Common to all microbial electrochemical cells (MXCs) are the anode-respiring bacteria (ARB), which transfer electrons to an anode and release protons that must transport out of the biofilm. Here, we develop a novel modeling platform, Proton Condition in BIOFILM (PCBIOFILM), with a structure geared towards mechanistically explaining: (1) how the ARB half reaction produces enough acid to inhibit the ARB by low pH; (2) how the diffusion of alkalinity carriers (phosphates and carbonates) control the pH gradients in the biofilm anode; (3) how increasing alkalinity attenuates pH gradients and increases current; and (4) why carbonates enable higher current density than phosphates. Analysis of literature data using PCBIOFILM supports the hypothesis that alkalinity limits the maximum current density for MXCs. An alkalinity criterion for eliminating low-pH limitation - 12 mg CaCO(3)/mg BOD - implies that a practical MXC can achieve a maximum current density with an effluent quality comparable to anaerobic digestion. (C) 2010 Elsevier Ltd. All rights reserved.