Analysis of the conformational dependence of mass-metric tensor determinants in serial polymers with constraints.
Analysis of the conformational dependence of mass-metric tensor determinants in serial polymers with constraints.
复制标题
具有约束条件的系列聚合物中质量计量张量行列式的构象依赖性分析。
作者：
A. Patriciu;G. Chirikjian;R. Pappu
众所周知，质量度量张量行列式det（G（s））影响键长和键角受限的聚合物的平衡统计和构象转变速率。现在的标准做法是将U（c）（q（s））比例、变量（-k（B）T/2）ln[det（G（s））]形式的Fixman型补偿势作为扭转空间分子动力学算法的一部分。这种优雅的策略有助于消除由于施加完整约束而产生的不必要的偏差。然而，det（G（s））以及ln[det（G（s））]随链构象和链长的变化的精确性质和程度从未被量化。这种类型的分析是至关重要的理解的性质的构象偏差，引入一个Fixman潜力的目的是消除。此外，det（G（s））的构象依赖性的详细分析将有助于解决关于在扭转空间蒙特卡罗模拟中的移动集设计中纳入与det（G（s））相关的术语的建议的歧义。在这项工作中，我们提出了一个系列的聚合物与固定的键长和键角作为链构象和链长的函数的变化det（G（s））的系统研究的结果。该分析需要设计用于快速计算det（G（s））的算法，该算法同时允许对det（G（s））的构象依赖性进行物理/几何解释。因此，我们提供了一个详细的讨论，我们适应的O（n）算法从机器人文学，这导致简单的递归关系直接评估det（G（s））。我们对det（G（s））的构象依赖性的分析产生了以下见解。(1)det（G（s））对于空间构象最大化，对于平面构象最小化。(2)以前的工作表明，这是合乎逻辑的预期，det（G（s））的构象依赖性变得更加明显，随着链长的增加。为了证明这一点，我们对这种依赖性的性质进行了系统的量化，并表明空间构象和平面构象之间的det（G（s））差异，即，det（G（s））的最大值和最小值之间的差随链长系统地增长。最后，我们提供了一个简短的讨论，我们的分析在蒙特卡洛模拟移动集的设计的影响。
It is well known that mass-metric tensor determinants det(G(s)) influence the equilibrium statistics and the rates of conformational transitions for polymers with constrained bond lengths and bond angles. It is now standard practice to include a Fixman-style compensating potential of the form U(c)(q(s)) proportional, variant(-k(B)T/2)ln[det(G(s))] as part of algorithms for torsional space molecular dynamics. This elegant strategy helps eliminate unwarranted biases that arise due to the imposition of holonomic constraints. However, the precise nature and extent of variation of det(G(s)) and hence ln[det(G(s))] with chain conformation and chain length has never been quantified. This type of analysis is crucial for understanding the nature of the conformational bias that the introduction of a Fixman potential aims to eliminate. Additionally, a detailed analysis of the conformational dependence of det(G(s)) will help resolve ambiguities regarding suggestions for incorporating terms related to det(G(s)) in the design of move sets in torsional space Monte Carlo simulations. In this work, we present results from a systematic study of the variation of det(G(s)) for a serial polymer with fixed bond lengths and bond angles as a function of chain conformation and chain length. This analysis requires an algorithm designed for rapid computation of det(G(s)) which simultaneously allows for a physical/geometric interpretation of the conformational dependence of det(G(s)). Consequently, we provide a detailed discussion of our adaptation of an O(n) algorithm from the robotics literature, which leads to simple recursion relations for direct evaluation of det(G(s)). Our analysis of the conformational dependence of det(G(s)) yields the following insights. (1) det(G(s)) is maximized for spatial conformers and minimized for planar conformations. (2) Previous work suggests that it is logical to expect that the conformational dependence of det(G(s)) becomes more pronounced with increase in chain length. Confirming this expectation, we provide systematic quantification of the nature of this dependency and show that the difference in det(G(s)) between spatial and planar conformers, i.e., between the maxima and minima of det(G(s)) grows systematically with chain length. Finally, we provide a brief discussion of implications of our analysis for the design of move sets in Monte Carlo simulations.
影响因子：
3.4
作者：
Mihailescu,Mihail;Gilson,MichaelK
通讯作者：
Gilson,MichaelK
影响因子：
3.6
作者：
Carlson, BX;Engblom, AC;Olsen, RW
通讯作者：
Olsen, RW