A noninteractive two-state model for ion channels in cell membranes is proposed using the pair approximation. The cell membrane is visualized as a two-dimensional sheet with a regular array of lattice sites and is described by a simple two-state system in which each channel is opened by a movement of single gating particle which carries a charge. Assuming that the particle is in one of the two positions associated with closed and open states, the free energy is calculated using the pair approximation and minimized with respect to the pair variables to obtain the steady-state activation curves. Using known parameters for sodium channels in giant squid axon as an example, the fractions of open channels are obtained by solving a self-consistent nonlinear algebraic equation for the pair variables and the effect of the lattice coordination number on the channel activation vs. voltage curve is investigated. Our numerical results are compared with the mean-field results as well as the experimental measurements by cut-open axon technique. (C) 2004 Elsevier B.V. All rights reserved.