The correlation length and lateral compressibility of phospholipid bilayers in the presence of thermodynamic density fluctuations

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Abstract
Pink’s ten state statistical model for the gel–fluid (main) phase transitions of phospholipid bilayers is used in conjunction with linear response theory to obtain expressions for the coherence length, ξ and the lateral compressibility χL for wet lipid bilayers in the presence of thermodynamic density fluctuations near the temperature Tf of the main phase transition. The advantage of this method is that the parameters of Pink’s model are known for several lipid systems from previous fitting to experimental data. ξ and χL can therefore be calculated numerically and the relative importance of the static and fluctuation contributions to χL can be examined. One conclusion of the article is that the coherence length and Tf is short and therefore that the contribution of thermodynamic density fluctuations to χL is about 13%. This implies that the free energy barrier EB experienced by an ion as it penetrates the bilayer has a dominant contribution from the static lateral compressibility, provided that the interaction between the ion and the polar heads of the lipid molecules is a δ‐force. However, it is further shown that the static and the density fluctuation effects contribute almost equally to EB at Tf when the range ξo of interaction between the ion and the polar heads is greater than half a molecule diameter. This remains true in the limit ξo→∞ as the coherence length ξ is quite short at any temperature.