I
I..
Theoretical model of micro-fluidic reactor system
According to the model which have been published by our lab [32] that we have constructed a novel home-made micro-fluidic system (Figure 6) for assay enzymatic kinetics parameter of immobilized enzyme. This novel model combined plug flow approximation, Michaelis-Menten equation, and surface reaction limited condition, to fit the kinetics of immobilized enzyme on one-side planar surface as eq (1).
where space time () is the time required to process the volume of reaction mixture
in reactor, K*m is the Michaelis constant (mol dm-3) for immobilized enzymes on the planar surface, V*max is maximum reaction rate per unit surface area of catalyst (mol dm-2 min-1), H is the height of rectangular channel reactor, is reaction conversion fraction, and [S]o is the substrate concentration at inlet of the channel. Surface reaction limited condition means that diffusion is fast compared to surface reaction.
To meet this requirement, the ratio of the reaction volume to the catalytic planar surface must be reduced. We built a micro-fluidic bioreactor with a much smaller channel height than the diffusion layer in semi-infinite diffusion process, and the corresponding dynamic model was discussed in detail in our past reference [32]. By using a series of variant flow rates (or space times), this equation could allow us to
31
precisely predict the kinetics of immobilized enzyme at different inlet concentration
of substrate; details are as followings:
If reaction conversion fraction, , is smaller than 1%, and [S]o is much higher than
K*m, then eq (1) can be degenerated as follows:
where the subscript H of [S]o,H refers to this saturating assay condition, the subscript 0
of 0
* max
H
V refers to initial approximation without regard to K*m factor. This
condition means that the highest available concentration of substrate is much larger than Km. If we could choose [S]o,H ≥ 19Km, then the error involved in the
deactivation of immobilized enzyme; therefore the any simultaneous value of
0
* max
H
V can be determined in experiment progress. Eq (1) obviously indicates that
we should choose as low as possible the [S]o concentration, as long as the output concentration of reporter is not beyond the limit of detection, to increase the accuracy of K*m evaluation after
H Vmax*
determined as above. Eq (1) can be arranged into the following eq:
32
where the subscript L of [S]o,L refers to at low concentration of substrate, the subscript 0 of Km* 0 refers to an initial approximation. With linear regression of eq (1.2),
and using a set of space time s and the corresponding measured data of conversion fraction s, we can derive estimated value forKm* 0, the slope of eq (1.2). If the
Nevertheless, the saturating substrate condition can’t always be achieved in some
assays because of high-substrate inhibition or limit of substrate solubility. If the highest available concentration of substrate is larger than the level of 3Km, then accurate estimates of kinetics for immobilized enzymes can still be achieved. For this case, considering an iterative scheme, we can re-arrange eq (1) as eq (1.3), and combine eq (1.3) with eq (1.2) to set up the following set of equations.
33
concentration of substrate, [S]o,H, and low inlet concentration of substrate, [S]o,L , respectively. After successively finite computing, we will get repetitions of decimal places being used for r
* max
H
V and K*m r, and these values are then the final
approximate solutions to eq (1.3) and eq (1.4), respectively.
As mentioned above, this method will fail or gain a large deviation from true value of kinetics when the highest available concentration of substrate is far lower than saturation (i.e., ≤ 3Km). This is similar to the limitations of Michaelis-Menten plot to
estimate the kinetic value of homogeneous catalytic reaction. The strategy of measurement and calculation is briefly outlined as Figure 7.
34
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26. Siek, G.C., Katz, L.S., Fishman, E.B., Korosi, T.S., Marquis, J.K. (1990) Molecular forms of acetylcholinesterase in subcortical areas of normal and Alzheimer disease brain. Biol Psychiatry. 27: 573-80.
27. Barshan Tashnizi, M., Ahmadian, S., Niknam, K., Torabi, S.F., Ranaei Siadat S.O. (2005) Covalent immobilization of Drosophila acetylcholinesterase for biosensor applications. Biotechnol Appl Biochem. 52: 257-64.
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28. Du, D., Chen, S., Cai, J., Zhang, A. (2007) Immobilization of acetylcholinesterase on gold nanoparticles embedded in sol-gel film for amperometric detection of organophosphorous insecticide. Biosens Bioelectron. 23: 130-4.
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30. Sahin, F., Demirel, G., Tumturk, H. (2005) A novel matrix for the immobilization of acetylcholinesterase. Int J Biol Macromol. 37: 148-53 31. Milkani, E., Khaing, A.M., Huang, F., Gibson, D.G., Gridley, S., Garceau, N.,
Lambert, C.R., McGimpsey, W.G. (2010) Immobilization of acetylcholinesterase in lipid membranes deposited on self-assembled monolayers. Langmuir. 26: 18884-92.
32. Lee, C.C., Chiang, H.P., Li, K.L., Ko, F.H., Su, C.Y., Yang, Y.S. (2009) Surface Reaction Limited Model for the Evaluation of Immobilized Enzyme on Planar Surfaces. Anal. Chem. 81: 2737-2744.
33. Marinov, I., Gabrovska, K., Velichkova, J., Godjevargova, T. (2009) Immobilization of acetylcholinesterase on nanostructure polyacrylonitrile membranes. Int J Biol Macromol. 44: 338-45.
34. Cesar, Mateo., Jose, M. Palomo., Gloria, Fernandez-Lorente., Jose, M. Guisan., Roberto, Fernandez-Lafuente. (2007) Improvement of enzyme activity, stability and selectivity via immobilization techniques. Enzyme and Microbial Technology. 40: 1451-1463.
35. Delouise, L.A., Miller, B.L. (2005) Enzyme immobilization in porous silicon:
quantitative analysis of the kinetic parameters for glutathione-S-transferases.
Anal Chem. 77: 1950-6.
36. Godjevargova, T., Nenkova, R., Dimova, N. (2008) Immobilization of
38
acetylcholinesterase on new modified acrylonitrile copolymer membranes.
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37. Sanllorente-Mendez., Dominguez-Renedo, S.O., Arcos-Martinez, M.J. (2010) Immobilization of acetylcholinesterase on screen-printed electrodes.
Application to the determination of arsenic(III). 10: 2119-28.
38. Fatranská, M., Kiss, A., Oprsalová, Z., Kvetnanský, R. (1989) Acetylcholinesterase and choline acetyltransferase activity in some hypothalamic nuclei under immobilization stress in rats. Endocrinol Exp. 23:
3-10.
39. Barr, R.D., Koekebakker, M., Lawson, A.A. (1998) Acetylcholinesterase in the human erythron. II. Biochemical assay. Am J Hematol. 28: 260-5.
40. Kiely, J.S., Moos, W.H., Pavia, M.R., Schwarz, R.D., Woodard, G.L. (1991) A silica gel plate-based qualitative assay for acetylcholinesterase activity: a mass method to screen for potential inhibitors. Anal Biochem. 196: 439-42.
39
Table 1. The percentage of elemental analysis at different stages of immobilization process. While the every immobilized step increases that the percentage of Si elemental analysis reduce, but the percentage of C elemental analysis raises. Thus, we could confirm that the enzyme immobilized onto surface silicon wafer, successfully.
40
Immobilized AChE Free AChE Assay condition
Immobilization support Silicon oxide none ATChI
Vmax (mole/min/mg) 7.2 0.6 159 5 0.1 mM DTNB
Km (M) 46 3 79 8 10 mM PB (pH 8)
Kcat (min-1) 433 36 44485 1541
Table 2. Experiment-determined catalytic parameters of turnover numbers (kcat) and Michaelis constants (Km) for the soluble and planar surface–immobilized AChE systems.
41
Figure 1. The mechanism of action of acetylcholinesteras (AChE) cholinergic nerve transmission is terminated by the enzyme acetylcholinesterase (AChE).
AChE is found both on the post-synaptic membrane of cholinergic synapses and in other tissues like red blood cells. Acetylcholine (ACh) binds to AChE and is hydrolysed to acetate and choline. This inactivates the ACh and the nerve impulse is halted. AChE inhibitors prevent the hydrolysis of ACh, which increases the concentration of ACh in the synaptic cleft; AChE inhibitors are widely used in the treatment of Alzheimer’s disease.
42
Figure 2. Percentage changes in selected causes of death (all ages) between 2000 and 2008 [1].
43
Figure 3. Schematic diagram of the immobilization of AChE onto silicon oxide surface. ThThee imimmmoobbiilliizzeedd enenzzyymmee ffuunnccttioionnaalliizzeedd onon sisilliiccoonn wawaffeerr nneeeeddeedd ththrreeee--sstteepp r
reeaaccttiioonn ooff ssuurrfafaccee momoddiiffiiccaattiioonn:: WeWe fifirrsstt mmooddiiffiieedd susurrffaaccee ofof sisilliiccoonn wawaffeerr byby 3-triethoxysilylpropylamine (APTES) that provided amine groups. At second step, we utilized glutaraldehyde to bind amine groups via covalent binding. At third step, according to Chemical characteristic of aldehyde group is able to bind amine groups of acetylcholinesterase (AChE) that would form disulfide bind via covalent binding.
44
Figure 4. ThThee ststeeppss ininvvoollvveedd inin esesttiimmaattiioonn ooff ACAChhEE acacttiivviittyy bbyy ususiinngg ElElllmmaann’’ss memetthhoodd.. AAcceettyytthhiioocchhoolliinnee (A(ATTCChhII)) isis bbrrookkeenn dodowwnn inin tthhee pprreesseennccee ofof a
acceettyyllcchhoolliinneesstteerraassee ((ACAChhEE)) ttoo rerelleeaassee ththiioocchhoolliinnee tthhaatt rreeaaccttss wiwitthh 5,5-dithiobis-(2-nitrobenzoic acid) (DTNB) to rapidly form thionitro benzoic acid (TNB) and detects its absorbance at 410 nm.
45
Figure 5. Schematic diagram of the home-made apparatus for immobilization of acetylcholinesterase onto the silicon dioxide surface.
46
Figure 6. Overview of home–made reactor system for measurement immobilized enzymatic kinetics. Reactor system design for the determination of kinetic constants of immobilized enzyme. Rectangular reactor with a catalytic surface on the silicon oxide wafer. The channel size is L(72.6cm)W(0.194cm)H (167m)(where
H W
L ).
47
Figure 7. A systematic and standardized data analysis. Flow chart showing the scheme of solving eq (1) to determine the apparent kinetics of immobilized enzyme when i) saturating condition is available; ii) enough high, but not saturating, concentration of substrate is available; iii) the highest available concentration of substrate is still lower than 3K*m. These conditions of choice can be also regarded as the final check for the reasonableness of calculating results.
48
(a) (b)
(c)
Figure 8. The first automatic program for modifying progress curves of immobilized-enzyme reaction cycles. (a) To key essential parameters: flow rate (l/min), space time (min), extinction coefficient of product () and substrate concentration (M). (b) Entering in the baseline of high/low concentration for background, respectively. (c) To key in reaction line of high concentration and select region for modification and subtract from baseline of high concentration that is operated as same as the low concentration of substrate.
49
(a) (b)
(c)
Figure 9. The second automatic program for computing initial approximation of
0
* max
H
V , Km* 0 and decay curve about the issue of deactivation of
immobilized enzyme. (a)(b) We entered qualified reaction line of high/low concentration and concentration of substrate into program. After computing for first time, we got the initial of 0
* max
H
V , decay curve of deactivation of immobilized
enzyme. (c) According to above parameters, we could figure out the initial Km* 0 of immobilized enzyme.
50
Figure 10. The third automatic program for finding the final value of < K*m >r
of immobilized enzyme. The value of final Km*r would find out after we entered qualified reaction line of high/low concentration, concentration of substrate and initial
< K*m >0 into third automatic program.
51
Figure 11. The XPS spectra of each immobilization step. After each immobilization step, we utilized XPS to scan the four element (Si, O, N, C) on surface of silicon wafer.
52 Time (sec)
0 10 20 30 40 50 60
A410
0.0 0.1 0.2 0.3 0.4
1 2 3 4
1 2 3 4
ATchI 5mM - + + +
DTNB 0.1mM + - + +
K-PB 10mM pH8 + + + +
AChE + + - +
total volume 1 ml 1 ml 1 ml 1 ml
Figure 12. Progress curves of enzyme assay for AChE. Complete reaction. (1) could observe an increase of absorbance at 410 nm but there is no change of absorbance for control reaction without ATChI (2), DTNB (3) and AChE (4). Detailed procedures are described in Materials and Methods.
53
Time (min)
0 5 10 15 20 25
A410
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Reaction solution removed from active surface Reaction solution removed from active surface
Figure 13. The absorbance of 2-nitro-5-thiobenzoic acid (TNB). Time course with two termination periods caused by removing reaction mixture from catalytic surface and the enzyme target sample (acetylcholinesterase immobilized onto the silicon oxide surface).
54
Figure 14. The overview of general crystal with vector coordinate. The crystal of general (triclinic) unit cell, with edges a, b, c and angles ,
55
AChE amount(nM)
0 1 2 3 4 5
Slope(A 410/min)
0.0 0.2 0.4 0.6 0.8 1.0
Figure 15. Effective range of AChE assay. AChE catalyzed by the variable amount of AChE (from 0.5 to 4.5 nM) was determined under the standard condition. Each point and bar represented the mean and SD, respectively, obtained from three experiments.
56
Michaelis-Menten
[ATChI] (mM)
0 1 2 3 4 5
Specific activity (umol/min/mg)
0 20 40 60 80 100 120 140
Immobilization Support ATChI
Vmax (umole/min/mg) 0.1mM DTNB
Km (mM) 10mM PB pH 8
kcat (min-1) kcat/Km
none 158.8±5.5 0.079±0.008
564962±38048 44485 ±1541
Free AChE Assay condition
Figure 16.Michaelis-Menten plots for hydrolysis reaction by free AChE. Lines of best fit were obtained from the data using Enzyme Kinetics Module software. Each point and bar represented the mean and SD, respectively, obtained from three experiments.
57
Progess time (min)
0 100 200 300 400
A410
0.0 0.2 0.4 0.6 0.8
[ATChI]0=1000 M [ATChI]0= 50 M
Figure 17. The typical progress curves of enzymatic assays. The absorbance measurements of time courses were obtained after setting zero on a control solution containing no ATChI substrate in the AChE assay.
58
S]0
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025
0.00 0.01 0.02 0.03 0.04 0.05 0.06
H1
V*max/H (M/min)=25.95 (Slope)
H2
V*max/H (M/min)=11.23 (Slope)
H3
V*max/H (M/min)=10.16 (Slope)
H4
V*max/H (M/min)=9.71 (slope)
ATChI]0=1000 M
Figure 18. AChE kinetics. According to the second automatic program, the versus /[S]o plot was used to determine initial V*max/H at high substrate concentration. Under saturating substrate condition, [ATChI]o = 1000 M >> Km, in the AChE assay, the slope of linear regression, V*max/H, were fitted to an exponential decay curve shown as the inset, which interpolated value was used to predict V*max/H at any time in the experimental intervals.
59
Figure 19. AChE kinetics. The typical iterative plots (a) and (b) were the output values of the second and third automatic programs. (a) for the solubility limit of substrate [ATChI]o in the AChE assay, [ATChI]o = 1000 M concentration used in this experiment, the initial approximation <V*max/H>0 (black symbol) were still obtained from eq (2), and fitted to the exponential decay curve (r = 0). The r = 1~4 curves mean the fitting curves of five successive approximations of eq (1.3); the red symbol means the optimum value of V*max/H, which has converged to three significant figures.
(b) The black symbol and red symbol mean the initial and the fourth approximations of eq (1.4), respectively. The value of K*m of immobilized AChE has converged to 46.92 M after four successive approximation (r = 1~4).
60
-Ln( 1-)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
V*max/H)-[pNPP] (uM)
0 2 4 6 8 10 12 14 16 18 20
n=1
K*m=46.22 M (slope) n=2
K*m=49.40 M (slope) n=3
K*m=42.62 M (slope)
y=49.40
y=46.22
y=42.62
Figure 20. Kinetics of immobilized AChE. The predicted values of K*m of immobilized AChE are the result of three set of independent experiment data (n = 1~3).