Many lipid membranes of eukaryotic cells are asymmetric, which means the two leaflets differ in at least one physical property, such as lipid composition or lateral stress. Maintaining this asymmetry is helped by the fact that ordinary phospholipids rarely transition between leaflets, but cholesterol is an exception: its flip-flop times are in the microsecond range, so that its distribution between leaflets is determined by a chemical equilibrium. In particular, preferential partitioning can draw cholesterol into a more saturated leaflet, and phospholipid number asymmetry can force it out of a compressed leaflet. Combining highly coarse-grained membrane simulations with theoretical modeling, we investigate how these two driving forces play against each other until cholesterol’s chemical potential is equilibrated. The theory includes two coupled elastic sheets and a Flory-Huggins mixing free energy with a $\chi$ parameter. We obtain a relationship between $\chi$ and the interaction strength between cholesterol and lipids in either of the two leaflets, and we find that it depends, albeit weakly, on lipid number asymmetry. The differential stress measurements under various asymmetry conditions agree with our theoretical predictions. Using the two kinds of asymmetries in combination, we find that it is possible to counteract the phospholipid number bias, and the resultant stress in the membrane, via the control of cholesterol mixing in the leaflets.

真核细胞的许多脂质膜是不对称的，这意味着两个小叶在至少一种物理特性上不同，例如脂质成分或侧向应力。普通磷脂很少在小叶之间转变，但胆固醇是一个例外：它的翻转时间在微秒范围内，因此它在小叶之间的分布是由化学平衡决定的，这一事实有助于维持这种不对称性。特别是，优先分配可以将胆固醇吸引到更饱和的小叶中，而磷脂数量不对称可以将其从压缩的小叶中挤出。将高度粗粒度的膜模拟与理论模型相结合，我们研究了这两种驱动力如何相互作用，直到胆固醇的化学势达到平衡。该理论包括两个耦合的弹性片和一个将自由能与$\chi$范围。我们获得之间的关系$\chi$以及两个小叶中胆固醇和脂质之间的相互作用强度，我们发现它依赖于脂质数量不对称性，尽管很弱。各种不对称条件下的差异应力测量结果与我们的理论预测一致。结合使用两种不对称性，我们发现可以通过控制小叶中胆固醇的混合来抵消磷脂数量偏差以及膜中由此产生的应力。