RNA Secondary Structures: Complex Statics and Glassy Dynamics

TL;DR

This paper investigates the complex static and dynamic properties of RNA secondary structures, using Monte Carlo simulations and exact polynomial-time computations, to understand their glassy behavior and benchmark algorithms.

Contribution

It introduces a detailed analysis of Monte Carlo methods applied to RNA secondary structures and relates their dynamics to static phase space properties, providing new insights and benchmarks.

Findings

Monte Carlo methods' tunneling times correlate with static phase space features

Exact polynomial-time calculations of density of states are feasible for RNA structures

RNA secondary structures serve as ideal models for studying glassy dynamics and benchmarking algorithms.

Abstract

Models for RNA secondary structures (the topology of folded RNA) without pseudo knots are disordered systems with a complex state-space below a critical temperature. Hence, a complex dynamical (glassy) behavior can be expected, when performing Monte Carlo simulation. Interestingly, in contrast to most other complex systems, the ground states and the density of states can be computed in polynomial time exactly using transfer matrix methods. Hence, RNA secondary structure is an ideal model to study the relation between static/thermodynamic properties and dynamics of algorithms. Also they constitute an ideal benchmark system for new Monte Carlo methods. Here we considered three different recent Monte Carlo approaches: entropic sampling using flat histograms, optimized-weights ensembles, and ParQ, which estimates the density of states from transition matrices. These methods were examined by comparing the obtained density of states with the exact results. We relate the complexity seen in the dynamics of the Monte Carlo algorithms to static properties of the phase space by studying the correlations between tunneling times, sampling errors, amount of meta-stable states and degree of ultrametricity at finite temperature.