Patent Publication Number: US-7917302-B2

Title: Determination of optimal local sequence alignment similarity score

Description:
FIELD OF INVENTION 
     The present invention relates to the comparison of biological sequences and, more specifically, the invention relates to a method, a computer readable device and an electronic device for determination of optimal local sequence similarity score in accordance with the claims. 
     BACKGROUND OF INVENTION 
     The rapidly increasing amounts of genetic sequence information available represent a as constant challenge to developers of hardware and software database searching and handling. The size of the GenBank/EMBL/DDBJ nucleotide database is now doubling at least every 15 months (Benson et al. 2000). The rapid expansion of the genetic sequence information is probably exceeding the growth in computing power available at a constant cost, in spite of the fact that computing resources also have been increasing exponentially for many years. If this trend continues, increasingly longer time or increasingly more expensive computers will be needed to search the entire database. 
     Searching databases for sequences similar to a given sequence is one of the most fundamental and important tools for predicting structural and functional properties of uncharacterised proteins. The availability of good tools for performing these searches is hence important. When looking for sequences in a database similar to a given query sequence, the search programs compute an alignment score for every sequence in the database. This score represents the degree of similarity between the query and database sequence. The score is calculated from the alignment of the two sequences, and is based on a substitution score matrix and a gap penalty function. A dynamic programming algorithm for computing the optimal local alignment score was first described by Smith and Waterman (1981), improved by Gotoh (1982) for linear gap penalty functions, and optimised by Green (1993). 
     Database searches using the optimal algorithm are unfortunately quite slow on ordinary computers, so many heuristic alternatives have been developed, such as FASTA (Pearson and Lipman, 1988) and BLAST (Altschul et al., 1990; Altschul et al., 1997). These methods have reduced the running time by a factor of up to 40 compared to the best-known Smith-Waterman implementation on non-parallel general-purpose computers, however, at the expense of sensitivity. Because of the loss of sensitivity, some distantly related sequences might not be detected in a search using the heuristic algorithms. 
     Due to the demand for both fast and sensitive searches, much effort has been made to produce fast implementations of the Smith-Waterman method. Several special-purpose hardware solutions have been developed with parallel processing capabilities (Hughey, 1996), such as Paracel&#39;s GeneMatcher, Compugen&#39;s Bioccelerator and TimeLogic&#39;s DeCypher. These machines are able to process more than 2 000 million matrix cells per second, and can be expanded to reach much higher speeds. However, such machines are very expensive and cannot readily be exploited by ordinary users. Some hardware implementations of the Smith-Waterman algorithm are described in patent publications, for instance U.S. Pat. Nos. 5,553,272, 5,632,041, 5,706,498, 5,964,860 and 6,112,288. 
     A more general form of parallel processing capability is available using Single-Instruction Multiple-Data (SIMD) technology. A SIMD computer is able to perform the same operation (logical, arithmetic or other) on several independent data sources in parallel. It is possible to exploit this by dividing wide registers into smaller units in the form of micro parallelism (also known as SIMD within a register—SWAR). However, modern microprocessors have added special registers and instructions to make the SIMD technology easier to use. With the introduction of the Pentium MMX (MultiMedia eXtensions) microprocessor in 1997, Intel made computing with SIMD technology available in a general-purpose microprocessor in the most widely used computer architecture—the industry standard PC. The technology is also available in the Pentium II and has been extended in the Pentium III under the name of SSE (Streaming SIMD Extensions) (Intel, 1999). Further extension of this technology has been announced for the Pentium 4 processor (also known as Willamette) under the name SSE2 (Streaming SIMD extensions 2) (Intel 2000). The MMX/SSE/SSE2 instruction sets include arithmetic (add, subtract, multiply, min, max, average, compare), logical (and, or, xor, not) and other instructions (shift, pack, unpack) that may operate on integer or floating-point numbers. This technology is primarily designed for speeding up digital signal processing applications like sound, images and video, but seems suitable also for genetic sequence comparisons. Several other microprocessors with SIMD technology are or will be made available in the near future, as shown in table 1 (Dubey, 1998). 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Examples of microprocessors with SIMD technology 
               
            
           
           
               
               
               
            
               
                 Manufacturer 
                 Microprocessor 
                 Name of technology 
               
               
                   
               
               
                 AMD 
                 K6/K6-2/K6-III 
                 MMX/3DNow! 
               
               
                   
                 Athlon/Duron 
                 Extended MMX/3DNow! 
               
               
                 Compaq 
                 Alpha 
                 MVI (Motion Video Instruction) 
               
               
                 (Digital) 
               
               
                 Hewlett 
                 PA-RISC 
                 MAX(−2) (Multimedia Acceleration 
               
               
                 Packard (HP) 
                   
                 eXtensions) 
               
               
                 HP/Intel 
                 Itanium 
                 SSE (Streaming SIMD Extensions)? 
               
               
                   
                 (Merced) 
               
               
                 Intel 
                 Pentium 
                 MMX (MultiMedia eXtensions) 
               
               
                   
                 MMX/II 
               
               
                   
                 Pentium III 
                 SSE (Streaming SIMD Extensions) 
               
               
                   
                 Pentium 4 
                 SSE2 (Streaming SIMD Extensions 2) 
               
               
                 Motorola 
                 PowerPC G4 
                 Velocity Engine (AltiVec) 
               
               
                 SGI 
                 MIPS 
                 MDMX (MIPS Digital Media 
               
               
                   
                   
                 eXtensions) 
               
               
                 Sun 
                 SPARC 
                 VIS (Visual Instruction Set) 
               
               
                   
               
            
           
         
       
     
     Several investigators have used SIMD technology to speed up the Smith-Waterman algorithm, but the increase in speed relative to the best non-parallel implementations have been limited. 
     The general dynamic programming algorithm for optimal local alignment score computation was initially described by Smith and Waterman (1981). 
     Gotoh (1982) described an implementation of this algorithm with affined gap penalties, where the gap penalty for a gap of size k is equal to q+rk, where q is the gap open penalty and r is the gap extension penalty. Under these restrictions the running time of the algorithm was reduced to be proportional to the product of the lengths of the two sequences. 
     Green (1993) wrote the SWAT program and applied some optimisations to the algorithm of Gotoh to achieve a speed-up of a factor of about two relative to a straightforward implementation. The SWAT-optimisations have also been incorporated into the SSEARCH program of Pearson (1991). 
     The Smith-Waterman algorithm has been implemented for several different SIMD computers. Sturrock and Collins (1993) implemented the Smith-Waterman algorithm for the MasPar family of parallel computers, in a program called MPsrch. This solution achieved a speed of up to 130 million matrix cells per second on a MasPar MP-1 computer with 4096 CPUs and up to 1 500 million matrix cells per second on a MasPar MP-2 with 16384 CPUs. Brutlag et al. (1993) also implemented the Smith-Waterman algorithm on the MasPar computers in a program called BLAZE. 
     Alpern et al. (1995) presented several ways to speed up the Smith-Waterman algorithm including a parallel implementation utilising micro parallelism by dividing the 64-bit wide Z-buffer registers of the Intel Paragon i860 processors into 4 parts. With this approach they could compare the query sequence with four different database sequences simultaneously. They achieved more than a fivefold speedup over a conventional implementation. 
     Wozniak (1997) presented a way to implement the Smith-Waterman algorithm using the VIS (Visual Instruction Set) technology of Sun UltraSPARC microprocessors. This implementation reached a speed of over 18 million matrix cells per second on a 167 MHz UltraSPARC microprocessor. According to Wozniak (1997), this represents a speedup of a factor of about 2 relative to the same algorithm implemented with integer instructions on the same machine. 
     Taylor (1998 and 1999) applied the MMX technology to the Smith-Waterman algorithm and achieved a speed of 6.6 million cell updates per second on an Intel Pentium III 500 MHz microprocessor. 
     Sturrock and Collins (2000) have implemented the Smith-Waterman algorithm using SIMD on Alpha microprocessors. However no details of their method has been published. They have achieved a speed of about 53 million cell updates per second using affine gap penalties. It is unknown exactly what computer this system is running on. 
     Recently, Barton et al. (2000) employed MMX technology to speed up their SCANPS implementation of the Smith-Waterman algorithm. They claim a speed of 71 million cell updates per second on a Intel Pentium III 650 MHz microprocessor. Only a poster abstract without any details of their implementation is currently available. 
     DISCLOSURE OF THE INVENTION 
     It is described an efficient parallelisation related to a method for computing the optimal local sequence alignment score of two sequences. Increased speed of the overall computation is achieved by performing several operations in parallel. 
     The invention enables Smith-Waterman based searches to be performed at a much higher speed than previously possible on general-purpose computers. 
     Using the MMX and SSE technology in an Intel Pentium III 500 MHz microprocessor, a speed of about 200 million cell updates per second was achieved when comparing a protein with the sequences in a protein database. As far as known, this is so far the fastest implementation of the Smith-Waterman algorithm on a single-microprocessor general-purpose computer. Relative to the commonly used SSEARCH program, which is consider as a reference implementation, it represents a speedup of about eight. It is believed that an implementation of the present invention on the forthcoming Intel Pentium 4 processor running at 1.4 GHz will obtain a speed of more than 1000 million cell updates per second. These speeds approach or equal the speed of expensive dedicated hardware solutions for performing essentially the same calculations. 
     Using the present invention, high speed is achieved on commonly available and inexpensive hardware, thus significantly reducing the cost and/or computation time of performing sequence alignment and database searching using an optimal local alignment dynamic programming approach. 
     The present invention is based on the principle that all calculations are performed using vectors that are parallel to the query sequence (“query-based vectors”) (see  FIG. 2   b ). This is in contrast to the traditional approach in which the calculations are performed using vectors that are parallel to the minor diagonal in the matrix (“diagonal vectors”) (see  FIG. 2   a ). In both cases, the vectors contain two or more elements that represent different cells in the alignment matrix. The values in the elements of the vectors represent score values, e.g. the h-, e- or f-variables in the recurrence relations described later. 
     The advantage of the traditional approach is that the calculations of the individual elements of the vectors are completely independent (see  FIG. 3   a ). Hence the use of this approach may seem obvious. The traditional approach is described in detail by Hughey (1996), Wozniak (1997) and Taylor (1998, 1999), and seems to be almost universal to all parallel implementations of the Smith-Waterman alignment procedure that are known in detail. However, there are several disadvantages with this approach, most notably the complexity of forming the vector of substitution score values. This problem is especially noticeable at high degrees of parallelism. The query-based vector approach has not been described earlier, in spite of numerous attempts to parallelise the Smith-Waterman algorithm. It is believed that the present invention is sufficiently novel and different from the current “state of the art”. 
     The disadvantage of the query-based vector approach is the dependence between the individual vector elements in some of the calculations (see  FIG. 3   b ). However, by exploiting a vector generalisation of the principles used in the SWAT-optimisations, these dependencies will only affect a small fraction of the calculations, and hence not have a major impact on the performance. The advantage of the query-based approach is the greatly simplified loading of the vector of substitution score values from memory when using a query sequence profile (also known as a query-specific score matrix). 
     The present invention method uses a query profile, which is a matrix of scores for all combination of query positions and possible sequence symbols. The scores are arranged in memory in such a manner that a vector representing the scores for matching a single database sequence symbol with a consecutive range of query sequence symbols can easily be loaded from memory into the microprocessor using a single instruction. This is achieved by first storing the scores for matching the first possible database sequence symbol with each of the symbols of the query sequence, followed by the scores for matching the second possible database sequence symbol with each query position, and so on. 
     The scores in the query profile are all biased by a fixed amount (e.g. 4, in case of the BLOSUM62 matrix) so that all values become non-negative, and stored as an unsigned integer. This allows subsequent calculations to be performed using unsigned arithmetic. The constant bias is later subtracted using an unsigned integer subtraction operation. 
     Vector elements are represented by few bits (e.g. 8), and may thus represent only a narrow range of scores. When the total vector size is limited to a specific number of bits (e.g. 64), narrow vector elements allows the vector to be divided into more elements (e.g. 8) than if wider elements were used. This allows more concurrent calculations to take place, further increasing speed. 
     In order to make the narrow score range useful even in cases where the scores are larger than what can be represented by a vector element, we employ saturated arithmetic to detect overflow in the score calculations. If overflow is detected, the entire alignment score is subsequently recomputed using an implementation with a wider score range, e.g. 16 bits. Because such high scores are relatively rare, the performance impact is small. 
     Score computations are performed using unsigned values. Unsigned score values allows the widest possible score range. This reduces the number of recomputations necessary as described above. 
     The computations are performed using saturated unsigned arithmetic. This allows easy clipping of negative results of subtractions at zero, an operation that is frequently performed in the calculations. 
     The method, the computer readable device and the electronic device have their respective characteristic features as stated in the claims. 
    
    
     
       BRIEF DESCRIPTIONS OF DRAWINGS 
         FIG. 1  illustrates computational dependencies in the Smith-Waterman alignment matrix, the arrows indicate dependencies between matrix cells that are involved in the computations of the h-, e- and f-values in each cell of the alignment matrix. 
         FIG. 2  illustrates vector arrangements in SIMD implementations of the Smith-Waterman algorithm, each column represent one symbol of the database sequence, and each row represents on symbol of the query sequence, where
         a) represent traditional approach with vectors parallel to the minor diagonal in the matrix, and   b) represents the novel approach with vectors parallel to the query sequence.       

         FIG. 3  illustrates vector calculation dependencies, the arrows indicates dependencies between matrix cells that are involved in the computations of the h-, e- and f-values in the elements of the vector using (a) the traditional and (b) the novel approach. 
         FIG. 4   a  illustrates pseudo-code for the new approach, the pseudo-code being just a detailed example showing how our method may be implemented in a computer program. 
         FIG. 4   b  illustrates a flow diagram of the pseudo-code in  FIG. 4   a   
       
         
           
             
                 
               
                 
                   TABLE 2 
                 
               
              
                 
                     
                 
                 
                   The symbols and phrases used in the pseudo-code. 
                 
              
             
             
                 
                 
              
                 
                   Phrase/statement/symbol 
                   Description 
                 
                 
                     
                 
                 
                   BYTE a 
                   Indicates that the variable a is represented by a byte (8 bits) 
                 
                 
                     
                   value 
                 
                 
                   INTEGER a 
                   Indicates that the variable a is a variable able to represent 
                 
                 
                     
                   integer values 
                 
                 
                   BYTE A[m] 
                   Indicates that A is an array of m elements, where each element 
                 
                 
                     
                   is represented by a byte value 
                 
                 
                   BYTE A[m][n] 
                   Indicates that A is a two-dimensional array (matrix), where 
                 
                 
                     
                   each element is represented by a byte value 
                 
                 
                   VECTOR A 
                   Indicates that A is a vector of containing eight elements, each 
                 
                 
                     
                   represented by a byte value 
                 
                 
                   a = b 
                   The variable a is assigned the value of expression b 
                 
                 
                   A = B 
                   The vector variable A is assigned the value of expression B. 
                 
                 
                     
                   Can be implemented using the MOVQ (move quadword) 
                 
                 
                     
                   instruction on processors supporting MMX technology. 
                 
                 
                   (A + B ) − C 
                   Parenthesises indicated expressions that take precedence in the 
                 
                 
                     
                   order of computation. 
                 
                 
                   FUNCTION a(b, c) 
                   The FUNCTION and RETURN statements indicate the 
                 
                 
                   ... 
                   beginning and ending of a function a taking b and c as 
                 
                 
                   RETURN c 
                   parameters and returning the resulting value c. 
                 
                 
                   FOR i = a TO b DO 
                   This FOR-statement indicates that the statements enclosed by 
                 
                 
                   { 
                   the brackets should be repeated (b−a+1) times, with a loop 
                 
              
             
             
                 
                 
                 
              
                 
                     
                   statements 
                   index variable i, taking consecutive integer values a., a+1, a+2, 
                 
              
             
             
                 
                 
              
                 
                   } 
                   ..., b−1, b. 
                 
                 
                   IF expression THEN 
                   This IF-statement indicates that the if-statements shall be 
                 
                 
                   { 
                   executed if the expression is true, and that the else-statements 
                 
              
             
             
                 
                 
                 
              
                 
                     
                   if-statements 
                   shall be executed if the expression is false. 
                 
              
             
             
                 
              
                 
                   } 
                 
                 
                   ELSE 
                 
                 
                   { 
                 
              
             
             
                 
                 
              
                 
                     
                   else-statements 
                 
              
             
             
                 
                 
              
                 
                   } 
                     
                 
                 
                   { ... } 
                   Brackets enclosing the statements of a for-loop, if-statements 
                 
                 
                     
                   and else-statements 
                 
                 
                   a + b 
                   An expression representing the sum of the values of a and b 
                 
                 
                   a − b 
                   An expression representing the value of b subtracted from the 
                 
                 
                     
                   value of a 
                 
                 
                   a * b 
                   Indicates scalar integer multiplication 
                 
                 
                   a/b 
                   Indicates scalar integer division 
                 
                 
                   max (a, b, c, ...) 
                   A scalar expression representing the largest of its arguments 
                 
                 
                   A + B 
                   A vector operation taking A and B as arguments and 
                 
                 
                     
                   representing a new vector where each element is equal to the 
                 
                 
                     
                   pair wise sum of the corresponding elements of vector A and B. 
                 
                 
                     
                   The computations are performed using unsigned saturated 
                 
                 
                     
                   arithmetic, meaning that if any resulting element is larger than 
                 
                 
                     
                   the highest representative number, that element is replaced by 
                 
                 
                     
                   the largest representative integer. 
                 
                 
                     
                   c i  = min(a i  + b i , 255) 
                 
                 
                     
                   Can be implemented using the PADDUSB (packed addition of 
                 
                 
                     
                   unsigned saturated bytes) instruction on processors supporting 
                 
                 
                     
                   MMX technology. 
                 
                 
                   A − B 
                   A vector operation taking A and B as arguments and resulting 
                 
                 
                     
                   in a new vector where each element is equal to the pair wise 
                 
                 
                     
                   difference between the corresponding elements of vector A and 
                 
                 
                     
                   B, when subtracting each value of B from the value of A. 
                 
                 
                     
                   The computations are performed using unsigned saturated 
                 
                 
                     
                   arithmetic, meaning that if the difference is negative, zero 
                 
                 
                     
                   replaces the result. 
                 
                 
                     
                   c i  = max(a i  − b i , 0) 
                 
                 
                     
                   Can be implemented using the PSUBUSB (packed subtract of 
                 
                 
                     
                   unsigned saturated bytes) instruction on processors supporting 
                 
                 
                     
                   MMX technology. 
                 
                 
                   MAX (A , B) 
                   A vector operation taking A and B as arguments and 
                 
                 
                     
                   representing a new vector where each element is equal to the 
                 
                 
                     
                   larger of two corresponding elements of A and B. 
                 
                 
                     
                   c i  = max(a i , b i ) 
                 
                 
                     
                   Can be implemented using the PMAXUB (packed maximum 
                 
                 
                     
                   unsigned byte) instruction processors supporting SSE 
                 
                 
                     
                   technology, or using the PSUBUSB instruction followed by the 
                 
                 
                     
                   PADDUSB (packed subtract/add unsigned saturated bytes) 
                 
                 
                     
                   instruction on processors supporting only MMX technology. 
                 
                 
                   A SHIFT b 
                   SHIFT is a vector operation taking the vector A and the scalar b 
                 
                 
                     
                   as arguments and resulting in a new vector where the elements 
                 
                 
                     
                   of vector A is shifted a number of positions. Element i of vector 
                 
                 
                     
                   A is placed at position i+b in the new vector. The remaining 
                 
                 
                     
                   elements of the resulting vector are assigned a value of zero. 
                 
                 
                     
                   Thus: 
                 
                 
                     
                   IF ( (i&gt;=b) AND (i&lt;b+x)) 
                 
              
             
             
                 
                 
              
                 
                     
                   { c i  = a i−b  } 
                 
              
             
             
                 
                 
              
                 
                     
                   ELSE 
                 
              
             
             
                 
                 
              
                 
                     
                   { c i  = 0 } 
                 
              
             
             
                 
                 
              
                 
                     
                   The sign of b hence indicates the direction of the shift, while 
                 
                 
                     
                   the magnitude of b indicates the number of positions the 
                 
                 
                     
                   elements shall be shifted. 
                 
                 
                     
                   On Intel Pentium processors and other little-endian 
                 
                 
                     
                   microprocessors, a positive b value corresponds to a left shift, 
                 
                 
                     
                   while a negative b-value corresponds to a right shift. On big- 
                 
                 
                     
                   endian microprocessors the shift direction is reversed. 
                 
                 
                     
                   Can be implemented using the PSLLQ and PSRLQ (packed 
                 
                 
                     
                   shift left/right logical quadword) instructions on processors 
                 
                 
                     
                   supporting MMX technology. 
                 
                 
                   A OR B 
                   Bit wise OR of all bits in vector A and B. 
                 
                 
                     
                   Used in combination with the SHIFT-operation to combine 
                 
                 
                     
                   elements from two vectors into a new vector. 
                 
                 
                   A[i] 
                   An expression representing element number i of vector or array A 
                 
                 
                   A[b .. c] 
                   An expression representing a vector containing elements at 
                 
                 
                     
                   position b to c of the array A. 
                 
                 
                   [a, b, c, d, e, f, g, h] 
                   An expression representing a vector consisting of elements with 
                 
                 
                     
                   values a, b, c, d, e, f, g, and h. 
                 
                 
                     
                 
              
             
           
         
       
     
    
    
     PREFERRED EMBODIMENT OF THE INVENTION 
     The preferred embodiment will be described with reference to the drawings. For each sequence in the database, a sequence similarity-searching program computes an alignment score that represent the degree of similarity between the query sequence and the database sequence. By also taking the length and composition of the query and database sequences into account, a statistical parameter can be computed and used to rank the database sequences in order of similarity to the query sequence. The raw alignment score is based on a substitution score matrix, (e.g. BLOSUM62), representing the similarity between two symbols, and an affined gap penalty function based on a gap open and a gap extension penalty. 
     In the following description vectors of 8 elements are used with 8 bits each, totalling 64 bits. However, this is only for the ease of description. Many other combinations of vector and element sizes are possible and can easily be generalised from the description below. Any number of vector elements larger than one, and any number of bits for each element is possible. However, an element size of 8 bits, and a vector size of 8, 16 or 32 elements are probably the most useful. 
     In the following description the method is illustrated with a possible implementation using Intel&#39;s microprocessors and their MMX and SSE technology. However, this is just for the ease of description. An implementation using other microprocessors and other SIMD technology is also possible. 
     The Smith-Waterman Algorithm 
     To compute the optimal local alignment score, the dynamic programming algorithm by Smith and Waterman (1981), as enhanced by Gotoh (1982), is used. Given a query sequence A of length m, a database sequence B of length n, a substitution score matrix Z, a gap open penalty q and a gap extension penalty r, the optimal local alignment score t can be computed by the following recursion relations:
 
 e   i,j =max{ e   i,j−1   , h   i,j−1   −q}−r  
 
 f   i,j =max{ f   i−1,j   , h   i−1,j   −q}−r  
 
 h   i,j =max{ h   i−1,j−1   +Z[A[i], B[j]], e   i,j   , f   i,j ,0}
 
t=max{h i,j }
 
     Here, e i,j  and f i,j  represent the maximum local alignment score involving the first i symbols of A and the first j symbols of B, and ending with a gap in sequence B or A, respectively. The overall maximum local alignment score involving the first i symbols of A and the first j symbols of B, is represented by h i,j . The recursions should be calculated with i going from 1 to m and j from 1 to n, starting with e i,j =f i,j =h i,j =0 for all i=0 or j=0. The order of computation of the values in the alignment matrix is strict because the value of any cell cannot be computed before the value of all cells to the left and above it has been computed, as shown by the data interdependence graph in  FIG. 1 . An implementation of the algorithm as described by Gotoh (1982) has a running time proportional to mn. 
     Parallelisation 
     The Smith-Waterman algorithm can be made parallel on two scales. It is fairly easy to distribute the processing of each of the database sequences on a number of independent processors in a symmetric multiprocessing (SMP) machine. On a lower scale, however, distributing the work involved within a single database sequence is a bit more complicated.  FIG. 1  shows the data interdependence in the alignment matrix. The final value, h, of any cell in the matrix cannot be computed before the value of all cells to the left and above it has been computed. But the calculations of the values of diagonally arranged cells parallel to the minor diagonal (see  FIGS. 2   a  and  3   a ) are independent and can be done simultaneously in a parallel implementation. This fact has been utilised in earlier SIMD implementations (Hughey, 1996; Wozniak, 1997). 
     The Inventive Approach 
     The main features of the implementation according to the invention, are:
         Vectors parallel to the query sequence   Vector generalisation of the SWAT-optimisations   8-way parallel processing with 8-bit values   Query sequence profiles   Unsigned arithmetics   Saturated arithmetics   General code optimisations       

     These concepts are described in detail below. In order to illustrate and exemplify the description, pseudo-code for the present method is shown in  FIG. 4 . 
     In the pseudo-code, the method according to the invention through  FIGS. 4   a  and  4   b , is illustrated using vectors of 8 elements, however the present invented method is general and can be implemented with vectors of any number of elements. 
     The pseudo-code assumes that the query sequence length (m) is a multiple of the vector size, 8. This can be achieved by padding the query sequence and query score profile. 
     All vector indices start at zero as is usual in programming languages (not one, as is usual in ordinary mathematics notation). 
     Upper case letters are generally used to represent vector or array variables or operations, while lower case letters are generally used to represent scalar variables or operations. 
     The S-matrix is an x times n query-specific score matrix representing the score for substituting any of the x different possible database sequence symbols with the query symbol at any of the n query positions. In general, x just represents the size of the alphabet from which the sequence symbols belong to. For amino acid sequences, x is typically 20 (representing the 20 natural amino acids) or slightly larger (to include also ambiguous and other symbols). For nucleotide sequences, x is typically 4 (representing the 4 nucleotides adenine, cytosine, guanine and thymine/uracil), or larger (to include also ambiguous and other symbols). The S-matrix is usually precomputed from a query sequence and a substitution score matrix, but may also represent a general query profile, which may be based on scores calculated from a multiple alignment of a protein sequence family. 
     The H-vectors holds the h-values, representing the optimal local alignment score for a given matrix cell. The H-vectors represent a part of the HH-array. The E-vector holds the e-values, representing scores from alignments involving a database sequence gap. The E-vectors represent a part of the EE-array. The F-vector holds the f-values, and temporary f-values, representing scores from alignments involving a query sequence gap. 
     In the LASTF vector, only a single element (at index 0) is used. It represents the potential score from previous rounds involving a gap in the query sequence. The actual value used has the gap opening penalty added, in order to simplify later calculations. 
     Vectors Parallel to the Query Sequence 
     Despite the loss of independence between the computations of each of the vector elements, it was decided to use vectors of cells parallel to the query sequence (as shown in  FIGS. 2   b  and  3   b ), instead of vectors of cells parallel to the minor diagonal in the matrix (as shown in  FIGS. 2   a  and  3   a ). The advantage of this approach is the much-simplified and faster loading of the vector of substitution scores from memory. The disadvantage is that data dependencies within the vector related to the f-value computations (see  FIG. 3   b ) must be handled. Eight cells are processed simultaneously along each column as indicated in  FIG. 2   b . Vectors are used to represent the h-, e- and f-values in the recurrence relations in groups of eight consecutive cells parallel to the query sequence. Vectors are also used to represent zero, q, r, q+r and other constants. Using vector processing, the value of eight h-, e- or f-values may be computed in parallel (the h, e and f as described in the equations on page 11). 
     Vector Generalisation of the SWAT-Optimisations 
     As already indicated, we have to take into account that each element in the vector is dependent on the element above it, as shown in  FIG. 3   b , because of the possible introduction of gaps in the query sequence. We employ a vector generalisation of the SWAT-optimisations and other optimisations to make the principle of query-parallel vectors efficient. The concept is illustrated in the pseudo-code in  FIG. 4 . 
     The f-values represent the score of an alignment ending at a cell with a gap in the query sequence. The f-values are dependent on the h- and f-values in the cells above it. Hence, the F-vector is dependent on the H- and F-vectors, and in addition, on the h- and f-value in the cell immediately above the vector. These dependencies make the calculations complex and hard to do in parallel in the general case. 
     However, because the h-value of a cell may only influence other cells if the h-value is larger than a threshold equal to the gap penalty of a single symbol gap (q+r), the calculations may be simplified in most cases. In practice, relatively few of the cells have h-values that are above the threshold, implying that simplified calculations can be used in most cases. These principles can be generalised in the vector case. 
     It is possible to quickly check if there is a possible dependency problem or not for the entire vector. If the check is negative (possible dependency), we have to do the complex calculations to find the correct h-, e- and f-values. If the check is positive (no dependency), most of the calculations can be skipped. 
     To check whether there is a possible dependency, it is first computed an initial H-vector without taking the f-values into account. By examining the initial H-vector and the h- and f-value from the cell immediately above the vector, it can be decided if there will be any dependence between the cells. If the value of any element in the H-vector is greater than the q+r threshold, there is a possible dependency. There is also a possible dependency if the h-value in the cell above the vector is greater than the q+r threshold, or if the f-value in the cell above the vector is greater than the gap extension penalty, r. 
     Actually, the bottom element of the initial H-vector cannot cause any intra-vector dependency, but we include it in the check, because it affects the E-vector and the vector containing the overall highest scores. 
     If the check is positive, the initial H-vector is also the final H-vector. In this case, the E-vector is also not dependent on the H-vector and can be computed simply by deducting the gap extension penalty from each element of the E-vector. If the check is positive, we can also skip updating the vector containing the overall highest scores (unless we are interested in final scores below q+r). 
     If the check is negative, the correct F-vector has to be computed based on the initial H-vector, and the h- and f-values from the cell above. This computation is performed by a lengthy series of subtraction-, shift-, and maximum-operations as described by the pseudo-code in  FIG. 4 . When the correct F-values have been computed, the correct H- and E-vectors must be updated. In addition the vector containing the overall highest scores must also be updated. 
     8-Way Parallel Processing with 8-Bit Values 
     The microprocessors provide for the SIMD instructions a set of registers (usually 64-bit wide) that can be divided into smaller units. The Pentium family of microprocessors contains several 64-bit registers that can be treated either as a single 64-bit (quad word) unit, or as two 32-bit (double word), four 16-bit (word), or eight 8-bit (byte) units. Operations on these units are independent. Hence, the microprocessor is able to perform up to eight independent additions or other operations simultaneously. 
     In order to optimise the speed of the calculations, the MMX-registers of the microprocessor could be divided into as many units as possible, i.e. eight 8-bit units. This allows eight concurrent operations to take place. Dividing the MMX-registers into eight 8-bit registers increases the number of parallel operations but limits the precision of the calculations to the range 0-255. Unless the sequences are long and very similar, this poses no problems. In the few cases where this score limit is surpassed, the use of saturation arithmetic (see below) will ensure that the overall highest score will stay at 255. For all sequences that reach a score of 255, the correct score may subsequently be recomputed by a different implementation with a larger score range (e.g. using a non-SIMD implementation). 
     Query Sequence Profiles 
     Initially we compute a query profile (also known as a query-specific score matrix) called S, which is an m times x matrix, with the following values:
 
 S[k, i]=Z[k, A[i]] 
 
     Here k is any of the possible symbols occurring in sequence B, and i is the query position. This profile is computed only once for the entire search. The score for matching e.g. symbol A (for alanine) in the database sequence B with each of the symbols in the query sequence is stored sequentially in the first matrix row, followed by the scores for matching symbol B (ambiguous) in the next row, and so on. This query sequence profile is used extensively in the inner loop of the algorithm and is usually small enough to be kept in the microprocessor&#39;s first level cache. 
     Unsigned Arithmetic 
     In most microprocessors, additions and subtractions can be performed in either unsigned or signed mode. In the inner loop of the algorithm, the query profile scores are added to the unsigned h-values. Using a signed addition, the h-values would have been restricted to the range of 0-127. Instead, all the values in the query sequence score profile were biased by a fixed amount (e.g., 4) so that no values were negative. One signed operation was then replaced by an unsigned addition followed by an unsigned subtraction of the bias. The useful data range was hence expanded to nearly 8 bits (e.g., 0-251). 
     Saturated Arithmetic 
     Unsigned arithmetic using SIMD technology can be performed in either a modular (also known as wrap-around) or in a saturated mode. When using 8-bit wide registers, subtracting 25 from 10 will give the result 241 (because 10-25=241-256) in modular mode and 0 in saturated mode. This is very useful in the inner loop calculations of the Smith-Waterman algorithm because zero in some of the calculations should replace negative results. Also, because of the limited precision of a single byte value, saturated arithmetics are useful to detect potential overflow in the calculations with very high scores. 
     The core of the Smith-Waterman algorithm repeatedly computes the maximum of two numbers. It is therefore important to make this computation fast. The SSE instruction set includes a special instruction (pmaxub) that computes the largest of two unsigned bytes. This instruction was not included in the original MMX instruction set, but can be replaced by an unsigned saturated subtraction (psubusb) followed by an unsigned saturated addition (paddusb). 
     General Code Optimisations 
     In order to get complete control over code optimisation and because of limited support for the SIMD instructions in high-level languages, the core of the algorithm should be written in assembly language. 
     The use of conditional jumps should be avoided when it is difficult for the microprocessor to predict whether to jump or not, because mispredictions require additional time. In addition, conditional jumps based on the results of MMX/SSE operations are not straightforward on the Intel architecture because the status flags are not set by these instructions. 
     In order to achieve the highest speed, the memory used repeatedly in the calculations should preferably be contained in the first level caches of the microprocessor. In addition to the query sequence score profile, the vectors storing the h and e values from the last column should also fit in the cache, but these are usually only about 400 bytes each for an average sequence. 
     The 64-bit memory accesses used with MMX registers should preferably be placed on 8 byte boundaries, in order to be as fast as possible. We have taken this into account when aligning the data structures. Code alignment also had substantial effects on the speed. 
     When the computer is equipped with enough internal memory to hold the entire database, the use of memory-mapped files is an effective way to read the database. The entire sequence file can then be mapped to particular address range in memory. Operating systems are usually optimised for reading sequential files in this way. 
     Application Areas and Industrial Utilisation 
     The present method can in general be used in any form of comparison of two linear sequences of symbols, representing one-dimensional signals, i.e. genetic or biological molecules, sound signals (e.g. speech, voice, music), text in any language (human, computer), or other phenomenon. However, comparison of nucleotide or amino acid sequences is the most obvious application. It can be used both for direct pair wise sequence comparison (alignment) and for database similarity searching. The method quantifies the amount of similarity between two sequences, and can be used to find which sequences in a database that is the most similar to a given sequence. The most similar sequences are often related or homologous to the query sequence. 
     The following types of comparisons and database searches are possible:
         Comparison/alignment of amino acid sequences (proteins, enzymes).   Comparison/alignment of nucleotide sequences (DNA, RNA, mRNA, cDNA, etc.).   Database searching, in which a nucleotide query sequence is compared to all nucleotide sequences in a database, a score is computed for each database sequence, and the database sequences with scores of interest are reported.   Database searching, in which an amino acid query sequence is compared to all amino acid sequences in a database.   Comparison of a protein query sequence with nucleotide sequences in a database, after translating the database sequences into all six frames, also taking possible frame shifts into account.   Comparison of a nucleotide query sequence with amino acid sequences in a database, after translating the query sequence into all six frames, also taking possible frame shifts into account.   Comparison of a nucleotide query sequence with nucleotide sequences in a database, after translating both the query sequence and the database sequences into all six frames, also taking possible frame shifts into account.       

     Other variants of the present invented method are also possible:
         Sequence alignment or database searching where the query sequence is replaced by a query profile, e.g. a matrix of scores for every combination of query position and possible database sequence symbol   Sequence alignment where our method is applied to a band or otherwise restricted area in the alignment matrix   Sequence database similarity searching where our method is applied to a subset of the database after a pre-filtering procedure is applied to all database sequences   Sequence database similarity searching where our method is applied to a query sequence that has been filtered or masked to remove regions of repetitive sequences, biased composition or other low-complexity regions   An implementation of the inventive method where the resulting scores for each database sequence is the basis for the calculation of a statistical parameter indicating the significance of each match, by also taking into account the length and/or composition of the query and database sequences, in addition to the scoring scheme (choice of substitution matrix and gap penalty function)   An implementation of the inventive method on a symmetric multiprocessing (SMP) computer   An implementation of the inventive method on a cluster of networked computers   An implementation of the inventive method on a microprocessor with missing or limited explicit instructions for SIMD operations, by using SIMD within a register (SWAR) or other forms of microparallelism   As a part of an iterative database homology search application, similar to e.g. PSIBLAST (Altschul et al 1997), in which the sequence information from a family of sequences is used to detect distantly related sequences       

     The present method can be used as a part of the following applications within bio informatics:
         Protein function prediction   Protein structure prediction   RNA function prediction   RNA structure prediction   Multiple sequence alignment   Sequence clustering   Protein family grouping/clustering   DNA sequence contig assembly   Detection of coding sequence regions in nucleotide sequences   Phylogenetic tree construction   Any other applications which involves computation of an accurate sequence alignment score       

     The present method can also be used in the following product:
         a general-purpose computer system containing software that implements the described algorithm.       

     Equivalents to the above product are:
         other computer systems using a digital signal processing device implementing the described method   dedicated hardware solutions in the form of electronic circuits that incorporates the described method, e.g. an application specific integrated circuit (ASIC), field-programmable gated arrays (FPGA), or custom very large scale integration (VLSI) chips. Using VHDL hardware description language of the method outlined in this disclosure of the invention, any form of electronic device implementation of the method can be achieved as long as the VHDL synthesize tool support the chosen technology as is well known to a person skilled in the art.       

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