Mathematical Model for a Three-Phase Enzymatic Reaction System

Abstract

The enzymatic reaction system with a solid−liquid−gas three-phase interface microenvironment allows oxygen to be directly supplied to the oxidase catalytic reaction from the gas phase, effectively improving enzyme kinetics as compared with the conventional two-phase system. For this new system, a mathematical model is developed in this work to describe the enzymatic reaction coupled with interphase mass transfer, by which the influences of three-phase interfacial microenvironment on reaction kinetics can be systematically and quantitatively explored. The numerical simulations reveal that the flux of oxygen transport across the interface between the gas phase and the enzyme layer dominantly determines the H 2 O 2 production rate. The porous substrate possessing larger porosity and smaller pores, when coated with a thick and concentrated enzyme layer, can potentially lead to higher oxygen supply and hence a higher H 2 O 2 production rate. Moreover, regardless of the pore diameter, the H 2 O 2 production rate remains constant after the porosity is greater than 0.8, and if the enzyme concentration is not less than 5 mol m −3 , the H 2 O 2 production rate no longer changes after the thickness of the enzyme layer is greater than 0.5 μm. This work offers a powerful in silico tool for the investigation of the three-phase enzymatic reaction system. The quantitative results and mechanistic findings will lead to optimized design of this promising system.

Modeling enzymatic and electrochemical cascade reactions at the three‐phase interface enzyme electrode

“…As shown in Figure 2A2, the production rate of H 2 O 2 remains high regardless of the porosity. Since the previous study 20 confirmed that the supply rate of oxygen dominantly determines the production rate of H 2 O 2 , this high production rate can be attributed to the fact that the supply rate of oxygen is sufficiently large (see Figure 2A1). Furthermore, the supply rate of oxygen is related to the structure of the porous substrate.…”

“…This phenomenon has been confirmed in the previous study. 20 In addition, the escape rate of H 2 O 2 also increases with increasing porosity. This is because the pore size increases with increasing porosity when the pore wall thickness is fixed.…”

“…The symbol i in the GDL only denotes oxygen since only oxygen in the gas phase participates in the enzymatic reaction. To simulate the mass transfer of oxygen in the porous substrate with pore sizes that are smaller than the mean free path of oxygen, the Knudsen diffusion 20 must be considered in the model. The effective diffusion coefficient of oxygen (D GDL,O2 ) is calculated via the Wilke-Bosanquet model, 27 1…”

“…Very recently, a novel model was also developed for the threephase enzymatic system based on glucose oxidase (GOx). 20…”

“…Very recently, a novel model was also developed for the three‐phase enzymatic system based on glucose oxidase (GOx) 20 . It described the interphase (oxygen dissolution) and intraphase (species diffusion) mass transfer, and the homogeneous enzymatic reaction within the system.…”