the repeat distance becomes contact at 6.45 nm, the same The behavior of dipalmitoyl phosphatidylcholine bilayers in value as that in I. When the concentration is reduced, the CaCl 2 aqueous solution found by Inoko et al. (Biochim. Biophys. transitions IV r III and III r II occur at the same concentra-Acta 413, 24 (1975)) is analyzed, with four states I-IV appearing tion as that mentioned above, but the transition II r I takes with increasing concentrations of CaCl 2 from 0 m M to 1 M. The place at a concentration close to 0 mM. This means that present theory takes into account the field-dependent association there is a hysteresis in the transition I-II. The experiments constant K of Ca 2/ ions to the membrane surface, which was were conducted at the temperature T Γ
5ΠC, below the transiderived from a theoretical investigation (Y. Izumitani, J. Colloid tion temperature (T c Γ
41ΠC) of the gel-to-liquid crystalline Interface Sci. 166, 143 (1994)) of the electrostatic cation-dipole phase for the dipalmitoyl lecithin. A quantitative explanation interaction. The present theory is based on the DLVO theory of colloid stability, which was also used in the analysis of this phe-for these phenomena was made by Ohshima and Mitsui (2) nomena by Ohshima and Mitsui (J. Colloid Interface Sci. 63, 525 on the basis of a DLVO-type theory with simple postulations. (1978)), but in the present theory, the transition of states I r II However, the observed values for the repeat distance of is conditioned by the membrane flexibility and the retardation the lamellar structure in state III were significantly smaller, effects are taken into account in the van der Waals interaction in especially at CaCl 2 concentration between 10 and 30 mM, the lamellar structure. The discrepancy between the observed valthan those predicted by their analysis using sets of parameues for the repeat distance of the lamellar phase and the theoretical ters of K and H A , the intrinsic association constant of Ca 2/ predictions of Ohshima's theory can be fairly well explained by ions to the bilayer surface and the Hamaker constant for the present theory with state III at 10-100 mM CaCl 2 concentranonretarded van der Waals attraction, respectively. tion. The undulation effect is neglected in our treatment but the This paper gives an explanation for the discrepancy of membrane flexibility can qualitatively explain the hysteresis in the the repeat distance, in which the effect of cation -dipole I-II transition.