this will become version 3 at arXiv

tex/minimap2.tex

@@ -34,7 +34,7 @@ \section{Motivation:} Recent advances in sequencing technologies promise
 length. Existing alignment programs are unable or inefficient to process such data
 at scale, which presses for the development of new alignment algorithms.
 
-\section{Results:} Minimap2 is a general-purpose mapper to align DNA or long
+\section{Results:} Minimap2 is a general-purpose alignment program to map DNA or long
 mRNA sequences against a large reference database. It works with accurate short
 reads of $\ge$100bp in length, $\ge$1kb genomic reads at error rate $\sim$15\%,
 full-length noisy Direct RNA or cDNA reads, and assembly contigs or closely
@@ -66,15 +66,22 @@ \section{Introduction}
 approximate mapping 50 times faster than BWA-MEM~\citep{Li:2016aa}.
 \citet{Suzuki130633} extended our work with a fast and novel algorithm on
 generating base-level alignment, which in turn inspired us to develop minimap2
-towards higher accuracy and more practical functionality.
+with added functionality.
 
 Both SMRT and ONT have been applied to the sequencing of spliced mRNAs (RNA-seq). While
 traditional mRNA aligners work~\citep{Wu:2005vn,Iwata:2012aa}, they are not
 optimized for long noisy sequence reads and are tens of times slower than
 dedicated long-read aligners. When developing minimap2 initially for aligning
-genomic DNA only, we realized minor modifications could make it competitive for
-aligning mRNAs as well. Minimap2 is a first RNA-seq aligner specifically
-designed for long noisy reads.
+genomic DNA only, we realized minor modifications could enable the base
+algorithm to map mRNAs as well. Minimap2 becomes a first RNA-seq aligner
+specifically designed for long noisy reads. We have also extended the original
+algorithm to map short reads at a speed faster than several mainstream
+short-read mappers.
+
+In this article, we will describe the minimap2 algorithm and its applications
+to different types of input sequences. We will evaluate the performance and
+accuracy of minimap2 on several simulated and real data sets and demonstrate
+the versatility of minimap2.
 
 \begin{methods}
 \section{Methods}
@@ -366,12 +373,12 @@ \subsection{Aligning spliced sequences}
 
 In the spliced alignment mode, minimap2 further increases the density of
 minimizers and disables banded alignment. Together with the two-round DP-based
-alignment, spliced alignment is several times slower than DNA sequence
+alignment, spliced alignment is several times slower than genomic DNA
 alignment.
 
 \subsection{Aligning short paired-end reads}
 
-During chainging, minimap2 takes a pair of reads as one read with a gap of
+During chainging, minimap2 takes a pair of reads as one fragment with a gap of
 unknown length in the middle. It applies a normal gap cost between seeds on the
 same read but is a more permissive gap cost between seeds on different reads.
 More precisely, the gap cost during chaining is:
@@ -423,9 +430,7 @@ \subsection{Aligning long genomic reads}
 and LAMSA~\citep{Liu:2017aa} because they either
 crashed or produced malformatted output. In this evaluation, minimap2 has
 higher power to distinguish unique and repetitive hits, and achieves overall
-higher mapping accuracy (Fig.~\ref{fig:eval}a). It is still the most accurate
-even if we skip DP-based alignment (data not shown), confirming chaining alone
-is sufficient to achieve high accuracy for approximate mapping. Minimap2 and
+higher mapping accuracy (Fig.~\ref{fig:eval}a). Minimap2 and
 NGMLR provide better mapping quality estimate: they rarely give repetitive hits
 high mapping quality.  Apparently, other aligners may
 occasionally miss close suboptimal hits and be overconfident in wrong mappings.
@@ -498,10 +503,10 @@ \subsection{Aligning long spliced reads}
 We have also evaluated spliced aligners on public Iso-Seq data (human Alzheimer
 brain from \href{http://bit.ly/isoseqpub}{http://bit.ly/isoseqpub}). The
 observation is similar: minimap2 is faster at higher junction accuracy.
-On a private Nanopore Direct RNA data set with $>$20\% sequencing error rate
-(M\"{u}ller et al, personal communication), minimap2 aligned 940,346 introns
-from 239,976 mapped reads with 88.5\% of them consistent with human gene
-annotations. In comparison, only 40.3\% of GMAP introns found in known gene
+On a private Nanopore Direct RNA data set with $\sim$17\% sequencing error rate
+(N. Loman, personal communication), minimap2 aligned 96\,467 introns
+from 37\,068 mapped reads with 95.4\% of them consistent with human gene
+annotations. In comparison, only 74.8\% of GMAP introns found in known gene
 annotations.
 
 We noted that GMAP and SpAln have not been optimized for noisy reads. We are
@@ -551,24 +556,23 @@ \subsection{Aligning short genomic reads}
 ERR1341796. In this evaluation, minimap2 has higher SNP false negative rate
 (FNR; 2.5\% of minimap2 vs 2.2\% of BWA-MEM), but fewer false positive SNPs per
 million bases (FPPM; 3.0 vs 3.9), lower 2--50bp INDEL FNR (7.3\% vs 7.5\%) and
-similar INDEL FPPM (both 1.0). In comparison, Bowtie2 has a SNP FNR of 4.7\%
-and INDEL FNR of 10.4\%. Minimap2 is broadly similar to BWA-MEM in the context
-of small variant calling.
+similar INDEL FPPM (both 1.0). Minimap2 is broadly similar to BWA-MEM in the
+context of small variant calling.
 
 \subsection{Other applications}
 
 Minimap2 retains minimap's functionality to find overlaps between long reads
 and to search against large multi-species databases such as \emph{nt} from
 NCBI. Minimap2 can also align similar genomes or different assemblies of the
 same species. It took 7 wall-clock minutes over 8 CPU cores to align a human
-SMRT assembly (AC:GCA\_001297185.1) to GRCh38, over 20 times as fast as
+SMRT assembly (AC:GCA\_001297185.1) to GRCh38, over 20 times faster
 MUMmer4~\citep{Kurtz:2004zr}.
 
 \section{Discussions}
 
 Minimap2 is a versatile mapper and pairwise aligner for nucleotide sequences.
 It works with short reads, assembly contigs and long noisy genomic and RNA-seq
-reads. It can be used as a read mapper, long-read overlapper or a full-genome
+reads, and can be used as a read mapper, long-read overlapper or a full-genome
 aligner. Minimap2 is also accurate and efficient, often outperforming other
 domain-specific alignment tools in terms of both speed and accuracy.
 
@@ -586,6 +590,17 @@ \section{Discussions}
 spliced reads and multiple reads per fragment. This gives us the opportunity to
 extend the same base algorithm to a variety of use cases.
 
+Modern mainstream aligners often use a full-text index, such as suffix array or
+FM-index, to index reference sequences. An advantage of this approach is that
+we can use exact seeds of arbitrary lengths, which helps to increase seed
+uniqueness and reduce unsuccessful extensions. Minimap2 indexes reference
+k-mers with a hash table instead. Such fixed-length seeds are inferior to
+variable-length seeds in theory, but can be computed much more efficiently in
+practice. When a query sequence has multiple seed hits, we can afford to skip
+some highly repetitive seeds without affecting the final accuracy. This further
+alleviates the concern with the uniqueness of seeds. Hash table is the ideal
+data structure for mapping long query sequences.
+
 \section*{Acknowledgements}
 We owe a debt of gratitude to H. Suzuki and M. Kasahara for releasing their
 masterpiece and insightful notes before formal publication. We thank M.