Statistical mechanics of secondary structures formed by random RNA sequences

Abstract

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.

24 pages, 16 figures

References in corpus (1)

• Reply to the Comment on `Glassy Transition in a Disordered Model for the RNA Secondary Structure'

Cited by in corpus (41)

• Single-molecule experiments in biological physics: methods and applications
• Statistical Physics of RNA-folding
• Synonymous mutations reduce genome compactness in icosahedral ssRNA viruses
• The collapse transition of randomly branched polymers -renormalized field theory
• The Freezing of Random RNA
• An intermediate phase in DNA melting
• A numerical approach to copolymers at selective interfaces
• Statistical mechanics of RNA folding: a lattice approach
• RNA denaturation: excluded volume, pseudoknots and transition scenarios
• RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses
• Quantification of the differences between quenched and annealed averaging for RNA secondary structures
• RNA secondary structure design
• Systematic Field Theory of the RNA Glass Transition
• Statistical mechanics of RNA folding: importance of alphabet size
• Random Euclidean matching problems in one dimension
• Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers
• A growth model for RNA secondary structures
• The effect of loops on the mean square displacement of Rouse-model chromatin
• Model for Folding and Aggregation in RNA Secondary Structures
• Dependence of RNA secondary structure on the energy model
• The Dyck bound in the concave 1-dimensional random assignment model
• Random copolymer adsorption: Morita approximation compared to exact numerical simulations
• Planar diagrams from optimization
• Scaling properties of RNA as a randomly branching polymer
• New alphabet-dependent morphological transition in a random RNA alignment
• Anomalous scaling in nanopore translocation of structured heteropolymers
• Freezing transition of the random bond RNA model: statistical properties of the pairing weights
• Analytical description of finite size effects for RNA secondary structures
• RNAlike polymer model: exact calculation on the Bethe lattice
• Interplay between single-stranded binding proteins on RNA secondary structure
• Random RNA under tension
• On the behavior of random RNA secondary structures near the glass transition
• Random walk models and probabilistic techniques for inhomogeneous polymer chains
• Cold denaturation of RNA secondary structures with loop entropy and quenched disorder
• Field Theory of the RNA Freezing Transition
• An exactly solvable model for a beta-hairpin with random interactions
• New phase transition in random planar diagrams and RNA-type matching
• Topological transition in disordered planar matching: combinatorial arcs expansion
• Summation test for gap penalties and strong law of the local alignment score
• RNA Secondary Structures: Complex Statics and Glassy Dynamics
• Pseudo-RNA with parallel aligned single-strands and periodic base sequence as a new universality class