Complex Media and Enzymatic Kinetics - ACS Publications - American

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Complex media and enzymatic kinetics Evangelos O. Bakalis, Alice Soldà, Marios K. Kosmas, Stefania Rapino, and Francesco Zerbetto Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b00343 • Publication Date (Web): 05 May 2016 Downloaded from http://pubs.acs.org on May 8, 2016

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Analytical Chemistry

Complex media and enzymatic kinetics Evangelos Bakalis,§,¶,* Alice Soldà,§,¶ Marios Kosmas,† Stefania Rapino,§,* and Francesco Zerbetto§,* §

Dipartimento di Chimica “G. Ciamician”, Università di Bologna, V. F. Selmi 2, 40126,

Bologna †

¶

Department of Chemistry, University of Ioannina, 45110 Ioannina, Greece

These authors equally contributed to this work

*

To whom correspondence should be addressed. Email: [email protected],

[email protected], [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Enzymatic reactions in complex environments often take place with concentrations of enzyme comparable to that of substrate molecules. Two such cases occur when an enzyme is used to detect low concentrations of substrate/analyte or inside a living cell. Such concentrations do not agree with standard in-vitro conditions, aimed at satisfying one of the founding hypothesis of the Michaelis-Menten reaction scheme, MM. It would be desirable to generalize the classical approach, and show its applicability to complex systems. A permeable micrometrically-structured hydrogel matrix was fabricated by protein cross-linking. Glucose oxidase enzyme (GOx) was embedded in the matrix and used as a prototypical system. The concentration of H2O2 was monitored in time and fitted by an accurate solution of the enzymatic kinetic scheme, which is expressed in terms of simple functions. The approach can also find applications in digital microfluidics and in systems biology where the kinetics response in the linear regimes often employed must be replaced.


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INTRODUCTION

An important issue for standard in vitro techniques used to assess enzymatic kinetics is the substantial amount of the biological compounds that is required. In the past decades miniaturized low-sample consuming assays have been developed in the area of biofuel cells, biotechnology, medical diagnostics and drug discovery. Nanoarrays were used to perform enzymatic analyses in 6.3 - 8 nL solutions1 and microfluidic devices were used to unravel the enzyme kinetics in a single shot experiment.2 Beside sample saving, the miniaturization and confinement of the reaction environment also allows the investigation of fast kinetics: for instance, an acoustofluidic approach in single bubbles stimulated by a piezoelectric transducer to generate vortices in the fluid was used for the characterization of enzymatic reaction constants. The reagents can be mixed in 100 ms by the vortices to yield the product.3 Alternatively, a droplet-based microfluidic chip with pneumatic valves was reported for the measuring of rapid, millisecond enzymatic kinetics using amperometric detection method and with a time resolution of about 0.05 s.4 Very recently, a new microfluidic platform for the study of enzymatic reactions using static droplets on demand was demonstrated. This system allows monitoring both fast and slow reactions using small amounts of reagents.5 A nanopore was used to disentangle the kinetics of single macromolecule enzymatic degradation.6 The confinement effects on enzymatic kinetics were also taken in account using new entrapping and sensing strategies.7, 8 In the present work we propose the use of a picolitre reaction chamber based on a proteic hydrogel, which can allocate enzyme and substrate in high concentrations with a relatively small use of the compounds. The detection of the enzymatic reaction products is integrated and is conducted by amperometric measurements employing a microelectrode, which also allows a high temporal resolution assay. The minimal model that describes an enzymatic reaction reads:

  → C  → E + P E + S← k k1

k2

−1

(1)

where E, S, C, and P are the enzyme, the substrate, the intermediate complex, and the product, and, ( ), ( ) and ( ) are the forward, the reverse, and the


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catalytic rates. A special regime of eq. (1) has been used by the long established Michaelis-Menten (MM) reaction scheme and its approximate solutions have been used to describe most of the in vitro enzymatic reactions. Recently, it has been pointed out that the description holds true even at single molecule level.9,

10

Many arguments can be

formulated in favor and against its validity and its standard solution.11 Gutiérrez introduced an alternative analytical treatment for the description of the kinetics in biological assays characterized by a heterogeneous feature of the reaction and a typical concentration of the enzyme larger than the one of the substrate12 This approach is based on the total quasi-steady-state approximation.13, 14 In the present work, we investigate enzymatic kinetics in a complex microenvironment. We use a micrometric assay/device with the following features: i) minimal use of biological compounds; ii) a hydrogel microenvironment for the enzymatic reaction; iii) an integrated amperometric detection employing microelectrodes, which increase the temporal resolution (due to fast double layer charging and hemi-spherical diffusion of the species at the electrode) and the sensitivity of the analyses. Furthermore, the confinement of the enzyme and the high sensitivity enable the investigation of substrate/enzyme ratios similar to the situations found in vivo. As a proof of concept, the glucose oxidase enzyme, Eox, (GOx) kinetics is investigated. GOx is a β-D-glucose:oxygen 1-oxidoreductase, which catalyzes the oxidation of β-Dglucose, S, to β-D-glucono-δ-lactone, P’, by utilizing oxygen as an electron acceptor with production of hydrogen peroxide. The reaction can be separated into a reductive and an oxidative step: (2)

(3) GOx binds specifically to β-D-glucose and does not act on α-D-glucose (the other hemiacetal form of glucose); however, it oxidises all glucose present in solution (at pH 7.0) because the equilibrium between α and β anomers is driven towards the β form as the latter is consumed by the reactions. The H2O2 product is readily monitored.


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The reaction follows the ping-pong mechanism where the enzyme exists in two states,

GOx − FAD and GOx – FADH2. In principle, secondary Lineweaver–Burk plots could be obtained by keeping constant glucose concentration and varying the oxygen content. In terms of eq. (1) the reaction, eqs. (2) and (3), is re-cast as

1 2   → ES k Eox + S ← → Ered + P ' k 

k

−1

k   → E O k→ E + H O E red + O2 ← red 2 ox 2 2 k 3

(4)

4

−3

(5)

which is reduced to the standard scheme if the second set of steps is fast enough. Standard values of these quantities are [O2]=0.25 mM, [β-D-glucose]=0.1 mM, [GOx – FAD]=4.0 µΜ, = 14000 , = 0 , = 1000 . If eq. (5) is represented as a single step, without formation of the complex, the association rate is 1.95x106 M-1s-1, which makes the overall reaction an effective Michaelis-Menten15 (see also discussion below). Effective reaction schemes occur often and pseudo-first-order rate constants are reported.16-18 Understanding enzyme functioning proceeds through the determination of the rate constants from the rate of the product formation, which is one of the measurable quantities of an enzymatic reaction. In the study of new enzymatic reactions, there is no guarantee that more complicated schemes will be reduced to effective MM. Furthermore, enzymes entrapped in complex matrices are extensively studied for biosensor applications, where the presence of a restricted environment can affect their kinetics19 and therefore the device response. Restricted Environment of Enzymatic Reaction. The complex environment is a hydrogel fabricated via protein cross-linking. The protein matrix is micrometrical both in thickness and diameter. The cross-linking is based on the covalent binding of two (or more) molecules by a cross-linker. Enzymes present a variety of functional groups that can be readily bound by many agents. The two main chemical functions are the amine (NH2) and carboxyl (-COOH) groups. Amino groups are present at the N-terminal end and at every lysine residue. Carboxylic groups are present at the C-terminal end and at every


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glutamic and aspartic acid residue. An important parameter to tune is the distance between the reactive groups of the linker. It determines the flexibility of the protein matrix and the degree of freedom that the enzyme retains once immobilized. Immobilization by covalent linking using glutaraldehyde is probably one of the most used coupling methods.20 It is a friendly procedure since the reaction proceeds in aqueous buffer solution under conditions close to physiological pH, ionic strength, and temperature.21 Glutaraldehyde bears two aldehydes groups and can rapidly react with amine groups of proteins and enzymes at a pH around neutrality. It is more efficient than other aldehydes in generating ramified three-dimensional networks that are thermally and chemically stable.22 A lysine-rich inert protein carrier (BSA) was added to the solution to avoid extensive modification of the enzyme within the matrix.22 The inert protein and its concentration were selected in order to favour intermolecular cross-linking between enzyme molecules rather than the formation of unwanted intra-molecular links. A Pt microdisk was the detection tool, located directly inside the matrix, which allowed direct measurements inside the micro-reactor (Figure 1).

Figure 1. (A) Schematic section of the confining environment for the enzymatic reaction. The lower part represents the micro-electrode detection system, in black the Pt wire (i.e. the electro-active surface), in grey the glass support, the upper part shows the hydrogel matrix, which encloses GOx enzymes (green stars). (B) Merged optical and fluorescent (green) images of the system; the fluorescent signal is due to GOx-FITC tagged protein in the hydrogel matrix. For details see Section VIII of SI.


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EXPERIMENTAL SECTION Chemicals and Materials. β-D-glucose BioXtra ≥ 99.5%, glucose oxidase (GOx) Type X-S from Aspergillus niger (100-250U/mg), glutaric dialdehyde (GDA) as 25% solution in water (GDA), potassium phosphate monobasic and dibasic, acetic acid and sodium acetate were purchased from Sigma Aldrich. Bovine serum albumin (BSA) from ID Bio, PBS (pH 7.4) from Lonza, Triton X-100 from VWR, and MQ water from Millipore. The commercially available D-glucose is composed exclusively by α-anomer, due to the high solubility of β-anomer. For this reason, the 50 mM D-glucose stock solution was prepared at least 24h before using, in order to permit its mutarotation23. Enzyme-based Microelectrodes Fabrication. The enzyme (8 mg/mL for GOx) and BSA (62.5 mg/mL) were dissolved in PBS (pH 7.4) containing 0.02% v/v Triton X-100. After enzyme and BSA dissolution, 28 µL/mL buffer of 25% w/w GDA was added and quickly mixed. This solution constitutes a protein-based hydrogel. After 1 min, the enzymatic solution was hand-casted onto the surface of a 10 µm Pt ultra-microelectrode (UME) by touching for 10 minutes the tip of the UME to a tiny droplet (5 µL) of the solution deposited in a plastic dish. A thin layer adhered to the UME surface and was let to air-dry for 2h. Optimal drying time varied depending on temperature, humidity and type of enzyme.24 Amperometric Measurements. The amperometric experiments (i vs t) were performed in PBS solution (pH 7.4) at room temperature (RT), where a known concentration of analyte, β-D-glucose, was added. The electric potential of the electrode was kept at E = +0.65 V vs Ag/AgCl 3M KCl, at which the oxidation of H2O2 takes place; the system was allowed to equilibrate at least for 300 s before any measurement. The current was recorded during each addition of the analyte, and it was proportional to H2O2 concentration, which is one of the products of the enzymatic reaction under investigation. Curves of product concentration versus time, for each substrate concentration, were obtained. Several ranges of concentration of the substrate, from very low, 1 µM, to relatively high, 1 mM, were explored. Instrumentation. Amperometric measurements were performed using a 910B SECM (CH Instruments Inc., Austin, TX) in a typical three-electrodes configuration


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electrochemical cell: the hydrogel enzyme-based electrode is the working electrode (WE), a platinum wire is the counter electrode (CE) and Ag/AgCl, 3 M KCl is the reference electrode (RE). All potentials are referred to the Ag/AgCl (KCl 3M). A bipotentiostat controls the potential (range ±10 V) of the UME versus the reference electrode and it is able of measuring a broad range of current responses (range ±10A): with sensitivity from pA (or even sub-pA) currents to mA currents. The instrument is mounted inside a Faraday cage to isolate it from electromagnetic noises. This kind of insulation is fundamental for low-current measurements (pA and sub-pA). The electrodes were cleaned before their use with 0.05 µm diamond paper and sonicated in MQ water for five minutes in a bath sonicator. The CHI900 software allows extensive experimental control and analysis of acquired data. For further data elaborations OriginPro7.5 was utilized. Theoretical Model. In homogeneous environments, considering that concentrations have no spatial dependency and that the rates are constant, the time evolution of eq. (1) is described by four coupled differential equations

d [E ] = − k1 [ E ][ S ]+ ( k −1 + k 2 )[ C ] dt

(6)

d [S ] = −k1 [ E ][ S ] + k −1 [ C ] dt

(7)

d [C ] = k1[ E ][ S ]− ( k− 1 + k 2 )[ C ] dt

(8)

d[P ] = k 2[C ] dt

(9)

which are usually accompanied by initial conditions [E](0) = E0, [S](0) = S0, [C](0) = 0 and [P](0) = 0. The constant value of the ’s implies equi-probable reaction events at each point of the environment where the process evolves. Comparison of and has been used to determine the analytical solutions of the set of eqs. (6), (7), (8) and (9).25 For inhomogeneous crowded environments, eqs. (6), (7), (8) and (9) can still describe enzymatic activity by a mean field approximation. A slight modification of eqs. (6), (7),


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(8) and (9) can take into account additional effects connected to inhomogeneity. For instance, changing , which appears in the right hand side of eqs. (6), (7) and (8), to we have the power law approximation.26-28 The rates are modified to = Γ where the ’s are the rates in homogeneous systems, and Γ’s the correction factors.29 The conventional solution, MM reaction scheme, of eqs. (6), (7), (8) and (9) hold under the condition ≪ + , where =

is the MM constant.

As aforementioned this is valid even at single molecule level.9, 10 Since the formulation of the problem, a century and more ago, only a handful of solutions have been given, which are valid in limited ranges of the sets of variables that describe the system.26,

30-37

Analytical studies based on perturbative schemes and/or suitable series have also been carried out.25, 38-41 Matter conservation requires ! !" ! !"

( + #)=0

(10)

( + # + $) = 0

(11)

Eqs. (9) and (10) used together with the dimensionless variables, % = (&)/ , = (&)/, ( = #(&)/ , ) = / , * = /, + = / ,and , = & reduce the initial system of eqs. (6), (7), (8) and (9) to only two equations !-

) !. = % − * ( !0 !.

(12)

= −% + + (

(13)

Eqs. (12) and (13) can be further reduced to a single equation25,

42

when they are

associated with initial conditions. For the present work, we use e(0) = 1, s(0) = 1, c(0) = 0, and [P](0) = 0. The equations are solved iteratively. The analytical description of the solution method is given elsewhere41 and its brief description is reported in SI material section I. According to the model41 the normalized product, 1(,) = $(,)/, as a function of time reads


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g (x , x ) g (x , x )  g1 (x1 , x2 ) x1τ  (e − 1) + 1 2 1 (e x2τ − 1) + 2 1 2 (e( x1 + x2 )τ − 1)   x2 x1 + x2 (kµ − kσ )  x1  p(τ ) =   g3 (x2 , x1 ) 2 x2τ g(x1 , x2 )  g3 (x1 , x2 ) 2 x1τ  + (e − 1) + (e − 1)   2x1 2x2

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(14)

where

      

g ( x , y ) = λ 2 xy( x - 2 y )( y − x ) 2 (2 x - y ) g1 ( x, y ) = x ( x − y )(2 x − y )(2 + x + 2 y + λ y ( x − 2 y )) g 2 ( x, y ) = (2 x − y )(2 y − x )( x + y )(2 + x + y) g3 ( x, y ) = 2 xy (1 + y )( x − 2 y )

(15)

and

x1,2 =

−(λ + kµ ) ± (λ − kµ )2 + 4 λ kσ 2λ

.

(16)

Eq. (14) can be used to fit experimental data and yield reaction rates together with initial enzyme concentration only if the initial substrate concentration is known. Eq. (14) is expressed in terms of simple functions, exponentials and polynomials as cofactors, and may be implemented even in a spreadsheet. The accuracy of eq. (14) depends on the values of the dimensionless variables ), * , + . These variables are, in principle, in the (0, ∞) range. However, for intracellular reactions this range is much narrower. For small molecules, the forward rate, , is estimated in the 108 - 109 M-1s-1 range, but the active sites of enzymes and their substrates may be accessible only over a limited range of collision geometries, and effectively reduce the forward rate to the 104 - 107 M-1s-1 range.43 The reverse and catalytic rates values are in the 10-2 - 104 s-1 range.44 Intracellular concentrations of enzyme are similar or greater than substrate concentrations. It was reported that substrate concentrations within cells are in the neighborhood of their values,45 and therefore 0.1 < * < 10. Similar arguments hold for + with the extra condition that + < * . Eq. (14) predicts with high accuracy the formation of the product in time for λ ≥ 1.


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For λ = 1 the largest percent error, 5 =

67898:;8: 79?@AB=>8: 6 79?@AB=>8:

C 100, is less than 10% for

kµ = 0.1 and decreases as the value of kµ increases. For λ > 1 the error becomes smaller and smaller, see discussion in SI material, Section II. For λ < 1, eq. (14) satisfactorily describes the formation of the product. However, it presents a high relative error during the early times of the reaction, which is subsequently significantly reduced. It should be also noticed that eq. (14) describes with high accuracy enzymatic reactions modeled in terms of stochastic events, see Section III of SI material.

RESULTS AND DISCUSSION

Experiments were conducted for several initial substrate concentrations, which ranged from 1 µM to 2 mM. In all experiments, the enzyme concentration is technically the same. However, the fraction of enzyme that participates in each experiment may differ, see below. The analysis of the results in terms of the century-old solution of the MM equation and its Lineweaver-Burk plot shows that unique linearization does not exist, see Figure 2B.

Figure 2. Reciprocal currents versus reciprocal initial substrate concentrations. (A) Lineweaver-Burk plot for substrate concentrations higher or equal to 80 µM shows a linear regime with an estimated Michaelis-Menten (MM) constant = 7.306 ± 0.150 mM. (B) A non-linear regime appears for concentrations ranging from 1 to 60 µM.


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For concentrations higher then 60 µM the Lineweaver-Burk linearization of the kinetics data gives a value of = 7.306 ± 0.150 mM (Figure 2A), with a very good correlation coefficient: R2 equal to 0.998. The value is in agreement with previously reported data for similar systems.46 For substrate concentrations from 1 µM to 60 µM, the dependency of the reciprocal of the product formation velocities with respect to the reciprocal of substrate concentrations is not linear (Figure 2B). The best achievable linear fit in the second region is obtained for concentrations from 2.5 µM to 40 µM and gives a value of 4.563 ± 1.143 µM, with a correlation coefficient R2 of 0.837, see other possible combinations of linear fits in Section VII of SI. The estimated value of in the low concentration region is three orders of magnitude lower than the one obtained for higher concentrations. The variation of the MM constant from one regime to the other is substantial. This difference suggests that the condition ≪ + , necessary for the validity of the classical MM description, is either weak or does not hold in the second regime. The implication is that there is not a unifying description of both regimes. In order to avoid artifacts due to the existence of the ping-pong mechanism, we performed numerical simulations using the Chemical Kinetics Simulator (CKS).47 The use of the effective constants of ref. 15 confirmed that the ping-pong mechanism of GOX enzyme is effectively reduced to a two step reaction scheme, namely the MM scheme, and that the curves of hydrogen peroxide and gluconic acid concentrations over time are perfectly superimposable (see section IV of SI). We investigated the validity of the condition ≪ + in the second regime, i.e. low substrate concentrations, by means of eq. (14), and analogously we estimated the rates and the amount of enzyme that participated in the reaction. The panel of Figure 3 illustrates the use of eq. (14) and the associated fits, which are obtained by relaxing completely any constraint, including the concentrations of substrate and enzyme. To avoid results that had no physical meaning, the concentrations were initially set to the nominal ones. The rationale for the introduction of these additional degrees of freedom is the presence of a micrometrically structured hydrogel matrix as reaction environment. The concentration of glucose oxidase can locally change. The percolation of glucose inside the matrix may also generate a gradient of concentration or local variations. The


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estimated kinetics values and related fitted curves (obtained using eq. (14)) of the experimental data are reported in Table 1. Both the experimental and fitted curves are illustrated in Figure 3.

Figure 3. Observed and estimated (using eq. (14)) normalized product formation in time. The nominal substrate concentrations are: (A) 0.93 µM; (B) 9.3 µM; (C) 15.5 µM; (D) 18.8 µM; (E) 33 µM; (F) 60 µM. Black lines for experimental data (obtained from amperometric curves), for each concentration, red lines show the fits.

Eq. (14) fits well each experiment, see Section V of SI material for fitting details, and reveals the MM constant, dissociation constant, as well as all the reaction rates and the amount of enzyme participating in the reaction, see Table 1 (the individual reaction rates are given in Section VII of SI). Both MM and dissociation constants follow a linear relation with the substrate concentration, see Figure 4. The latter denotes that the apparent constants / and ! / are practically unchanged. Instead, the values of , , (see Section VII. Table S1) change from experiment to experiment and these changes show that the increase of the substrate concentration, in confined geometries, enhances additional mechanisms, such as diffusivity, excluded volume effects and


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percolation. These mechanisms, potentially present at all concentrations, do not affect the reaction process, but alter the reaction rates.

Table 1. Substrate, enzyme concentration, Michaelis-Menten constant and dissociation constant obtained by using eq. (14) to fit each experiments. The last column reports the arithmetic value of ( + )/, MM assumption holds true only if this values is much greater than one.

#Exp

DE (µM)

FE (µΜ)

GH (µΜ)

GI (µΜ)

GH /DE

(GH + DE )/ FE

1

0.93

0.153 ± 0.001

0.118 ± 0.001

0.046 ± 0.001

0.202 ± 0.001

7.31

2

9.3

1.618 ± 0.013

2.130 ± 0.013

0.930 ± 0.013

0.229 ± 0.001

7.06

3

15.6

2.902 ± 0.017

4.664 ± 0.017

1.560 ± 0.017

0.299 ± 0.001

6.99

4

18.8

3.929 ± 0.040

4.832 ± 0.040

1.880 ± 0.040

0.257 ± 0.002

6

5

33

4.620 ± 0.022

9.504 ± 0.022

3.300 ± 0.022

0.288 ± 0.001

9.2

6

60

8.400 ± 0.263

18.060 ± 0.263

0.600 ± 0.263

0.301 ± 0.004

9.29

Our analysis shows that the formal assumption of the MM model is poor in this range: i) for all the experiments, eq. (14) gives enzyme concentrations lower than those of the substrates and the / ratio is in the 0.2 - 0.3 range. This condition is met in intracellular reactions where the value of is in the neighborhood of the value of ; ii) for this group of experiments, the estimated concentration of the enzyme, based on the use of eq. (14), is smaller than the sum of and , e.g. the ( + )/ is between 6 and 10, an arithmetic value not much higher than one, which is a necessary condition, ≪ + , for the validity of Michaelis-Menten model. If we take into account the experiments from 2.5 µM to 40 µM the mean average value for is 5.281 ± 0.013 µM and for ! is 1.917 ± 0.013. For S0 [2.5 – 40] µM we estimated the value of either by using classical approach, 4.563 ± 1.143 µM, or by applying eq. (14), 5.281 ± 0.013 µM. The estimated values are in good agreement, although higher accuracy is achieved by eq. (14), while for Lineweaver-Burk plot the error is much higher, which denotes that the MM assumption does not hold strongly for this regime of concentrations.


14

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Figure 4. (A) Linear dependency of and (B) dissociation constant (! ) versus the initial substrate concentration, S0.

CONCLUSION

Experiments have been designed and conducted in a complex environment with concentrations of enzymes comparable to that of the substrate. Such environment may cause a change in the conformational state of the enzymes from periphery to the core of the medium. An electrode, where the detection of the product occurs, is located at the centre of the micrometric device. For low initial substrate concentrations, the enzymatic reaction takes mainly place at the periphery of the device, and the product requires time to diffuse and to be detected. The increase of leads to an increase of product flux from periphery to the bulk and the product is more quickly detected. Eq. (14) has been developed to analyze the results. It is a mean field approach. Diffusivity, percolation and other effects are not explicitly taken into account. The model, however, describes with high accuracy enzymatic reaction modeled in terms of stochastic events and is able to detect a dependency of the Michaelis-Menten, backward, and catalytic reaction rates on the initial concentration of the substrate. Fabrication of complex matrices, such as that presented here, supported by the development of new kinetic models such, i.e. eq. (14), can be used to shed light on the inner working processes of living cells. Assays/devices based on the present work can be


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used to investigate the enzymatic mechanism of further proteins and can be employed in biotechnological and medical application such as drug discovery and medical diagnosis.

ASSOCIATED CONTENT

Supporting Information In the Supporting Information we briefly discuss the mathematical model and we present the range of the variables where it can be successfully applied to determine kinetics rates (Section I and II). In Section III, we demonstrate the applicability of the model to a limited number of molecules. Furthermore, we describe the numerical simulation of the enzymatic reaction (Section IV), the fitting protocol (Section V) and the estimation of errors with respect to experimentally observed data (Section VI). We report the individual reaction rates: , , for each single experiment (Section VII). Finally, in Section VIII, we show the form of the microstructure of the enzyme-based hydrogel matrix by using fluorescence.

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