid mixing of enzyme
and substrate is not the goal, as it will result in homogeneous
reactions similar to those taking place in well-mixed conditions
in batch. Indeed, as the studied reaction is an enzymatic
proteolysis, the main goal remains to take advantage of the
strong diffusive conditions in order to conduct a diffusion-
dependant reaction that could be modulated in term of
kinetic selectivity, i.e. in term of peptides appearance kinetics.
In fact, because of the huge variety of peptides generated during
proteolysis, the control of specic bioactive peptides appear-
ance is desirable. Due to the large number of sequential and
parallel reactions occurring during protein hydrolysis by
protease, the enzymatic proteolysis constitutes a typical reac-
tion that might be affected by microuidics and the resulting
dominant diffusion effect.
The microreactor used in this study was fabricated by a glass/
silicon/glass technological process. First, a 350 mm-thick
silicon wafer was bonded to a 700 mm borosilicate glass
substrate. Then, microchannels were etched in silicon wafer by
a Deep Reactive Ion Etching (DRIE) process. Finally, the
microchannels were covered by another glass substrate to get a
buried Y-shaped microuidic circuit. The specicity of this
technological process is due to its parallel biosensor function.
Indeed, combined with an integrated electromagnetic sensor,
the obtained microuidic platform allowed us to perform
measurements at sub-THz frequencies.41 Details on the tech-
nological process have already been reported.41,42
2.2. Experimental procedure
The enzymatic reaction was the hydrolysis of bovine hemo-
globin (64.5 kDa, Sigma Chemicals Co.) by porcine pepsin (E.C.
3.4.23.1, 3.440 U mgꢀ1, 35 kDa, Sigma Chemicals Co.), protease
belonging to the family of aspartic acid proteases and which
preferentially catalyzes the cleavage of peptide bonds at the
carboxyl side of aromatic and hydrophobic amino acids. This
proteolytic reaction leads to the appearance of product mole-
cules called peptides. Hemoglobin was prepared under dena-
turing conditions at pH3.0 by adding 2 M HCl for a 20 mg mLꢀ1
nal concentration. All aqueous solutions were prepared in 18.2
MU Milli-Q water (Millipore). The introduction of the reagents
in the microreactor was achieved by a syringe pump (New Era
Enzymatic hydrolysis of natural proteins (animal or plant
origins) interests food and pharmaceutical industries, espe-
cially for functional property improvement of proteins such as
taste, solubility, emulsication, gelation,27–29 or to obtain bio-
logically active peptides.28–31 These bioactive peptides are inac-
tive within the sequence of parent protein and can be released
during controlled enzymatic hydrolysis of the proteins.32
Hemoglobin constitutes a good example of protein which can
be considered as an attractive source of peptides with several
biological properties such as antioxidant,33 antihypertensive,34
antimicrobial35 and opioid.36 Under controlled conditions, the
hydrolysis of bovine hemoglobin by porcine pepsin enables to
isolate a vast variety of peptides which are produced at different
advancement states of the reaction. Selectivity modulation of
this reaction has already been studied by using organic solvents
such as alcohols,37 urea or acidic conditions.38 In these condi-
tions, studies have shown that, in the course of hemoglobin
hydrolysis, modication of the peptidic populations was due to
the modication of the hemoglobin native conformation.39 In
fact, hemoglobin hydrolysis involves two main mechanisms
depending on its structure: in denatured state, the hydrolysis
proceeds by a “zipper” mechanism that leads to the formation
and successive cleavage of intermediate peptides whereas in
native state, hemoglobin is hydrolyzed in small size peptides
according to a “one-by-one” mechanism.39,40
Fig. 1 Experimental protocol for microfluidic mode reaction and
analysis. Pepsin (E) and hemoglobin (S) are injected by a syringe pump
in the microreactor. The product of the stopped reaction is collected
before its chromatographic and mass analysis. PP stands for peptidic
Considering that the hydrolysis of hemoglobin by pepsin is
highly modulated by the spatial structure, we hypothesized that
a kinetic behavior resulting from exclusive diffusion can profile.
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Pump Systems Inc., Farmingdale, NY, USA) (Fig. 1) and the ow which the spectra were recorded in the range of m/z 150–3000
rate was xed for both enzyme and substrate solution at 1 mL with a resolution of 30 000. An external calibration of the
minꢀ1 and next 0.5 mL minꢀ1 for two distinct hydrolysis equipment for mass accuracy was carried out the day before the
experiments, each repeated at least 6 times. The outlet fused- analysis according to the manufacturer guidelines.
silica capillary (75 mm I.D. ꢁ 150 mm O.D.) was in contact
with a disodium tetraborate buffer solution (0.32 M, pH 9.0)
that caused enzyme denaturation and thus reaction stopping.
3. Results and discussion
3.1. Comparison of the peptidic proles
Recovery of the solution from the outlet of the ow channel was
started aer an initial 30 mL pre-sending delay to reach steady-
state ow in microreactor.
Analysis and comparison of peptidic proles from hemoglobin
hydrolysis by pepsin in batch and microuidic modes were
performed (Fig. 2). Since the retention times result from the
reversed-polarity, the x-axis of the chromatograms is relatively
comparable to the size of the eluted molecules. In batch mode
(Fig. 2B and C), the a- and b-chains of hemoglobin are rapidly
hydrolyzed in peptides, eluted between 30 and 43 minutes. As it
was previously shown,36 these peptides are called “transient
peptides” since they become substrate of the pepsin to give
smaller peptides. Linderstrøm-Lang has developed a model to
explain these phenomena frequently observed during the
hydrolysis of globular proteins, i.e. that the pepsin hydrolyzes
denatured hemoglobin by a mechanism called “zipper”, a
mechanism that involves a rapid conversion of the whole
protein in intermediate peptides followed by a progressive
cleavage of these intermediates in reduced-size peptides.
Moreover, pepsin prefers long substrates when accessible, since
it recognizes eight substrate residues,43 which could explain the
large increase in intensity of the peaks from 38 to 43 minutes
retention time for 15 and 30 seconds reaction in batch mode
(frames 1 and 2, Fig. 2B and C). In microuidic mode (Fig. 2D
and E), with the same reaction conditions as in batch mode (pH,
concentrations, reaction times), more intact hemoglobin
remains in the microreactor and the peptidic proles strongly
differ. For 15 seconds reaction, only peptides between 28 and 38
minutes of retention time are eluted (frame 3, Fig. 2D). Aer 30
seconds reaction, small nal peptides with low retention times
from approximately 17 to 28 minutes (frame 4, Fig. 2E) and at 8
minutes (frame 5, Fig. 2E) combined with the absence of a large
part of intermediate peptides (from 38 to 43 min of retention
time) are indicative that the enzymatic reaction proceeds
differently than in batch mode, probably due to the microuidic
ow regime and the diffusional properties of the enzyme,
substrate and produced peptides during the reaction. The
identication of the peptides present in the hydrolysates can
serve in order to understand and propose a model of hydrolysis
within the microreactor.
2.3. Reversed-phase-HPLC analysis
The produced peptides were analyzed by liquid chromato-
graphic system that consisted of a Waters 600E automated
gradient controller pump module, a Waters Wisp 717 automatic
sampling device and a Waters 996 photodiode array detector.
Spectral and chromatographic data were stored on a NEC image
466 computer. Millennium soware was used to plot, acquire
and analyze chromatographic data. Detection of produced
peptides was carried out at 215 nm by reverse phase HPLC (RP-
HPLC) on a C4-column (Vydak 0.46 ꢁ 25 cm, 3 mm I.D.) for
0.5 mL minꢀ1 ow-rate. The mobile phase was water–tri-
uoroacetic acid (100 : 0.1, v/v) as eluent A and acetronitrile–
water–triuoroacetic acid (60 : 40 : 0.1, by vol) as eluent B. The
applied gradient was 0–67% (v/v) B over 30 min, then 67–87%
(v/v) B over 35 min, and nally 100% B over 25 min. On-line UV
absorbance scans were performed between 200 and 400 nm at a
rate of one spectrum per second with a resolution of 1.2 nm. All
common chemicals and reagents were of analytical grade and
purchase from Sigma Chemicals Co. and Flandres Chimie.
2.4. LC-MS analysis by one-line UPLC-ESI-MS
The analysis were performed on a Accela UPLC system acquired
from Fisher Scientic (Thermo Fisher Scientic, Bremen, Ger-
many) that consisted of an autosampler equipped with a
column oven and a tray compartment cooler and a quaternary
pump with a built-in solvent degasser, all piloted by Xcalibur
soware. The chromatographic separation was performed on a
C4-column (Vydak 0.46 ꢁ 25 cm, 3 mm I.D.). 10 mL of samples
were injected in a no waste injection mode. The separations
were performed using the same solvent gradient as previously
described for the simple RP-HPLC analysis. The column oven
and tray cooler temperatures were set to 25 ꢂC and 4 ꢂC
respectively. The Accela UPLC system was hyphenated with an
Orbitrap Exactive mass spectrometry system (Thermo Fisher
Scientic, Bremen, Germany). A ow divider called “splitter”
used as the output rate of UPLC is higher than that tolerated by
3.2. Identication of bioactive peptides
the mass spectrometer. The ow was split to give approximately LC/MS analysis of the peptidic hydrolysates allowed the detec-
100 mL minꢀ1 directed into the mass spectrometer via the tion of several biological active peptides previously reported in
electrospray interface. The system was equipped with an ESI the literature.30,44 Different peptides are produced in the course
interface that was used in positive ionization mode with the of hemoglobin hydrolysis by pepsin in the microreactor:
following conditions: capillary temperature and voltage at hydrophobic peptides are detected for short residence time of
275 ꢂC and 9 V respectively, ion spray voltage at 3.3 kV and tube enzyme and substrate in the microreactor (15 s which is
lens voltage at 95 V. Nitrogen (N2) was used as sheath gas and equivalent to a ow-rate of 1 mL minꢀ1) whereas small hydro-
helium (He) as auxiliary gas with ow-rates of 20 and 5 arbitrary philic peptides are detected for longer residence time (30 s
units. For the MS experiments, full MS scan was applied, for which is equivalent to a ow-rate of 0.5 mL minꢀ1).
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Fig. 2 RP-HPLC chromatograms of unreacted hemoglobin (A) and peptidic hydrolysates from batch (B and C) and microfluidic (D and E) modes.
40 mL samples were fractionated on a C4 column for 15 s reaction (B and D) and 30 s reaction (C and E).
Thank to MS base-peak chromatogram of hemoglobin (Fig. 3C), a99–106 at m/z 455.79 [M + 2H]2+, a84–98 at m/z 582
digestion in microreactor, biological active peptides have been [M + 3H]3+and b126–145 at m/z 549.79 [M + 4H]4+ (Table 1).45 In
identied in the peptidic proles (Fig. 2D and E) and are pre- the frame 4 (Fig. 2E), corresponding to the 0.5 mL minꢀ1 ow-
sented in Table 1. The biological active peptides identied for rate, the peptide b140–145 was identied with a m/z 399.25
1 mL minꢀ1 are present in the frame 3 (Fig. 2D) which includes [M + 2H]2+ and is detected in appreciable quantity. This peptide
the peptides eluted between 30 and 43 minutes of retention is not detected in batch for the same reaction time (Fig. 2C).
times. An MS base-peak chromatogram of a hemoglobin Moreover, peptidic products originating from the hydrolysis of
digestion shows the spectrum of the peptide LVVYPWTQRF the a1–32 sequence by pepsin have been identied among the
originating from the hemoglobin b-chain with a m/z 654.86 [M + peptides present in the frame 4 (Fig. 2E). Identication of the
2H]2+ (1307.71 Da) and called LVV-hemorphin-7 (Fig. 3A).44 The a1–23 sequence (Fig. 3D) clearly shows that the peptide a1–32
peptide VVYPWTQRF called VV-hemorphin-7 was also detected present at 1 mL minꢀ1 (Fig. 2D, frame 3) was hydrolyzed in a1–23
with a m/z 598.31 [M + 2H]2+ (1194.63 Da) (Fig. 3B).44 We iden- (Fig. 2E, frame 4) which is an antimicrobial sequence.35 Finally,
tied the antimicrobial peptides a1–32 at m/z 652.34 [M + 5H]5+ it was detected in frame 5 (Fig. 2E) at m/z 654.14 [M + H]+
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Table 1 Bioactive peptides generated after digestion in batch or microreactor identified by LC-MS analysis
Peptide present
in frame
Peptide mass
[M + H]+ (Da)
Hydrolysis
in batch
Hydrolysis in
microreactor
Sequence
Biological activity
Position
3
3
3
LVVYPWTQRF (LVV-hemorphin-7)
VVYPWTQRF (VV-hemorphin-7)
VLSAADKGNVKAAWGK
VGGHAAEYGAEALERM
VLSAADKGNVKAAWG
KVGGHAAE
Opioid
Opioid
Antimicrobial
b31–40
b32–40
a1–32
1308.71
1195.63
3257.70
Yes
Yes
Yes
Yes
Yes
Yes
4
Antimicrobial
a1–23
2237.20
No
Yes
3
4
4
3
5
KLLSHSLL
LAHRYH
SDLHAHKLRVDPVNF
QADFQKVVAGVANALAHRYH
TSKYR (neokyotorphin)
Antimicrobial
Antimicrobial
Antimicrobial
Antimicrobial
Antimicrobial
a99–106
b140–145
a84–98
b126–145
a137–141
910.56
797.50
1744.00
2196.16
654.14
Yes
No
No
Yes
No
Yes
Yes
Yes
Yes
Yes
(653.14 Da) the peptide TSKYR called neokyotorphin which is between 28 and 38 minutes of retention time. Using the peptide
originated from the a-chain of hemoglobin, while absent for the a1–32 as marker, its kinetic evolution can be monitored
batch hydrolysates. Indeed, the minimal antimicrobial through its fraction area evolution. Its concentration decreases
sequence KYR has been previously identied as a nal product with residence time and shows that this peptide is rapidly
of the a-chain hydrolysis.46 Its sequence a137–141 constitutes consumed in order to generate smaller peptides, in particular
thus a nal peptide derived from the a-chain hydrolysis and is the peptide a1–23. This behavior reects the intermediate
absent from the hydrolysis in microreactor at 1 mL minꢀ1 and character of the peptide a1–32 (frame 3, Fig. 2D) which is
from the hydrolysis in the same conditions in batch mode. This rapidly consumed by pepsin to generate smaller peptides such
bioactive peptide is typically obtained in appreciable quantity in as the peptide a1–23 (frame 4, Fig. 2E), whose concentration
batch aer several hours of denatured hemoglobin pepsic increases with residence time. The same behavior is observed
hydrolysis.47
for the generation of the peptide LVV-h7 and its hydrolysis in
VV-h7. For batch experiments of denatured hemoglobin
hydrolysis (at acidic pH or in the presence of urea), this kinetic
behavior is apparent for longer kinetics.48 Peptides present in
frames 4 and 5 (Fig. 2E) are produced faster than they could be
generated in batch mode. It suggests a rapid proteolysis at the
interface of the solution of enzymes and substrates in the
microuidic device.
3.3. Inuence of the ow-rate on the evolution of the
proteolysis in the microreactor
The two distinct chromatograms (Fig. 2D and E) allow
discerning the evolution of the reaction and the peptide
appearance kinetics in microuidics because the peaks areas
containing peptide fractions change with the ow-rates. The
rst peptides generated at 1 mL minꢀ1 are expected to come
directly from the a- and b-chains of hemoglobin. According to
the “zipper” mechanism occurring in acidic conditions
described by Linderstrøm-Lang, a large part of these generated
peptides are consumed for 0.5 mL minꢀ1 ow-rate. Thus, the
global evolution of the proteolysis in the microreactor seems to
proceed rstly by the rapid digestion of the initial substrate
molecules located close to the interface in intermediate
peptides (Fig. 2D, frame 3), whose molecular weights vary
between 1.5 and 3.5 kDa approximately (Fig. 4). Then, the
proteolysis continues with the hydrolysis of these intermediate
peptides just produced and accessible in small nal peptides
(Fig. 2E, frames 4 and 5). No intermediate peptide of more than
3.5 kDa is observed for these reaction times, suggesting a rapid
reaction at the interface. In consequence, the appearance
kinetics of these small nal peptides in the microreactor
appears faster than in batch.
3.4. Evaluation of the substrate-enzyme mixing by
simulation
In order to explain the difference observed between batch and
microuidic congurations, simulations of the subtrate-
enzyme mixing inside microchannels have been performed
with COMSOL Multiphysics soware. Substrate and enzyme
concentrations are predicted by solving the advection–diffusion
equation for the experiment conditions described before
(Fig. 5). In this conguration, an interface appears because
enzyme and substrate do not mix immediately. We suppose that
this interface is the origin of the peptidic prole differences
between batch and microuidic modes.
3.5. Modelisation of the proteolysis in the microreactor
The classic Michaelis–Menten equation provides a highly
Through their appearance/disappearance, couples of bioac- satisfactory description of enzymatic kinetics for large ensem-
tive peptides can serve as markers to monitor the hydrolysis of bles of enzyme molecules.50 According to the general scheme of
the rst generated peptides in small nal peptides: a1–32/a1–23 enzyme-catalyzed reaction, a substrate S binds reversibly with
and LVVh-7/VVh-7. In the 15 rst seconds, the population of the an enzyme E to form a complex ES which then undergoes
rst intermediate peptides increases, which results in unimolecular decomposition to form a product P, and E is
increasing the peaks areas corresponding to the peptides eluted regenerated for the next cycle:
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Fig. 3 ESI-MS spectra showing opioid peptides (A and B) and antimicrobial peptides (C and D). (A) LVV-hemorpin 7 (b31–40) (B) VV-hemorphin 7
(b32–40) (C) a1–23 (D) a1–32. MS measurements were performed in positive ion mode using electrospray ionization (ESI).
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n
n
k1
kcat
ƒƒƒ!
*
E þ Sn )
ðESÞ
E þ Snþ1 þ Fn
(c)
n
n
k
ꢀ1
n
n
k1
kcat
ƒƒƒ!
*
E þ Sn )
ðESÞ
E þ 2F
(d)
n
n
n
kꢀ1
with k1 , k 1 and kcat1 in (a) and k1n, k n and kcatn in (b), (c) and
1
ꢀ1
ꢀ1
(d). S1 represents the rst substrate molecules, i.e. the initial a-
and b-chains of hemoglobin, whereas Sn (with n s1) is assumed
to represent the substrate of pepsin in reaction (b), (c) and (d).
Fig. 4 Average distribution of molecular weight profiles of peptides in
hydrolysates as function of their retention time in RP-HPLC.
S
n+1 represents the next substrate molecule which becomes the
new Sn that will be hydrolyzed by forming a new complex (ES)n,
up to the formation of two nal fragments without cleavage site
Fn. Thus, the product of reaction (a), (b) or (c), i.e. amino acids
sequence, is also the substrate of pepsin in reaction (b), (c) and
(d). The reactions in (b) and (c) occur up to the whole
consumption of the substrate in (d).
Enzymatic reactions kinetics can generally be expressed by
the Michaelis–Menten equation as follow:50
dP kcat½Eꢃ½Sꢃ
Vmax½Sꢃ
¼
¼ V0 ¼
(1)
dt
Km þ ½Sꢃ
Km þ ½Sꢃ
where V0, [S], [E], Vmax and Km represent the initial rate of
product generation, the substrate concentration, the total
enzyme concentration, the maximum rate, and the Michaelis–
Menten constant (Km h (kꢀ1 + kcat)/k1), respectively. V0 increases
as [S] increases asymptotically approaching the maximum rate
of an enzyme-mediated reaction Vmax. The substrate concen-
tration at which V reaches half of Vmax is dened as Km. Because
of the saturation of all the active sites of the enzyme, the initial
velocity of the reaction V0 in eqn (1) cannot be increased in-
nitely. Hence, the plot of V0 against [S] shows the shape of a
rectangular hyperbola where, at low substrate concentration
([S] ꢄ Km), V0 varies linearly with the substrate concentration
and eqn (1) is simplied to
Vmax½Sꢃ kcat½Eꢃ½Sꢃ
Fig. 5 Substrate and enzyme concentration profile in batch (A) and
simulated by COMSOL in microfluidic mode (B). Simulations were
V0 ¼
¼
(2)
Km
Km
performed with a diffusion coefficient D ¼ 1 ꢁ 10ꢀ10 m2
s
ꢀ1, approx-
where kcat and [E] represent the turnover number and the total
concentration of enzyme respectively. For high substrate
concentrations ([S] [ Km), the rate of the reaction is
independent of the substrate concentration and eqn (1) is
simplied to
imated by the Wilke–Chang formula.49 The interface extent is defined
when the concentrations of enzyme and substrate are between 10 and
90% of their maximal value.
k1
k2
kcat
E þ S )
ES
E0 þ P; E0
E
*
ꢀ1
V0 ¼ Vmax ¼ kcat[E]
(3)
ƒƒ!
ƒƒƒ!
k
To model the substrate hydrolysis kinetics in microuidic
and batch modes, a stochastic algorithm based on Michaelis–
Menten kinetics was used and is depicted in Fig. 6. Some bio-
logical phenomena such as enzyme reactions can be appreci-
ated by stochastic approaches.51,52 Indeed, the very basic step of
every molecular reaction can be described only in terms of its
probability of occurrence. Moreover, the diffusion of molecules
is a realization of a random walk process called “Brownian
motion”. Thus, according to the intrinsic noise, i.e. the proba-
bilistic nature of biochemical reactions, the dynamical
description below is assumed to represent a discrete and
with k1, kꢀ1, kcat and k2 the complex formation constant, the
complex dissociation constant, the catalytic constant and
the enzyme regeneration constant respectively. However,
considering here a proteolysis, the reaction scheme can be
appreciated by:
1
1
k1
kcat
ƒƒƒ!
*
E þ S1 )
ðESÞ
E þ 2S
(a)
(b)
2
1
1
kꢀ1
n
n
k1
kcat
ƒƒƒ!
*
E þ Sn )
ðESÞ
E þ 2S
nþ1
n
n
kꢀ1
stochastic description inspired by Gillespie algorithm,
a
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reaction probability pm1 between a substrate molecule and an
enzyme is low because only substrate and enzyme molecules
present at the interface between the uids can react. Since the
interface extent li is about a h of the microchannel width lc
(Fig. 5), and since interface conguration is the same as batch
conguration, it comes pm1 ¼ pb/5; (iii) in microuidic mode,
once a substrate molecule S1 is hydrolyzed, the resulting
peptides can react with enzymes with a probability pm2 [ pb.
Indeed, peptides Sn that are generated during enzymatic
hydrolysis are located close to the interface and, due to their
smaller size, their diffusivity becomes higher than the initial
substrate molecule S1 (according to the well known relationship
between l, s, and D dened by s ꢅ l2/D, with s the diffusion time,
l the length and D the diffusion coefficient22). Therefore, they
can diffuse to other unsaturated enzyme molecules in the
“enzyme compartment” ([Sn]3 ꢄ Km, where Km is the Michaelis
constant and considering that the substrate S1 is hydrolyzed at
the interface); (iv) according to the results of mass spectrometry
(Table 1), the lengths of the peptides generated in the course of
the enzyme reaction are randomly chosen between l0 (initial
Fig. 6 Algorithm used to compute hemoglobin hydrolysis in micro-
fluidic mode. [Sn]3 represents the substrate concentration in the
“enzyme compartment”.
Monte-Carlo method. The equivalence between the discrete length) and l0/25.
description and the master equation has been demonstrated by
Evaluation of probabilities has thus been made using the
Gillespie,53 who proposed an exact simulation stochastic algo- Michaelis–Menten equation, with the following equation for pb:
rithm to solve the chemical master equations (CMEs). The basic
d½Pꢃ
kcat½E0ꢃ
b
½Sꢃ b ½Sꢃ þ Km
pb$dt ¼
¼
dt
(4)
working principles of the Gillespie algorithm derive from the
description of the collision of particles in a vessel. Here, the
formation of peptides close to the junction where substrate and
enzyme are rst brought together depends on the diffusivity of
both substrate and enzyme. A region where the species are
mixed by (inter)diffusion is dened as 1/5 of the whole channel
width (Fig. 5). In this interface region, all the diffusive terms in
classic ordinary differential equations describing the proteol-
ysis vanish (ODEs are the natural language for representing
mass action kinetics and the kinetics of enzyme-catalyzed
reactions is usually modeled by a set of coupled differential
equations), so the governing equations reduce to those used in
the classical Michaelis–Menten analysis.13 Moreover, the tricky
transformation of ODEs in terms of probabilities implies the
use of the constant k1 which results in a novel approximation (k1
is commonly approximated between 104 and 108 Mꢀ1 sꢀ1),13,52,54
whereas the Michaelis–Menten formula requires just the known
constants kcat and Km.55,56 Hence, the dynamical system was
considered to follow an equilibrium derived by the usual
approximation initially formulated by Briggs–Haldane that the
concentration of species is quasi steady-state (QSSA).57 Usually
considered as valid if [E] ꢄ [S] + Km, its availability was extended
to [E] [ [S] + Km, renamed by total QSSA (tQSSA).58–60 Here, the
tQSSA assure the validity of the use of Michaelis–Menten
equation and of the following model by the fact that this
approximation is at least roughly valid for any substrate and
enzyme concentrations,60 since the reaction takes place in an
environment where substrate molecules can react with non-
saturated enzymes (in the enzyme compartment, Fig. 5 and 6).
The underlying assumptions for the modelisation of the
peptic hydrolysis were: (i) in batch mode, all the substrate
molecule and resulted peptides have the same probability pb to
react with an enzyme molecule; (ii) in microuidic mode,
b
b
[P]b, [S]b and [E0]b are respectively the product, substrate and
initial enzyme concentrations in batch mode. From previous
studies, Km ¼ 0.1 mM has been chosen.55,56 In microuidic
mode, it has been shown that pm1 ¼ pb/5 due to the interface
extent. Moreover, the probability pm2 of products hydrolysis by
enzyme in the “enzyme compartment” is given by:
kcat½E0ꢃ
kcat½E0ꢃ
2kcat½E0ꢃ
3
pm2$dt ¼
dt ꢅ
3 dt ¼
b dt
(5)
Km þ ½Snꢃ
Km
Km
3
since: (i) all the enzyme molecules are not saturated (Km
[
[Sn]3) in the “enzyme compartment”; (ii) the initial enzyme
concentration in the enzyme compartment is [E0]3 ¼ 2.[E0]b
because the enzyme compartment volume is half the whole
microreactor volume.
Then, a Scilab algorithm has been written to predict the
microuidic and batch peptide contents. At the beginning, the
solution is composed of enzymes and N0 substrate molecules
with a l0 length. For each time step dt, substrate molecules and
produced peptides can be cleaved or not, depending on prob-
abilities dened before.
The peptidic proles were determined aer T ¼ 30 s for
microuidic and batch modes for kcat ¼ 0.5 sꢀ1 (Fig. 7).55 Three
main points are in good agreement with Fig. 2C and E: (1) in the
microuidic mode, peptides with an intermediate length are
very few compared to batch mode, (2) aer the same reaction
time, there are more small peptides obtained in the micro-
uidic mode than in the batch mode, (3) the initial substrate
molecules are more consumed in batch than in microreactor.
However, due to assumptions (i) and (iv), small peptides
appearance in batch mode is over-estimated by computation
compared to experimental results. Indeed, the pb probability
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diffusion enhanced effect specic to microuidics. We show
that microuidics causes an acceleration of the enzymatic
proteolysis kinetics for a part of the initial substrate population,
resulting in a different kinetic selectivity. A mechanism of
hydrolysis occurring within the microchannel is proposed as a
basis for future studies. The stochastic nature of the model is
adapted because the mechanism to be described is based on the
interaction of few molecules, in contrast with deterministic
models for which the phenomena under consideration involve a
large number of molecules and describe thus an average effect.
Microuidics is therefore a good tool that can modulate an
enzymatic proteolysis for the rapid kinetic screening of protein
enzymatic digestion and the search of bioactive peptides in
combination with LC/MS analysis. Thus, perspectives are to
further explore this approach for determining the kinetics of
bioactive peptides appearance during hemoglobin hydrolysis by
pepsin in order to provide a reliable methodology to guide
peptides preparation. Indeed, in batch mode, peptides
screening and preparation from hydrolysates can be very slow,
typically until 2 hours or more for some hydrolysates containing
specic small peptides (neokyotorphin in the case of hemo-
globin hydrolysis). Thus, a rapid and advanced hydrolysis can
be easily realized in parallel laminar co-ow microreactor in
order to obtain a rapid production of small size peptides or a
rapid kinetic screening of specic peptides appearance. More
than time-saving, microuidics can offer some advantages
including greater efficiency, real-time monitoring, possible
parallelization for production or on-line optimal extraction or
purication.
Fig. 7 Microfluidic and batch solution contents after 30 s reaction.
Results from Scilab computation.
may depends on the peptide length and preferential cleavage
sites exist in proteins.43 Nevertheless, the model presented here
is able to give with a good agreement a simple explanation of
kinetic behavior differences that are experimentally observed
in batch mode and microuidic ow regime in co-ow
conguration.
3.6. Comparison with immobilized pepsin experimental
conguration
Previous study about hydrolysis of hemoglobin by immobilized
pepsin in microuidic device has been realized by Stigter et al.
in 2008.61 In the same conditions of reaction time, pH and
temperature, it was observed that peptidic proles obtained in
microreactor were similar to reaction carrying out in batch.
Moreover, no kinetic selectivity modulation was observed when
the ow rate of hemoglobin solution varied. These results
showed that enzymatic kinetics was not altered with immobi-
lized pepsin, probably due to the saturation of the enzyme
molecules by hemoglobin substrate. However, in our study, only
the enzymes located close to the interface are able to react with
hemoglobin molecules due to the mass-transfer resistance of
pepsin and hemoglobin. The other enzyme molecules located in
the “enzyme compartment” can be qualied as “unsaturated”
since they react with some produced peptides coming from the
interface but are unable to react with the initial hemoglobin
substrate. Thus, substrate molecules located close to the inter-
face are rapidly and completely digested by pepsin whereas
substrate molecules away from the interface are not hydrolyzed.
This result indirectly underscores the inuence of a parallel co-
ow microuidic conguration on the hydrolysis kinetic selec-
tivity modulation. Diffusion effect is enhanced when the uids
are in co-ow conguration because of the interface effect.
Acknowledgements
´
We are grateful to Dr Gabrielle Chataigne for technical assis-
tance in LC-MS analysis.
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