A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: I

Free energy-based model of CTCF-mediated chromatin looping in the human genome

In recent years, high-throughput techniques have revealed considerable structural organization of the human genome with diverse regions of the chromatin interacting with each other in the form of loops. Some of these loops are quite complex and may encompass regions comprised of many interacting chain segments around a central locus. Popular techniques for extracting this information are chromatin interaction analysis by paired-end tag sequencing (ChIA-PET) and high-throughput chromosome conformation capture (Hi-C). Here, we introduce a physics-based method to predict the three-dimensional structure of chromatin from population-averaged ChIA-PET data. The approach uses experimentally-validated data from human B-lymphoblastoid cells to generate 2D meta-structures of chromatin using a dynamic programming algorithm that explores the chromatin free energy landscape. By generating both optimal and suboptimal meta-structures we can calculate both the free energy and additionally the relative thermodynamic probability. A 3D structure prediction program with applied restraints then can be used to generate the tertiary structures. The main advantage of this approach for population-averaged experimental data is that it provides a way to distinguish between the principal and the spurious contacts. This study also finds that euchromatin appear to have rather precisely regulated 2D meta-structures compared to heterochromatin. The program source-code is available at https://github.com/plewczynski/looper.

A method for finding optimal rna secondary structures using a new entropy model (vsfold)

We are developing a program to calculate optimal RNA secondary structures. The model uses di-nucleotide pairing energies as with most traditional approaches. However, for long-range entropy interactions, the approach uses an entropy-loss model based on the accumulated sum of the entropy of bonding between each base-pair weighted inversely by the correlation of the RNA sequence (the Kuhn length). Stiff RNA forms very different structures from flexible RNA. The results demonstrate that the long-range folding is largely governed by this entropy and the Kuhn length.

Analysis of the conformational energy landscape of human snRNA with a metric based on tree representation of RNA structures

It is an outstanding problem to clarify how the RNA sequence is related to its structure and biological functions. We developed a simplified definition of a metric for tree representation of RNA secondary structures and analyzed the conformational energy landscapes of human spliceosomal snRNAs. We discuss the structural properties of the biological sequence by calculating the conformational energy landscapes based on the structural distance between each of the pairs in the set of suboptimal structures. The new index value is introduced for estimating the shapes of distribution patterns in conformational energy landscapes. We apply our method to the five human snRNAs and show that U1 snRNA has a multi-valley profile of the landscape, whereas the landscapes of the other four snRNAs have one steep valley. This result reflects different biological functions of these snRNAs in the pre-mRNA splicing process. The results of analyzing tRNAs and rRNAs show that the conformational energy landscapes of these sequences have multi-valley profiles.

A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: II

In Part I, cross-linking entropy (CLE) was proposed as a mechanism that limits the size of functional domains of RNA. To test this hypothesis, the theory is developed into an RNA secondary structure prediction filter which is applied to nearest-neighbor secondary structure (NNSS) algorithms that utilize a free energy (FE) minimization strategy. (The NNSS strategies are also referred to as the dynamic programming algorithm in the literature.) The cross-linking entropy for RNA is derived from a generalized Gaussian polymer chain model where the entropic contributions caused by the formation of base pairs (stacking) in RNA are analysed globally. Local entropic contributions are associated with the freezing out of degrees of freedom in the links. Both global and local entropic effects are strongly influenced by the persistence length. The cross-linking entropy provides a physical origin for the size of functional domains in long nucleic acid sequences and may go further to explain as to why the majority of the domain regions in typical sequences tend to be less than 600 nucleotides in length. In addition, improvements were observed in the "best guess" predictive capacity over NNSS prediction strategies. The thermodynamic distribution is more representative of the expected structures and is strongly governed by such physical parameters as the persistence length and the excluded volume. The CLE appears to generalize the tabulated penalties used in NNSS algorithms. The principal parameter influencing this entropy is the persistence length. The model is shown to accomodate a variable persistence length and is capable of describing the folding dynamics of RNA. A two-state kinetic model based on the CLE principle is used to help elucidate the folding kinetics of functional domains in the group I introns.