Rote of Ca²⁺ in the formation of an excitable membrane on the surface of a protoplasmic droplet of nitella

A theory is presented for a phase transition between resting and depolarized states of a protoplasmic droplet of Nitella induced by variation of Ca²⁺ and Na⁺ concentrations. In the theory, a membrane formed on a surface of the droplet by lipids and proteins is regarded as a kind of adsorbed bilayer. Effects of bridging among adsorbed molecules through Ca²⁺ are taken into account, besides an electrostatic interaction between polar groups of adsorbed molecules and monovalent and divalent cations. It is shown that an excitable membrane is stabilized only in a certain range of Ca²⁺ and Na⁺ concentrations, where a phase separation through the Ca²⁺-bridging occurs between Ca²⁺-rich membranous and Ca²⁺-depleted domains. This kind of phase separation is mainly subject to a competitive effect between monovalent cations and Ca²⁺ at lower Ca²⁺ concentrations but an ionic strength at higher Ca²⁺ concentrations. The present results can explain fairly well quantitative features of existing observed data.