Genus distribution and thermodynamics of a random matrix model of RNA with Penner interaction

摘要

The nonlinear Penner external interaction is introduced and studied in the random matrix model of homonRNA. A numerical technique is developed to study the partition function, and a general formula is obtained fornall lengths. The genus distribution function for the system is obtained, plotted, and compared with the genusndistribution for the real RNA structures found from the protein databank. The genus distribution shows that thennonlinear interaction favors the formation of low genus structures and matches the result for real RNA structures.nThe distribution of structure with temperature suggests that nonlinear interaction is biased toward the planarnstructures. The variation of chemical potential with temperature and interaction strength indicates the presencenof additional molecules in the system other than the magnesium ions and possibly represents a phase transition.nThe specific heat has a bump and its derivatives shows a double-peak behavior at a particular temperature. Onnanalyzing the specific heat and derivatives for each genus separately, the planar structure (genus zero) is shownnto contribute the most to the bump and double peak. This observation in the nonlinear model is similar to thatnobserved in the unfolding experiments on RNA.