Enhancement of product selectivity via enzyme immobilization in sequential degradation reactions of polymeric substrates

The balance equations pertaining to the modelling of a slap-shaped bead containing immobilized enzyme uniformly distributed which catalyzes the sequential reactions of degradation of a polymeric substrate were written and analytically solved in dimensionless form. The effect of the Thiele modulus on the selectivity of consumption of each multimeric product was studied for a simple case. Whereas plain diffusional regime leads to lower selectivities than plain kinetic regime, improvements in selectivity of species A_i relative to species A_i+1 may be obtained at the expense of higher Thiele moduli within a limited range when the diffusivity of A_i is larger than that of A_i+1, or when the pseudo first order kinetic constant describing the rate of consumption of A_i is lower than that of A_i+1.List of Symbols A_i polymeric substrate containing i monomeric subunits - C_i mol·m^–3 normalized counterpart of C_i - C_i mol·m^–3 concentration of substrate A_i - C_i,0 mol·m^–3 initial concentration of substrate A_i - C_i,0 normalized counterpart of C_i,0 - D_ap,i m²·s^–1 apparent diffusivity of substrate A_i - k_i s^–1 pseudo-first order rate constant - K_m,i mol·m^–3 Michaelis-Menten constant associated with substrate A_i - L m half-thickness of the catalyst slab - N number of monomeric subunits of the largest substrate molecule - Th Thiele modulus - V_i mol·m^–3·s^–1 rate of rection of substrate A_i - V_max,i mol·m^–3·s^–1 maximum rate of reaction under saturating conditions of substrate A_i - x m longitudinal coordinate - S_i,i+1 selectivity of enzyme with respect to substrates with consecutive numbers of monomeric subunitsGreek Symbols _i ratio of maximum rates of reaction - _i ratio of apparent diffusivities