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Heng Li 2018-02-07 11:07:08 -05:00
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@ -1,6 +1,6 @@
\documentclass{bioinfo}
\copyrightyear{2017}
\pubyear{2017}
\copyrightyear{2018}
\pubyear{2018}
\usepackage{graphicx}
\usepackage{hyperref}
@ -89,11 +89,11 @@ the versatility of minimap2.
Minimap2 follows a typical seed-chain-align procedure as is used by most
full-genome aligners. It collects minimizers~\citep{Roberts:2004fv} of the
reference sequences and indexes them in a hash table. Then for each query
sequence, minimap2 takes query minimizers as \emph{seeds}, finds matches to the
reference, and identifies sets of colinear seeds, which are called
sequence, minimap2 takes query minimizers as \emph{seeds}, finds exact matches
(i.e. \emph{anchors}) to the reference, and identifies sets of colinear anchors as
\emph{chains}. If base-level alignment is requested, minimap2 applies dynamic
programming (DP) to extend from the ends of chains and to close unseeded
regions between adjacent seeds in chains.
programming (DP) to extend from the ends of chains and to close
regions between adjacent anchors in chains.
Minimap2 uses indexing and seeding algorithms similar to
minimap~\citep{Li:2016aa}, and furthers the predecessor with more accurate
@ -122,8 +122,8 @@ In implementation, a gap of length $l\not=0$ costs
\[
\gamma_c(l)=0.01\cdot \bar{w}\cdot|l|+0.5\log_2|l|
\]
where $\bar{w}$ is the average seed length. For $n$ anchors, directly computing all $f(\cdot)$ with
Eq.~(\ref{eq:chain}) takes $O(n^2)$ time. Although theoretically faster
where $\bar{w}$ is the average seed length. For $N$ anchors, directly computing all $f(\cdot)$ with
Eq.~(\ref{eq:chain}) takes $O(N^2)$ time. Although theoretically faster
chaining algorithms exist~\citep{Abouelhoda:2005aa}, they
are inapplicable to generic gap cost, complex to implement and usually
associated with a large constant. We introduced a simple heuristic to
@ -133,7 +133,7 @@ We note that if anchor $i$ is chained to $j$, chaining $i$ to a predecessor
of $j$ is likely to yield a lower score. When evaluating Eq.~(\ref{eq:chain}),
we start from anchor $i-1$ and stop the process if we cannot find a better
score after up to $h$ iterations. This approach reduces the average time to
$O(h\cdot n)$. In practice, we can almost always find the optimal chain with
$O(hN)$. In practice, we can almost always find the optimal chain with
$h=50$; even if the heuristic fails, the optimal chain is often close.
\subsubsection{Backtracking}
@ -379,6 +379,16 @@ alignment between the two subsequences involved in the global alignment, but
this time with the one subsequence reverse complemented. This additional
alignment step may identify short inversions that are missed during chaining.
\subsubsection{Filtering out misplaced anchors}
Due to sequencing errors and local homology, some anchors in a chain may be
wrong. If we blindly align regions between two misplaced anchors, we will
produce a suboptimal alignment. To reduce this artifact, we filter out
anchors that lead to a $>$10bp insertion and a $>$10bp deletion at the same
time, and filter out terminal anchors that lead to a long gap towards the ends
of a chain. These heuristics greatly alleviate the issues with misplaced
anchors, but they are unable to fix all such errors. Local misalignment is a
limitation of minimap2 which we hope to address in future.
\subsection{Aligning spliced sequences}
The algorithm described above can be adapted to spliced alignment. In this
@ -623,7 +633,7 @@ simulated data set than Bowtie2 and SNAP but less accurate than BWA-MEM
(Fig.~\ref{fig:eval}b). Closer investigation reveals that BWA-MEM achieves
a higher accuracy partly because it tries to locally align a read in a small
region close to its mate. If we disable this feature, BWA-MEM becomes slightly
less accurate than minimap2. We might consider to implement a similar heuristic
less accurate than minimap2. We might implement a similar heuristic
in minimap2 in future.
To evaluate the accuracy of minimap2 on real data, we aligned human reads
@ -643,11 +653,10 @@ context of small variant calling.
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. QUAST~\citep{Gurevich:2013aa}
v5.0 will use minimap2 to evaluate the quality of assemblies against a
reference genome.
NCBI. Minimap2 also aligns similar genomes or different assemblies of the
same species. It can map a human SMRT assembly (AC:GCA\_001297185.1) to
GRCh38 in 7 minutes using 8 CPU cores. QUAST~\citep{Gurevich:2013aa} v5.0 will
use minimap2 to evaluate the quality of assemblies against a reference genome.
\section{Discussions}