Batch tests have been most commonly employed to investigate the biosorption isotherms of heavy metals. There is evidence showing that the biosorption isotherm is influenced by initial metal and biosorbent concentrations, namely C-o and X-o. However, a quantitative description of the effect of initial conditions on biosorption isotherms still remained elusive. According to the thermodynamics of the biosorption process, an initial condition-dependent isotherm equation for biosorption of heavy metals was derived and verified by experimental data. This model demonstrated that the biosorption isotherms of heavy metals by aerobic granules were a function of the C-o/X-o ratio. The biosorption constant involved in the proposed model had a clearly defined physical meaning; this constant was found to be equal to the inverse of the thermodynamic equilibrium constant of the biosorption process. (C) 2004 Society of Chemical Industry.