Derivation of nonsteady-state analytical solution for surface enzyme kinetics

A mathematical modeling of real-time surface plasmon resonance (SPR) imaging measurements of surface enzymatic reactions on DNA microarrays are examined using a kinetics model that couples the contribution of both enzyme adsorption and surface enzyme reaction kinetics. The enzymatic reaction can be described in terms of classical Langmuir adsorption and Michaelis–Menten concepts and three rate constants: enzyme adsorption (ka), enzyme desorption (kd) and enzyme catalysis (kcat). In this paper, the analytical solution of the fractional surface coverage for the three surface species ES, S* and S are derived. In the presence of catalytic activity, the numerical solution of the problem is also reported using Matlab software program. All the analytical results are compared with our numerical results.