The interchange of the protons with the cell wall-bound calcium and magnesium ions at the interface of solution/bacterial cell surface in the biosorption system at various concentrations of protons has been studied in the present work. A mathematical model for establishing the correlation between concentration of protons and active sites was developed and optimized. The sporadic limited residence time reactor was used to titrate the calcium and magnesium ions at the individual data point. The accuracy of the proposed mathematical model was estimated using error functions such as nonlinear regression, adjusted nonlinear regression coefficient, the chi-square test, P-test and F-test. The values of the chi-square test (0.042-0.017), P-test (<0.001-0.04), sum of square errors (0.061-0.016), root mean square error (0.01-0.04) and F-test (2.22-19.92) reported in the present research indicated the suitability of the model over a wide range of proton concentrations. The zeta potential of the bacterium surface at various concentrations of protons was observed to validate the denaturation of active sites.