Related papers: Scaling properties of RNA as a randomly branching …
Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…
The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…
Myriad viruses use positive-strand RNA molecules as their genomes. Far from being only a repository of genetic material, viral RNA performs numerous other functions mediated by its physical structure and chemical properties. In this…
Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…
Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have…
The statistics of randomly branching double-folded ring polymers are relevant to the secondary structure of RNA, the large-scale branching of plectonemic DNA (and thus bacterial chromosomes), the conformations of single-ring polymers…
RNA secondary structures of increasing complexity are probed combining single molecule stretching experiments and stochastic unfolding/refolding simulations. We find that force-induced unfolding pathways cannot usually be interpretated by…
We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second order phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a…
The branching of an RNA molecule is an important structural characteristic yet difficult to predict correctly, especially for longer sequences. Using plane trees as a combinatorial model for RNA folding, we consider the thermodynamic cost,…
Our work is concerned with the generation and targeted design of RNA, a type of genetic macromolecule that can adopt complex structures which influence their cellular activities and functions. The design of large scale and complex…
We study the statistical mechanics of RNA secondary structures designed to have an attraction between two different types of structures as a model system for heteropolymer aggregation. The competition between the branching entropy of the…
We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched…
A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the…
A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of…
Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of…
A hierarchical model for the growth of planar arch structures for RNA secondary structures is presented, and shown to be equivalent to a tree-growth model. Both models can be solved analytically, giving access to scaling functions for large…
The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on…
While stretching of most polymer chains leads to rather featureless force-extension diagrams, some, notably DNA, exhibit non-trivial behavior with a distinct plateau region. Here we propose a unified theory that connects force-extension…
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc-…
Randomly branching polymers with {\em annealed} connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present…