Penner Matrix Models Inspired by Interacting RNA

The nonlinear Penner type external interaction is introduced and studied in the random matrix model of homo Ribo Nucleic Acid (RNA). The Penner interaction originally appeared in the studies of moduli space of punctured surfaces and has been applied here (for the first time) in addressing the problem of interacting RNA folding. An exact analytic formula for the generating function is derived using the orthogonal polynomial method. The partition function derived from the generating function for a given length enumerates all possible interacting RNA structure of possible topologies as well as the pairing. A numerical technique is developed to study the partition function and a general formula is obtained for all lengths. The asymptotic large length distribution functions are found and show a change in the critical exponent of the secondary structure contribution from $L^3/2$ for large $N$ (size of matrix, $N > L$, where $L$ is the length of the RNA chain ) to $L^1/2$ for small $N$. This observation in the nonlinear model is similar to that observed in the unfolding experiments on RNA with osmolytes and monovalent cations.

Preliminary results on biological networks for an enzyme will be briey discussed.

[1] H. Orland, A. Zee, Nucl. Phys. B [FS]620, 456 (2002).
[2] G. Vernizzi, Henri Orland, A. Zee, Phys. Rev. Lett. 94, 168103 (2005).
[3] P. Bhadola, I. Garg and N. Deo, Nucl. Phys. B [FS]870, 384 (2013).
[4] P. Bhadola and N. Deo, Phys. Rev. E 88, 032706 (2013).
[5] P. Bhadola and N. Deo, In preparation.