EM algorithm for reconstructing 3D structures of human chromosomes from chromosomal contact data

Abstract

Recent research suggested that chromosomes have preferred spatial conformations to facilitate necessary long-range interactions and regulations within a nucleus. So that, getting the 3D shape of chromosomes of a genome is very important for understanding how the genome folds and how the genome interact, which can know more about the secrete of life. The introduction of the chromosome conformation capture (3C) based techniques has risen the development of construct the 3D structure of chromosome model. Several works have been done to build the 3D model, among which can be divided into two groups one is consensus methods in early work, the other is ensemble method. In this paper I proposed an ensemble method for reconstructing the 3D structure of chromosome structure. First step is to process Hi-C data, and then do normalization. After that I applied the Bayesian inference model to get an objective function. Finally I used EM based algorithm along with using gradient descent method which is applied in expectation step. I applied the objective function and the optimization method to all 23 Hi-C chromosomal data at a resolution of 1MB.