The developed model is based on non-stationary reaction-diffusion equations [34�C36]. By changing input parameters the output results were numerically analyzed at transition and steady state conditions.2.?Mathematical ModelWe consider the reaction scheme of the optical biosensor involving hydrogen peroxide (H2O2) reaction with peroxidase (E) to form compound I (cmpI) and water (H2O) with the constant reaction rate k1. The compound I interacts with the substrate (S) to form product (P) and free enzyme (E) assuming the constant reaction rate k2,E+H2O2?k1cmpI+H2O,(1)cmpI+S?k2E+P.(2)The product (P) absorbs light and therefore the response of the biosensor increases during the reaction as the product forms. The concentration of the analyte (S) can be directly determined from the absorbance of the product (P) [37].

Assuming the symmetrical geometry of the biosensor and homogeneous distribution of immobilized enzyme, the mass transport and the reaction kinetics in the enzyme layer can be described by the following system of the reaction-diffusion equations (0 < x < d, t > 0),?Se?t=DSe?2Se?x2?k2CSe,(3)?Pe?t=DPe?2Pe?x2+k2CSe,(4)?He?t=DHe?2He?x2+k1EHe,(5)?E?t=?k1EHe+k2CSe,(6)?C?t=k1EHe?k2CSe,(7)where x and t stand for space and time, Se(x, t), Pe(x, t), He(x, t), E(x, t), C(x, t); are the substrate, product, hydrogen peroxide, peroxidase and compound I concentrations in the enzyme layer, d is the thickness of the enzyme layer, and Dse, Dpe, DHe are the diffusion coefficients. The enzyme and the formed compound I are immobilized and therefore there are no diffusion terms in the enzyme and compound I equations.

Outside the enzyme layer only mass transport by diffusion of the substrate, product and hydrogen peroxide takes place. We assume that the external mass transport obeys a finite diffusion regime (d < x < d + ��, t > 0),?Sb?t=DSb?2Sb?x2,(8)?Pb?t=DPb?2Pb?x2,(9)?Hb?t=DHb?2Hb?x2,(10)where �� is the thickness of the diffusion layer, Sb(x, t), Pb(x, t), Hb(x, t) are the substrate, product and Dacomitinib hydrogen peroxide concentrations in the diffusion layer, and DSb, DPb, DHb are the diffusion coefficients.The diffusion layer (d < x < d + ��) may be treated as the Nernst diffusion layer [38]. According to the Nernst approach a layer of thickness �� remains unchanged with time. It was assumed that away from it the solution is uniform in concentration.Let x = 0 represents the plate surface, while x = d is the boundary between the enzyme layer and the buffer solution. The biosensor operation starts when some substrate appears in the bulk solution.