Matrix models with Penner interaction inspired by interacting ribonucleic acid
Matrix models with Penner interaction inspired by interacting ribonucleic acid
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受相互作用核糖核酸启发的具有 Penner 相互作用的矩阵模型
DOI：
10.1007/s12043-014-0920-5
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
N. Deo
中科院分区：
文献类型：
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作者：
P. Bhadola;N. Deo
本文介绍了在穿孔黎曼曲面模空间研究中已知的Penner相互作用，并在随机矩阵模型的背景下研究了该相互作用。给出了生成函数的解析推导和相应的配分函数的数值推导。得到了结构组合因子对N（与矩阵的大小和相互作用强度有关）的附加依赖性。在低氮条件下，这一因素对结构组合学有很强的影响。扫描数据库中的真实的核糖核酸（RNA）结构，并通过计算提取这些RNA结构的配对信息。然后计算每个结构的亏格，并绘制为长度的函数。将亏格分布函数与非线性（NL）模型的预测结果进行了比较。由NL模型计算的比热和结构随温度的分布表明NL相互作用偏向于平面结构。比热的二阶导数使相变从小N时的双峰函数变为大N时的单峰函数。详细的分析揭示了双峰的存在，仅对于属0结构，较高的属1与N的行为正常。在涉及RNA与渗透剂和单价阳离子在展开实验中的相互作用的研究中发现了类似的行为。
The Penner interaction known in studies of moduli space of punctured Riemann surfaces is introduced and studied in the context of random matrix model of homo RNA. An analytic derivation of the generating function is given and the corresponding partition function is derived numerically. An additional dependence of the structure combinatorics factor on N (related to the size of the matrix and the interaction strength) is obtained. This factor has a strong effect on the structure combinatorics in the low N regime. Databases are scanned for real ribonucleic acid (RNA) structures and pairing information for these RNA structures is computationally extracted. Then the genus is calculated for every structure and plotted as a function of length. The genus distribution function is compared with the prediction from the nonlinear (NL) model. The specific heat and distribution of structure with temperature calculated from the NL model shows that the NL interaction is biased towards planar structures. The second derivative of specific heat changes phase from a double peaked function for small N to a single peak for large N. Detailed analysis reveals the presence of the double peak only for genus 0 structures, the higher genii behave normally with N. Comparable behaviour is found in studies involving interactions of RNA with osmolytes and monovalent cations in unfolding experiments.