227 lines
12 KiB
TeX
227 lines
12 KiB
TeX
\documentclass{bioinfo}
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\copyrightyear{2021}
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\pubyear{2021}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{url}
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\usepackage{amsmath}
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\usepackage[ruled,vlined]{algorithm2e}
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\newcommand\mycommfont[1]{\footnotesize\rmfamily{\it #1}}
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\SetCommentSty{mycommfont}
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\SetKwComment{Comment}{$\triangleright$\ }{}
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\usepackage{natbib}
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\bibliographystyle{apalike}
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\DeclareMathOperator*{\argmax}{argmax}
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\begin{document}
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\firstpage{1}
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\title[Improvements to minimap2]{New strategies to improve minimap2 alignment accuracy}
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\author[Li]{Heng Li$^{1,2}$}
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\address{$^1$Dana-Farber Cancer Institute, 450 Brookline Ave, Boston, MA 02215, USA,
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$^2$Harvard Medical School, 10 Shattuck St, Boston, MA 02215, USA}
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\maketitle
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\begin{abstract}
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\section{Summary:} We present several recent improvements to minimap2, a
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versatile pairwise aligner for nucleotide sequences. Now minimap2 v2.22 can
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more accurately map long reads to highly repetitive regions and align through
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insertions or deletions up to 100kb by default, addressing major weakness in
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minimap2 v2.18 or earlier.
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\section{Availability and implementation:}
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\href{https://github.com/lh3/minimap2}{https://github.com/lh3/minimap2}
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\section{Contact:} hli@ds.dfci.harvard.edu
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\end{abstract}
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\section{Introduction}
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Minimap2~\citep{Li:2018ab} is widely used for maping long sequence
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reads and assembly contigs. \citet{Jain:2020aa} found minimap2 v2.18 or earlier occasionally
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misaligned reads from highly repetitive regions as minimap2 ignored seeds of
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high occurrence. They also noticed minimap2 may misplace reads with structural
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variations (SVs) in such regions~\citep{Jain2020.11.01.363887}. These
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misalignments have become a pressing issue in the advent of
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temolere-to-telomore human assembly~\citep{Miga:2020aa}. Meanwhile, old minimap2
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was unable to efficiently align long insertions/deletions (INDELs) and often
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breaks an alignment around variable-number tandem repeats (VNTRs). This has
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inspired new chaining algorithms~\citep{Li:2020aa,Ren:2021aa} which are not
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integrated into minimap2. Here we will describe recent efforts implemented
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in v2.19 through v2.22 to improve mapping results.
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\begin{methods}
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\section{Methods}
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\subsection{Rescuing high-occurrence $k$-mers}
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Minimap2 keeps all $k$-mer minimizers during indexing. Its original
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implementation only selected low-occurrence minimizers during mapping. The
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cutoff is a few hundred for mapping long reads against a human genome. If a
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read habors only a few or even no low-occurrence minimizers, it will fail
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chaining due to insufficient anchors.
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To resolve this issue, we implemented a new heuristic to add additional
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minimizers. Suppose we are looking at two adjacent low-occurence $k$-mers
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located at position $x_1$ and $x_2$, respectively. If $|x_1-x_2|\ge500$,
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minimap2 v2.22 additionally selects $\lfloor|x_1-x_2|/500\rfloor$ minimizers
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of the lowest occurrence among minimizers between $x_1$ and $x_2$.
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We use a binary heap data
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structure to select minimizers of the lowest occurrence in this interval.
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This strategy adds necessary anchors at the cost of increasing total alignment
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time by a few percent on real data.
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\subsection{Aligning through longer INDELs}
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The original minimap2 may fail to align long INDELs due to its chaining
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heuristics. Briefly, minimap2 applies dynamic programming (DP) to chain
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minimizer anchors. This is a quadratic algorithm, which is slow for chaining
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contigs. For acceptable performance, the original minimap2 uses a 500bp band by
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default. If there is an INDEL longer than 500bp and the two chains around the INDEL
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have no overlaps on either the query or the reference sequence, minimap2 may
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join the two short chains later at a later step. We call it the
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long-join heuristic. This heuristic may fail around VNTRs because short chains
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often have overlaps in VNTRs. More subtly, minimap2 may escape the inner DP
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loop early, again for performance, if the chaining result is not improved for
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50 iterations. When there is a copy number change in a long segmental
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duplication, the early escape may break around the event even if users
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specify a large band.
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In minigraph~\citep{Li:2020aa}, we developed a new chaining algorithm that
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finds short INDELs with DP-based chaining and goes through long INDELs with a
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subquadratic algorithm~\citep{DBLP:conf/wabi/AbouelhodaO03}. We ported the same
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algorithm to minimap2 for contig mapping. For long-read mapping, the minigraph
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algorithm is slower. Minimap2 v2.22 now still uses the DP-based algorithm to
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find short chains and then invokes the minigraph algorithm to rechain anchors in
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these short chains. The rechaining step achieves the same goal as long-join
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but is more reliable as it can resolve overlaps between short chains. The old
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long-join heuristic has since been removed.
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\subsection{Properly mapping long reads with SVs}
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The original minimap2 ranks an alignment by its Smith-Waterman score and
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outputs the best scoring alignment. However, when there are SVs on the read,
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the best scoring alignment is sometimes not the correct alignment.
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\citet{Jain2020.11.01.363887} resolved this dilemma by altering the mapping
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algorithm.
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In our view, this problem is rooted in impropriate scoring: affine-gap penalty
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over-penalizes a long INDEL that was often evolutionarily created in one event.
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We should not penalize a SV linearly in its length. Minimap2 v2.22 rescores
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an alignment with the following scoring function. Suppose an alignment consists
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of $M$ matching bases, $N$ substitutions and $G$ gap opens, we empirically
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score the alignment with
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$$
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M-\frac{N+G}{2d}-\sum_{i=1}^G\log_2(1+g_i)
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$$
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where $g_i\ge1$ is the length of the $i$-th gap and
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$$
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d=\max\left\{\frac{N+G}{M+N+G},0.02\right\}
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$$
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Here $d$ approximates per-base sequence divergence with the smallest value set
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to 2\%. As an analogy to affine-gap scoring, the matching score in our scheme
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is 1, the mismatch and gap open penalties are both $1/2d$ and the gap extension
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penalty is a logarithm function of the gap length. Our scoring gives a long SV
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a much milder penalty. In terms of time complexity, scoring an alignment is
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linear in the length of the alignment. Time spent on rescoring is negligible in
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practice.
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%If we assume sequences evolve under a duplication-mutation model, we may have a
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%better way to choose the best alignment. If a long read can be mapped to $n$
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%loci, we can take the read as the template and build a
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%pseudo-multi-sequence-alignment (pMSA) of $n+1$ sequences. In this pMSA, we say
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%a site on the read is informative if the $n$ reference subsequences differ at
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%the position.
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\end{methods}
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\section{Results}
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\begin{table}
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\processtable{Evaluation of minimap2 v2.22}
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{\footnotesize\label{tab:1}\begin{tabular}{p{4.2cm}rrrr}
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\toprule
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$[$Benchmark$]$ Metric & v2.22 & v2.18 & Winno & lra \\
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\midrule
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$[$sim-map$]$ \% mapped reads at Q10 & 97.9 & 97.6 & {\bf 99.0} & 97.3 \\
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$[$sim-map$]$ err. rate at Q10 (phredQ) & {\bf 52} & {\bf 52} & 38 & 24 \\
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$[$winno-cmp$]$ rate of diff. (phredQ) & {\bf 41} & 37 & N/A & 18 \\
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$[$sim-sv$]$ \% false negative rate & {\bf 0.5} & 2.0 & {\bf 0.5} & 1.4 \\
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$[$sim-sv$]$ \% false discovery rate & {\bf 0.0} & 0.1 & {\bf 0.0} & 0.1 \\
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$[$real-sv-1k$]$ \% false negative rate & {\bf 7.3} & 20.0 & 13.0 & N/A \\
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$[$real-sv-1k$]$ \% false discovery rate & 2.7 & {\bf 2.4} & 2.7 & N/A \\
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\botrule
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\end{tabular}}
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{In $[$sim-map$]$, 152,713 reads were simulated from the CHM13 telomere-to-telomere assembly v1.1
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(AC: GCA\_009914755.3) with pbsim2~\citep{Ono:2021aa}: ``pbsim2 -{}-hmm\_model R94.model -{}-length-min
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5000 -{}-length-mean 20000 -{}-accuracy-mean 0.95''. Alignments of mapping quality
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10 or higher were evaluated by ``paftools.js mapeval''. The mapping error rate
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is measured in the phred scale: if the error rate is $e$, $-10\log_{10}e$ is
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reported in the table. In $[$winno-cmp$]$, 1.39 million CHM13 HiFi reads from
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SRR11292121 were mapped against CHM13. 99.3\% of them were mapped by Winnowmap2
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at mapping quality 10 or higher and were taken as ground truth to evaluate
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minimap2 and lra with ``paftools.js pafcmp''. $[$sim-sv$]$ simulated 1,000
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50bp to 1000bp INDELs from chr8 in CHM13 using SURVIVOR~\citep{Jeffares:2017aa} and simulated Nanopore
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reads at 30 folds with the same pbsim2 command line. SVs were called with
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``sniffles -q 10''~\citep{Sedlazeck:2018ab} and compared to the simulated truth with ``SURVIVOR eval
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call.vcf truth.bed 50''. In $[$real-sv-1k$]$, small and long variants were
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called by dipcall-0.3~\citep{Li:2018aa} for HG002 assemblies (AC: GCA\_018852605.1 and
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GCA\_018852615.1) and compared to the GIAB truth~\citep{Zook:2020aa} using ``truvari -r 2000 -s
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1000 -S 400 -{}-multimatch -{}-passonly'' which sets the minimum INDEL size to 1kb in evaluation. }
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\end{table}
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We evaluated minimap2 v2.22 along with v2.18, Winnowmap2 v2.03 and lra v1.3.2
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(Table~\ref{tab:1}). Both versions of minimap2 achieved high mapping accuracy on
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simulated Nanopore reads (sim-map). Winnowmap2 aligned more reads at mapping
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quality 10 or higher (mapQ10). However, it may occasionally assign a high mapping
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quality to a read with multiple identical best alignments. This reduced its
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mapping accuracy.
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In lack of groud truth for real data, so we took Winnowmap2 mapping as ground
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truth to evaluate other mappers (winno-cmp). Out of 1,378,092 reads with mapQ10
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alignments by Winnowmap2, minimap2 v2.22 could map all of them. 118 reads, less
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than 0.01\% of all reads, were mapped differently by v2.22. 51 of them have
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multiple identical best alignments. We believe these are more likely to be
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Winnowmap2 errors. Most of the remaining 67 (=118-51) reads have multiple
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highly similar but not identical alignments. We are not sure what are real
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mapping errors.
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The two benchmarks above only evaluate read mappings without variations.
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To measure the mapping accuracy in the presence of SVs (sim-sv), we reproduced
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the results by~\citep{Jain2020.11.01.363887}. Minimap2 v2.22 is as good as
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Winnowmap2 now. Note that we were setting the Sniffles mapping quality
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threshold to 10 in consistent with the benchmarks above. If we used the
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default threshold 20, v2.22 would miss additional 0.5\% SVs, suggesting
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minimap2 v2.22 could map variant reads correctly but with conservative mapping
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quality. This observation is more about the interaction between mappers and
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callers. Furthermore, the simulation here only considers a simple scenario in
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evolution. Non-allelic gene conversions, which happen often in segmental
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duplications~\citep{Harpak:2017aa}, would obscure the optimal mapping
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strategies. How much such simple SV simulation informs real-world SV calling
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remains a question.
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To see if minimap2 v2.22 could improve long INDEL alignment, we ran dipcall on
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contig-to-reference alignments and focused on INDELs longer than 1kb
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(real-sv-1k). v2.22 is more sensitive at comparable specificity, confirming its
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advantage in more contiguous alignment. lra is supposed to handle long INDELs
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better, too. However, we could not get lra to work well with dipcall, so did
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not report the numbers.
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Minimap2 spends most computing time on base alignment. As recent improvements
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in v2.22 incur little additional computing and do not change the base alignment
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algorithm, the new version has similar performance to older verions. It is
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consistently faster than Winnowmap2 by several times. Our simple heuristics can
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be as effective as more complex solutions on real data and may help the
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development of future sequence aligners.
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\section*{Acknowledgements}
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We thank Arang Rhie and Chirag Jain for providing motivating examples where
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older minimap2 underperforms.
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\paragraph{Funding\textcolon} This work is funded by NHGRI grant R01HG010040.
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\bibliography{minimap2}
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\end{document}
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