Related papers: Viral RNA as a branched polymer
We describe quantitatively a RNA molecule under the influence of an external force exerted at its two ends as in a typical single-molecule experiment. Our calculation incorporates the interactions between nucleotides by using the…
Researchers have repeatedly found that the ends of an RNA sequence are significantly closer than expected for a random linear chain. However, we prove that the ends of a branched structure are almost certainly close. Our results are…
Recent single-molecule pulling experiments have shown how it is possible to manipulate RNA molecules using optical tweezers force microscopy. We investigate a minimal model for the experimental setup which includes a RNA molecule connected…
At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…
In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the…
We have prepared a homologous series of filamentous viruses with varying contour length using molecular cloning techniques. These viruses are monodisperse enough to form a stable smectic phase. Two systems are studied. The first system…
Using data from contact maps of the DNA-polymer of $E. Coli$ (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain.…
The combinatorics of RNA plays a central role in biology. Mathematical biologists have several commonly-used models for RNA: words in a fixed alphabet (representing the primary sequence of nucleotides) and plane trees (representing the…
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…
The encapsulation of polyanions, whether single-stranded RNAs or synthetic polymers, is primarily driven by attractive electrostatic interactions between the positively charged, structurally disordered RNA-binding domains of virus coat…
Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
Loop formation in long molecules occurs many places in nature, from solutions of carbon nanotubes to polymers inside a cell. In this article, we review theoretical studies of the static and dynamic properties of polymer loops. For example,…
Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single…
We extend recent methods for parametric sequence alignment to the parameter space for scoring RNA folds. This involves the construction of an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common…
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…
Polymer filaments form the foundation of biology from cell scaffolding to DNA. Their study and fabrication play an important role in a wide range of processes from tissue engineering to molecular machines. We present a simple method to…
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication…