Determination of the inherent kinetics of immobilized glucose oxidase using a diffusion cell

The enzyme glucose oxidase (GO) was covalently immobilized onto a poly(vinyl alcohol) hydrogel, cross-linked with glutardialdehyde and a polyazonium salt. To compare the kinetic parameters of immobilized GO with the known kinetic parameters of soluble GO, the diffusion cell method was used.Between two compartments, containing solutions with different glucose concentrations, a GO-containing hydrogel membrane was placed. Simultaneous diffusion through and enzymatic reaction in the membrane occurred. In this way diffusional effects of the membrane could be eliminated from the effective kinetic parameters to yield the inherent kinetic parameters.It appeared that the enzymatic reaction is independent of the oxygen concentration at oxygen concentrations 0.22 mol m^–3 (Michaelis constant for oxygen < 0.22 mol m^–3). Further, the Michaelis constant for glucose does not change dramatically after immobilizing the enzyme. The maximal reaction rate is depending on the enzyme concentration. As the enzyme concentration in the membrane is not exactly known (mainly due to leakage of enzyme out of the membrane during membrane preparation), only an estimation of the turnover number can be made.The diffusion cell method is easy to carry out. Still, some recommendations can be made on the performance.List of Symbols _g, _0x partition coefficient of glucose and oxygen, respectively - thickness of the wetted membrane (m) - A_m surface area of membrane (m^–2) - C constant (mol² m^–3) - c_g, c_0x concentration of glucose and oxygen, respectively (mol m^–3) - c_g,0c_g, glucose concentration at the filter-paper/membrane interface next to compartment A and B, respectively (mol m^–3) - c_{g, A}c_{g, B} glucose concentration in compartment A and B, respectively (mol m^–3) - c_GO glucose oxidase concentration (mol m^–3) - D_eff effective diffusion coefficient (m² s^–1) - D_m, D_sl diffusion coefficient in, respectively, the membrane and the solution layer (m² s^–1) - d_dl, d_df, d_sl thickness of, respectively, the diffusion layer, the filter-paper and the solution layer (m) - h_B initial slope of concentration versus time curve of compartment B (mol m^–3 s^–1) - J flux (mol m^–2 s^–1) - J₀ flux in the membrane at membrane/filter-paper interface next to compartment A and B, respectively (mol m^–2 s^–1) - J_A, J_B flux leaving compartment A and entering compartment B, respectively (mol m^–2 s^–1) - J_m flux through the membrane (mol m^–2 s^–1) - k total mass transfer coefficient (m s^–1) - k₁, k₂ rate constant of a particular reaction step (m³ mol^–1 s^–1) - k_–1, k_–2 rate constant of a particular reaction step (s^–1) - k_cat (intrinsic) catalytic constant of turnover number (s^–1) - k_cat^* inherent catalytic constant, determined by inserting D_m(s^–1) - k_cat^** inherent catalytic constant, determined by inserting D_eff (s^–1) - k_m(g) (intrinsic) Michaelis constant for glucose (mol m^–3) - k_m(o) (intrinsic) Michaelis constant for oxygen (mol m^–3) - k_m^*(g) inherent Michaelis constant for glucose (mol m^–3) - k_m^*(o) inherent Michaelis constant for oxygen (mol m^–3) - m_GO number of moles of GO present (mol) - P_m permeability of glucose in the mebrane (m s^–1) - P_eff effective permeability (m s^–1) - V volume (m³) - v₀ initial reaction velocity (mol m^–3 s^–1) - V_max^** inherent maximal reaction velocity, determined by inserting D_eff (mol m^–3 s^–1) - x distance (m)