Principal Curve Approaches for Inferring 3D Chromatin Architecture

• Activity Number: 496 - Dimension Reduction
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Elena Tuzhilina* and Trevor Hastie and Mark Segal
• Companies: Stanford University, Department of Statistics and Stanford University, Department of Statistics and UCSF, Department of Epidemiology and Biostatistics
• Keywords: Chromatin conformation reconstruction; Principal Curves; Poisson model; Weighted low rank approximation ; Multi-dimensional scaling; Genome reconstruction

Abstract

The 3D spatial organization of chromatin is crucial for numerous cellular processes. The recent advent of Hi-C assay, which yield so-called contact matrices, has enabled us to infer 3D structure at increasing resolution. There are many MDS-based algorithms that operate on contact matrices producing reconstructed 3D configurations in the form of polygonal chain. However, none of the methods exploit the fact that the target solution is a smooth curve in 3D: this contiguity attribute is either ignored or indirectly addressed via smoothness penalties. In our work we introduce Principal Curve Metric Scaling (PCMS), a novel approach modeling chromatin directly by a smooth curve. Subsequently, we develop a weighted generalization of the PCMS technique and demonstrate its application to the Poisson Model for contact counts. The resulting algorithm, PoisMS, combines advantages of Multidimensional Scaling, Poisson Model and smoothness penalties whereas being computationally efficient. The performance of the algorithm is illustrated on real Hi-C data computed for chromosomes 20-21 and evaluated by means of orthogonal multiplex FISH imaging.