Non-linear interaction in random matrix models of RNA

• Main Authors: Garg, Itty, Bhadola, Pradeep, Deo, N
• Format: Journal Article
• Language: English
• Published: 29-03-2011
• Subjects: Physics - Statistical Mechanics; Quantitative Biology - Biomolecules
• DOI: 10.48550/arxiv.1103.5601

A non-linear Penner type interaction is introduced and studied in the random
matrix model of homo-RNA. The asymptotics in length of the partition function
is discussed for small and large $N$ (size of matrix). The interaction doubles
the coupling ($v$) between the bases and the dependence of the combinatoric
factor on ($v,N$) is found. For small $N$, the effect of interaction changes
the power law exponents for the secondary and tertiary structures. The specific
heat shows different analytical behavior in the two regions of $N$, with a
peculiar double peak in its second derivative for N=1 at low temperature.
Tapping the model indicates the presence of multiple solutions.