RNA Secondary Structure Boltzmann Distribution

Years and Authors of Summarized Original Work

• 2005; Miklós, Meyer, Nagy

Problem Definition

This problem is concerned with computing features of the Boltzmann distribution over RNA secondary structures in the context of the standard Gibbs free energy model used for RNA Secondary Structure Prediction by Minimum Free Energy (cf. corresponding entry). Thermodynamics state that for a system with configuration space Ω and free energy given by ${ E \colon \Omega \mapsto \mathbf{R} }$, the probability of the system being in state ${ \omega \in \Omega }$ is proportional to ${ \mskip2mu\mathrm{e}^{-E(\omega) / RT} }$ where R is the universal gas constant and T the absolute temperature of the system. The normalizing factor

$$ Z = \sum_{\omega \in \Omega} \mskip2mu\mathrm{e}^{-E(\omega) / RT} $$

(1)

is called the full partition function of the system.

Over the past several decades, a model approximating the free energy of a structured RNA molecule by independent contributions of its...