Sequence Similarity between Genetic Codes using Improved Longest Common Subsequence Algorithm

International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 57 – 60
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57
IJRITCC | July 2017, Available @ http://www.ijritcc.org
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Sequence Similarity between Genetic Codes using Improved Longest Common
Subsequence Algorithm
A. Murugan
Associate Professor, PG & Research Department
of Computer Science
DrAmbedkar Government Arts College,
Vyasarpadi, Chennai – 600 039, Tamilnadu.
e-mail: amurugan1972@gmail.com
U. Udayakumar
M.Phil Research Scholar, PG & Research Department
of Computer Science
DrAmbedkar Government Arts College,
Vyasarpadi, Chennai – 600 039, Tamilnadu.
e-mail: udaya.vijay13@gmail.com
Abstract— Finding the sequence similarity between two genetic codes is an important problem in computational biology. In this paper, we
developed an efficient algorithm to find sequence similarity between genetic codes using longest common subsequence algorithm. The algorithm
takes the advantages over the edit distance algorithm and improves the performance. The proposed algorithm is tested on randomly generated
DNA sequence and finding the exact DNA sequence comparison. The DNA genetic code sequence comparison can be used to discover
information such as evolutionary divergence and ways to apply genetic codes from one DNA sequence to another sequence.
Keywords-Dynamic Programming, DNA sequence comparison, DNA Similarity algorithms, Longest Common Subsequence.
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I. INTRODUCTION
DNA is the hereditary material found in almost all
organisms [1]. DNA resides in every cell in the body of
organism. The DNA is a double helix like structure made up of
two twisted strands. A single strand carries a nucleotide bases,
these bases are adenine (A), guanine (G), cytosine (C), thymine
(T). These chemical letters are in the form of triplets which
defines a meaningful code. The triplets give arise to specific
amino acid which later helps in the formation of protein[2]. An
important property of DNA is that it can replicate, or make
copies of itself. Each strand of DNA in the double helix can
serve as a pattern for duplicating the sequence of bases as
shown in Fig.1. This is critical when cells divide because each
new cell needs to have an exact copy of the DNA present in the
old cell.
Figure 1. Structure of DNA
The knowledge of a DNA sequence and gene analysis can be
used in several biological, medicine and agriculture research
fields such as: possible disease or abnormality diagnoses,
forensic science, pattern matching, biotechnology, etc[3][4].
The analysis and comparison studies for DNA sequences
connected information technology tools and methods to
accelerate findings and knowledge in biological related
sciences.
II. LITERATURE SURVEY
There are many traditional pattern matching methodologies
available in literature, they are Naive Brute force, Boyer
Moore, Knuth Morris Pratt and Dynamic algorithms[2]. Pattern
matching is used in various processes, like codon optimization
which is carried out to enhance the efficiency of the DNA
expression vectors used in DNA vaccination by increasing
protein expression[5].
A. Naive Brute force
It is one of the simplest algorithm having complexity
O(m*n). In this, first character of pattern P(with length m) is
aligned with first character of text T (with length n). Then
scanning is done from left to right. As shifting is done at each
step it gives less efficiency[6].
B. Boyer-Moore Algorithm
It performs larger shift-increment whenever mismatch is
detected. It differs from Naïve in the way of scanning. It scans
the string from right to left; unlike Naive i.e. P is aligned with
T such that last character of P will be matched to first character
of T. If character is matched then pointer is shifted to left to
very rest of the characters of the pattern[7][8]. If a mismatch is
detected at character c, in T which is not in P, then P is shifted
right to m positions and P is aligned to the next character after
c. If c is part of P, then P is shifted right so that c is aligned
with the right most occurrence of c in P. The worst time
complexity is still O(m+n).
C. Knuth-Morris-Pratt
This algorithm is based on automaton theory. First a finite
state automata model M is being created for the given pattern
P. The input string T with Σ= {A, C, T, G} is processed
through the model. If the pattern is present in text, the text is
accepted otherwise rejected.

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III. EFFICIENT LCS ALGORITHM
The longest common subsequence problem is to find a
substring that is common to the two given strings. Given two
sequences, find the length of the longest subsequence present in
both of them. A subsequence is a sequence that appears in the
same relative order, but not necessarily contiguous [16].
In LCS problem, we eliminate the operation of substitution
and allow only insertions and deletions. A Subsequence of a
string v is simply an ordered sequence of characters from v. For
example, if v = ATTGCTA, then AGCA and ATTA are
subsequences of v whereas TGTT and TCG are not. Where
ATGC denotes Adenine, Thymine, Guanine, Cytosine.
Formally, we define the common subsequence of strings[9].
1 ≤ i1 ≤ i2< . . . ik ≤ n (1)
and a sequence of positions in w,
1 ≤ j1 ≤ j2< . . . jk ≤ m (2)
Let si,j be the length of an LCS between v1...vi, the i-prefix of v
and w1...wj, the j-prefix of w. Clearly, si,0 = s0,j = 0 for all 1 ≤ i
≤ n and 1 ≤ i ≤ n one can see that si,j satisfy the following
recurrence:
si,j = max
si-1,j
si,j-1
si-1,j-1+1, if vi=wj
(3)
Note that one can "rewrite" these recurrences by adding some
zeros
si,j=max
si-1,j+0
si,j-1+0
si-1,j-1+1, if vi=wj
(4)
The LCS computation is like the recurrence given at the
equations (3) and (4), if we were to build particularly gnarly
version of Manhattan and gave horizontal and vertical edges
weights of 0, and set the weights of diagonal edges equal to +
1[10].
The following is the efficient algorithm for solving longest
common subsequence problem [15] that improves the time
complexity and performance.
Algorithm Backtracking Pointers and stored three values up,
right and diagonal in Multidimensional array
while x! := ―0‖ then
ifsolna,b == ―Diagonal‖ then
a := a - 1
b := b - 1
else
b := b - 1
a := a - 1
end if
return LCS[A.length][B.length]
end while
The following Fig. 2 shows Multidimensional array
representation of the LCS algorithm
Figure 2. Multidimensional Array representation for efficient
LCS Algorithm
The following Fig. 3 shows LCS Time Complexity and
Performance
Figure 3. LCS Time Complexity and Performance
IV. DNA SEQUENCE SIMILARITY
We proposed an algorithm to find the similarity between
DNA genetic code sequences. In DNA sequence similarity,
find the matching percentage between DNA genetic codes. In
this paper, we proposed a new method for DNA sequence
similarity.
A modified Longest Common Subsequences algorithm is
proposed in [15] and which is applied in the edit distance
algorithm, which is an existing algorithm.
The following is the modified edit distance algorithm used
to find the similarity between two genetic codes.
Algorithm 1: Edit Distance for DNA genetic code
AlgorithmeditDistance(s1,s2)
cost[] : = s2.length + 1
for i:= 0 to s1.length do
lastvalue := i
for j:= 0 to s2.length do
if(i == j)
cost[j] : = j
elseif(j > 0)
newValue : = costs[j - 1]
costs[j - 1] : = lastValue
lastValue : = newValue
end if
end for
end for
end algorithm

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The following Fig. 4 explain the entire process of finding
DNA sequence similarity
Figure 4. Implementing LCS Algorithm in DNA Genetic Code
Sequence Similarity
The computation of the similarity score s(v,w) between v and
w, while the table on the right presents the computation of the
edit distance between v and w under the assumption that
insertions and deletions are the only allowed operations[14].
The following TABLE Ishows DNA genetic code sequence
similarity
TABLE I. GENETIC CODE SIMILARITY BETWEEN SEQUENCES
Human DNA Animals DNA
% of
matching
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACGATTTGGGGGATGC
TTCTGGCTC------A
100.00%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACGATTTGGGGGA
TGCTTCTGGCTC------A-
100.00%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACGATTTGGGAGA
TGCTTCTGGCTC-----G-
91.67%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCAGAATTTGGGGGA
TGCTTCTGGCTC-----T-
88.89%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCAGAATTTGGGGGA
TGCTTCTGGCTC-----T-
88.89%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCAGAATTTGGGGGA
TGCTTCTGGCTC-----T-
88.89%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
ATCACAGTTGGGGGAT
GCCACTGGCCT-----C-
75.00%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
ATCACAA-TTGGGGG-
TGCCACGGTCCT-----C-
69.44%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
ATCACAATTTGGGGAA
CACCACTGGCAT-----C-
69.44%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACAATTTGGAGGA
TGTTACTGGCAT-----C-
77.78%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACAGTTTGGAGGA
TGTTACTGACAT-----C-
72.22%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCATAGTTT----
GATTATATGGGCTT-----
C-
58.33%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACAATTTGGGGGA
TACTACTGGCAT-----C-
80.56%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACAGTTTAGGGGG
TACTACTGGCAT-----C-
72.22%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GTCACAATTTAGGAAG
TGCCACTGGCCT-----C-
72.22%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
GCCTCTCTTT-----------
CTGCCCTGCAGGC-
33.33%
GTCACGATTTGGGGGATGC
TTCTGGCTC------A-
----------------
TGCTACTAATAT-----T-
36.11%
Algorithm 2: genetic code similarity
Algorithmsimilarity(s1, s2)
longer := s1, shorter := s2
if (s1.length() < s2.length())
longer := s2
shorter : = s1
longerLength := longer.length();
if (longerLength == 0)
return (longerLength - editDistance(longer, shorter)) /
(double) longerLength;
end if
end algorithm
The following Fig. 6 shows the Output for Similarity
Sequences between genetic codes
Figure 5. Output for DNA Genetic Code Similarity Sequences
A. Time Complexity
The Time Complexity of Sequence Similarity Algorithms
TC(DSSA) = max{TC(LCS), TC(EDA), TC(SS)}
TC(DSSA) = max{O(n2
), O(n2
), O(n2
)}
So the time complexity of the DNA Sequence Similarity
Algorithm is O(n2
)
The best case and average case time complexity
T(n) = max((O(n2
) and O(levelnumber)), O(|n|).
The Worst case time complexity
T(n) = max((O(n3
) and O(levelnumber)), O(|n|).
The following Figure 7 shows Graphical Representation of
DNA Genetic Code between Human and Animals

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60
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Figure 6. Graphical Representation of DNA Genetic Code
Similarity Sequences
V. DNA SEQUENCE SIMILARITY
In this paper, we proposed an algorithm for finding similarity
between two strings. It calculate the matching percentage
between two strings by using longest common subsequence
(LCS) and edit distance approach by avoiding unnecessary
comparisons that reduces its time complexity. The running
time is better than dynamic programming based algorithms
and it is due to time control parameter. The DNA sequence
similarity algorithm is tested on 50 samples with two input
DNA genetic code sequence strings and selected randomly in
Pentium processor machine is used and it shows good results.
In future the algorithm is implemented in Multiple Longest
Common Subsequences which will also have many
applications.
REFERENCES
[1] Neil C.Jones and Pavel A.Pevzner, "An Introduction to Bioinformatics
Algorithms" (2004)
[2] Jiaoyun Yang, Yun Xu, Yi Shang, ―An Efficient Parallel Algorithm for
Longest Common Subsequence Problem on GPUs‖, World Congress
Engineering, 2010.
[3] Maier. D, ―The Complexity of some problems on subsequences and
super sequences‖, ACM, (25), 1978, 332-336.
[4] B.Lavanya and A.Murugan, "Mining Longest Common Subsequence
and other related patterns using DNA operations", International Journal
of Computer Application, (18), 2012, 38-44.
[5] Hirosawa et al, "Comprehensive study on iterative algorithms of
multiple sequence alignment". Computational Applications in
Biosciences, 1995, 13-18.
[6] Mahdi Esmaieli and Mansour Tarafdar, "Sequential Pattern Mining from
multidimensional sequence data in parallel", International journal of
Computer theory and engineering, 2010, 730-733.
[7] Stormo. G, "DNA binding sites: representation and discovery".
Bioinformatics, 2000, 16:16-23
[8] Kyle Jensen. L., Mark Styczynski. P., Isidore Rigoutsos, and Gregory
Stephanopoulos. V, "A generic motif discovery algorithm for sequential
data". Bioinformatics, 22(1) 2006, 21-28.
[9] Wang. L. and Jiang. T, "On the complexity of multiple sequence
alignment". Journal of Computational Biology, 1994, 337-348.
[10] Nan Li and Tompa. M, "Analysis of computational tools for motif
discovery". Algorithms of molecular biology, 2006, 1-8.
[11] Suyama. M., Nishioka. T., and Junichi. O, "Searching for common
sequence patterns among distantly related proteins". Protein
Engineering, 1995,1075-1080.
[12] Smith. H. O., Annau. T. M., and Chandrasegaran.S, "Finding sequence
motifs in groups of functionally related proteins". Proceedings of
National Academy (USA), 1990, 826-830.
[13] Bin Ma, "A polynomial time approximation scheme for the closest
substring problem". LCNS Springer, 2000, 99-107.
[14] Martinez. M, "An efficient method to find repeats in molecular
sequences". Nucleic Acid Research, 1983, 4629-4634.
[15] U. Udayakumar and A. Murugan "An Efficient Algorithm For Solving
Longest Common Subsequence Problem", IJESMR, 2017,4(5).
[16] www.geeksforgeeks.org/dynamic-programming-set-4-longest-common-
subsequence

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