Chung Hoi Sung, Tokmakoff Andrei
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Proteins. 2008 Jul;72(1):488-97. doi: 10.1002/prot.22042.
To provide evidence for the interpretation of temperature-dependent unfolding kinetics and the downhill unfolding scenario presented in the accompanying experimental article (Part I), the free energy surface of ubiquitin unfolding is calculated using statistical mechanical models of the Muñoz-Eaton (ME) form. The models allow only two states for each amino acid residue, folded or unfolded, and permutations of these states generate an ensemble of microstates. One-dimensional free energy curves are calculated using the number of folded residues as a reaction coordinate. The proposed sequential unfolding of ubiquitin's beta-sheet is tested by mapping the free energy onto two reaction coordinates inspired by the experiment as follows: the number of folded residues in ubiquitin's stable beta-strands I and II and those of the less stable strands III-V. Although the original ME model successfully captures folding features of zipper-like one-dimensional folders, it misses important tertiary interactions between residues that are far from each other in primary sequence. To take tertiary contacts into account, partially folded microstates based on a spherical growth model are included in the calculation and compared with the original model. By calculating the folding probability of each residue for a given point on the free energy surface, the unfolding pathway of ubiquitin is visualized. At low temperature, thermal unfolding occurs along a sequential unfolding pathway as follows: disruption of the beta-strands III-V followed by unfolding of the strands I and II. At high temperature, multiple unfolding routes are formed. The heterogeneity of the transition state explains the global nonexponential unfolding observed in the T-jump experiment at high temperature. The calculation also reports a high stability for the alpha-helix of ubiquitin.
为了解释随附实验文章（第一部分）中提出的温度依赖性解折叠动力学和下坡解折叠情况提供证据，使用Muñoz-Eaton（ME）形式的统计力学模型计算泛素解折叠的自由能表面。这些模型每个氨基酸残基仅允许两种状态，折叠或未折叠，并且这些状态的排列产生微状态的集合。使用折叠残基的数量作为反应坐标计算一维自由能曲线。通过将自由能映射到受实验启发的两个反应坐标上来测试泛素β-折叠的提议顺序解折叠，如下所示：泛素稳定β-链I和II中以及较不稳定链III-V中的折叠残基数量。虽然原始的ME模型成功捕获了拉链状一维折叠体的折叠特征，但它忽略了在一级序列中彼此相距很远的残基之间的重要三级相互作用。为了考虑三级接触，基于球形生长模型的部分折叠微状态被纳入计算并与原始模型进行比较。通过计算自由能表面上给定点处每个残基的折叠概率，可视化泛素的解折叠途径。在低温下，热解折叠沿着以下顺序解折叠途径发生：β-链III-V的破坏，随后是链I和II的解折叠。在高温下，形成多个解折叠途径。过渡态的异质性解释了在高温下T跳跃实验中观察到的全局非指数解折叠。计算还报告了泛素α-螺旋的高稳定性。
