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56-455: The algorithm was first proposed by Temple F. Smith and Michael S. Waterman in 1981. Like the Needleman–Wunsch algorithm , of which it is a variation, Smith–Waterman is a dynamic programming algorithm. As such, it has the desirable property that it is guaranteed to find the optimal local alignment with respect to the scoring system being used (which includes the substitution matrix and

112-632: A n {\displaystyle A=a_{1}a_{2}...a_{n}} and B = b 1 b 2 . . . b m {\displaystyle B=b_{1}b_{2}...b_{m}} be the sequences to be aligned, where n {\displaystyle n} and m {\displaystyle m} are the lengths of A {\displaystyle A} and B {\displaystyle B} respectively. Smith–Waterman algorithm aligns two sequences by matches/mismatches (also known as substitutions), insertions, and deletions. Both insertions and deletions are

168-760: A publicly available white paper . Accelerated version of the Smith–Waterman algorithm, on Intel and Advanced Micro Devices (AMD) based Linux servers, is supported by the GenCore 6 package, offered by Biocceleration . Performance benchmarks of this software package show up to 10 fold speed acceleration relative to standard software implementation on the same processor. Currently the only company in bioinformatics to offer both SSE and FPGA solutions accelerating Smith–Waterman, CLC bio has achieved speed-ups of more than 110 over standard software implementations with CLC Bioinformatics Cube . The fastest implementation of

224-525: A 2x speed-up over software implementations. A similar method has already been implemented in the Biofacet software since 1997, with the same speed-up factor. Several GPU implementations of the algorithm in NVIDIA 's CUDA C platform are also available. When compared to the best known CPU implementation (using SIMD instructions on the x86 architecture), by Farrar, the performance tests of this solution using

280-664: A PhD in 1969 in the Physics Department, University of Colorado at Boulder . After his PhD, Smith did postdoctoral research from March 1969 to August 1971 in the Department of Biophysics and Genetics, University of Colorado Medical School, Boulder. His research is centered on the application of various computer science and mathematical methods for the discovery of the syntactic and semantic patterns in nucleic acid and amino acid sequences. In recent years this has focus on molecular evolution of protein families. such as

336-683: A different path if this element is traced back. In case of multiple highest scores, traceback should be done starting with each highest score. The traceback process is shown below on the right. The best local alignment is generated in the reverse direction. The alignment result is: An implementation of the Smith–Waterman Algorithm, SSEARCH, is available in the FASTA sequence analysis package from UVA FASTA Downloads . This implementation includes Altivec accelerated code for PowerPC G4 and G5 processors that speeds up comparisons 10–20-fold, using

392-409: A different recursive divide-and-conquer strategy than the one used by Hirschberg. The resulting algorithm runs faster than Myers and Miller's algorithm in practice due to its superior cache performance. Take the alignment of sequences TACGGGCCCGCTAC and TAGCCCTATCGGTCA as an example. When linear gap penalty function is used, the result is (Alignments performed by EMBOSS Water. Substitution matrix

448-564: A genome project. Genome assembly refers to the process of taking a large number of short DNA sequences and reassembling them to create a representation of the original chromosomes from which the DNA originated. In a shotgun sequencing project, all the DNA from a source (usually a single organism , anything from a bacterium to a mammal ) is first fractured into millions of small pieces. These pieces are then "read" by automated sequencing machines. A genome assembly algorithm works by taking all

504-423: A genome, and what those genes do. There may also be related projects to sequence ESTs or mRNAs to help find out where the genes actually are. Historically, when sequencing eukaryotic genomes (such as the worm Caenorhabditis elegans ) it was common to first map the genome to provide a series of landmarks across the genome. Rather than sequence a chromosome in one go, it would be sequenced piece by piece (with

560-594: A modification of the Wozniak, 1997 approach, and an SSE2 vectorization developed by Farrar making optimal protein sequence database searches quite practical. A library, SSW, extends Farrar's implementation to return alignment information in addition to the optimal Smith–Waterman score. Cray demonstrated acceleration of the Smith–Waterman algorithm using a reconfigurable computing platform based on FPGA chips, with results showing up to 28x speed-up over standard microprocessor-based solutions. Another FPGA-based version of

616-514: A new genome sequence has steadily fallen (in terms of cost per base pair ) and newer technology has also meant that genomes can be sequenced far more quickly. When research agencies decide what new genomes to sequence, the emphasis has been on species which are either high importance as model organism or have a relevance to human health (e.g. pathogenic bacteria or vectors of disease such as mosquitos ) or species which have commercial importance (e.g. livestock and crop plants). Secondary emphasis

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672-586: A scoring matrix, and a traceback process. Three main differences are: One of the most important distinctions is that no negative score is assigned in the scoring system of the Smith–Waterman algorithm, which enables local alignment. When any element has a score lower than zero, it means that the sequences up to this position have no similarities; this element will then be set to zero to eliminate influence from previous alignment. In this way, calculation can continue to find alignment in any position afterwards. The initial scoring matrix of Smith–Waterman algorithm enables

728-681: A single NVidia GeForce 8800 GTX card show a slight increase in performance for smaller sequences, but a slight decrease in performance for larger ones. However, the same tests running on dual NVidia GeForce 8800 GTX cards are almost twice as fast as the Farrar implementation for all sequence sizes tested. A newer GPU CUDA implementation of SW is now available that is faster than previous versions and also removes limitations on query lengths. See CUDASW++ . Eleven different SW implementations on CUDA have been reported, three of which report speedups of 30X. Finally, other GPU-accelerated implementations of

784-657: A single long gap. Therefore, connected gaps forming a long gap usually is more favored than multiple scattered, short gaps. In order to take this difference into consideration, the concepts of gap opening and gap extension have been added to the scoring system. The gap opening score is usually higher than the gap extension score. For instance, the default parameters in EMBOSS Water are: gap opening = 10, gap extension = 0.5. Here we discuss two common strategies for gap penalty. See Gap penalty for more strategies. Let W k {\displaystyle W_{k}} be

840-523: A very efficient implementation was presented. Using one PCIe FPGA card equipped with a Xilinx Virtex-7 2000T FPGA, the performance per Watt level was better than CPU/GPU by 12-21x. Lawrence Livermore National Laboratory and the United States (US) Department of Energy's Joint Genome Institute implemented an accelerated version of Smith–Waterman local sequence alignment searches using graphics processing units (GPUs) with preliminary results showing

896-445: Is DNAfull (similarity score: +5 for matching characters otherwise -4). Gap opening and extension are 0.0 and 1.0 respectively): When affine gap penalty is used, the result is (Gap opening and extension are 5.0 and 1.0 respectively): This example shows that an affine gap penalty can help avoid scattered small gaps. The function of the scoring matrix is to conduct one-to-one comparisons between all components in two sequences and record

952-545: Is a negative expectation score. The expectation score is defined as the average score that the scoring system ( substitution matrix and gap penalties ) would yield for a random sequence. Another motivation for using local alignments is that there is a reliable statistical model (developed by Karlin and Altschul) for optimal local alignments. The alignment of unrelated sequences tends to produce optimal local alignment scores which follow an extreme value distribution. This property allows programs to produce an expectation value for

1008-411: Is being scored, only the gap penalties from the elements that are directly adjacent to this element need to be considered. An affine gap penalty considers gap opening and extension separately: W k = u k + v ( u > 0 , v > 0 ) {\displaystyle W_{k}=uk+v\quad (u>0,v>0)} , where v {\displaystyle v}

1064-443: Is fairly demanding of time: To align two sequences of lengths m {\displaystyle m} and n {\displaystyle n} , O ( m 2 n + n 2 m ) {\displaystyle O(m^{2}n+n^{2}m)} time is required. Gotoh and Altschul optimized the algorithm to O ( m n ) {\displaystyle O(mn)} steps. The space complexity

1120-563: Is over six times more rapid than software based on Farrar's 'striped' approach. It is faster than BLAST when using the BLOSUM50 matrix. Temple F. Smith Temple Ferris Smith (born March 7, 1939) is an emeritus professor in biomedical engineering who helped to develop the Smith-Waterman algorithm with Michael Waterman in 1981. The Smith-Waterman algorithm serves as the basis for multi sequence comparisons, identifying

1176-503: Is quite demanding of time. Gotoh optimized the steps for an affine gap penalty to O ( m n ) {\displaystyle O(mn)} , but the optimized algorithm only attempts to find one optimal alignment, and the optimal alignment is not guaranteed to be found. Altschul modified Gotoh's algorithm to find all optimal alignments while maintaining the computational complexity. Later, Myers and Miller pointed out that Gotoh and Altschul's algorithm can be further modified based on

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1232-621: Is replaced in favor of computationally more efficient alternatives such as (Gotoh, 1982), ( Altschul and Erickson, 1986), and (Myers and Miller, 1988). In 1970, Saul B. Needleman and Christian D. Wunsch proposed a heuristic homology algorithm for sequence alignment, also referred to as the Needleman–Wunsch algorithm. It is a global alignment algorithm that requires O ( m n ) {\displaystyle O(mn)} calculation steps ( m {\displaystyle m} and n {\displaystyle n} are

1288-442: Is the difficulty of obtaining correct alignments in regions of low similarity between distantly related biological sequences, because mutations have added too much 'noise' over evolutionary time to allow for a meaningful comparison of those regions. Local alignment avoids such regions altogether and focuses on those with a positive score, i.e. those with an evolutionarily conserved signal of similarity. A prerequisite for local alignment

1344-418: Is the gap opening penalty, and u {\displaystyle u} is the gap extension penalty. For example, the penalty for a gap of length 2 is 2 u + v {\displaystyle 2u+v} . An arbitrary gap penalty was used in the original Smith–Waterman algorithm paper. It uses O ( m 2 n ) {\displaystyle O(m^{2}n)} steps, therefore

1400-467: Is the process of identifying attaching biological information to sequences , and particularly in identifying the locations of genes and determining what those genes do. When sequencing a genome, there are usually regions that are difficult to sequence (often regions with highly repetitive DNA ). Thus, 'completed' genome sequences are rarely ever complete, and terms such as 'working draft' or 'essentially complete' have been used to more accurately describe

1456-436: Is usually more complicated than that of the bases. See PAM , BLOSUM . Gap penalty designates scores for insertion or deletion. A simple gap penalty strategy is to use fixed score for each gap. In biology, however, the score needs to be counted differently for practical reasons. On one hand, partial similarity between two sequences is a common phenomenon; on the other hand, a single gene mutation event can result in insertion of

1512-730: The Core microarchitecture the SSE2 implementation achieves a 20-fold increase. Farrar's SSE2 implementation is available as the SSEARCH program in the FASTA sequence comparison package. The SSEARCH is included in the European Bioinformatics Institute 's suite of similarity searching programs . Danish bioinformatics company CLC bio has achieved speed-ups of close to 200 over standard software implementations with SSE2 on an Intel 2.17 GHz Core 2 Duo CPU, according to

1568-408: The gap-scoring scheme). The main difference to the Needleman–Wunsch algorithm is that negative scoring matrix cells are set to zero. Traceback procedure starts at the highest scoring matrix cell and proceeds until a cell with score zero is encountered, yielding the highest scoring local alignment. Because of its cubic time complexity, it often cannot be practically applied to large-scale problems and

1624-598: The Smith-Waterman can be found in NVIDIA Parabricks , NVIDIA's software suite for genome analysis. In 2000, a fast implementation of the Smith–Waterman algorithm using the single instruction, multiple data ( SIMD ) technology available in Intel Pentium MMX processors and similar technology was described in a publication by Rognes and Seeberg. In contrast to the Wozniak (1997) approach,

1680-454: The Smith–Waterman algorithm shows FPGA (Virtex-4) speedups up to 100x over a 2.2 GHz Opteron processor. The TimeLogic DeCypher and CodeQuest systems also accelerate Smith–Waterman and Framesearch using PCIe FPGA cards. A 2011 Master's thesis includes an analysis of FPGA-based Smith–Waterman acceleration. In a 2016 publication OpenCL code compiled with Xilinx SDAccel accelerates genome sequencing, beats CPU/GPU performance/W by 12-21x ,

1736-716: The WD-repeat beta propellers, translation associated GTPase, and the ribosomal proteins. He is known for the creation of the Smith-Waterman algorithm . Smith has held the following appointments: Smith was awarded the ISCB Senior Scientist Award and elected ISCB Fellow in 2009 by the International Society for Computational Biology . Im 2002, he was inducted into American Institute for Medical and Biological Engineering (AIMBE) “for extraordinary contributions in defining and advancing

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1792-562: The algorithm on CPUs with SSSE3 can be found the SWIPE software (Rognes, 2011), which is available under the GNU Affero General Public License . In parallel, this software compares residues from sixteen different database sequences to one query residue. Using a 375 residue query sequence a speed of 106 billion cell updates per second (GCUPS) was achieved on a dual Intel Xeon X5650 six-core processor system, which

1848-466: The alignment of any segment of one sequence to an arbitrary position in the other sequence. In Needleman–Wunsch algorithm, however, end gap penalty also needs to be considered in order to align the full sequences. Each base substitution or amino acid substitution is assigned a score. In general, matches are assigned positive scores, and mismatches are assigned relatively lower scores. Take DNA sequence as an example. If matches get +1, mismatches get -1, then

1904-549: The cache performance of the algorithm while keeping the space usage linear in the total length of the input sequences. In recent years, genome projects conducted on a variety of organisms generated massive amounts of sequence data for genes and proteins, which requires computational analysis. Sequence alignment shows the relations between genes or between proteins, leading to a better understanding of their homology and functionality. Sequence alignment can also reveal conserved domains and motifs . One motivation for local alignment

1960-406: The collective DNA sequences of each chromosome in the organism. For a bacterium containing a single chromosome, a genome project will aim to map the sequence of that chromosome. For the human species, whose genome includes 22 pairs of autosomes and 2 sex chromosomes, a complete genome sequence will involve 46 separate chromosome sequences. The Human Genome Project is a well known example of

2016-497: The field of bioinformatics, with emphasis on novel engineering methods to predict protein structure and function”. Genome project Genome projects are scientific endeavours that ultimately aim to determine the complete genome sequence of an organism (be it an animal , a plant , a fungus , a bacterium , an archaean , a protist or a virus ) and to annotate protein-coding genes and other important genome-encoded features. The genome sequence of an organism includes

2072-757: The gap length. When linear gap penalty is used, the Smith–Waterman algorithm can be simplified to: H i j = max { H i − 1 , j − 1 + s ( a i , b j ) , H i − 1 , j − W 1 , H i , j − 1 − W 1 , 0 {\displaystyle H_{ij}=\max {\begin{cases}H_{i-1,j-1}+s(a_{i},b_{j}),\\H_{i-1,j}-W_{1},\\H_{i,j-1}-W_{1},\\0\end{cases}}} The simplified algorithm uses O ( m n ) {\displaystyle O(mn)} steps. When an element

2128-414: The gap penalty function for a gap of length k {\displaystyle k} : A linear gap penalty has the same scores for opening and extending a gap: W k = k W 1 {\displaystyle W_{k}=kW_{1}} , where W 1 {\displaystyle W_{1}} is the cost of a single gap. The gap penalty is directly proportional to

2184-461: The goal of sequencing a genome is to obtain information about the complete set of genes in that particular genome sequence. The proportion of a genome that encodes for genes may be very small (particularly in eukaryotes such as humans, where coding DNA may only account for a few percent of the entire sequence). However, it is not always possible (or desirable) to only sequence the coding regions separately. Also, as scientists understand more about

2240-461: The large genomes of plants and animals . The resulting (draft) genome sequence is produced by combining the information sequenced contigs and then employing linking information to create scaffolds. Scaffolds are positioned along the physical map of the chromosomes creating a "golden path". Originally, most large-scale DNA sequencing centers developed their own software for assembling the sequences that they produced. However, this has changed as

2296-416: The length of the other sequence plus 1. The additional first row and first column serve the purpose of aligning one sequence to any positions in the other sequence. Both the first line and the first column are set to 0 so that end gap is not penalized. The initial scoring matrix is: Take the alignment of DNA sequences TGTTACGG and GGTTGACTA as an example. Use the following scheme: Initialize and fill

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2352-558: The lengths of the two sequences being aligned). It uses the iterative calculation of a matrix for the purpose of showing global alignment. In the following decade, Sankoff, Reichert, Beyer and others formulated alternative heuristic algorithms for analyzing gene sequences. Sellers introduced a system for measuring sequence distances. In 1976, Waterman et al. added the concept of gaps into the original measurement system. In 1981, Smith and Waterman published their Smith–Waterman algorithm for calculating local alignment. The Smith–Waterman algorithm

2408-414: The method that was published by Hirschberg in 1975, and applied this method. Myers and Miller's algorithm can align two sequences using O ( n ) {\displaystyle O(n)} space, with n {\displaystyle n} being the length of the shorter sequence. Chowdhury, Le, and Ramachandran later showed how to run Gotoh's algorithm cache-efficiently in linear space using

2464-473: The new implementation was based on vectors parallel with the query sequence, not diagonal vectors. The company Sencel Bioinformatics has applied for a patent covering this approach. Sencel is developing the software further and provides executables for academic use free of charge. A SSE2 vectorization of the algorithm (Farrar, 2007) is now available providing an 8-16-fold speedup on Intel/AMD processors with SSE2 extensions. When running on Intel processor using

2520-399: The operations that introduce gaps, which are represented by dashes. The Smith–Waterman algorithm has several steps: The Smith–Waterman algorithm finds the segments in two sequences that have similarities while the Needleman–Wunsch algorithm aligns two complete sequences. Therefore, they serve different purposes. Both algorithms use the concepts of a substitution matrix, a gap penalty function,

2576-428: The optimal alignment results. The scoring process reflects the concept of dynamic programming. The final optimal alignment is found by iteratively expanding the growing optimal alignment. In other words, the current optimal alignment is generated by deciding which path (match/mismatch or inserting gap) gives the highest score from the previous optimal alignment. The size of the matrix is the length of one sequence plus 1 by

2632-416: The optimal local alignment of two sequences, which is a measure of how often two unrelated sequences would produce an optimal local alignment whose score is greater than or equal to the observed score. Very low expectation values indicate that the two sequences in question might be homologous , meaning they might share a common ancestor. Let A = a 1 a 2 . . .

2688-457: The pieces and aligning them to one another, and detecting all places where two of the short sequences, or reads , overlap. These overlapping reads can be merged, and the process continues. Genome assembly is a very difficult computational problem, made more difficult because many genomes contain large numbers of identical sequences, known as repeats . These repeats can be thousands of nucleotides long, and occur different locations, especially in

2744-464: The prior knowledge of approximately where that piece is located on the larger chromosome). Changes in technology and in particular improvements to the processing power of computers, means that genomes can now be ' shotgun sequenced ' in one go (there are caveats to this approach though when compared to the traditional approach). Improvements in DNA sequencing technology have meant that the cost of sequencing

2800-405: The role of this noncoding DNA (often referred to as junk DNA ), it will become more important to have a complete genome sequence as a background to understanding the genetics and biology of any given organism. In many ways genome projects do not confine themselves to only determining a DNA sequence of an organism. Such projects may also include gene prediction to find out where the genes are in

2856-414: The scoring matrix, shown as below. This figure shows the scoring process of the first three elements. The yellow color indicates the bases that are being considered. The red color indicates the highest possible score for the cell being scored. The finished scoring matrix is shown below on the left. The blue color shows the highest score. An element can receive score from more than one element, each will form

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2912-514: The segment with the maximum local sequence similarity, see sequence alignment . This algorithm is used for identifying similar DNA , RNA and protein segments. He was director of the BioMolecular Engineering Research Center at Boston University for twenty years and is now professor emeritus . Smith obtained his bachelor's degree in 1963 from the Physics Department, Purdue University , followed by

2968-461: The software has grown more complex and as the number of sequencing centers has increased. An example of such assembler Short Oligonucleotide Analysis Package developed by BGI for de novo assembly of human-sized genomes, alignment, SNP detection, resequencing, indel finding, and structural variation analysis. Since the 1980s, molecular biology and bioinformatics have created the need for DNA annotation . DNA annotation or genome annotation

3024-418: The status of such genome projects. Even when every base pair of a genome sequence has been determined, there are still likely to be errors present because DNA sequencing is not a completely accurate process. It could also be argued that a complete genome project should include the sequences of mitochondria and (for plants) chloroplasts as these organelles have their own genomes. It is often reported that

3080-556: The substitution matrix is: This substitution matrix can be described as: s ( a i , b j ) = { + 1 , a i = b j − 1 , a i ≠ b j {\displaystyle s(a_{i},b_{j})={\begin{cases}+1,\quad a_{i}=b_{j}\\-1,\quad a_{i}\neq b_{j}\end{cases}}} Different base substitutions or amino acid substitutions can have different scores. The substitution matrix of amino acids

3136-404: Was optimized by Myers and Miller from O ( m n ) {\displaystyle O(mn)} to O ( n ) {\displaystyle O(n)} (linear), where n {\displaystyle n} is the length of the shorter sequence, for the case where only one of the many possible optimal alignments is desired. Chowdhury, Le, and Ramachandran later optimized

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