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This paper presents computational modeling of response kinetics of bioelectroanalytical system based on solid supported lipase substrate and lipase interaction. The model assumes that lipase substrate is formed by dripping and drying a small amount of the ethanol solution of 9-(5′-ferrocenylpentanoyloxy)nonyl disulfide (FPONDS) and that lipase is capable of cleaving FPONDS ester bonds via hydrolysis mechanism. Two mathematical models have been developed and evaluated trough computational simulation series by comparing them to experimental data. The results of simulation demonstrate that a good fitting might be obtained only taking into account non-linear substrate wash off process.

Lipolytic enzymes are one of the most important components of the biochemical processes. At the same time, triacylglycerol acylhydrolases (EC 3.1.1.3) that hydrolyze triacylglycerols at the oil/water interface have wide applications as detergent additives, digestive aids, as well as in the paper and food industries [

Recently, a novel electrochemical technique for the assay of lipase activity has been described [_{2})_{4}COO(CH_{2})_{9}S-]_{2}, where Fc is the ferrocene) on the gold electrode surface modified by a hexanethiol self-assembled monolayer. The redox-active ferrocene group of FPONDS generates the amperometric signal, the intensity of which is proportional to the number of FPONDS molecules at the interface. Electrochemical and surface-enhanced infrared absorption spectroscopic data, as well as control experiments with an engineered, deactivated mutant enzyme, have demonstrated that the wild-type lipase from

However, in exclusively experimental work [

This paper analyzes bioelectroanalytical system that is significantly different from recently discussed amperometric system of lipase activity determination [

The processes that occur at the interface of zones 2 and 3 could be described in the following schematic form which is most commonly used for the description of lipase interfacial activation [

where E is the enzyme in solution, E * is the enzyme attached to the surface of substrate (at the interface of zones 2 and 3 in

It is assumed that lipase solution is distributed evenly and its diffusion could be not taken into account. It is also assumed that the redox-active reaction product (ferrocene-based) leaves sensor surface quite fast and its diffusion could be estimated as instantaneous. The system under discussion can be described by classical mathematical model of reaction kinetics:
_{p}_{D}_{1} is the rate constant of enzyme-substrate complex (E*U) formation, _{-1} is the rate constant of E*U dissociation, _{2} is the catalytic rate constant of enzymatic reaction, and

This model allowed good fitting only for a part of experimental data available (data not shown), which had strongly expressed exponential character of substrate concentration decrease (

However, another part of experimental data exhibited ^{-1} (

Thus, slightly modified system of non-linear differential equations can be written by _{u} is the substrate wash off rate constant and _{0} is the initial substrate concentration on the electrode surface.

Non-linear wash off term is quite unusual, but it could be explained in a simplified way as complex outcome of two different linear wash off rates: one for the electrode surface/substrate boundary (stronger bond, lower wash off rate) and second (weaker attraction, much higher wash off rate) for, say, substrate/substrate boundary. It is possible that during the process of modified electrode preparation substrate forms only very few substrate/substrate boundaries (pseudo-multilayer interfacial structure). Thus, initially wash off rate could be seen as linearly (in respect to the substrate concentration) dropping from high value for the substrate/substrate boundary, down to low value for the electrode/substrate boundary, and the whole process then becomes second order with respect to the substrate concentration. By way of illustration, let's assume that the wash-off rate constant _{0}

The series of computational simulations were performed to investigate how electrode readings would differ if this amperometric biosensor worked under presented model and how they would match experimental data (experimental results were obtained as described in [^{3}, _{2} = 75 s^{-1}, _{-1} = 10 s^{-1}, _{p}^{-1}, _{D}^{-1}, _{A}^{-2} cm^{2}, _{B}^{-2} cm^{2}, _{C}^{-2} cm, _{D}^{-2} cm^{2}. The values of four kinetic constants selected as a starting point for modeling were the same as in paper [_{0}_{0}. The values of initial _{0}_{0}_{1}_{u}

Experimental data and simulation results are presented in

Experimental data were analyzed as logarithmic and ^{-1} graphs. These graphs reveal that experiments A, C and D strongly exhibit inverse dependence on time, whereas the data of experiment B has more exponential character. Such different graph characters could be explained as two term competition in

Finally, it is worth noting that the values of kinetic constant _{1} obtained in this work are lower by ca. three orders of magnitude compared to the value reported in our earlier study [_{1} reflects molecular event of substrate binding in the enzyme active center.

The results of the foregoing computational experiments enable us to make the following conclusions:

The proposed reaction kinetic model of response of the FPONDS-based electrode, used for the electrochemical determination of

According to the results of our study, experimental data exhibit two distinct types of substrate (FPONDS) concentration decay: one exponential (in respect to time) and the other of t^{-1}-type. This indicates that, in the

Numeric simulations have revealed that a good fitting might be obtained only taking into account non-linear substrate wash off process, which could be explained in a simplified way as a complex outcome of two different linear wash off rates: one for the electrode surface/substrate boundary (stronger bond, lower wash off rate) and the other (weaker attraction, much higher wash off rate) for the substrate/substrate layer boundary. In this model of interface, it is assumed that substrate forms only very few substrate/substrate boundaries (pseudo-multilayer interfacial structure), thus wash off rate could be seen as linearly (with respect to the substrate concentration) dropping from high value for substrate/substrate boundary, down to low value for electrode surface/substrate boundary, therefore the whole process then becomes second order with respect to the substrate concentration.

We would like to acknowledge Aleksandr Kašliakov as his initial research on this problem allowed us to better understand specific properties of the problem.

Cross-section scheme of the model used in the present study:

Experiment A and B data analysis: ▲- 1/U dependency on time; ▼- ln(U) dependency on time.

U dependency on time: solid line - simulation results, points – experimental data.

Initial concentrations and best-fitted constants.

_{0}^{-2} |
_{0}^{12}, mol cm^{-3} |
_{1}×10^{-6}, mol cm^{-2} s^{-1} |
_{u}×10^{13}, mol cm^{-2} s^{-1} | |
---|---|---|---|---|

A | 3.88 | 58.0 | 0.41 | 2.26 |

B | 8.43 | 5.80 | 1.20 | 2.13 |

C | 3.51 | 0.58 | 1.17 | 2.06 |

D | 0.44 | 8.30 | 0.75 | 2.34 |