A theory of equilibrium states of a biomembrane with particles in its channels that takes into account "bilateral" channel-particle interactions has been developed within a thermodynamic scheme. The aim of the proposed theory is to explain the existence of the multiple steady states which have long been observed experimentally. The existence of such states is postulated in the majority of the current theories which kinetically describe transitions between such states. The governing equations have been derived from basic physics under the requirement that the conformation of the channel changes to minimize the system's free energy which includes the elastic conformation energy together with the electrostatic interaction between the (hydrated) ion and the channel. It has been shown that in certain regions of a control parameter such minimization can give rise to bifurcation of the equilibrium state, i.e. to the coexistence of at least two equilibrium states. The value of the control parameter can be changed by an external action (gating), which can be either mechanical, or electrical, or even thermal.