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A novel RNA structural alignment method has been proposed based on profile-csHMMs. In principle, the profile-csHMM based approach can handle any kind of RNA secondary structures including pseudoknots, and it has been shown that the proposed approach can find highly accurate RNA alignments. In order to find the optimal alignment, the method employs...
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... proceeding with the discussion, let us first define the concept of adjoining rules. As the name suggests, an adjoining rule describes how we can adjoin two nonoverlapping subse- quences to obtain a longer subsequence. Examples of adjoining rules are shown in Fig. 3. For example, let us consider the ad- joining rule shown on the left-hand side of Fig. 3(a). This rule shows how we can adjoin a subsequence with two intervals (se- quence a) and a subsequence with a single base (sequence b) to obtain a new subsequence that has also two intervals (sequence c). Similarly, the rule illustrated in Fig. ...
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... proceeding with the discussion, let us first define the concept of adjoining rules. As the name suggests, an adjoining rule describes how we can adjoin two nonoverlapping subse- quences to obtain a longer subsequence. Examples of adjoining rules are shown in Fig. 3. For example, let us consider the ad- joining rule shown on the left-hand side of Fig. 3(a). This rule shows how we can adjoin a subsequence with two intervals (se- quence a) and a subsequence with a single base (sequence b) to obtain a new subsequence that has also two intervals (sequence c). Similarly, the rule illustrated in Fig. 3(b) shows how we can adjoin a subsequence with two intervals (sequence a) and an- other ...
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... shown in Fig. 3. For example, let us consider the ad- joining rule shown on the left-hand side of Fig. 3(a). This rule shows how we can adjoin a subsequence with two intervals (se- quence a) and a subsequence with a single base (sequence b) to obtain a new subsequence that has also two intervals (sequence c). Similarly, the rule illustrated in Fig. 3(b) shows how we can adjoin a subsequence with two intervals (sequence a) and an- other subsequence with two intervals that consists of a single base-pair (sequence b) to get a longer subsequence with two in- tervals (sequence c). Another rule depicted in Fig. 3(c) shows how we can adjoin two neighboring subsequences each with a single ...
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... that has also two intervals (sequence c). Similarly, the rule illustrated in Fig. 3(b) shows how we can adjoin a subsequence with two intervals (sequence a) and an- other subsequence with two intervals that consists of a single base-pair (sequence b) to get a longer subsequence with two in- tervals (sequence c). Another rule depicted in Fig. 3(c) shows how we can adjoin two neighboring subsequences each with a single interval (sequences a and b) to obtain a new sequence that has only one interval (sequence c). Let us consider the adjoining order shown in Fig. 2 (left-hand side). We can obtain the par- tial RNA in STEP-2 by applying the adjoining rule in Fig. 3(a). Similarly, ...
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... Another rule depicted in Fig. 3(c) shows how we can adjoin two neighboring subsequences each with a single interval (sequences a and b) to obtain a new sequence that has only one interval (sequence c). Let us consider the adjoining order shown in Fig. 2 (left-hand side). We can obtain the par- tial RNA in STEP-2 by applying the adjoining rule in Fig. 3(a). Similarly, we can obtain the partial RNAs shown in STEP-3 and STEP-4 by using the rules in Fig. 3(b) and (c), ...
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... interval (sequences a and b) to obtain a new sequence that has only one interval (sequence c). Let us consider the adjoining order shown in Fig. 2 (left-hand side). We can obtain the par- tial RNA in STEP-2 by applying the adjoining rule in Fig. 3(a). Similarly, we can obtain the partial RNAs shown in STEP-3 and STEP-4 by using the rules in Fig. 3(b) and (c), ...
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... rules for adjoining "symbol sequences" (shown on the left-hand side of Fig. 3) are ultimately used for adjoining the "optimal state sequences" (shown on the right-hand side of Fig. 3) that correspond to certain portions of the pro- file-csHMM. As an example, let us again focus on the adjoining rule in Fig. 3(a). Consider a subsequence with two intervals, where the first interval consists of only one symbol at ...
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... rules for adjoining "symbol sequences" (shown on the left-hand side of Fig. 3) are ultimately used for adjoining the "optimal state sequences" (shown on the right-hand side of Fig. 3) that correspond to certain portions of the pro- file-csHMM. As an example, let us again focus on the adjoining rule in Fig. 3(a). Consider a subsequence with two intervals, where the first interval consists of only one symbol at position and the second interval is located between positions and . Assume that the underlying state at ...
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... rules for adjoining "symbol sequences" (shown on the left-hand side of Fig. 3) are ultimately used for adjoining the "optimal state sequences" (shown on the right-hand side of Fig. 3) that correspond to certain portions of the pro- file-csHMM. As an example, let us again focus on the adjoining rule in Fig. 3(a). Consider a subsequence with two intervals, where the first interval consists of only one symbol at position and the second interval is located between positions and . Assume that the underlying state at position is and the states at positions and are and , respectively. How can we find the optimal state sequence of the given ...
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... of only one symbol at position and the second interval is located between positions and . Assume that the underlying state at position is and the states at positions and are and , respectively. How can we find the optimal state sequence of the given subsequence by combining shorter optimal state sequences? As shown on the right-hand side of Fig. 3(a), we can adjoin the optimal state sequence with two intervals (where the first interval has only one symbol at position with underlying state , and the second interval is located between and whose left and right terminal states are and , respectively) and the optimal state sequence with a single base (located at with underlying state ). ...
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... at with underlying state ). When adjoining the two optimal state sequences, we consider all possible transitions from state at position to state at position and choose the one that maximizes the observation probability. 3 This exactly corresponds to STEP-2B shown on the right-hand side of Fig. 2. In a similar manner, the adjoining rule shown in Fig. 3(b) [or Fig. 3(c)] can be used to find the optimal sate sequence corresponding to the portion of the profile-csHMM shown in STEP-3B(or ...
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... state ). When adjoining the two optimal state sequences, we consider all possible transitions from state at position to state at position and choose the one that maximizes the observation probability. 3 This exactly corresponds to STEP-2B shown on the right-hand side of Fig. 2. In a similar manner, the adjoining rule shown in Fig. 3(b) [or Fig. 3(c)] can be used to find the optimal sate sequence corresponding to the portion of the profile-csHMM shown in STEP-3B(or ...
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... RNA structural alignment, also known as RNA sequence-structure alignment, is the challenging area of bioinformatics, which becomes more challenging and advantageous if the pseudoknots are also considered in the structure. The literature available on pseudoknotted structural alignment of RNA includes simulated annealing [1]; dynamic programming [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]; genetic algorithm [17][18][19]; integer linear programming [20][21][22][23]; graph approach [24][25][26][27]; tree construction [28][29][30][31]; stochastic sampling [32]; Markov chain Monte Carlo [33] and formal grammar [34][35][36]. ...
A two-level particle swarm optimization (TL-PSO) algorithm is proposed for training stochastic context-sensitive hidden Markov model (cs-HMM), that addresses a thrust area of bioinformatics i.e. structural alignment of pseudoknotted non-coding RNAs (ncRNAs). Due to the well-conserved sequences and corresponding secondary structures of ncRNAs, the structural information becomes imperative for performing their alignments. Proposed approach is unique in the sense: it is the first idea so far which works on optimization of the model length; also it is the first swarm intelligence technique that is proposed for training csHMM. The two-level strategy with training and cross training sets helps in increasing the diversity of the particles so as to avoid trapping in local optima, yields more accurate estimation parameters, preserves the structure of the model and provides the best compression from the model. TL-PSO yields a trained stochastic model with position-dependent probabilities that achieves high prediction ratios than the compared non-stochastic scoring matrix based csHMM approaches. TL-PSO is also tested solely for sequence alignment of proteins, by training the conventional HMMs. TLPSO-HMM produces an effective framework for sequence alignment in terms of alignment quality and prediction accuracy than the competitive state-of-the-art and family of PSO based algorithms. Conjointly, TLPSO-csHMM finds higher prediction measures than competitive RNA structural alignment techniques for pseudoknotted and non-pseudoknotted RNA structures of diverse complexities.
... Then they employed a DP algorithm called the SCA (sequential component adjoining) algorithm for the optimal alignment of profile-csHMMs. [61] proposed a few modifications in profile-csHMM for the adjoining order in SCA algorithm for fast RNA structural alignments with minimum computational cost. Hamada et al. (2009) [62] presented CentroidAlign, a novel estimator for structural multiple sequence alignments, based on maximizing the expected accuracy of predictions. ...
... The approach claims to capture the features missing in the conventional CMs and generally achieving significantly improved accuracy. Yoon (2009) [66] proposed constraints into its previously developed profile-csHMM [61]. The profile-HMM was used to identify the seed regions that can be aligned with high confidence. ...
... Only these regions will be passed to a more complex model, such as a covariance model (CM; profile-SCFG) [3] or a profile context-sensitive HMM (profile-csHMM) [16, 17], for further inspection. In fact, these are just a few examples, and there also exist other approaches for making RNA alignment and RNA search algorithms faster [18, 19]. Recently, we proposed an efficient RNA structural alignment algorithm based on profile-csHMMs, which can also be used for aligning RNAs that contain pseudoknots [17]. ...
... We can also handle the RNAs outside the Rivas and Eddy class by incorporating additional adjoining rules. See [19] for further discussions on adjoining rules and the descriptive capability of profile-csHMMs.Table 4 shows that all three profilecsHMM-based approaches yielded accurate alignment results for Flavi pk3 RNAs. By comparing the performance of the profile-csHMM method with different constraints, we can note that incorporating the proposed alignment constraint virtually did not affect the alignment accuracy. ...
When aligning RNAs, it is important to consider both the secondary structure similarity and primary sequence similarity to find an accurate alignment. However, algorithms that can handle RNA secondary structures typically have high computational complexity that limits their utility. For this reason, there have been a number of attempts to find useful alignment constraints that can reduce the computations without sacrificing the alignment accuracy. In this paper, we propose a new method for finding effective alignment constraints for fast and accurate structural alignment of RNAs, including pseudoknots. In the proposed method, we use a profile-HMM to identify the "seed" regions that can be aligned with high confidence. We also estimate the position range of the aligned bases that are located outside the seed regions. The location of the seed regions and the estimated range of the alignment positions are then used to establish the sequence alignment constraints. We incorporated the proposed constraints into the profile context-sensitive HMM (profile-csHMM) based RNA structural alignment algorithm. Experiments indicate that the proposed method can make the alignment speed up to 11 times faster without degrading the accuracy of the RNA alignment.
... 2) Unlike the Viterbi algorithm that proceeds " left-to-right " or the CYK algorithm that proceeds " inside-to-outside " , the SCA algorithm allows us to explicitly describe how the optimal subsequence of shorter subsequences can be extended and adjoined to find the optimal state sequence of longer subsequences. The specific order that describes how we should proceed to find the final optimal state sequence is called the adjoining order [19], [20]. For example,Fig. 3 shows the adjoining order for the profile-csHMM shown inFig. 2 (c). ...
... 2. By following these steps, we can ultimately find the optimal state sequence for the entire profile-csHMM. Detailed discussion on adjoining orders can be found in [19] and [20]. Unlike the Viterbi algorithm and the CYK algorithm, the SCA algorithm has a variable computational complexity that depends on the adjoining order [19]. ...
... However, finding the optimal adjoining order can be quite difficult for profile-csHMMs that represent complex secondary structures, and we need an efficient method that can automatically find the optimal order for a given profile-csHMM. In fact, such an algorithm has been proposed in [20], and it can be used to find the best order that minimizes the computational cost of the SCA algorithm. It was shown that using the optimal adjoining order can improve the alignment speed up to 3.6 times for RNA pseudoknots [20]. ...
Noncoding RNAs (ncRNAs) are RNA molecules that function without being translated into proteins. Systematic research on ncRNAs has shown that there exist many ncRNAs that are actively involved in various biological processes, playing key roles in controlling them. As the annotation of ncRNAs is still at an early stage, developing efficient computational tools for finding ncRNAs is of great importance. One effective way for finding new ncRNAs is to look for new RNAs that resemble the RNAs that have already been identified. Recently, a new model called the profile context-sensitive HMM (proflle-csHMM) has been proposed, and it has been shown that they can provide a convenient framework for finding RNA homologues. In this paper, we give a brief review of proflle-csHMMs and their application in RNA similarity search. We also introduce a number of recent advances related to proflle-csHMMs and proflle-csHMM based search.
