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 inter-action 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.
Volume 96, 2022
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