JILA, National Institute of Standard and Technology and University of Colorado, Boulder, Colorado 80309, USA.
J Chem Phys. 2018 Mar 28;148(12):123313. doi: 10.1063/1.5009108.
Precisely quantifying the energetics that drive the folding of membrane proteins into a lipid bilayer remains challenging. More than 15 years ago, atomic force microscopy (AFM) emerged as a powerful tool to mechanically extract individual membrane proteins from a lipid bilayer. Concurrently, fluctuation theorems, such as the Jarzynski equality, were applied to deduce equilibrium free energies (ΔG) from non-equilibrium single-molecule force spectroscopy records. The combination of these two advances in single-molecule studies deduced the free-energy of the model membrane protein bacteriorhodopsin in its native lipid bilayer. To elucidate this free-energy landscape at a higher resolution, we applied two recent developments. First, as an input to the reconstruction, we used force-extension curves acquired with a 100-fold higher time resolution and 10-fold higher force precision than traditional AFM studies of membrane proteins. Next, by using an inverse Weierstrass transform and the Jarzynski equality, we removed the free energy associated with the force probe and determined the molecular free-energy landscape of the molecule under study, bacteriorhodopsin. The resulting landscape yielded an average unfolding free energy per amino acid (aa) of 1.0 ± 0.1 kcal/mol, in agreement with past single-molecule studies. Moreover, on a smaller spatial scale, this high-resolution landscape also agreed with an equilibrium measurement of a particular three-aa transition in bacteriorhodopsin that yielded 2.7 kcal/mol/aa, an unexpectedly high value. Hence, while average unfolding ΔG per aa is a useful metric, the derived high-resolution landscape details significant local variation from the mean. More generally, we demonstrated that, as anticipated, the inverse Weierstrass transform is an efficient means to reconstruct free-energy landscapes from AFM data.
精确量化驱动膜蛋白折叠成脂质双层的能量仍然具有挑战性。15 年前，原子力显微镜（AFM）作为一种强大的工具出现，可以从脂质双层中机械提取单个膜蛋白。与此同时，波动定理（如 Jarzynski 等式）被应用于从非平衡单分子力谱记录中推断平衡自由能（ΔG）。这两项单分子研究的进展相结合，推断了模型膜蛋白细菌视紫红质在其天然脂质双层中的自由能。为了以更高的分辨率阐明这个自由能景观，我们应用了最近的两项进展。首先，作为重建的输入，我们使用了比传统的膜蛋白 AFM 研究高 100 倍的时间分辨率和 10 倍的力精度获得的力-延伸曲线。接下来，通过使用逆 Weierstrass 变换和 Jarzynski 等式，我们去除了与力探针相关的自由能，并确定了研究分子细菌视紫红质的分子自由能景观。所得的景观产生了每个氨基酸（aa）的平均展开自由能为 1.0 ± 0.1 kcal/mol，与过去的单分子研究一致。此外，在较小的空间尺度上，这个高分辨率的景观也与细菌视紫红质中特定的三个氨基酸跃迁的平衡测量结果一致，得到 2.7 kcal/mol/aa，这是一个出人意料的高值。因此，虽然每个氨基酸的平均展开 ΔG 是一个有用的指标，但得出的高分辨率景观细节显示出与平均值相比存在显著的局部变化。更一般地说，我们证明了，正如预期的那样，逆 Weierstrass 变换是从 AFM 数据重建自由能景观的有效方法。
