Convex hulls in hamming space enable efficient search for similarity and clustering of genomic sequences

David S Campo,Yury Khudyakov

doi:10.1186/s12859-020-03811-z

Abstract

BackgroundIn molecular epidemiology, comparison of intra-host viral variants among infected persons is frequently used for tracing transmissions in human population and detecting viral infection outbreaks. Application of Ultra-Deep Sequencing (UDS) immensely increases the sensitivity of transmission detection but brings considerable computational challenges when comparing all pairs of sequences. We developed a new population comparison method based on convex hulls in hamming space. We applied this method to a large set of UDS samples obtained from unrelated cases infected with hepatitis C virus (HCV) and compared its performance with three previously published methods.ResultsThe convex hull in hamming space is a data structure that provides information on: (1) average hamming distance within the set, (2) average hamming distance between two sets; (3) closeness centrality of each sequence; and (4) lower and upper bound of all the pairwise distances among the members of two sets. This filtering strategy rapidly and correctly removes 96.2% of all pairwise HCV sample comparisons, outperforming all previous methods. The convex hull distance (CHD) algorithm showed variable performance depending on sequence heterogeneity of the studied populations in real and simulated datasets, suggesting the possibility of using clustering methods to improve the performance. To address this issue, we developed a new clustering algorithm, k-hulls, that reduces heterogeneity of the convex hull. This efficient algorithm is an extension of the k-means algorithm and can be used with any type of categorical data. It is 6.8-times more accurate than k-mode, a previously developed clustering algorithm for categorical data.ConclusionsCHD is a fast and efficient filtering strategy for massively reducing the computational burden of pairwise comparison among large samples of sequences, and thus, aiding the calculation of transmission links among infected individuals using threshold-based methods. In addition, the convex hull efficiently obtains important summary metrics for intra-host viral populations.

Highlights

In molecular epidemiology, comparison of intra-host viral variants among infected persons is frequently used for tracing transmissions in human population and detecting viral infection outbreaks
L a=1 i =j faifai n2 − n /2 where n is the number of sequences, l is the length, number of positions, fai is the frequency of nucleotide i at position a and faj is the frequency of nucleotide j at position a. 2 CCh of each sequence The average distance from each sequence h to all others within the population, its closeness centrality CCh, is an important measure of centrality that is computationally challenging, as we need to make n2 − n /2 pairwise comparisons and calculate the average of each sequence
CCh = fa a=1 where l is the length and fa is the population frequency of the nucleotide present at sequence h, position a. 3 Average distance between two populations The average hamming distance (ADpq) among all sequences of two populations, p and q, is a very common statistic in population genetics that is the basis for several measures of genetic relatedness

Summary

Introduction

Comparison of intra-host viral variants among infected persons is frequently used for tracing transmissions in human population and detecting viral infection outbreaks. We developed a new population comparison method based on convex hulls in hamming space We applied this method to a large set of UDS samples obtained from unrelated cases infected with hepatitis C virus (HCV) and compared its performance with three previously published methods. Phylogenetic analysis of viral sequences is frequently used in investigation of outbreaks and transmission chains [2,3,4,5,6], usually using a single sequence per infected individual. Many viruses such as hepatitis C virus (HCV) exist as a population of numerous genetic variants in each infected individual. Statistical analysis of intra-host HCV variants obtained from epidemiologically characterized outbreaks allowed for the development of a simple and accurate threshold-based approach for detecting HCV transmissions [7]

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