Thermodynamic analysis of interacting nucleic acid strands
Thermodynamic analysis of interacting nucleic acid strands
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DOI：
10.1137/060651100
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发表时间：
2007-03-01
期刊：
影响因子：
10.2
通讯作者：
Pierce, Niles A.
中科院分区：
文献类型：
--
作者：
Dirks, Robert M.;Bois, Justin S.;Pierce, Niles A.
受自然和工程DNA和RNA系统分析的激励，我们提出了计算多个相互作用核酸链的非假结复合体配分函数的第一个算法。这个动态程序是基于二级结构模型对多链情况的严格扩展，解决单链结构没有出现的表示和可区分性问题。然后，我们推导出含有核酸复合物的稀释溶液的固定体积的配分函数的形式。这个表达式可以明确地评估少量的链，允许计算平衡种群分布的每个物种的络合物。另外，对于大型系统（例如试管），我们证明了通过求解凸规划问题可以获得与热力学平衡相对应的唯一复合浓度。配分函数和浓度信息可用于计算平衡碱基对观测值。这些问题的基础物理和数学公式导致了一种有趣的方法混合，包括来自图论、群论、动态规划、组合学、凸优化和拉格朗日对偶的思想。
Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality.