Reconstruction Of Chromosome 3D Structure Based On Maximum Likelihood Algorithm Of Cauchy Distribution

The spatial structure of the genome is closely related to transcription activities to ensure that cells perform normal functions.Therefore,the analysis and research of genome spatial conformation has become an important subject in bioinformatics and computational biology.In recent years,with the development of high-throughput chromosome conformation capture(Hi-C)technology and the reduction of high-throughput sequencing cost,the data volume of whole-genome interaction has increased rapidly,and the resolution of interaction map keeps improving.Great progress has been made in the research of 3D structure modeling of chromosomes and genomes.Several methods have been proposed to construct the chromosome structure from chromosome conformation capture data.In this paper,through the analysis of the related literature of chromosome three-dimensional structure reconstruction,the principle of the classical algorithm 3DMAX is summarized.On this basis,this paper completes the following parts:(1)The current representative gradient iterative optimization algorithms are systematically studied,and the advantages and disadvantages of various gradient optimization algorithms are comprehensively compared.On this basis,a new stochastic gradient ascent algorithm XNadam is proposed.(2)3DMax1,3DMax Nadam and 3DMax XNadam algorithms were obtained by combining the maximum likelihood algorithm with Adagrad,Nadam and XNadam algorithms respectively.3DMax1,3DMax Nadam and 3DMax XNadam algorithms were used to reconstruct the three-dimensional structure of yeast chromosomes.(3)Based on(1)and(2),a new maximum likelihood algorithm based on Cauchy distribution is proposed to reconstruct the three-dimensional structure of chromosome: Firstly,the shortest path algorithm is used to complement the distance matrix converted from contact frequency matrix to satisfy the triangle relation;Assuming that each distance data point obeys Cauchy distribution,the log-likelihood objective function is obtained;Then,the random gradient rising algorithm xnadam log-likelihood objective function is used to optimize.You get a more accurate three-dimensional structure.(4)To compare the performance of the model,in this paper,Distance Root Mean Squared Deviation and Distance Spearman Correlation Coefficient,Distance Pearson Correlation Coefficient,Kullback-Leibler Divergence to quantify the similarity of the structure.To measure the performance of the prediction method.