Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore.
School of Biological Sciences, Nanyang Technological University, Singapore, 637371, Singapore.
Sci Rep. 2020 Jun 16;10(1):9685. doi: 10.1038/s41598-020-66710-6.
It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate dramatically different properties in a protein folding process. Even with the enormous theoretical and experimental research work on these two osmolytes, various aspects of their underlying mechanisms still remain largely elusive. In this paper, we propose to use the weighted persistent homology to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a local topological perspective. We consider two weighted models, i.e., localized persistent homology (LPH) and interactive persistent homology (IPH). Boltzmann persistent entropy (BPE) is proposed to quantitatively characterize the topological features from LPH and IPH, together with persistent Betti number (PBN). More specifically, from the localized persistent homology models, we have found that TMAO and urea have very different local topology. TMAO is found to exhibit a local network structure. With the concentration increase, the circle elements in these networks show a clear increase in their total numbers and a decrease in their relative sizes. In contrast, urea shows two types of local topological patterns, i.e., local clusters around 6 Å and a few global circle elements at around 12 Å. From the interactive persistent homology models, it has been found that our persistent radial distribution function (PRDF) from the global-scale IPH has same physical properties as the traditional radial distribution function. Moreover, PRDFs from the local-scale IPH can also be generated and used to characterize the local interaction information. Other than the clear difference of the first peak value of PRDFs at filtration size 4 Å, TMAO and urea also shows very different behaviors at the second peak region from filtration size 5 Å to 10 Å. These differences are also reflected in the PBNs and BPEs of the local-scale IPH. These localized topological information has never been revealed before. Since graphs can be transferred into simplicial complexes by the clique complex, our weighted persistent homology models can be used in the analysis of various networks and graphs from any molecular structures and aggregation systems.
人们早就观察到三甲胺 N-氧化物（TMAO）和尿素在蛋白质折叠过程中表现出截然不同的性质。尽管对这两种渗透物进行了大量的理论和实验研究，但它们的各种潜在机制在很大程度上仍然难以捉摸。在本文中，我们建议使用加权持久同调从局部拓扑角度系统地研究渗透物分子聚集及其氢键网络。我们考虑了两种加权模型，即局部持久同调（LPH）和交互持久同调（IPH）。玻尔兹曼持久熵（BPE）被用来定量地描述 LPH 和 IPH 的拓扑特征，以及持久贝蒂数（PBN）。更具体地说，从局部持久同调模型中，我们发现 TMAO 和尿素具有非常不同的局部拓扑。TMAO 表现出局部网络结构。随着浓度的增加，这些网络中的圆形元素总数明显增加，相对大小减小。相比之下，尿素显示出两种局部拓扑模式，即 6 Å 左右的局部簇和 12 Å 左右的少数全局圆形元素。从交互持久同调模型中，我们发现全局规模 IPH 的持久径向分布函数（PRDF）具有与传统径向分布函数相同的物理性质。此外，还可以生成局部规模 IPH 的 PRDF，并用于描述局部相互作用信息。除了过滤尺寸为 4 Å 的 PRDF 的第一个峰值的明显差异外，TMAO 和尿素在过滤尺寸为 5 Å 到 10 Å 的第二个峰值区域也表现出非常不同的行为。这些差异也反映在局部规模 IPH 的 PBN 和 BPE 中。这些局部拓扑信息以前从未被揭示过。由于图可以通过团复合转化为单纯复形，因此我们的加权持久同调模型可以用于分析来自任何分子结构和聚集系统的各种网络和图。
