- Proceedings
- Open Access
A hybrid method for the exact planted (l, d) motif finding problem and its parallelization
- Mostafa M Abbas^{1}Email author,
- Mohamed Abouelhoda^{2, 3}Email author and
- Hazem M Bahig^{4}
https://doi.org/10.1186/1471-2105-13-S17-S10
© Abbas et al.; licensee BioMed Central Ltd. 2012
- Published: 13 December 2012
Abstract
Background
Given a set of DNA sequences s_{1}, ..., s_{ t }, the (l, d) motif problem is to find an l-length motif sequence M , not necessary existing in any of the input sequences, such that for each sequence s_{ i }, 1 ≤ i ≤ t, there is at least one subsequence differing with at most d mismatches from M. Many exact algorithms have been developed to solve the motif finding problem in the last three decades. However, the problem is still challenging and its solution is limited to small values of l and d.
Results
In this paper we present a new efficient method to improve the performance of the exact algorithms for the motif finding problem. Our method is composed of two main steps: First, we process q ≤ t sequences to find candidate motifs. Second, the candidate motifs are searched in the remaining sequences. For both steps, we use the best available algorithms. Our method is a hybrid one, because it integrates currently existing algorithms to achieve the best running time. In this paper, we show how the optimal value of q is determined to achieve the best running time. Our experimental results show that there is about 24% speed-up achieved by our method compared to the best existing algorithm. Furthermore, we also present a parallel version of our method running on shared memory architecture. Our experiments show that the performance of our algorithm scales linearly with the number of processors. Using the parallel version, we were able to solve the (21, 8) challenging instance using 8 processors in 20.42 hours instead of 6.68 days of the serial version.
Conclusions
Our method speeds up the solution of the exact motif problem. Our method is generic, because it can accommodate any new faster algorithm based on traditional methods. We expect that our method will help to discover longer motifs. The software we developed is available for free for academic research at http://www.nubios.nileu.edu.eg/tools/hymotif.
Keywords
- Problem Instance
- Input Sequence
- Exact Algorithm
- Parallel Version
- Motif Problem
Background
DNA motifs are short sequences in the genome that play important functional roles in gene regulation. Due to their short length, it is difficult to identify these regions using features intrinsic in their composition. Assuming that the motifs are conserved in closely related species due to the importance of their function, it is possible to discover them by comparing the respective DNA sequences to identify the sub-sequences that are very similar to each other.
There are two common combinatorial formulations that identify the motifs: The first is the consensus motif problem which made its first appearance in 1984 [1], while the second is the planted (l, d)-motif problem that was presented in 2000 [2]. It is worth noting that the latter formulation is a special case of the former. The exact definitions are as follows:
Given a set of t sequences s_{ i } where 1 ≤ i ≤ t defined over an alphabet ∑. The consensus motif problem is to find an l-length motif sequence M such that in each sequence s_{ i }, 1 ≤ i ≤ t, there is at least one subsequence p_{ i } differing with at most d mismatches from M; i.e., d_{ H }(p_{ i } , M) ≤ d, where d_{ H } is the hamming distance between p_{ i } and M.
The planted (l, d) motif problem is a special case of the consensus problem in which we restrict that p_{ i } occurs only once in s_{ i }.
Due to its combinatorial nature, the consensus motif problem and its variant defined above is extremely challenging. Over a benchmark data of 20 sequences, each of length 600 characters, large instances of (15, 5), (17, 6), (19, 7) and (21, 8) have been addressed and many algorithms have been developed to solve them one after another. These algorithms can be classified into two major categories: approximation algorithms [2–12] and exact algorithms [13–30]. Approximation algorithms are based on probabilistic local search techniques, such as Gibbs Sampling, Expectation Maximization, etc. Although these algorithms may solve the challenging instances in practice, there is no guarantee that the motif can be found even when l is short.
Exact algorithms are based on exhaustive search techniques. The brute force algorithm proceeds by testing all possible motifs of length l using pattern matching, leading to O (l n t 4^{ l }) time complexity. This algorithm, however, is not suitable for discovering long motifs in practice, and many algorithms have been developed to provide faster solutions. Examples of these algorithms are CENSUS [23], PMS1 [26], PMSP [27], PMSprune [29], PMS5 [30], SMILE [19], RISO [24], RISOTTO [28], and Voting [25]. In the following we briefly review the most efficient ones and the ones related to our work.
The algorithms SMILE [19], RISO [24], and RISOTTO [28] are based on the use of suffix tree. The time complexity of these algorithms is the same and it is O(t^{2}Nv(l, d)), where $v(l,\phantom{\rule{0.1em}{0ex}}d)={\displaystyle \sum _{d}^{i=0}{C}_{i}{}^{l}{3}^{i}}$ is the size of the d-mismatch neighbourhood of motifs of length l and $N={\displaystyle \sum _{t}^{i=1}{n}_{i}}$, n_{ i } is the length of sequence i from input sequences. RISOTTO improved the time complexity of SMILE and RISO in the average case and solved some challenging instances such as (15, 5) and (17, 6).
PMSP [27] is based on exploring the neighbourhood of the l-mer of the first sequence and checking whether the elements of such neighbourhoods are (l, d) motifs. The time complexity is $O\left(\frac{1}{w}t{n}^{2}v\left(l,d\right)\right)$. It is able to solve some challenging instances such as (15, 5) and (17, 6). PMSprune [29, 31] is an improved version of the PMSP algorithm, based on the branch and bound strategy. Although it has the same worst-case time complexity as PMSP algorithm, it is more efficient in practice and it could tackle the (17, 6) and (19, 7) instances for the first time. PMS5 [30] is based on computing the common d-neighbourhood of three l-mers using integer programming formulation. It combines this novel idea with the algorithms PMS1 and PMSPrune. PMS5 can tackle the large challenging instances (19, 7), (21, 8) and (23, 9). The only drawback of PMS5, it requires larger amount of internal memory to finish computation.
Our contribution
In a previous work [32, 33], we have introduced an idea composed of two stages to speed up the exact algorithms: In the first stage, we generate a set of candidate motifs by applying one of the exact algorithms based on the neighbourhood method (like Voting [25] or PMSP [27] algorithms) using q ≤ t sequences. In the second stage, for each candidate motif we check if it is a valid motif or not using pattern matching on the reminder (t - q) sequences. This dramatically reduces the search space and leads to significant speed up. The bottleneck in this approach, however, was the determination of the q value that yields the fastest running time. That is, the user has to guess the value of q, which might lead to non-optimal running time and even no speed up compared to the traditional methods. Also, the authors in [34] have used the same idea on PMS1, RISOTTO, and PMSprune algorithms.
In this paper, we present a theoretical method which can be used to determine the appropriate value of q. Then we apply this strategy on PMSprune algorithm and solve some big challenging instances such as (21, 8). Furthermore, we propose a parallel version of our algorithm to present a practical solution to the challenging instances of the motif problem. Our parallel version further speeds up the solution of the (21, 8) instance.
Definitions and related work
In this section, we introduce some notations and definitions that will help us to describe our algorithm and related work in a concise manner.
Definition 1 adapted from [29]: For any string x, with |x| = l, let B_{ d }(x) = {y: |y| = l, d_{ H }(y, x) ≤ d}, where d_{ H } denotes the Hamming distance and B_{ d }(x) denotes the set of neighbourhoods of x. We also write v(l, d) to refer to |B_{ d }(x)|.
Definition 2 adapted from [29]: Let s denote a string of length n and let x denote another string of length l, l <n. We define the minimum distance between s and x as ${\stackrel{\u0304}{d}}_{H}\left(x,s\right)=\underset{{x}^{\prime}{\u22b2}_{l}s}{\mathsf{\text{min}}}{d}_{H}\left(x,{x}^{\prime}\right)$, where x ⊲_{ l } s denotes that x is a substring of s with length l.
Definition 3 adapted from [29]: Given an l-length string x and a set of strings S = {s_{1}, ..., s_{ t }} with |s_{ i }| = n for i = 1, ..., t and l <n, we define the distance between S and x as ${\stackrel{\u0304}{d}}_{H}\left(x,S\right)=\underset{i=1}{\overset{t}{\mathsf{\text{max}}}}\left\{{\stackrel{\u0304}{d}}_{H}\left(x,{s}_{i}\right)\right\}=\underset{i=1}{\overset{t}{\mathsf{\text{max}}}}\left\{\underset{r{\u22b2}_{l}{s}_{i}}{\mathsf{\text{min}}}\left\{{d}_{H}\left(x,r\right)\right\}\right\}$
- 1)
${\stackrel{\u0304}{d}}_{H}\left(x,S\right)\le d.$
- 2)
$\exists y{\u22b2}_{l}{s}_{1}:x\in {B}_{d}\left(y\right)\wedge {\stackrel{\u0304}{d}}_{H}\left(x,\left\{{s}_{1},....,{s}_{t}\right\}\right)\le d.$
Proposition 1 adapted from [10]: Let u and v be two random strings of length l over an alphabet of 4 characters with equal probability of occurrence. The probability p_{ d } that d_{ H }(u, v) ≤ d is ${p}_{d}=\sum _{i=0}^{d}\left(\begin{array}{c}\hfill l\hfill \\ \hfill i\hfill \end{array}\right){\left(3/4\right)}^{i}{\left(1/4\right)}^{l-i}$, and the probability that ${\stackrel{\u0304}{d}}_{H}\left(x,S\right)\ge d$is (1-(1-p_{ d })^{n-l+1})^{ t }. The expected number of l-length motifs that occur at least once in each of the t sequences with up to d substitutions is E(l, d, t, n) = 4^{ l }(1-(1-p_{ d })^{n-l+1})^{ t }.
PMSprune Algorithm
Because the first stage of our method will depend on the PMSprune algorithm. We will review the basic steps of it in the notions presented above.
where p_{2d}is the probability that the hamming distance between two strings is at most 2d, and it is defined in Proposition 1. For fixed values of t, n, and l, value d' was estimated such that the probability of ${\stackrel{\u0304}{d}}_{H}\left(x,S\right)\ge {d}^{\prime}$ is close to 1. (The probability of ${\stackrel{\u0304}{d}}_{H}\left(x,S\right)\ge {d}^{\prime}$ is given in Proposition 1 and it is ${\left(1-{\left(1-{p}_{d}^{\prime}\right)}^{n-l+1}\right)}^{t}$).
Implementation
Our proposed strategy
Our new strategy, referred to as hybrid exact pattern motif search (HEP), is composed of three steps: first, we determine the value q, corresponding to the size of a subset of input sequences, as explained below. Second, we apply an exact exhaustive algorithm £ (like, PMSprune) on the set of q sequences to find the set of d-neighbourhood B_{ d }(x) (review definition 1 for exact definition of d-neighbourhood). We call this set the candidate motif set. Finally, we apply a pattern search algorithm over the remaining sequences to verify each motif. Note that our algorithm is generic in the sense that it takes the program £ also as input in addition to the input sequences and user parameters. A pseudo code for this strategy using the exact algorithm £ is as follows:
Algorithm 2: HEP (£, s_{1},..., s_{ t }, n, l, d)
- 1)
Determine the number of sequences q using the method given below.
- 2)
Implement the exact algorithm £ on q input sequences. Let C be the set of candidate motifs found in the q sequences.
- 3)
For each pattern v in C, check if v is a valid motif or not in the reminder (t - q) input sequences using pattern matching Algorithm.
End.
Theorem 1: Algorithm 2 correctly finds all (l, d) motifs in a given t input sequences.
Proof: Step 2 of the algorithm is exhaustive and finds the whole set of d-neighborhood for the q sequences. Therefore, and by definition of the (l, d) motif problem, any (l, d) motif belongs to this set, even if q = 1. In Step 3, each candidate motif is verified by comparison to each substring in the remaining sequences. This step is conducted by an approximate pattern matching algorithm for each l-length substring in the candidate motif set and each l-length substring in the remaining sequences such that the hamming distance between these two substrings is ≤ d. This guarantees that no motif is missing.
where T_{£(q)}is the running time of step 2 involving the use of an exact algorithm £ on the q input sequences and l(t - q) (n - l + 1) E(l, d, q, n) is the running time of step 3 such that E(l, d, q, n) is the number of elements in the set C, which is estimated to be 4l(1- (1 - p_{ d })^{n - l + 1})^{ q }. Note that the complexity of step 1 takes constant time, as we will explain below. Note that the running time of the brute force algorithm is acquired if q = 0 in equation 2. The running time of the exact algorithm £ is acquired if q = t in equation 2.
Determination of the best q
Definition 5: We define mns as the minimum number of sequences q that yields better running time; i.e., the first value of q that verifies the inequality. We also define ons as the optimal number of sequences q that yields the best running time; i.e., the value of q such that T_{ HEP } is minimum over 1 ≤ q ≤ t.
Implementing HEP based on PMSprune
We decided to use PMSprune for implementing the first step in our method, because of its superiority compared to other algorithms as discussed in [31]. However, we stress that our approach is generic and can be used with any better algorithm that appears in future. In the following, we will refer to our method based on PMSprune as HEP_PMSprune. If q = mns we will denote it with HEP_PMSprune(mns), and if q = ons we will denote it with HEP_PMSprune(ons).
Determining mns for PMSprune
Determining ons for PMSprune
For fixed values of t, n, l and d, ons can be calculated for PMSprune by selecting the value of q that minimizes the total number of operations T_{HEP _PMSprune}for 1 ≤ q ≤ t. The following algorithm computes the value of ons for each instance (l, d).
Algorithm 3: Find ons
- 1)
q = ons = 1
- 2)
$E\left(l,d,q,n\right)={4}^{l}{\left(1-{(1-(\sum _{i=0}^{d}\left(\begin{array}{c}\hfill l\hfill \\ \hfill i\hfill \end{array}\right){\left(3/4\right)}^{i}{\left(1/4\right)}^{l-i}))}^{n-l+1}\right)}^{q}$
- 3)
${T}_{\mathsf{\text{min}}}=q{\left(n-l+1\right)}^{2}(l+{p}_{2d}\sum _{i=1}^{2d-{d}^{\prime}+1}\left(\begin{array}{c}\hfill l\hfill \\ \hfill i\hfill \end{array}\right){3}^{i})+l\left(t-q\right)\left(n-l+1\right)E\left(l,d,q,n\right)$
- 4)for q = mns to t do$E\left(l,d,q,n\right)={4}^{l}{\left(1-{(1-(\sum _{i=0}^{d}\left(\begin{array}{c}\hfill l\hfill \\ \hfill i\hfill \end{array}\right){\left(3/4\right)}^{i}{\left(1/4\right)}^{l-i}))}^{n-l+1}\right)}^{q}$$T=q{\left(n-l+1\right)}^{2}(l+{p}_{2d}\sum _{i=1}^{2d-{d}^{\prime}+1}\left(\begin{array}{c}\hfill l\hfill \\ \hfill i\hfill \end{array}\right){3}^{i})+l\left(t-q\right)\left(n-l+1\right)E\left(l,d,q,n\right)$
if T <T_{min} then
T_{min} = T
- 5)
return ons
End
The above algorithm computes q in O(t) time. In practice, the time for computing q takes negligible time with respect to the rest of motif finding steps; it took maximum one second for all experiments included in this paper with simulated and real datasets. To save some time, our implementation includes a look-up table containing pre-computed values of q for different values of l, n, and d, where l < 20, d < 3, and selected values of n with n = 300, n = 350, 400, ..., n = 700. For other values of l, n, and d, we compute the best q using the above algorithm.
Parallel version of HEP_PMSprune(ons)
We propose a parallel version for HEP_PMSprune(ons) called PHEP_PMSprune(ons). The two main steps of HEP_PMSprune(ons) can be parallelized as follows:
We parallelize the PMSprune algorithm by assigning a set of l-mers from s_{1} to each processor for establishing the set of neighboring motifs. The resulting sets are stored in candidate motif lists C_{ i }, i ∈ {1, 2, ..., p}, where p is the number of processors. After each processor finishes computation, the C_{ i } lists are merged together in a larger set C, such that each motif is represented once in this list; i.e., all repetitions are removed. Creating the C list is done in linear time with respect to the number of candidate motifs and it is achieved as follows:
We incrementally construct the partial list C_{ j } that contains the L_{ j } lists, 1 ≤ j ≤ p, by appending the list L_{ j } at the end of the list C_{j- 1}such that all elements in L_{ j } existing in C_{j-1}are discarded. This continues until j = p; i.e., C_{ p } is C. Discarding a repeated element is done efficiently as follows: For small values of l, we create a look-up table with size Σ^{ l }, where Σ is the alphabet size. Each possible l-length string can be mapped to a number in the range between zero and Σ^{ l } in O(l) time. The i^{th} entry in this table contains one if a string in C_{j- 1}is mapped to i. Otherwise, it contains zero. The strings in C_{ j } are queried against this look-up table to discard repetitions and set entries they are mapped to with value one. For longer values of l, we use the Aho-Corasick automaton to index all l-length motifs in C_{j- 1}, and check if a strings in C_{ j } exists in the automaton or not and add the new strings of C_{ j } to the automaton. For these string matching algorithms, we refer the reader to [35].
In the second step, we validate each candidate motif independently in parallel over the available processors. The running time of this algorithm is O(T_{s}/p +|C|), where T_{ s } is the sequential running time and |C| is the size of set C.
The first step in the parallel algorithm does not lead to loss of any motifs. This is because the set C includes the d-neighborhood set of the q-sequences. The reason is that we run PMSprune in parallel against the strings (x, s_{2}, s_{3}, ..., s_{ q }), where x is a substring of s_{1}. That is, each substring is not processed. The second step in the parallel algorithm is also correct, because the elements in C are independent of each other and checking the validity of each candidate motif can be safely run in parallel. Our experimental results confirm the correctness of our parallelization procedure.
Results and discussion
Experiments on simulated datasets
We used the simulated data sets that are used in many articles [25–30, 32–34] with t = 20 sequences and n = 600 characters, where the alphabet size is 4. Each (l, d) input instance dataset is generated as follows: We generate random strings with length (n-l) each, where the characters appear randomly with equal probability. Then we generate randomly an l-length string M and plant a copy of it in each sequence at random position after mutating it with at most d random mutations. We tested the algorithms for varying n, l, and d values and for the following challenging instances: (11, 3), (13, 4), (15, 5), (17, 6), (19, 7), and (21, 8).
Experiments overview
Our experiments address three major issues: The first is the performance of our method compared to the use of PMSprune only. The second, we show that our method for selecting q, already achieves the best running time. The third is the performance of the parallel version and its scalability. The algorithms are implemented on a 2 Quad-core processors (2.5 GHz each) machine. The programs are coded in C language. In the parallel version, we use openMP directives for parallelizing the code.
Performance of HEP on PMSprune
Time Comparison of PMSPrune and HEP_PMSprune(mns) with the Challenging Instances
l | d | T _{ PMSprune } | mns | T_{ HEP_PMSprune }(_{ mns }) | Improvement |
---|---|---|---|---|---|
11 | 3 | 1.92 s | 9 | 1.4 s | 27.1 % |
13 | 4 | 33.95 s | 7 | 26.05 s | 23.27 % |
15 | 5 | 7.7 m | 6 | 6.4 m | 16.8 % |
17 | 6 | 1.55 h | 7 | 1.26 h | 18.5 % |
19 | 7 | 18.62 h | 6 | 14.93 h | 19.8 % |
21 | 8 | 8.59 dy | 6 | 6.68 dy | 22.23 % |
Time Comparison of PMSPrune and HEP_PMSprune(ons) with the Challenging Instances
l | D | T _{ PMSprune } | ons | T_{ HEP_PMSprune }(_{ ons }) | Improvement |
---|---|---|---|---|---|
11 | 3 | 1.92 s | 10 | 1.34 s | 30 % |
13 | 4 | 33.95 s | 9 | 24.55 s | 27.69 % |
15 | 5 | 7.7 m | 7 | 6.02 m | 21.8 % |
17 | 6 | 1.55 h | 8 | 1.26 h | 18.65 % |
19 | 7 | 18.62 h | 7 | 14.39 h | 22.74 % |
21 | 8 | 8.59 dy | 6 | 6.68 dy | 22.23 % |
Evaluating the choice of q
In this section, we experimentally evaluate our algorithm for determining the best q that minimizes the running time of the HEP_PMSprune(q) algorithm. To achieve this, we will follow the following steps:
1. We run HEP_PMSprune(q), mns ≤ q ≤ t for the problem instances (11, 3), (13, 4), (15, 5), (17, 6), (19, 7), and (21, 8) and determine the value of q that minimizes the running time; we will refer to this value with ons_{exp}.
2. Compare the ons_{exp} against our ons computed theoretically.
The performance of the HEP_PMSprune(ons) for different values of n and l
n | d | l | ons | T_ons | ons_exp | T_onsexp | T_pms |
---|---|---|---|---|---|---|---|
300 | 3 | 11 | 9 | 0.0001 | 3-20 | 0.0001 | 0.0001 |
600 | 3 | 11 | 10 | 1.34 | 10 | 1.34 | 1.92 |
900 | 3 | 11 | 14 | 4 | 11-16 | 4 | 5 |
1200 | 3 | 11 | 17 | 7 | 17 | 7 | 8 |
1500 | 3 | 11 | 20 | 16 | 20 | 16 | 16 |
300 | 3 | 12 | 6 | 0.05 | 4-20 | 0.05 | 0.05 |
600 | 3 | 12 | 8 | 0.83 | 4-20 | 0.83 | 0.83 |
900 | 3 | 12 | 8 | 1.5 | 6-20 | 1.5 | 1.5 |
1200 | 3 | 12 | 9 | 3 | 6-15 | 3 | 4 |
1500 | 3 | 12 | 10 | 5 | 8-12 | 5 | 7 |
300 | 4 | 13 | 7 | 3 | 5-20 | 3 | 3 |
600 | 4 | 13 | 9 | 24.55 | 9 | 24.55 | 33.95 |
900 | 4 | 13 | 11 | 81 | 11 | 81 | 109 |
1200 | 4 | 13 | 14 | 190 | 14 | 190 | 217 |
1500 | 4 | 13 | 17 | 353 | 17-19 | 356 | 360 |
300 | 4 | 14 | 6 | 1 | 4-20 | 1 | 1 |
600 | 4 | 14 | 7 | 6.5 | 7-18 | 6.5 | 7 |
900 | 4 | 14 | 8 | 21.5 | 8-9 | 21.5 | 24 |
1200 | 4 | 14 | 8 | 54 | 8 | 54 | 67 |
1500 | 4 | 14 | 9 | 107 | 9 | 107 | 146 |
300 | 4 | 15 | 5 | 0.25 | 4--20 | 0.25 | 0.25 |
600 | 4 | 15 | 5 | 1.25 | 4-20 | 1.25 | 1.25 |
900 | 4 | 15 | 6 | 5 | 5-20 | 5 | 5 |
1200 | 4 | 15 | 6 | 12 | 8 | 10 | 13 |
1500 | 4 | 15 | 7 | 16.5 | 7-13 | 16.5 | 20 |
300 | 4 | 16+ | 5 | 0.002 | 3-20 | 0.002 | 0.002 |
600 | 4 | 16+ | 5 | 0.25 | 4-20 | 0.25 | 0.25 |
900 | 4 | 16+ | 5 | 1 | 4-20 | 1 | 1 |
1200 | 4 | 16+ | 6 | 2.34 | 5-20 | 2.34 | 2.34 |
1500 | 4 | 16+ | 6-8 | 4.89 | 5-20 | 4.89 | 4.89 |
300 | 5 | 15 | 7 | 38 | 6-10 | 38 | 46 |
600 | 5 | 15 | 8 | 361.2 | 8 | 360 | 462 |
900 | 5 | 15 | 9 | 1250 | 9 | 1250 | 1847 |
1200 | 5 | 15 | 11 | 2976 | 11 | 2976 | 4060 |
1500 | 5 | 15 | 13 | 5829 | 13 | 5829 | 6969 |
300 | 5 | 17 | 5 | 2 | 5-20 | 2 | 2 |
600 | 5 | 17 | 6 | 27 | 13-20 | 19 | 19 |
900 | 5 | 17 | 5 | 103 | 7-20 | 92 | 92 |
1200 | 5 | 17 | 6 | 231 | 6-8 | 224 | 264 |
1500 | 5 | 17 | 6 | 439 | 6-8 | 439 | 552 |
300 | 5 | 18+ | 5 | 1 | 5-20 | 1 | 1 |
600 | 5 | 18+ | 6 | 5 | 6-20 | 4 | 4 |
900 | 5 | 18+ | 6-7 | 14 | 6-20 | 14 | 14 |
1200 | 5 | 18+ | 6-7 | 33 | 6-20 | 33 | 33 |
1500 | 5 | 18+ | 6-8 | 74 | 6-20 | 74 | 74 |
Note that it was not feasible to list the results for all possible values n, l, and d in Table 3. But in other instances with different values of n, l, and d, we found that ons and its time were consistent with ons_{exp} and its time published in this table.
Performance of PHEP_PMSprune(ons)algorithm
Running time of PHEP_PMSprune(ons) using different number of processors p for some challenging instances
l | d | Time | |||||||
---|---|---|---|---|---|---|---|---|---|
P = 2 | P = 3 | P =4 | P = 5 | P = 6 | P = 7 | P = 8 | |||
13 | 4 | 24.86 s | 12.4 s | 8.35 s | 6.1 s | 4.95 s | 4.35 s | 3.6 s | 3.2 s |
15 | 5 | 6.34 m | 3.19 m | 2.13 m | 1.61 m | 1.28 m | 1.07 m | 55.2 s | 48.5 s |
17 | 6 | 1.28 h | 38.28 m | 25.58 m | 19.16 m | 15.34 m | 12.81 m | 10.98 m | 9.61 m |
19 | 7 | 14.56 h | 7.24 h | 4.81 h | 3.61 h | 2.98 h | 2.42 h | 2.07 h | 1.82 h |
21 | 8 | 6.68 dy | 3.33 dy | 2.23 dy | 1.67 dy | 1.34 dy | 1.12 dy | 23.18 h | 20.42 h |
Experiments on real datasets
We used two collections of real datasets used in previous research papers [10, 26, 29, 36]. The first collection is a dataset including a number of the upstream regions of yeast genes [37] affected by certain transcription factors. The transcription factors are from the SCPD [38] database and the paper [39]. The upstream DNA sequences were extracted using the Saccharomyces Genome Database [37]. The second collection includes the dataset of Blanchette [36] which includes the upstream DNA regions of many genes from different species. This dataset is available at http://bio.cs.washington.edu/supplements/FootPrinter and a copy of it is available with our software tool for testing.
Application of the PHEP_PMSprune(ons) on the real yeast dataset
Transcription Factor | Genes | Detected motif (s) & parameters | Published Motif (s) & reference(s) | Time |
---|---|---|---|---|
PHO4 (600 bp) | PHO5, PHO8, PHO81, PHO84, | CACGTG (6,0) | CACGT[G|T] [38] | 38 (5%) |
HSE_HSTF (600 bp) | SSA1, HSP26, SSA4, HSC82, SIS1, CUP1-1 | TTCAGTGAA (9,2) | TTCNNGAA [38] TTCNNNGAA [38] | 37 (35%) |
PDR (600 bp) | PDR3, SNQ2, PDR15, HXT9, HXT11, PDR5, YOR1 | TCCGTGGA (8,1) TCCGCGGA (8,1) | TCCG[C|T]GGA [38] | 27(13%) |
MCB (600 bp) | CDC2, CDC9, CDC6, CLN1, POL1, CDC21 | ACGCGT (6,0) | [A|T]CGCG[A|T] [38] | 31(20%) |
ECB (600 bp) | SWI4, MCM5 MCM7, CDC6 CLN3 | TTTCCCATTAAGGAAA (16,3) | 41(49%) |
Application of the PHEP_PMSprune(ons) on the Blanchette real dataset
DNA region | Seq. no. | Detected motif | Published Motif | Time |
---|---|---|---|---|
Insulin family 5' promoter (500 bp) | 8 | CCTCAGCCCC (10, 1) | 87(10%) | |
AAGACTCTAA (10,2) | ||||
GCCATCTGCC (10,1) | ||||
CTATAAAG (8,0) | CTATAAAG [36, GB] | |||
GGGAAATG (8,1) | ||||
Metallothionein 5'UTR+Promoter (590 bp) | 26 | TTTGCACACGC (11,3) | 7.87(1%) | |
TGCACAC (7,1) | ||||
Interleukin-3 5'UTR+Promoter 490 bp | 6 | TTGAGTACT (9,2) | ||
GATGAATAAT (10,1) | ||||
TCTTCAGAG, (9,2) | ||||
AGGACCAG, (8,1) | 466(10%) | |||
AGGTTCCATGTCAGATAAAG, ATGGAGGTTCCATGTCAGAT, CTATGGAGGTTCCATGTCAG, GAGGTTCCATGTCAGATAAA, GGAGGTTCCATGTCAGATAA, TATGGAGGTTCCATGTCAGA, TGGAGGTTCCATGTCAGATA, all these motifs found with (20,0) | Novel | |||
Growth-hormone 5^{'}UTR+promoter (380 bp) | 16 | AACTTATCCAT (11,3) | 3.43(0%) | |
ATAAATGTAAA (11,3) | ||||
TATAAAAAG (9,2) | ||||
c-fos 5^{'} UTR+promoter (800bp) | 6 | CCATATTAGGAC (12,3) | 350(15%) | |
GAGTTGGCTGC (11,3) | GAGTTGGCTG [36] | |||
CACAGGATGT (10,2) | ||||
AGGACATCTGCT (12,3) | ||||
c-myc 5'+promoter (100bp) | 7 | GTTTATTC (8,1) | GTTTATTC [36] | 83.5(42%) |
CTTGCTGGG (9,2) | TTGCTGGG [36] | |||
TGTTTACATC (10,2) | ||||
CCCTCCCC (8,1) | ||||
Histone H1 5^{'}UTR+Promoter 650 bp | 4 | CAATCACCAC, (10,2) | CAATCACCAC, [36, GB] | 47.6(9%) |
AAACAAAAGT (10,1) | AAACAAAAGT, [36, GB] |
Tables 5 and 6 also include the running times (in seconds) of running our method for the listed problem instances and the improvement in time compared to the PMSprune method. The running time for one problem instance is the time needed to run our program in the (l, d) parameters range from (6, 0) until (21, 3), i.e., there are 64 invocations of our program. The results show that our program is superior to the PMSprune for large instances.
Conclusions
In this paper, we introduced an efficient method that can enhance the performance of exact algorithms for the motif finding problem. Our method depends on dividing the sequence space into two sets. Over the first set, we generate a set of candidate motifs. Then, we use the remaining set of sequences to verify if each candidate motif is a real one. The experimental results show that our method is superior to the best methods available so far and could tackle large problems like (21, 8). Finally, we introduced a scalable and efficient parallel version for the proposed method. Our tool is available for free for academic research at http://www.nubios.nileu.edu.eg/tools/hymotif.
Availability and requirements
Project name: hymotif.
Project home page: http://www.nubios.nileu.edu.eg/tools/hymotif
Operating system(s): Linux.
Programming language: C.
Other requirements: C/C++ libraries.
License: GPL.
Any restrictions to use by non-academics: No restrictions.
Declarations
Acknowledgements
The authors are grateful to M.M. Mohie Eldin for useful discussion. The authors also thank Sanguthevar Rajasekaran for providing us with the source code of PMSprune and real datasets.
This article has been published as part of BMC Bioinformatics Volume 13 Supplement 17, 2012: Eleventh International Conference on Bioinformatics (InCoB2012): Bioinformatics. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcbioinformatics/supplements/13/S17.
Authors’ Affiliations
References
- Waterman MS, Aratia R, Galas DJ: Pattern recognition in several sequences: consensus and alignment. Bulletin of Mathematical Biology. 1984, 46 (4): 515-527.View ArticlePubMedGoogle Scholar
- Pevzner P, Sze SH: Combinatorial approaches to finding subtle signals in DNA sequences. Proceedings of Eighth International Conference on Intelligent Systems for Molecular Biology. 2000, 269-278.Google Scholar
- Lawrence C, Reilly A: An expectation maximization (EM) algorithm for the identification and characterization of common sites in unaligned biopolymer sequences. Proteins: Structure, Function and Genetics. 1990, 7: 41-51. 10.1002/prot.340070105.View ArticleGoogle Scholar
- Lawrence C, Altschul S, Boguski M, Liu J, Neuwald A, Wootton J: Detecting subtle sequence signals: A Gibbs Sampling strategy for multiple alignment. Science. 1993, 262: 208-214. 10.1126/science.8211139.View ArticlePubMedGoogle Scholar
- Bailey T, Elkan C: Unsupervised learning of multiple motifs in biopolymers using Expectation Maximization. Machine Learning. 1995, 21: 51-80.Google Scholar
- Fraenkel Y, Mandel Y, Friedberg D, Margalit H: Identification of common motifs in unaligned DNA sequences: application to Escherichia coli Lrp regulon. Bioinformatics. 1995, 11: 379-387. 10.1093/bioinformatics/11.4.379.View ArticleGoogle Scholar
- Rigoutsos I, Floratos A: Combinatorial pattern discovery in biological sequences: the TEIRESIAS algorithm. Bioinformatics. 1998, 14: 55-67. 10.1093/bioinformatics/14.1.55.View ArticlePubMedGoogle Scholar
- Hertz GZ, Stormo GD: Identifying DNA and protein patterns with statistically significant alignments of multiple sequences. Bioinformatics. 1999, 15: 563-577. 10.1093/bioinformatics/15.7.563.View ArticlePubMedGoogle Scholar
- Gelfand M, Koonin E, Mironov A: Prediction of transcription regulatory sites in archaea by a comparative genomic approach. Nucleic Acid Res. 2000, 28: 695-705. 10.1093/nar/28.3.695.PubMed CentralView ArticlePubMedGoogle Scholar
- Buhler J, Tompa M: Finding motifs using random projections. Journal of Computational Biology. 2002, 9 (2): 225-242. 10.1089/10665270252935430.View ArticlePubMedGoogle Scholar
- Price A, Ramabhadran S, Pevzner PA: Finding subtle motifs by branching from sample strings. Bioinformatics. 2003, 19 (2): ii149-ii155. 10.1093/bioinformatics/btg1072.PubMedGoogle Scholar
- Huang C, Lee W, Hsieh S: An improved heuristic algorithm for finding motif signals in DNA sequences. IEEE/ACM Transactions on Computational Biology and Bioinformatics. 2011, 8 (4): 959-975.View ArticlePubMedGoogle Scholar
- Galas DJ, Eggert M, Waterman MS: Rigorous pattern-recognition methods for DNA sequences: analysis of promoter sequences from Escherichia coli. Journal of Molecular Biology. 1985, 186 (1): 117-128. 10.1016/0022-2836(85)90262-1.View ArticlePubMedGoogle Scholar
- Staden R: Methods for discovering novel motifs in nucleic acid sequences. Computer Applications in the Biosciences. 1989, 5 (4): 293-298.PubMedGoogle Scholar
- Brazma A, Jonassen I, Vilo J, Ukkonen E: Predicting gene regulatory elements in silico on a genomic scale. Genome Research. 1998, 15: 1202-1215.Google Scholar
- Sagot MF: Spelling approximate repeated or common motifs using a suffix tree. Latin'98: Theoretical informatics, LNCS. Edited by: Lucchesi CL, Moura AV. 1998, 1380: 111-127.Google Scholar
- Van Helden J, Andre B, Collado-Vides J: Extracting regulatory sites from the upstream region of yeast genes by computational analysis of oligonucleotide frequencies. Journal of Molecular Biology. 1998, 281 (5): 827-842. 10.1006/jmbi.1998.1947.View ArticlePubMedGoogle Scholar
- Tompa M: An exact method for finding short motifs in sequences with application to the ribosome binding site problem. Proceedings of seventh International Conference on Intelligent Systems for Molecular Biology. 1999, 262-271.Google Scholar
- Marsan L, Sagot MF: Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification. Journal of Computational Biology. 2000, 7 (3-4): 345-362. 10.1089/106652700750050826.View ArticlePubMedGoogle Scholar
- Sinha S, Tompa M: A statistical method for finding transcription factor binding sites. Proceedings of Eighth International Conference on Intelligent Systems for Molecular Biology. 2000, 344-354.Google Scholar
- Blanchette M: Algorithms for phylogenetic footprinting. Proceedings of Fifth International Conference Computational Biology (RECOMB 2001). 2001Google Scholar
- Eskin E, Pevzner PA: Finding composite regulatory patterns in DNA sequences. Bioinformatics. 2002, 18 (1): 354-363. 10.1093/bioinformatics/18.suppl_1.S354.View ArticleGoogle Scholar
- Evans PA, Smith A: Toward optimal motif enumeration. Proceedings of Eighth International Workshop Algorithms and Data Structures (WADS03). 2003, 47-58.Google Scholar
- Carvalho AM, Freitas AT, Oliveira AL, Sagot MF: A highly scalable algorithm for the extraction of CIS-Regulatory regions. Proceedings of Third Asia Pacific Bioinformatics Conference. 2005, 273-282.View ArticleGoogle Scholar
- Chin FYL, Leung HCM: Voting algorithms for discovering long motifs. Proceedings of Third Asia Pacific Bioinformatics Conference. 2005, 261-271.View ArticleGoogle Scholar
- Rajasekaran S, Balla S, Huang C-H: Exact algorithms for planted motif problems. Journal of Computational Biology. 2005, 12 (8): 1117-1128. 10.1089/cmb.2005.12.1117.View ArticlePubMedGoogle Scholar
- Davila J, Balla S, Rajasekaran S: Space and time efficient algorithms for planted motif search. Proceedings of Second International Workshop on Bioinformatics Research and Applications (LNCS 3992). 2006, 822-829.Google Scholar
- Pisanti N, Carvalho A, Marsan L, Sagot MF: RISOTTO: fast extraction of motifs with mismatches. Proceedings of Seventh Latin American Theoretical Informatics Symposium. 2006, 757-768.Google Scholar
- Davila J, Balla S, Rajasekaran S: Fastand practical algorithms for planted (l, d) motif search. IEEE/ACM Transactions on Computational Biology and Bioinformatics. 2007, 544-552.Google Scholar
- Dinh H, Rajasekaran S, Kundeti V: PMS5: an efficient exact algorithm for the (l, d)-motif finding problem. BMC Bioinformatics. 2011, 12: 410-420. 10.1186/1471-2105-12-410.PubMed CentralView ArticlePubMedGoogle Scholar
- Sharma D, Rajasekaran S, Dinh H: An experimental comparison of PMSprune and other algorithms for motif search. CoRR abs. 2011, 1108.5217-Google Scholar
- Abbas MM, Bahig HM: Performance and analysis of modified voting algorithm for planted motif search. Proceedings of Seventh ACS/IEEE International Conference on Computer Systems and Applications. 2009, 725-731.Google Scholar
- Bahig HM, Abbas MM, Bhery A: Experimental study of modified voting algorithm for planted (l, d)-motif problem. Experimental Medicine and Biology, special issue Advanced in Computational Biology, Springer. 2010, 65-73.Google Scholar
- Rajasekaran S, Dinh H: A speedup technique for (l, d)-motif finding algorithms. BMC Research Notes. 2011, 54-61. 4Google Scholar
- Gusfield D: Algorithms on strings, trees, and sequences: computer science and computational biology. Cambridge university Press, New York. 1977Google Scholar
- Blanchette J, Tompa M: Discovery of regulatory elements by a computational method for phylogenetic footprinting. Genome Research. 2002, 12 (5): 739-748. 10.1101/gr.6902.PubMed CentralView ArticlePubMedGoogle Scholar
- Cherry JM, Adler C, Ball C, Chervitz SA, Dwight SS, Hester ET, Jia Y, Juvik G, Roe T, Schroeder M, Weng S, Botstein D: SGD: Saccharomyces Genome Database. Nucleic Acid Res. 1998, 26: 73-79. 10.1093/nar/26.1.73. [http://www.yeastgenome.org/]PubMed CentralView ArticlePubMedGoogle Scholar
- Zhu J, Zhang M: SCPD: A Promoter Database of the Yeast Saccha-Romyces Cerevisiae. Bioinformatics. 1999, 15 (7-8): 607-611. [http://cgsigma.cshl.org/jian/]View ArticlePubMedGoogle Scholar
- McInerny CJ, Partridge JF, Mikesell GE, Creemer DP, Breeden LL: A novel Mcm1-dependent element in the SWI4, CLN3, CDC6, and CDC47 promoters activates M/G1-specific transcription. Genes Dev. 1997, 11 (10): 1277-1288. 10.1101/gad.11.10.1277.View ArticlePubMedGoogle Scholar
- Wingender E, Dietze P, Karas H, Knuppel R: TRANSFAC: a database on transcription factors and their DNA binding sites. Nucleic Acids Research. 1996, 24 (1): 238-241. 10.1093/nar/24.1.238. [http://transfac.gbf-braunschweig.de/TRANSFAC/]PubMed CentralView ArticlePubMedGoogle Scholar
- Natesan S, Gilman M: YY1 facilitates the association of serum response factor with the c-fos serum response element. Mol Cell Biol. 1995, 15 (11): 5975-5982.PubMed CentralView ArticlePubMedGoogle Scholar
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