The shape of chromatin: insights from computational recognition of geometric patterns in Hi-C data.

The three-dimensional organization of chromatin plays a crucial role in gene regulation and cellular processes like deoxyribonucleic acid (DNA) transcription, replication and repair. Hi-C and related techniques provide detailed views of spatial proximities within the nucleus. However, data analysis is challenging partially due to a lack of well-defined, underpinning mathematical frameworks. Recently, recognizing and analyzing geometric patterns in Hi-C data has emerged as a powerful approach. This review provides a summary of algorithms for automatic recognition and analysis of geometric patterns in Hi-C data and their correspondence with chromatin structure. We classify existing algorithms on the basis of the data representation and pattern recognition paradigm they make use of. Finally, we outline some of the challenges ahead and promising future directions.

Chanalyzer: A Computational Geometry Approach for the Analysis of Protein Channel Shape and Dynamics.

Morphological analysis of protein channels is a key step for a thorough understanding of their biological function and mechanism. In this respect, molecular dynamics (MD) is a very powerful tool, enabling the description of relevant biological events at the atomic level, which might elude experimental observations, and pointing to the molecular determinants thereof. In this work, we present a computational geometry-based approach for the characterization of the shape and dynamics of biological ion channels or pores to be used in combination with MD trajectories. This technique relies on the earliest works of Edelsbrunner and on the NanoShaper software, which makes use of the alpha shape theory to build the solvent-excluded surface of a molecular system in an aqueous solution. In this framework, a channel can be simply defined as a cavity with two entrances on the opposite sides of a molecule. Morphological characterization, which includes identification of the main axis, the corresponding local radius, and the detailed description of the global shape of the cavity, is integrated with a physico-chemical description of the surface facing the pore lumen. Remarkably, the possible existence or temporary appearance of fenestrations from the channel interior towards the outer lipid matrix is also accounted for. As a test case, we applied the present approach to the analysis of an engineered protein channel, the mechanosensitive channel of large conductance.