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Steffen Neumann authored on 30/03/2012 05:51:40
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+@Article{boecker08decomp,
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+author = {Sebastian B\"ocker and Zsuzsanna Lipt\'ak and Marcel Martin and Anton Pervukhin and Henner Sudek},
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+title = {{DECOMP}---from interpreting Mass Spectrometry peaks to solving the {Money} {Changing} {Problem}},
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+journal = {Bioinformatics},
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+year = {2008},
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+volume = {24},
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+number = {4},
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+pages = {591-593},
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+url = {http://bioinformatics.oxfordjournals.org/cgi/reprint/24/4/591?ijkey=1lM50Bkzz4SCLsa&keytype=ref},
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+doi = {10.1093/bioinformatics/btm631},
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+abstract = {We introduce DECOMP, a tool that computes the sum formula
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+                  of all molecules whose mass equals the input
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+                  mass. This problem arises frequently in biochemistry
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+                  and mass spectrometry (MS), when we know the
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+                  molecular mass of a protein, DNA, or metabolite
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+                  fragment but have no other information. A closely
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+                  related problem is known as the Money Changing
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+                  Problem (MCP), where all masses are positive
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+                  integers. Recently, efficient algorithms have been
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+                  developed for the MCP, which DECOMP applies to real
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+                  valued MS data. The excellent performance of this
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+                  method on proteomic and metabolomic MS data has
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+                  recently been demonstrated. DECOMP has an
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+                  easy-to-use graphical interface, which caters for
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+                  both types of users: those interested in solving MCP
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+                  instances and those submitting MS data.},
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+} 
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+
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+@Article{boecker09sirius,
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+author = {Sebastian B\"ocker and Matthias Letzel and Zsuzsanna Lipt{\'a}k and Anton Pervukhin},
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+title = {{SIRIUS}: Decomposing isotope patterns for metabolite identification},
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+journal = {Bioinformatics},
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+year = {2009},
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+volume = {25},
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+number = {2},
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+pages = {218--224},
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+url = {http://bioinformatics.oxfordjournals.org/cgi/content/full/25/2/218},
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+doi = {10.1093/bioinformatics/btn603},
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+abstract = {Motivation: High-resolution mass spectrometry (MS) is
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+                  among the most widely used technologies in
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+                  metabolomics. Metabolites participate in almost all
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+                  cellular processes, but most metabolites still
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+                  remain uncharacterized. Determination of the sum
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+                  formula is a crucial step in the identification of
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+                  an unknown metabolite, as it reduces its possible
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+                  structures to a hopefully manageable set. Results:
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+                  We present a method for determining the sum formula
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+                  of a metabolite solely from its mass and the natural
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+                  distribution of its isotopes. Our input is a
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+                  measured isotope pattern from a high resolution mass
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+                  spectrometer, and we want to find those molecules
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+                  that best match this pattern. Our method is
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+                  computationally efficient, and results on
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+                  experimental data are very promising: For orthogonal
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+                  time-of-flight mass spectrometry, we correctly
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+                  identify sum formulas for more than 90\% of the
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+                  molecules, ranging in mass up to 1000
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+                  Da. Availability: SIRIUS is available under the LGPL
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+                  license at
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+                  http://bio.informatik.uni-jena.de/sirius/. Contact:
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+                  anton.pervukhin@minet.uni-jena.de},
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+} 
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+
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+@Inproceedings{boecker06decomposing,
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+author = {Sebastian B\"ocker and Matthias Letzel and Zsuzsanna Lipt{\'a}k and Anton Pervukhin},
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+title = {Decomposing metabolomic isotope patterns},
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+booktitle = {Proc. of Workshop on Algorithms in Bioinformatics (WABI 2006)},
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+publisher = {Springer, Berlin},
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+year = {2006},
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+volume = {4175},
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+pages = {12--23},
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+series = {Lect. Notes Comput. Sci.},
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+url = {http://bio.informatik.uni-jena.de/bib2html/downloads/2006/BoeckerEtAl_DecomposingMetabolomicIsotopePatterns_WABI_2006.pdf},
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+abstract = {We present a method for determining the sum formula of
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+                  metabolites solely from their mass and isotope
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+                  pattern. Metabolites, such as sugars or lipids,
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+                  participate in almost all cellular processes, but
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+                  the majority still remains uncharacterized. Our
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+                  input is a measured isotope pattern from a high
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+                  resolution mass spectrometer, and we want to find
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+                  those molecules that best match this
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+                  pattern. Determination of the sum formula is a
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+                  crucial step in the identification of an unknown
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+                  metabolite, as it reduces its possible structures to
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+                  a hopefully manageable set. Our method is
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+                  computationally efficient, and first results on
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+                  experimental data indicate good identification rates
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+                  for chemical compounds up to 700 Dalton. Above 1000
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+                  Dalton, the number of molecules with a certain mass
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+                  increases rapidly. To efficiently analyze mass
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+                  spectra of such molecules, we define several
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+                  additive invariants extracted from the input and
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+                  then propose to solve a joint decomposition
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+                  problem.},
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+} 
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+
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+@Article{boecker07fast,
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+author = {Sebastian B\"ocker and Zsuzsanna Lipt{\'a}k},
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+title = {A fast and simple algorithm for the {M}oney {C}hanging {P}roblem},
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+journal = {Algorithmica},
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+year = {2007},
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+volume = {48},
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+number = {4},
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+pages = {413-432},
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+doi = {10.1007/s00453-007-0162-8},
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+abstract = {The Money Changing Problem (MCP) can be stated as follows:
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+                  Given $k$ positive integers $a_1< \ldots < a_k$ and
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+                  a query integer $M$, is there a linear combination
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+                  $\sum_i c_ia_i = M$ with non-negative integers
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+                  $c_i$, a \emph{decomposition} of $M$? If so, produce
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+                  one or all such decompositions. The largest integer
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+                  without such a decomposition is called the
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+                  \emph{Frobenius number} $g(a_1,\ldots,a_k)$. A data
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+                  structure called {\em residue table} of $a_1$ words
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+                  can be used to compute the Frobenius number in time
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+                  $O(a_1)$. We present an intriguingly simple
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+                  algorithm for computing the residue table which runs
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+                  in time $O(ka_1)$, with no additional memory
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+                  requirements, outperforming the best previously
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+                  known algorithm. Simulations show that it performs
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+                  well even on 'hard' instances from the
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+                  literature. In addition, we can employ the residue
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+                  table to answer MCP decision instances in constant
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+                  time, and a slight modification of size $O(a_1)$ to
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+                  compute one decomposition for a query $M$. Note that
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+                  since both, computing the Frobenius number and MCP
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+                  (decision) are NP-hard, one cannot expect to find an
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+                  algorithm that is polynomial in the size of the
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+                  input, i.e., in $k,\log a_k$, and $\log M$. We then
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+                  give an algorithm which, using a modification of the
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+                  residue table, also constructible in $O(ka_1)$ time,
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+                  computes all decompositions of a query integer
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+                  $M$. Its worst-case running time is $O(ka_1)$ for
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+                  each decomposition, thus the total runtime depends
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+                  only on the output size and is independent of the
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+                  size of query $M$ itself. We apply our latter
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+                  algorithm to interpreting mass spectrometry (MS)
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+                  peaks: Due to its high speed and accuracy, MS is now
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+                  the method of choice in protein
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+                  identification. Interpreting individual peaks is one
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+                  of the recurring subproblems in analyzing MS data;
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+                  the task is to identify sample molecules whose mass
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+                  the peak possibly represents. This can be stated as
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+                  an MCP instance, with the masses of the individual
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+                  amino acids as the $k$ integers $a_1,\ldots,
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+                  a_k$. Our simulations show that our algorithm is
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+                  fast on real data and is well suited for generating
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+                  candidates for peak interpretation.},
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+} 
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