We present a simple dynamical model for the transmembrane potential in non-excitable mammalian cells. This model allows us to mimic the effect of nanoparticles on the transmembrane potential, by decreasing the permeability of potassium ion channels. We show that our model agrees with the trends observed in our experiments. However, it also exhibits opposing trends under certain conditions, which were not seen in the experiments. This indicates that the membrane potential can be bistable. We analyze the cellular conditions which may cause this apparent bistability. The effects of adding nanoparticles on sodium and chloride ion channels are also studied using the proposed model. We hypothesize that nanoparticles may also block the sodium and chloride ion channels but the extent of blockage of these ion channels may differ from that of potassium ion channels.