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important probabilistic data structure developed in the 70s by Burton H. Bloom in this paper \cite{bloom1970space}. This data structure is usually used to check the membership of an item in a set, one of its advantages is that it can't have false negatives but it can have false positives.\\ +The idea behind the bloom filters is that we have an array of bits with size $m$ and all the bits are set to 0. We also have $h$ hash functions that are independent. For each item, the all the hash function are used which map to different parts of the array, and the bits are changed from 0 to 1. Therefore, a false positive can happen if another item mapped to some part of the array and switched that part of the array to 1. However, false negatives can't happen, because if the same hash functions are used for that item, it will map to the same parts in the array which should be set to 1.\\ +The false positive rate of bloom filters can be approximated using this equation $\left ( 1 - e^{-h\frac{n}{m}} \right )^{h}$, where $n$ is the number of unique elements added to the filter, $m$ is the bit array size, and $h$ is the number of independent hash functions. We can see that if we wanted more accuracy we can change $m$ or $h$ but with some trade off, increasing $m$ means more memory and more $h$ means more calculations. +\section{$\ell$-mminimizer} \label{l_minimizer} +For a string $x$ with length $k$ characters, the left minimizer of $x$ or lmm($x$) with $\ell < k$ is the $\ell$-minimizer of the prefix $(k-1)$-mer, and the right minimizer or rmm($x$) is the $\ell$-minimizer of the suffix $(k-1)$-mer. + +\section{GFA Files} \label{gfa_files} +GFA is short for Graphical Fragment Assembly, this format is used for the representation of genomic assembly graphs. It is a simple, text-based format that is tab-delimited. First column contains one capital letter that describes the type of the line, and there are several types of lines: +\begin{enumerate} +\item \textbf{H}: for a header line, which has one mandatory column which is "H", and an optional column can be added for the version number. +\item \textbf{L}: for an edge or link line, has 6 mandatory columns, first column is "L" for the line type, then we have the "from" node id, followed by its orientation (+ or - for normal overlap or reverse complement), then we have the "to" nod id followed by the orientation, and the last column is the overlap size. Can have several optional fields such as mapping quality, number of mismatches, etc... +\item \textbf{S}: for a segment or a node line, has 3 mandatory columns, first column is "S" for the type of line, followed by the node name or ID, then the sequence. Can have many optional columns such as sequence length, node count, k-mer count, and so on. +\item \textbf{C}: for a containment line, in case one node or sequence was fully contained in another one, this line has 7 mandatory columns, first column is the identifier "C", followed by the "container" node, then the orientation (whether the sequence is contained in it is current sequence or the reverse complement one), then the "contained" node and it is orientation, the 6th column has an integer for the position where the contained sequence starts in the container sequence, and the last column is the overlap. +\item \textbf{P}: for a path line, has 4 mandatory columns, first is "P", followed by the path unique ID, the a comma separated list of node ids and orientation of this path, and the last column is also a comma separated list of overlaps. +\end{enumerate} +Comment lines start with a hash \#.\\ +Table \ref{tab:gfa_example} is a small example of a GFA file with 3 edges, 3 nodes (ACCTT, TCAAGG, CTTGATT), and one path. We can see for example that node 1 overlaps with 4 base pairs with the reverse complement of node 2. The path line discribes a path between ACCTT (node 1) CCTTGA (reverse complement of node 2) and CTTGATT (node 3) and their respective overlaps in this orientation, this path gives back after removing the overlaps ACCTTGATT. GFA file specification and example adapted from \texttt{http://gfa-spec.github.io/GFA-spec/GFA1.html}. + +\begin{table}[h] +\centering +\setlength{\tabcolsep}{1.7em} +\begin{tabular}{ +>{\columncolor[HTML]{E8F1FD}}l +>{\columncolor[HTML]{E8F1FD}}l +>{\columncolor[HTML]{E8F1FD}}l +>{\columncolor[HTML]{E8F1FD}}l +>{\columncolor[HTML]{E8F1FD}}l +>{\columncolor[HTML]{E8F1FD}}l } +H & VN:Z:1.0 & & & & \\ +S & 1 & ACCTT & & & \\ +S & 2 & TCAAGG & & & \\ +S & 3 & CTTGATT & & & \\ +L & 1 & + & 2 & - & 4M \\ +L & 2 & - & 3 & + & 5M \\ +L & 1 & + & 3 & + & 3M \\ +P & 4 & 11+,12-,13+ & 4M,5M & & +\end{tabular} +\caption{Example of a tab separated GFA file with} +\label{tab:gfa_example} +\end{table} + +\section{Extra Tables} +\renewcommand{\arraystretch}{2} +\begin{sidewaystable} +\centering +\begin{tabular}{|c|c|} + +\hline +Long Read$_1$& +\verb|m141228_203435_42248_c100724252550000001823140404301566_s1_p0/124717/534_16502 | \\ \hline %1 +Long Read$_2$& \verb|m140817_090215_42175_c100689561270000001823145102281512_s1_p0/77789/1261_15093 | \\ \hline %0 +Long Read$_3$ & \verb|$m140730_234813_42161_c100693980030000001823147103241540_s1_p0/62995/10187_28465| \\ \hline %1 +Long Read$_4$ & \verb|$m150119_034210_42225_c100724262550000001823140404301552_s1_p0/146960/5678_25609| \\ \hline %0 +Long Read$_5$ & \verb|$m150114_041139_42248_c100723882550000001823140404301566_s1_p0/14429/8164_19894 | \\ \hline %1 +Long Read$_6$ & \verb|$m150103_220523_42248_c100723822550000001823140404301525_s1_p0/52501/1323_16658 | \\ \hline %1 +\end{tabular} +\caption{PacBio long reads IDs from NA19420 sample used to construct table \ref{tab:mec_bubble_chain} for the bubble chain in figure \ref{fig:bubble_chain} } +\label{tab:long_reads} +\end{sidewaystable} diff --git a/Bibliography.bib b/Bibliography.bib new file mode 100644 index 0000000..6d56be4 --- /dev/null +++ b/Bibliography.bib @@ -0,0 +1,354 @@ +@article{garg_graph, + title={A graph-based approach to diploid genome assembly.}, + author={Garg, S and Rautiainen, M and Novak, AM and Garrison, E and Durbin, R and Marschall, T}, + journal={Bioinformatics (Oxford, England)}, + volume={34}, + number={13}, + pages={i105--i114}, + year={2018}, + publisher={Oxford University Press} +} + +@inproceedings{klau2017guided, + title={A guided tour to computational haplotyping}, + author={Klau, Gunnar W and Marschall, Tobias}, + booktitle={Conference on Computability in Europe}, + pages={50--63}, + year={2017}, + organization={Springer} +} + +@inproceedings{medvedev2007computability, + title={Computability of models for sequence assembly}, + author={Medvedev, Paul and Georgiou, Konstantinos and Myers, Gene and Brudno, Michael}, + booktitle={International Workshop on Algorithms in Bioinformatics}, + pages={289--301}, + year={2007}, + organization={Springer} +} + +@article{cilibrasi2007complexity, + title={The complexity of the single individual SNP haplotyping problem}, + author={Cilibrasi, Rudi and Van Iersel, Leo and Kelk, Steven and Tromp, John}, + journal={Algorithmica}, + volume={49}, + number={1}, + pages={13--36}, + year={2007}, + publisher={Springer} +} + +@article{crawford2005definition, + title={Definition and clinical importance of haplotypes}, + author={Crawford, Dana C and Nickerson, Deborah A}, + journal={Annu. Rev. Med.}, + volume={56}, + pages={303--320}, + year={2005}, + publisher={Annual Reviews} +} + +@article{browning2011haplotype, + title={Haplotype phasing: existing methods and new developments}, + author={Browning, Sharon R and Browning, Brian L}, + journal={Nature Reviews Genetics}, + volume={12}, + number={10}, + pages={703}, + year={2011}, + publisher={Nature Publishing Group} +} + +@article{rhee2016survey, + title={Survey of computational haplotype determination methods for single individual}, + author={Rhee, Je-Keun and Li, Honglan and Joung, Je-Gun and Hwang, Kyu-Baek and Zhang, Byoung-Tak and Shin, Soo-Yong}, + journal={Genes \& Genomics}, + volume={38}, + number={1}, + pages={1--12}, + year={2016}, + publisher={Springer} +} + +@article{manolio2010genomewide, + title={Genomewide association studies and assessment of the risk of disease}, + author={Manolio, Teri A}, + journal={New England journal of medicine}, + volume={363}, + number={2}, + pages={166--176}, + year={2010}, + publisher={Mass Medical Soc} +} + +@inproceedings{lancia2001snps, + title={SNPs problems, complexity, and algorithms}, + author={Lancia, Giuseppe and Bafna, Vineet and Istrail, Sorin and Lippert, Ross and Schwartz, Russell}, + booktitle={European symposium on algorithms}, + pages={182--193}, + year={2001}, + organization={Springer} +} + +@article{bonizzoni2016minimum, + title={On the minimum error correction problem for haplotype assembly in diploid and polyploid genomes}, + author={Bonizzoni, Paola and Dondi, Riccardo and Klau, Gunnar W and Pirola, Yuri and Pisanti, Nadia and Zaccaria, Simone}, + journal={Journal of Computational Biology}, + volume={23}, + number={9}, + pages={718--736}, + year={2016}, + publisher={Mary Ann Liebert, Inc. 140 Huguenot Street, 3rd Floor New Rochelle, NY 10801 USA} +} + +@article{sohn2016present, + title = "{The present and future of de novo whole-genome assembly}", + author = {Sohn, Jang-il and Nam, Jin-Wu}, + journal = {Briefings in Bioinformatics}, + volume = {19}, + number = {1}, + pages = {23-40}, + year = {2016}, + month = {10}, + doi = {10.1093/bib/bbw096}, + publisher={Briefings in Bioinformatics} +} + +@article{miller2010assembly, + title={Assembly algorithms for next-generation sequencing data}, + author={Miller, Jason R and Koren, Sergey and Sutton, Granger}, + journal={Genomics}, + volume={95}, + number={6}, + pages={315--327}, + year={2010}, + publisher={Elsevier} +} + +@article{schlebusch2012next, + title={Next generation shotgun sequencing and the challenges of de novo genome assembly}, + author={Schlebusch, Stephen and Illing, Nicola}, + journal={South African Journal of Science}, + volume={108}, + number={11-12}, + pages={62--70}, + year={2012}, + publisher={Academy of Science of South Africa} +} +%bcalm paper +@article{chikhi2016compacting, + title={Compacting de Bruijn graphs from sequencing data quickly and in low memory}, + author={Chikhi, Rayan and Limasset, Antoine and Medvedev, Paul}, + journal={Bioinformatics}, + volume={32}, + number={12}, + pages={i201--i208}, + year={2016}, + publisher={Oxford University Press} +} + +@article{compeau2011bruijn, + title={Why are de Bruijn graphs useful for genome assembly?}, + author={Compeau, Phillip EC and Pevzner, Pavel A and Tesler, Glenn}, + journal={Nature biotechnology}, + volume={29}, + number={11}, + pages={987}, + year={2011}, + publisher={NIH Public Access} +} + +@inproceedings{iliopoulos2016popping, + title={Popping superbubbles and discovering clumps: recent developments in biological sequence analysis}, + author={Iliopoulos, Costas S and Kundu, Ritu and Mohamed, Manal and Vayani, Fatima}, + booktitle={International Workshop on Algorithms and Computation}, + pages={3--14}, + year={2016}, + organization={Springer} +} + +@article{paten2018superbubbles, + title={Superbubbles, ultrabubbles, and cacti}, + author={Paten, Benedict and Eizenga, Jordan M and Rosen, Yohei M and Novak, Adam M and Garrison, Erik and Hickey, Glenn}, + journal={Journal of Computational Biology}, + volume={25}, + number={7}, + pages={649--663}, + year={2018}, + publisher={Mary Ann Liebert, Inc. 140 Huguenot Street, 3rd Floor New Rochelle, NY 10801 USA} +} + +@article{heather2016sequence, + title={The sequence of sequencers: The history of sequencing DNA}, + author={Heather, James M and Chain, Benjamin}, + journal={Genomics}, + volume={107}, + number={1}, + pages={1--8}, + year={2016}, + publisher={Elsevier} +} + +@article{kececioglu1995combinatorial, + title={Combinatorial algorithms for DNA sequence assembly}, + author={Kececioglu, John D and Myers, Eugene W}, + journal={Algorithmica}, + volume={13}, + number={1-2}, + pages={7}, + year={1995}, + publisher={Springer} +} + +@article{pevzner2001eulerian, + title={An Eulerian path approach to DNA fragment assembly}, + author={Pevzner, Pavel A and Tang, Haixu and Waterman, Michael S}, + journal={Proceedings of the national academy of sciences}, + volume={98}, + number={17}, + pages={9748--9753}, + year={2001}, + publisher={National Acad Sciences} +} + +@inproceedings{onodera2013detecting, + title={Detecting superbubbles in assembly graphs}, + author={Onodera, Taku and Sadakane, Kunihiko and Shibuya, Tetsuo}, + booktitle={International Workshop on Algorithms in Bioinformatics}, + pages={338--348}, + year={2013}, + organization={Springer} +} + +@article{song2014lighter, + title={Lighter: fast and memory-efficient sequencing error correction without counting}, + author={Song, Li and Florea, Liliana and Langmead, Ben}, + journal={Genome biology}, + volume={15}, + number={11}, + pages={509}, + year={2014}, + publisher={BioMed Central} +} + +@article{koboldt2006distribution, + title={Distribution of human SNPs and its effect on high-throughput genotyping}, + author={Koboldt, Daniel C and Miller, Raymond D and Kwok, Pui-Yan}, + journal={Human mutation}, + volume={27}, + number={3}, + pages={249--254}, + year={2006}, + publisher={Wiley Online Library} +} + +@article{guo2005distribution, + title={The distribution of SNPs in human gene regulatory regions}, + author={Guo, Yongjian and Jamison, D Curtis}, + journal={Bmc Genomics}, + volume={6}, + number={1}, + pages={140}, + year={2005}, + publisher={BioMed Central} +} + +@article{melsted2014kmerstream, + title={KmerStream: streaming algorithms for k-mer abundance estimation}, + author={Melsted, P{\'a}ll and Halld{\'o}rsson, Bjarni V}, + journal={Bioinformatics}, + volume={30}, + number={24}, + pages={3541--3547}, + year={2014}, + publisher={Oxford University Press} +} + +@article{zerbino2008velvet, + title={Velvet: algorithms for de novo short read assembly using de Bruijn graphs}, + author={Zerbino, Daniel R and Birney, Ewan}, + journal={Genome research}, + volume={18}, + number={5}, + pages={821--829}, + year={2008}, + publisher={Cold Spring Harbor Lab} +} + +@article{rautiainen2018bit, + title={Bit-parallel sequence-to-graph alignment}, + author={Rautiainen, Mikko and M{\"a}kinen, Veli and Marschall, Tobias}, + journal={bioRxiv}, + pages={323063}, + year={2018}, + publisher={Cold Spring Harbor Laboratory} +} + +@article{wick2015bandage, + title={Bandage: interactive visualization of de novo genome assemblies}, + author={Wick, Ryan R and Schultz, Mark B and Zobel, Justin and Holt, Kathryn E}, + journal={Bioinformatics}, + volume={31}, + number={20}, + pages={3350--3352}, + year={2015}, + publisher={Oxford University Press} +} + +@article{chikhi2013informed, + title={Informed and automated k-mer size selection for genome assembly}, + author={Chikhi, Rayan and Medvedev, Paul}, + journal={Bioinformatics}, + volume={30}, + number={1}, + pages={31--37}, + year={2013}, + publisher={Oxford University Press} +} + +@article{martin2016whatshap, + title={WhatsHap: fast and accurate read-based phasing}, + author={Martin, Marcel and Patterson, Murray and Garg, Shilpa and Fischer, Sarah O and Pisanti, Nadia and Klau, Gunnar W and Schoenhuth, Alexander and Marschall, Tobias}, + journal={BioRxiv}, + pages={085050}, + year={2016}, + publisher={Cold Spring Harbor Laboratory} +} + +@inproceedings{patterson2014whatshap, + title={Whatshap: Haplotype assembly for future-generation sequencing reads}, + author={Patterson, Murray and Marschall, Tobias and Pisanti, Nadia and van Iersel, Leo and Stougie, Leen and Klau, Gunnar W and Sch{\"o}nhuth, Alexander}, + booktitle={International Conference on Research in Computational Molecular Biology}, + pages={237--249}, + year={2014}, + organization={Springer} +} + +@article{lee2016third, + title={Third-generation sequencing and the future of genomics}, + author={Lee, Hayan and Gurtowski, James and Yoo, Shinjae and Nattestad, Maria and Marcus, Shoshana and Goodwin, Sara and McCombie, W Richard and Schatz, Michael}, + journal={BioRxiv}, + pages={048603}, + year={2016}, + publisher={Cold Spring Harbor Laboratory} +} + +@inproceedings{jain2019complexity, + title={On the complexity of sequence to graph alignment}, + author={Jain, Chirag and Zhang, Haowen and Gao, Yu and Aluru, Srinivas}, + booktitle={International Conference on Research in Computational Molecular Biology}, + pages={85--100}, + year={2019}, + organization={Springer} +} + +@article{bloom1970space, + title={Space/time trade-offs in hash coding with allowable errors}, + author={Bloom, Burton H}, + journal={Communications of the ACM}, + volume={13}, + number={7}, + pages={422--426}, + year={1970}, + publisher={ACM} +} \ No newline at end of file diff --git a/Chapters/._Introduction.tex b/Chapters/._Introduction.tex new file mode 100644 index 0000000000000000000000000000000000000000..f335f9f74e04bb4a81229d643f88392328c63986 GIT binary patch literal 4096 zcmZQz6=P>$Vqox1Ojhs@R)|o50+1L3ClDJkFz{^v(m+1nBL)UWIUt(=a103vvYvJF zKST$^0-$mMG%bukK2%&PIX_n~v7jI)RWB#8xTLf=H6$Vqox1Ojhs@R)|o50+1L3ClDJkFz{^v(m+1nBL)UWIUt(=a103vvYvJF zKST$^0-$mMG%bukK2%&PIX_n~v7jI)RWB#8xTLf=H6ukeOGKnpcvUpO=`EQ>l=XnpUEal#`g34eSd;bq#3>)&Fp>$S}zL G{|^A5)GHzY literal 0 HcmV?d00001 diff --git a/Chapters/._Motivation.tex b/Chapters/._Motivation.tex new file mode 100644 index 0000000000000000000000000000000000000000..0887b62891d916c7746a0b3fe3b67eb236efc816 GIT binary patch literal 4096 zcmZQz6=P>$Vqox1Ojhs@R)|o50+1L3ClDJkFz{^v(m+1nBL)UWIUt(=a103vvYvJF zKST$^0-$mMG%bukK2%&PIX_n~v7jI)RWB#8xTLf=H6$Vqox1Ojhs@R)|o50+1L3ClDJkFz{^v(m+1nBL)UWIUt(=a103vvYvJF zKST$^0-$mMG%bukK2%&PIX_n~v7jI)RWB#8xTLf=H6{\adjustbox{angle=#1,lap=\width-(#2)}\bgroup}% + l% + <{\egroup}% +} +\newcommand*\rot{\multicolumn{1}{R{45}{1em}}}% no optional argument here, please! + +The data used in all the results presented here were taken from the 1000 genomes project. The main sample used is the HG00733 sample that belongs to a female individual from Puerto Rico with American ancestry\footnote{https://www.internationalgenome.org/data-portal/sample/HG00733}. For this sample, short and long reads were available, the short reads were used to build the De Bruijn graph and the long reads for phasing and resolving variants. This individual's parents were also part of the 1000 genomes project with HG00731 being the father sample and HG00732 being the mother sample. + +\section{Superbubbles and Bubble chains Statistics} +\subsection{Selecting $k$} +As one of the first steps of the pipeline is filtering the data using \texttt{Lighter}, the parameter $k$ for the $k$-mers counted in the tool need to be chosen (with maximum of 31 assigned by the tool). \texttt{BCALM2} tool that is used to build the De Bruijn graphs also needs the parameter $k$ as discussed in section \ref{build_dbg}. For this task, we ran several combinations of both $k$s and checked how the choice of $k$ affected the length of bubble chains discovered and the sequence covered by these bubble chains.\\ +Table \ref{tab:statistics} shows all the combinations tested on the HG00733 short reads, with the following columns: +\begin{enumerate} +\item \textbf{\texttt{Lighter} $k$}: The different values used for the $k$ parameter of \texttt{Lighter}. +\item \textbf{De Bruijn $k$}: The different values used for the $k$ parameter of \texttt{BCALM}. +\item \textbf{Longest Chain}: How many bubbles the longest chain had according to the parameters used. +\item \textbf{Longest Chain Untipped}: The same graph but after untipping (tip clipping). We can clearly see an increase in longest chain, which is expected as some tips can form between two bubble chains causing the algorithm to abort. +\item \textbf{Node Percentage}: The percentage of nodes part of the bubble chains compared to the total number of nodes. +\item \textbf{Node Percentage Untipped}: The same as the previous column but after removing tips. +\item \textbf{Longest Seq}: What was the longest sequence covered by a bubble chain. Note, that longest chain bubble-wise is not always the same as the longest chain sequence-wise. Because, a chain can have many bubbles with smaller nodes. +\item \textbf{Longest Seq Untipped}: The same as the previous column but after removing tips. +\item \textbf{Seq Percentage}: The percentage of total sequences covered by the bubble chains compared to the total number of sequences in the graph. We can see that in the node percentage, the bubble chains only cover up to 37\% of the total nodes. However, the bubble chains usually contain longer nodes as the sequence percentage is much higher of up to 66\% +\item \textbf{Seq Percentage Untipped}: The same as the previous column but after untipping. +\end{enumerate} +Looking at the big \ref{tab:statistics} Table we can see some clear patterns: +\begin{itemize} +\item The $k$-mer size for building the graph has a big effect as mentioned in methods in section \ref{selecting_k}, starting from 41 to 91 with 10 increments, we see that the numbers of longest chain bubble wise and sequence wise reach their peak at 61 or 71. +\item The different choices of $k$ for \texttt{Lighter} had some effect but not as drastic as the $k$-mer size choice. +\item Longest chain bubble-wise and sequence-wise increase after untipping which is expected and discussed in methods section \ref{tip_clipping}, what is not expected is the percentages drop after untipping. Unfortunately, after double-checking the codes, I am still not sure why the numbers drop while chains become longer as expected. +\end{itemize} +For the further results presented, a \texttt{Lighter} $k$ of 21 and $k$-mer size of 61 was chosen on the HG00733 sample as it had the longest chain bubble-wise and one of the highest chains sequence-wise, and covered a good percentage both before and after untipping.\\ + +\begin{table}[htbp] +\centering +%\begin{adjustbox}{angle=90} +{\small +\begin{tabular}{p{1.3cm}|p{1.2cm}|p{1.35cm}|p{1.35cm}|p{1.2cm}|p{1.2cm}|p{1.35cm}|p{1.35cm}|p{1.2cm}|p{1.2cm}} +\textbf{\texttt{Lighter} $k$}& \textbf{De Bruijn $k$} & \textbf{Longest Chain} & \textbf{Longest Chain untipped} & \textbf{Node percentage} & \textbf{Node percentage untipped}& \textbf{Longest Seq} & \textbf{Longest Seq untipped} & \textbf{Seq percentage} & \textbf{Seq Percentage untipped} \\ + \hline + 11 & 41 & 45 & 68 & 26 & 15 & 19631 & 43770 & 60 & 53 \\ + 11 & 51 & 49 & 80 &31 & 21 & 25595 & 56203 & 61 & 57 \\ + \hline + 11 & 61 & 73 & 110 & 34 & 26 & 40546 & 63160 & 62 & 59 \\ + \hline + 11 & 71 & 55 & 64 & 36 & 27 & 37319 & 53348 & 59 & 56 \\ + 11 & 81 & 38 & 47 & 32 & 20 & 43087 & 55344 & 48 & 42 \\ + 11 & 91 & 21 & 52 & 21 & 9 & 32271 & 42440 & 27 & 71 \\ + 15 & 41 & 40 & 68 & 26 & 15 & 19190 & 43770 & 60 & 53 \\ + 15 & 51 & 49 & 80 & 31 & 21 & 25595 & 56203 & 61 & 57 \\ + \hline + 15 & 61 & 73 & 109 & 34 & 26 & 40546 & 63160 & 62 & 59 \\ + \hline + 15 & 71 & 55 & 64 & 36 & 27 & 37319 & 53348 & 59 & 56 \\ + 15 & 81 & 38 & 47 & 32 & 20 & 43082 & 55344 & 48 & 42 \\ + 15 & 91 & 21 & 52 & 21 & 9 & 32271 & 42440 & 27 & 17 \\ + 19 & 41 & 53 & 67 & 24 & 14 & 35457 & 43770 & 59 & 52 \\ + + 19 & 51 & 54 & 77 & 29 & 21 & 36287 & 55801 & 62 & 57 \\ + \hline + 19 & 61 & 60 & 110 & 34 & 27 & 39287 & 63159 & 64 & 61 \\ + \hline + 19 & 71 & 58 & 92 & 37 & 30 & 44268 & 61114 & 63 & 60 \\ + 19 & 81 & 55 & 65 & 35 & 25 & 40038 & 56848 & 54 & 49 \\ + 19 & 91 & 29 & 40 & 25 & 13 & 28375 & 57163 & 34 & 24 \\ + 23 & 41 & 67 & 47 & 23 & 14 & 34547 & 43745 & 58 & 51 \\ + 23 & 51 & 63 & 78 & 28 & 20 & 41550 & 55399 & 63 & 57 \\ + \hline + \textbf{23} & \textbf{61} & \textbf{80} & \textbf{113} & 34 & 27 & 45756 & \textbf{64685} & \textbf{66} & 62 \\ + \hline + 23 & 17 & 68 & 94 & 37 & 31 & 45653 & 61862 & 65 & 62 \\ + 23 & 81 & 55 & 54 & 35 & 27 & 31617 & 59576 & 57 & 51 \\ + 23 & 91 & 29 & 52 & 26 & 14 & 31908 & 57163 & 37 & 26 \\ + 27 & 41 & 66 & 66 & 22 & 13 & 43806 & 43739 & 57 & 51 \\ + 27 & 51 & 68 & 77 & 28 & 20 & 46246 & 55198 & 62 & 57 \\ + \hline + 27 & 61 & 74 & 111 & 34 & 27 & 53322 & 63406 & 65 & 62 \\ + \hline + 27 & 71 & 70 & 96 & 38 & 32 & 48081 & 72174 & 65 & 62 \\ + 27 & 81 & 57 & 55 & 36 & 28 & 34142 & 62819 & 58 & 53 \\ + 27 & 91 & 30 & 52 & 26 & 15 & 36931 & 57163 & 38 & 27 \\ + 31 & 41 & 65 & 65 & 21 & 13 & 43316 & 43739 & 56 & 51 \\ + 31 & 51 & 68 & 78 & 27 & 20 & 45773 & 55600 & 62 & 57 \\ + \hline + 31 & 61 & 81 & 112 & 33 & 27 & 53603 & 63641 & 65 & 62 \\ + \hline + 31 & 71 & 70 & 95 & 38 & 32 & 53603 & 73874 & 65 & 63 \\ + 31 & 81 & 55 & 83 & 36 & 28 & 62819 & 76508 & 58 & 53 \\ + 31 & 91 & 30 & 52 & 27 & 15 & 34142 & 57163 & 38 & 28 +\end{tabular} +} +%\end{adjustbox} +\caption{Statistics on the effect of different $k$ choices in error correction and graph building on the quality of bubble chains detected.} +\label{tab:statistics} +\end{table} + +\subsection{Statistics} +The importance of tip clipping and removal can be demonstrated with the number of nodes and sequences covered by nodes before and after removing the tips. For the HG00733 sample, the De Bruijn graph was built using the short reads and with the parameters mentioned previously (\texttt{Lighter} $k = 23$, $k$-mer size $=$ 61). Looking at table \ref{tab:percentages} we notice the following important information: +\begin{itemize} +\item The raw graph has about 31 million nodes and when the sequences added up for each node after removing the overlap it is about 3 billion base pairs which is close to the size of the human genome. +\item By taking only the biggest connected component in the graph, we lose about 10\% both node-wise and sequence-wise. However, the small unconnected components represent erroneous $k$-mers probably and it is better to keep the biggest component for any further analysis. +\item After removing the tips, some unipaths might emerge that need to be compacted, looking back at figure \ref{fig:untipping} for example, we see that there is a bubble with two branches, one branch has 4 nodes and 3 tips, when these tips are removed we get a unipath of 4 nodes that need to be compacted. We notice that after untipping and compacting we now only have about 60\% of the original number of nodes but kept about 85\% of the sequences, indicating that there is a large number of tips with very short sequences that need to be removed. +\end{itemize} + +\begin{table}[htbp] +\centering +{\small +\begin{tabular}{|l|c|c|c|c|} +\hline +\textbf{} & \textbf{Nodes} & \textbf{Sequence} & \multicolumn{2}{c|}{\textbf{Percentage of Raw}} \\ \hline +\textbf{Raw Graph} & 31,337,981 & 3,026,036,607 & 100\% & 100\% \\ \hline +\textbf{Biggest Component} & 28,222,365 & 2,697,634,238 & 90.05\% & 89.14\% \\ \hline +\textbf{Untipped and Compacted} & 18,977,487 & 2,596,708,278 & 60.55\% & 85.81\% \\ \hline +\end{tabular}} +\caption{Filtering and untipping effect on the graph nodes number and sequence content.} +\label{tab:percentages} +\end{table} + +Table \ref{tab:running_alg_stats} contains statistics about running the pipeline, this was only ran on one core and no multithreading, it used about 8.9 Gigabytes of memory but was relatively fast, detecting bubble chains and superbubbles did not take more than 140 seconds once the graph is loaded to memory. Also, we can notice from the table that the number of bubble chains drops after using Superbubbls to merge chains together as explained in section \ref{merging_chains}, which is expected as some chains merge so the total number of chains drops but we get longer chains. + +\begin{table}[htbp] +\centering +{\small +\begin{tabular}{|l|l|} +\hline +\textbf{} & \textbf{HG00733 sample graph} \\ \hline +\textbf{Superbubble Detection Time} & 94.13 seconds \\ \hline +\textbf{Bubble Chains Detection time} & 34 seconds \\ \hline +\textbf{Total Memory Used} & 8.9 gigabyte \\ \hline +\textbf{Number of Superbubbles} & 46,307 \\ \hline +\textbf{Number of Bubble Chains} & 489,831 \\ \hline +\textbf{Number of Bubbles} & 1,556,852 \\ \hline +\textbf{Number of Bubble Chains after merging} & 475,071 \\ \hline +\end{tabular}} +\caption{Statistics on running the Bubble Chains and Superbubbles detection algorithm on the graph built using the short reads from the HG00733 sample.} +\label{tab:running_alg_stats} +\end{table} +%\renewcommand{\arraystretch}{2} + + + +\subsection{Plots} +The following histograms were made on the graph produced from short reads of the HG00733 sample: + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 1 +\begin{itemize} +\item Figure \ref{fig:nodes_len_dist} plots the distribution of nodes size (i.e. contigs size) in the graph. As expected, we see that the shorter the node is, the higher the frequency. Due to the complicated nature of the human genome graph, there are not many unipaths that can be compacted to form longer contigs. +\end{itemize} + +\begin{figure}[ht] +\small +\center +\includegraphics[scale=0.9]{nodes_len_dist.png} +\caption{Distribution of nodes length, i.e. contigs length distribution in the graph.} +\label{fig:nodes_len_dist} +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 2 +\begin{itemize} +\item Figure \ref{fig:bchain_len_dist} plots the distribution of the length of chains bubble wise, we can see that the longest chain is about 110 bubbles but only one chain with that length, and the majority of bubble chains have up to 20 bubbles. +\end{itemize} + +\begin{figure}[ht] +\small +\center +\includegraphics[scale=0.9]{bchain_len_dist.png} +\caption{Distribution of chain length bubble-wise.} +\label{fig:bchain_len_dist} +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 3 +\begin{itemize} +\item Figure \ref{fig:chain_seq_len_dist} plots the distribution of the length of chains bubble sequence wise, similar to the previous plots, smaller chains have high frequency compared to longer bubbles. +\end{itemize} + +\begin{figure}[ht] +\small +\center +\includegraphics[scale=0.9]{chain_seq_len_dist.png} +\caption{Distribution of chains sequence-wise.} +\label{fig:chain_seq_len_dist} +\end{figure} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 4 +%\begin{itemize} +%\item Figure \ref{fig:edit_dist_distribution} +%\end{itemize} +% +%\begin{figure}[ht] +%\small +%\center +%\includegraphics[scale=0.9]{edit_dist_distribution.png} +%\caption{igv stuff} +%\label{fig:edit_dist_distribution} +%\end{figure} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 5 +\begin{itemize} +\item Figure \ref{fig:hamming_dist_distribution} shows the distribution of the hamming distance between the two branches of a bubble, as mentioned in table \ref{tab:running_alg_stats}, we have around 1.5 million bubbles around 1.4 million of them have branches with the same size. Moreover, more than 90\% of them have a hamming distance not more than 10, and only few bubbles with higher hamming distance. This can happen either if there are several variants with very high proximity from each other or several errors near each other that can be covered by one read. However, as expected, most of the bubbles cover 1 variant (more than 1 million bubble of the 1.5 million bubbles detected). +\end{itemize} + +\begin{figure}[ht] +\small +\center +\includegraphics[scale=0.9]{hamming_dist_distribution.png} +\caption{Distribution of hamming distance between the branches of the bubbles that have the same size.} +\label{fig:hamming_dist_distribution} +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 6 +\begin{itemize} +\item Figure \ref{fig:sb_len_dist} shows the distribution of the size of the superbubbles detected. Again, most of the Superbubbles have relatively small size, and only very few Superbubbles have size over 100 nodes. This follows the results presented in \cite{onodera2013detecting}. +\end{itemize} + +\begin{figure}[ht] +\small +\center +\includegraphics[scale=0.9]{sb_len_dist.png} +\caption{Distribution of the size of Superbubbles detected.} +\label{fig:sb_len_dist} +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure 7 +\begin{itemize} +\item Figure \ref{fig:bubbles_and_seq} shows that there is a clear relationship between the size of the chain bubble-wise and its length sequence wise, the more bubbles the chain has the longer sequence it covers. That's why it is important to make the chains as long as possible, and try to merge any potential neighbouring chains. +\end{itemize} + +\begin{figure}[ht] +\small +\center +\includegraphics[scale=0.9]{bubbles_and_seq.png} +\caption{Comparing the distribution of length of chains bubble-wise and sequence-wise. The upper part is sequence-wise and the bottom part is bubble-wise. } +\label{fig:bubbles_and_seq} +\end{figure} + +\section{Long Reads Alignment} +Long reads for the HG00733 sample were used to align to the graph produced by the short reads, the alignment output was used to build the fragment matrices later.\\ +The results from \texttt{GraphAligner} tool were positive, it reported the following: +\begin{itemize} +\item About 99\% of the long reads had an alignment with the bubble chains, meaning that the bubble chains that covered around 66\% of the sequences of the graph, attracted almost all the long reads. +\item About 68\% of the sequences in the reads were aligned, meaning that some reads were only partially aligned. This can happen in situation like the branching presented in figure \ref{fig:branching_long_reads}, we can see that the middle section of the read does not have an alignment, or the long read can align to a a bubble chain in the middle with one or both the ends of the read not aligned. However, this can be useful, as long as the read have covered some bubbles, it can be used in the fragment matrix and bipartitioned, meaning that we can use the bipartitioned reads to rebuilt the haplotypes. For example, again in figure \ref{fig:branching_long_reads}, we know that a read can come from one of the two haplotypes. Therefore, when bipartitioning the reads, the middle gap is covered now by the reads and we can construct more sequences than the ones present in the nodes. +\end{itemize} + + +\section{Phasing} +To validate the phasing, we use the sequences extracted from the bubble chains after solving the fragment matrix, where theoretically, each sequence will represent one haplotype. We align these sequences back to a reference genome to get an alignment file (BAM file), then using a variant calls file (VCF file) generated using the real data from the parents (sample HG00732 and sample HG00731), we can check if these sequences actually represent the true haplotypes. Using \texttt{WhatsHap} we provide the BAM file and the un-phased VCF file, and the output is a phased VCF file with haplotype information for each SNP (0 or 1), using the compare tool provided by \texttt{WhatsHap} we can compare this output VCF file with a truly phased VCF using the parents information. Unfortunately, the results were not good, with switch error rates of about 12\% and flip error rates of about 9\%.\\ +More than one reason can/should be investigated to hopefully understand why the switch and flip errors were bad: +\begin{itemize} +\item Due to the many repeats in the genome, ordering bubbles in a chain is not a straight forward task, and it is related to resolving repeats. Therefore, the presence of a repetitive bubble in a chain might have an overall effect on the chain and the phasing, where a repetitive bubble can be identified by looking at how many long reads aligned to its nodes compared to the other bubbles in the chain \cite{garg_graph}. +\item Long reads that branch out to more than one chain as mentioned before can be useful. However, again, due to repeats they might wrongly connect two chains that are not in reality close to each other and should not be phased together. +\item Wrong implementation, as it might happen, something might have gone wrong during the building of the fragment matrices and more testing needs to be done. +\end{itemize} + +Figure \ref{fig:igv} is a snapshot of the genome visualizer tool called IGV, we can load the alignment file (BAM file) to the tool, and the reference genome to visualize where our alignments are located on the genome, we see that extracting the two paths from a bubble chain resulted in a clear two sequences that aligned exactly to the same location in the genome (grey strips) with coloured strips indicating where the SNPs are, which is expected as this is what the bubble chain is representing. The blue bar in the bottom of the figure represent the switch error that happened in this block. +\begin{figure}[ht] +\small +\center +\includegraphics[width=1.1\textwidth]{igv.png} +\caption{Snapshot of IGV genome visualizer with sequences extracted from the bubble chains aligned (grey bands) and switch errors (blue bands).} +\label{fig:igv} +\end{figure} + +%chain_seq_len_dist.png +%edit_dist_distribution.png +%hamming_dist_distribution.png +%sb_len_dist.png +%bubbles_and_seq diff --git a/Figures/._UniLogo.pdf b/Figures/._UniLogo.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4958bc450ff7a27c779d41e6420ce237bbc1bb85 GIT binary patch literal 4096 zcmZQz6=P>$Vqox1Ojhs@R)|o50+1L3ClDJkFz{^v(m+1nBL)UWIUt(=a103vvYvJF zKST$^0ibdTz45G>Txq68O1v#mDg{6r_iFqZNd8r`f*ML}nfk6r(pOaWz zQd*pvl9E`GsvHmuQe$Vqox1Ojhs@R)|o50+1L3ClDJkFz{^v(m+1nBL)UWIUt(=a103vvYvJF zKST$^0ibdTz45G>Txq68O1v#mDg{6r_iFqZNd8r`f*ML}nfk6r(pOaWz 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