Title: Effective stiffness and formation of secondary structures in a protein-like model Show Chinese title

Title: 有效刚度和蛋白质模型中二级结构的形成

Abstract: We use Wang-Landau and replica exchange techniques to study the effect of an increasing stiffness on the formation of secondary structures in protein-like systems. Two possible models are considered. In both models, a polymer chain is formed by tethered beads where non-consecutive backbone beads attract each other via a square-well potential representing the tendency of the chain to fold. In addition, smaller hard spheres are attached to each non-terminal backbone bead along the direction normal to the chain to mimic the steric hindrance of side chains in real proteins. The two models, however, differ in the way bending rigidity is enforced. In the first model, partial overlap between consecutive beads is allowed. This reduces the possible bending angle between consecutive bonds thus producing an effective entropic stiffness that competes with a short-range attraction, and leads to a formation of secondary structures characteristic of proteins. We discuss the low-temperature phase diagram as a function of increasing interpenetration, and find a transition from a planar, beta-like structure, to helical shape. In the second model, an energetic stiffness is explicitly introduced by imposing an infinitely large energy penalty for bending above a critical angle between consecutive bonds, and no penalty below it. The low-temperature phase of this model does not show any sign of protein-like secondary structures. At intermediate temperatures, however, where the chain is still in the coil conformation but stiffness is significant, we find the two models to predict a quite similar dependence of the persistence length as a function of the stiffness. This behaviour is rationalized in terms of a simple geometrical mapping between the two models. Finally, we discuss the effect of shrinking side chains to zero, and find the above mapping to still hold true. Show Chinese abstract

Abstract: 我们使用Wang-Landau和副本交换技术来研究增加刚度对蛋白质样系统中二级结构形成的影响。考虑了两种可能的模型。在两种模型中，聚合物链由连接的珠子组成，非连续的主链珠子通过平方势阱相互吸引，代表链折叠的趋势。此外，沿链方向垂直的方向上，在每个非末端的主链珠子上附着较小的硬球，以模拟真实蛋白质中侧链的空间位阻。然而，这两种模型在弯曲刚度的实现方式上有所不同。在第一个模型中，允许连续珠子的部分重叠。这减少了连续键之间的可能弯曲角度，从而产生一种有效的熵性刚度，与短程吸引力竞争，并导致形成蛋白质特征的二级结构。我们讨论了随着相互穿透增加的低温相图，并发现从平面状的β样结构向螺旋形状的转变。在第二个模型中，通过施加一个无限大的能量惩罚来引入能量刚度，当连续键之间的角度超过临界角时，而在其下方则没有惩罚。该模型的低温相不显示任何类似蛋白质的二级结构的迹象。然而，在中间温度下，当链仍处于无规线团构象但刚度显著时，我们发现两种模型预测的持久长度随刚度变化的依赖关系非常相似。这种行为可以通过两个模型之间的简单几何映射来解释。最后，我们讨论了将侧链缩小到零的影响，并发现上述映射仍然成立。