Förster resonance energy transfer (FRET) is a powerful tool for investigating heterogeneity in lipid bilayers. In model membrane studies, samples are frequently unilamellar vesicles with diameters of 20−200 nm. It is well-known that FRET efficiency is insensitive to vesicle curvature in uniformly mixed lipid bilayers, and consequently theoretical models for FRET typically assume a planar geometry. Here, we use a spherical harmonic expansion of the acceptor surface density to derive an analytical solution for FRET between donor and acceptor molecules distributed on the surface of a sphere. We find excellent agreement between FRET predicted from the model and FRET calculated from corresponding Monte Carlo simulations, thus validating the model. An extension of the model to the case of a non-uniform acceptor surface density (i.e., a phase-separated vesicle) reveals that FRET efficiency depends on vesicle size when acceptors partition between the coexisting phases, and approaches the efficiency of a uniformly mixed bilayer as the vesicle size decreases. We show that this is an indirect effect of constrained domain size, rather than an intrinsic effect of vesicle curvature. Surprisingly, the theoretical predictions were not borne out in experiments: we did not observe a statistically significant change in FRET efficiency in phase-separated vesicles as a function of vesicle size. We discuss factors that likely mask the vesicle size effect in extruded samples.

Förster 共振能量转移 (FRET) 是研究脂质双层异质性的有力工具。在模型膜研究中，样品通常是直径为 20-200 nm 的单层囊泡。众所周知，FRET 效率对均匀混合的脂质双层中的囊泡曲率不敏感，因此 FRET 的理论模型通常假设为平面几何。在这里，我们使用受体表面密度的球谐展开来推导出分布在球体表面上的供体和受体分子之间的 FRET 解析解。我们发现从模型预测的 FRET 与从相应的 Monte Carlo 模拟计算的 FRET 之间非常吻合，从而验证了模型。模型扩展到非均匀受体表面密度的情况（即，相分离的囊泡）表明，当受体在共存相之间分配时，FRET 效率取决于囊泡的大小，并且随着囊泡大小的减小接近均匀混合双层的效率。我们表明这是受约束域大小的间接影响，而不是囊泡曲率的内在影响。令人惊讶的是，理论预测并未在实验中得到证实：我们没有观察到相分离囊泡中 FRET 效率作为囊泡大小的函数的统计学显着变化。我们讨论了可能掩盖挤压样品中囊泡尺寸效应的因素。我们表明这是受约束域大小的间接影响，而不是囊泡曲率的内在影响。令人惊讶的是，理论预测并未在实验中得到证实：我们没有观察到相分离囊泡中 FRET 效率作为囊泡大小的函数的统计学显着变化。我们讨论了可能掩盖挤压样品中囊泡尺寸效应的因素。我们表明这是受约束域大小的间接影响，而不是囊泡曲率的内在影响。令人惊讶的是，理论预测并未在实验中得到证实：我们没有观察到相分离囊泡中 FRET 效率作为囊泡大小的函数的统计学显着变化。我们讨论了可能掩盖挤压样品中囊泡尺寸效应的因素。