Theoretical Biological Physics, Department of Theoretical Physics, Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden.
Chem Phys Lipids. 2013 Apr;169:2-8. doi: 10.1016/j.chemphyslip.2012.12.005. Epub 2013 Jan 17.
Membrane inclusion interactions are studied within the scope of continuum theory. We show that the free energy functional for the membrane thickness can be rewritten as a constant times a dimensionless integral. For cylindrical inclusions, the resulting differential equation gives a thickness profile that depends on the radius of the cylinder and one single lipid property, a correlation length that is determined by the ratio of the thickness compressibility and bending moduli. The solutions decay in a non-monotonic fashion with one single observable minimum. A solution for planar geometry may either be explicitly constructed or obtained by letting the radius of the cylinder go to infinity. In dimensionless units the initial derivative of the thickness profile is universal and equal to -1/√2. In physical units, the derivative depends on the size of the hydrophobic mismatch as well as the membrane correlation length and will usually be fairly small but clearly non-zero. The line tension between the protein inclusion and a fluid phase membrane will depend on the hydrophobic mismatch and be of the order of 10 pN (larger for the gel phase). This results in free energy costs for the inclusion that will be up to tens of kJ/mol (in the fluid phase).
在连续体理论的范围内研究了膜包含物相互作用。我们表明，膜厚度的自由能泛函可以重写为常数乘以无量纲积分。对于圆柱包含物，所得微分方程给出了一个厚度分布，该厚度分布取决于圆柱的半径和一个单一的脂质特性，即相关长度，它由厚度压缩模量和弯曲模量的比值决定。解以非单调的方式衰减，只有一个可观察到的最小值。对于平面几何形状的解，可以通过将圆柱的半径取为无穷大来显式构造或获得。在无量纲单位中，厚度分布的初始导数是普遍的，等于-1/√2。在物理单位中，导数取决于疏水性失配以及膜相关长度的大小，通常相当小但显然不为零。蛋白质包含物与流体相膜之间的线张力将取决于疏水性失配，并将处于 10 pN 左右（凝胶相更大）。这导致包含物的自由能成本高达数十 kJ/mol（在流体相）。
