Shityakov Sergey, Skorb Ekaterina V, Nosonovsky Michael
Infochemistry Scientific Center (ISC), ITMO University, 9 Lomonosova St., St Petersburg 191002, Russia.
R Soc Open Sci. 2022 Jul 13;9(7):220160. doi: 10.1098/rsos.220160. eCollection 2022 Jul.
Scaling relationships for polymeric molecules establish power law dependencies between the number of molecular segments and linear dimensions, such as the radius of gyration. They also establish spatial topological properties of the chains, such as their dimensionality. In the spatial domain, power exponents = 1 (linear stretched molecule), = 0.5 (the ideal chain) and = 0.333 (compact globule) are significant. During folding, the molecule undergoes the transition from the one-dimensional linear to the three-dimensional globular state within a very short time. However, intermediate states with fractional dimensions can be stabilized by modifying the solubility (e.g. by changing the solution temperature). Topological properties, such as dimension, correlate with the interaction energy, and thus by tuning the solubility one can control molecular interaction. We investigate these correlations using the example of a well-studied short model of Trp-cage protein. The radius of gyration is used to estimate the fractal dimension of the chain at different stages of folding. It is expected that the same principle is applicable to much larger molecules and that topological (dimensional) characteristics can provide insights into molecular folding and interactions.
聚合物分子的标度关系建立了分子链段数量与线性尺寸（如回转半径）之间的幂律依赖关系。它们还确定了链的空间拓扑性质，如维度。在空间域中，幂指数 ν = 1（线性拉伸分子）、ν = 0.5（理想链）和 ν = 0.333（紧密球体）具有重要意义。在折叠过程中，分子在极短时间内从一维线性状态转变为三维球状状态。然而，通过改变溶解度（如改变溶液温度），可以稳定具有分数维的中间状态。诸如维度等拓扑性质与相互作用能相关，因此通过调节溶解度可以控制分子间相互作用。我们以一个经过充分研究的短 Trp 笼蛋白模型为例来研究这些相关性。回转半径用于估计折叠不同阶段链的分形维数。预计相同原理适用于大得多的分子，并且拓扑（维度）特征可为分子折叠和相互作用提供见解。
