Curvature-related processes are of major importance during protein–membrane interactions. The illusive simplicity of membrane reshaping masks a complex molecular process crucial for a wide range of biological functions like fusion, endo- and exocytosis, cell division, cytokinesis, and autophagy. To date, no functional expression of a reaction coordinate capable of biasing molecular dynamics simulations to produce membrane curvature has been reported. This represents a major drawback given that the adequate identification of proper collective variables to enhance sampling is fundamental for restrained dynamics techniques. In this work, we present a closed-form equation of a collective variable that induces bending in lipid bilayers in a controlled manner, allowing for straightforward calculation of free energy landscapes of important curvature-related events, using standard methods such as umbrella sampling and metadynamics. As a direct application of the collective variable, we calculate the bending free energies of a ternary lipid bilayer in the presence and the absence of a Bin/Amphiphysin/Rvs domain with an N-terminal amphipathic helix (N-BAR), a well-known peripheral membrane protein that induces curvature.

中文翻译：

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弯曲的脂质双层：定量生物学中有效自由能景观的封闭形式的集体变量。

与曲率有关的过程在蛋白质-膜相互作用中至关重要。膜重塑的虚幻简单性掩盖了复杂的分子过程，该过程对于融合，内吞和胞吐作用，细胞分裂，胞质分裂和自噬等广泛的生物学功能至关重要。迄今为止，还没有报道能够偏向分子动力学模拟以产生膜曲率的反应坐标的功能表达。鉴于充分识别适当的集体变量以增强采样对于约束动力学技术至关重要，因此这是一个主要缺陷。在这项工作中，我们提出了一个集体变量的封闭形式方程，该方程以受控方式在脂质双层中引起弯曲，使用标准方法（例如伞形采样和元动力学），可以直接计算重要曲率相关事件的自由能态势。作为集合变量的直接应用，我们计算了在存在和不存在具有N末端两亲性螺旋（N-BAR）的Bin / Amphiphysin / Rvs域的情况下三元脂质双层的弯曲自由能。已知会引起弯曲的外周膜蛋白。