Statistical geometry of lattice chain polymers with voids of defined shapes: sampling with strong constraints

Computational construction of 3D chromatin ensembles and prediction of functional interactions of alpha-globin locus from 5C data

Conformation capture technologies measure frequencies of interactions between chromatin regions. However, understanding gene-regulation require knowledge of detailed spatial structures of heterogeneous chromatin in cells. Here we describe the nC-SAC (n-Constrained-Self Avoiding Chromatin) method that transforms experimental interaction frequencies into 3D ensembles of chromatin chains. nC-SAC first distinguishes specific from non-specific interaction frequencies, then generates 3D chromatin ensembles using identified specific interactions as spatial constraints. Application to α-globin locus shows that these constraints (∼20%) drive the formation of ∼99% all experimentally captured interactions, in which ∼30% additional to the imposed constraints is found to be specific. Many novel specific spatial contacts not captured by experiments are also predicted. A subset, of which independent ChIA-PET data are available, is validated to be RNAPII-, CTCF-, and RAD21-mediated. Their positioning in the architectural context of imposed specific interactions from nC-SAC is highly important. Our results also suggest the presence of a many-body structural unit involving α-globin gene, its enhancers, and POL3RK gene for regulating the expression of α-globin in silent cells.

Structure Prediction of RNA Loops with a Probabilistic Approach

The knowledge of the tertiary structure of RNA loops is important for understanding their functions. In this work we develop an efficient approach named RNApps, specifically designed for predicting the tertiary structure of RNA loops, including hairpin loops, internal loops, and multi-way junction loops. It includes a probabilistic coarse-grained RNA model, an all-atom statistical energy function, a sequential Monte Carlo growth algorithm, and a simulated annealing procedure. The approach is tested with a dataset including nine RNA loops, a 23S ribosomal RNA, and a large dataset containing 876 RNAs. The performance is evaluated and compared with a homology modeling based predictor and an ab initio predictor. It is found that RNApps has comparable performance with the former one and outdoes the latter in terms of structure predictions. The approach holds great promise for accurate and efficient RNA tertiary structure prediction.

Spatial confinement is a major determinant of the folding landscape of human chromosomes

The global architecture of the cell nucleus and the spatial organization of chromatin play important roles in gene expression and nuclear function. Single-cell imaging and chromosome conformation capture-based techniques provide a wealth of information on the spatial organization of chromosomes. However, a mechanistic model that can account for all observed scaling behaviors governing long-range chromatin interactions is missing. Here we describe a model called constrained self-avoiding chromatin (C-SAC) for studying spatial structures of chromosomes, as the available space is a key determinant of chromosome folding. We studied large ensembles of model chromatin chains with appropriate fiber diameter, persistence length and excluded volume under spatial confinement. We show that the equilibrium ensemble of randomly folded chromosomes in the confined nuclear volume gives rise to the experimentally observed higher-order architecture of human chromosomes, including average scaling properties of mean-square spatial distance, end-to-end distance, contact probability and their chromosome-to-chromosome variabilities. Our results indicate that the overall structure of a human chromosome is dictated by the spatial confinement of the nuclear space, which may undergo significant tissue- and developmental stage-specific size changes.

RNA fragment modeling with a nucleobase discrete-state model

In this work we develop an approach for predicting the tertiary structures of RNA fragments by combining an RNA nucleobase discrete state (RNAnbds) model, a sequential Monte Carlo method, and a statistical potential. The RNAnbds model is designed for optimizing the configuration of nucleobases with respect to their preceding ones along the sequence and their spatial neighbors, in contrast to previous works that focus on RNA backbones. The tests of our approach with the fragments taken from a small RNA pseudoknot and a 23S ribosome RNA show that for short fragments (<10 nucleotides), the root mean square deviations (RMSDs) between the predicted and the experimental ones are generally smaller than 3 Å; for slightly longer fragments (10-15 nucleotides), most RMSDs are smaller than 4 Å. The comparison of our method with another physics-based predictor with a testing set containing nine loops shows that ours is superior in both accuracy and efficiency. Our approach is useful in facilitating RNA three-dimensional structure prediction as well as loop modeling. It also holds the promise of providing insight into the structural ensembles of RNA loops.

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

Accurate free energy estimation is essential for RNA structure prediction. The widely used Turner's energy model works well for nested structures. For pseudoknotted RNAs, however, there is no effective rule for estimation of loop entropy and free energy. In this work we present a new free energy estimation method, termed the pseudoknot predictor in three-dimensional space (pk3D), which goes beyond Turner's model. Our approach treats nested and pseudoknotted structures alike in one unifying physical framework, regardless of how complex the RNA structures are. We first test the ability of pk3D in selecting native structures from a large number of decoys for a set of 43 pseudoknotted RNA molecules, with lengths ranging from 23 to 113. We find that pk3D performs slightly better than the Dirks and Pierce extension of Turner's rule. We then test pk3D for blind secondary structure prediction, and find that pk3D gives the best sensitivity and comparable positive predictive value (related to specificity) in predicting pseudoknotted RNA secondary structures, when compared with other methods. A unique strength of pk3D is that it also generates spatial arrangement of structural elements of the RNA molecule. Comparison of three-dimensional structures predicted by pk3D with the native structure measured by nuclear magnetic resonance or X-ray experiments shows that the predicted spatial arrangement of stems and loops is often similar to that found in the native structure. These close-to-native structures can be used as starting points for further refinement to derive accurate three-dimensional structures of RNA molecules, including those with pseudoknots.