Adenylate Kinase Potential of Mean Force

Adenylate kinase (AdK) is a enzyme that undergoes a large hinge-like motion. Because of an abundance of structural and functional data, it has become a standard system to test computational methods for sampling conformational transitions.1 In 2009, we studied the conformational transition between open and closed E. coli AdK without substrate, i.e. “apo AdK”, with a variety of computational methods.2 As part of the study we also produced a free energy landscape (a potential of mean force or PMF) as a function of two collective variables, the angles formed by the LID and NMP domains with the CORE domain.3 We 2 and others4,5 have used this PMF to compare methods that sample transition paths to the underlying free energy landscape. Terms of Use The data are made available under a Attribution-ShareAlike 4.0 International licence (include the following when using the data): Adenylate Kinase Potential of Mean Force by O Beckstein, EJ Denning, JR Perilla, TB Woolf is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Based on a work at http://becksteinlab.physics.asu.edu/file_download/11/free_bw2_tol1e-05.dat. When you make use of the data (contained in the file free_bw2_tol1e-05.dat) in published work, cite the paper2 O. Beckstein, E. J. Denning, J. R. Perilla, and T. B. Woolf. Zipping and unzipping of adenylate kinase: Atomistic insights into the ensemble of open ? closed transitions. J. Mol. Biol., 394(1):160–176, 2009. Data The file free_bw2_tol1e-05.dat contains the PMF data shown in Fig. 4a of the JMB paper2. The image shows the data plotted with cubic spline smoothing. File format free_bw2_tol1e-05.dat is the output from WHAM. The important data columns are NMP-core angle (degrees) LID-core angle (degrees) free energy in kcal/mol (Other columns are output from wham and can be ignored.) Methods Conformations of E. coli AdK were umbrella-sampled in the space of the NMP-core and LID-core angles.3 The protein was modelled in implicit solvent with the ACE2 electrostatics model. The resulting umbrella data were unbiased using Alan Grossfield’s wham code with bin size 2º tolerance of the self consistency procedure 1e-5 kT limits 34º < NMP < 80º and 94º < LID < 156º The first 2000 frames (200ps) of each window were discarded as equilibration and the remaining 3000 frames were used for the PMF. For further details please see the paper.2 References S. L. Seyler and O. Beckstein, O. Sampling large conformational transitions: adenylate kinase as a testing ground. Mol. Simul., 40(10–11): 855–877, 2014. O. Beckstein, E. J. Denning, J. R. Perilla, and T. B. Woolf. Zipping and unzipping of adenylate kinase: Atomistic insights into the ensemble of open / closed transitions. J. Mol. Biol., 394(1):160–176, 2009. See the 2009 paper2 for the definitions and the MDAnalysis tutorial’s Exercise 4 for Python code to calculate the angles. M. Gur, J. D. Madura, and I. Bahar. Global transitions of proteins explored by a multiscale hybrid methodology: Application to adenylate kinase Biophysical Journal, 105(7):1643 – 1652, 2013. A. Uyar, N. Kantarci-Carsibasi, T. Haliloglu, and P. Doruker. Features of large hinge-bending conformational transitions. Prediction of closed structure from open state. Biophysical Journal, 106(12):2656 – 2666, 2014

腺苷酸激酶（Adenylate kinase, AdK）是一类具有显著铰链样构象运动的酶。由于其结构与功能数据较为丰富，该体系已成为测试构象转变采样计算方法的标准模型系统¹。2009年，本团队采用多种计算方法，针对无底物状态下大肠杆菌腺苷酸激酶（E. coli AdK）的开放态与闭合态构象转变展开研究，即脱辅基腺苷酸激酶（apo AdK）²。作为该研究的一部分，我们还基于两个集体变量构建了自由能景观（平均力势，Potential of Mean Force, PMF），这两个变量分别为LID结构域与CORE结构域、NMP结构域与CORE结构域所形成的夹角³。本团队²及其他研究者⁴,⁵已利用该PMF对构象转变路径采样方法与底层自由能景观的匹配程度进行对比分析。

使用条款
本数据集采用署名-相同方式共享4.0国际许可协议（Creative Commons Attribution-ShareAlike 4.0 International License, CC BY-SA 4.0）进行授权，使用数据时需注明如下信息：O Beckstein、EJ Denning、JR Perilla与TB Woolf所提供的腺苷酸激酶平均力势数据集，采用知识共享署名-相同方式共享4.0国际许可协议进行授权。本数据集基于http://becksteinlab.physics.asu.edu/file_download/11/free_bw2_tol1e-05.dat 发布的工作成果。若在已发表的研究中使用本数据集（包含于文件free_bw2_tol1e-05.dat中），请引用以下文献²：O. Beckstein, E. J. Denning, J. R. Perilla与T. B. Woolf. 腺苷酸激酶的开合过程：原子级解析开放闭合态的转变机制. 分子生物学杂志（J. Mol. Biol.）, 394(1):160–176, 2009.

数据集
文件free_bw2_tol1e-05.dat包含JMB论文²中图4a所示的PMF数据，该图采用三次样条平滑法对数据进行绘制。

文件格式
文件free_bw2_tol1e-05.dat为WHAM软件的输出文件，其中关键数据列依次为：NMP-CORE夹角（单位：度）、LID-CORE夹角（单位：度）以及自由能（单位：千卡/摩尔，kcal/mol），其余列均为WHAM软件的额外输出内容，可忽略。

方法
大肠杆菌腺苷酸激酶的构象通过在NMP-CORE与LID-CORE夹角空间内的伞形采样获得³。蛋白质采用ACE2静电模型的隐式溶剂模型进行建模。利用Alan Grossfield开发的WHAM代码对所得伞形采样数据进行无偏化处理，自洽程序的步长为2°，收敛阈值为1e-5 kT，约束范围为34° < NMP-CORE夹角 < 80°以及94° < LID-CORE夹角 < 156°。每个采样窗口的前2000帧（对应200皮秒，200ps）作为平衡阶段数据被舍弃，剩余的3000帧用于计算PMF。更多细节请参见原文²。

参考文献
1. S. L. Seyler与O. Beckstein. 大规模构象转变采样：以腺苷酸激酶为测试模型. 分子模拟（Mol. Simul.）, 40(10–11): 855–877, 2014.
2. O. Beckstein, E. J. Denning, J. R. Perilla与T. B. Woolf. 腺苷酸激酶的开合过程：原子级解析开放闭合态的转变机制. 分子生物学杂志（J. Mol. Biol.）, 394(1):160–176, 2009. 有关夹角的定义请参见该2009年论文，Python计算代码可参考MDAnalysis教程的练习4。
3. M. Gur, J. D. Madura与I. Bahar. 多尺度混合方法探索蛋白质全局构象转变：以腺苷酸激酶为例. 生物物理学报（Biophysical Journal）, 105(7):1643–1652, 2013.
4. A. Uyar, N. Kantarci-Carsibasi, T. Haliloglu与P. Doruker. 大规模铰链弯曲构象转变的特征：从开放态预测闭合态结构. 生物物理学报（Biophysical Journal）, 106(12):2656–2666, 2014.