The current-potential response of the enzyme-catalyzed, redox polymer mediated kinetic scheme pertaining to biofuel cells is analyzed. The ping-pong reaction scheme is solved analytically using the homotopy method for estimating the current density. The validity of the approach is demonstrated using the known experimental data for a series of osmium based redox polymers, involving oxygen as the substrate with laccase being the enzyme for biocathode fuel cell reactions. The significance of the results has been demonstrated by suggesting two new graphical procedures for estimating the Michaelis-Menten constants and catalytic rate constants from the experimental current densities. (C) 2014 Elsevier B.V. All rights reserved.