Fast Structural Similarity Search of Noncoding RNAs Based on Matched Filtering of Stem Patterns

Transcription

1 Fast Structural Siilarity Search of Noncoding RNs Based on Matched Filtering of Ste Patterns Byung-Jun Yoon Dept. of Electrical Engineering alifornia Institute of Technology Pasadena, 91125, S Eail: bjyoon@caltech.edu P. P. Vaidyanathan Dept. of Electrical Engineering alifornia Institute of Technology Pasadena, 91125, S Eail: ppvnath@systes.caltech.edu bstract Many noncoding RNs (ncrns) have characteristic secondary structures that give rise to coplicated base correlations in their priary sequences. Therefore, when perforing an RN siilarity search to find new ebers of a ncrn faily, we need a statistical odel such as the profilecshmm or the covariance odel (M) that can effectively describe the correlations between distant bases. However, these odels are coputationally expensive, aking the resulting RN search very slow. To overcoe this proble, various prescreening ethods have been proposed that first use a sipler odel to scan the database and filter out the dissiilar regions. Only the reaining regions that bear soe siilarity are passed to a ore coplex odel for closer inspection. It has been shown that the prescreening approach can ake the search speed significantly faster at no (or a slight) loss of prediction accuracy. In this paper, we propose a novel prescreening ethod based on atched filtering of ste patterns. nlike any existing ethods, the proposed ethod can prescreen the database solely based on structural siilarity. The proposed ethod can handle RNs with arbitrary secondary structures, and it can be easily incorporated into various search ethods that use different statistical odels. Furtherore, the proposed approach has a low coputational cost, yet very effective for prescreening, as will be deonstrated in the paper. I. INTRODTION Recent studies on various genoes have revealed that there exist a large nuber of noncoding RNs (ncrns), which are RN olecules that function without being translated into proteins [6]. nlike RNs (essenger RNs) that passively carry protein-coding inforation, the ncrns actively participate in diverse biological processes. lthough exaples such as the trns (transfer RNs) and rrns (ribosoal RNs) have been known for a long tie, systeatic research on ncrns shows that the nuber of RNs and the variety and extent of their roles are uch larger than it was previously thought [6]. s the annotation of ncrns is still at an early stage, it is of great iportance to develop coputational tools that can be used for screening the genoe to identify new RNs. n effective way for finding new ncrns is to search for RNs that look siilar to already known RNs. iven a set of related RNs that belong to the sae faily, we ay construct a statistical odel that represents the RN faily, and use this odel to find siilar regions in a genoe database. This is usually called a siilarity search or a hoology search. For a successful RN siilarity search, we need a suitable statistical odel that can effectively describe the ain characteristics of ncrns. One distinguishing feature of any ncrns is the conservation of their secondary structures. s the secondary structure of a ncrn plays a crucial role in carrying out its biological function, any RN failies have characteristic secondary structures that are coonly shared by their ebers [1]. For this reason, it is iportant to consider both sequence siilarity as well as structural siilarity when perforing an RN siilarity search. In fact, using a scoring schee that can reasonably cobine sequence and structural siilarities can considerably increase the discriinative power of the search [1], [9]. The secondary structure of an RN can be described in ters of correlations between distant bases in its priary sequence [9]. Therefore, in order to represent ncrn failies and develop a scoring schee that can cobine contributions fro sequence siilarity and structural siilarity, we need a statistical odel that can describe these base correlations. Exaples of such odels are the M 1 (covariance odel) [1] and the profile-cshmm (profile context-sensitive HMM) [8], [11]. nfortunately, the coputational cost for using these odels is often too high for scanning a large genoe database. In order to solve this proble, a nuber of ethods have been proposed to expedite the RN siilarity search [3], [4], [7], [10]. The ain idea underlying these ethods is to prescreen the database using a sipler odel (e.g., a profile-hmm) to filter out the dissiilar regions as uch as possible. Only the reaining regions that bear soe siilarity are passed to a ore coplex (hence, ore discriinative) odel, such as the profile-cshmm or the M, for further inspection. It has been shown that this prescreening approach can ake the search speed significantly faster, either without any loss of accuracy [3], [4], [10] or at a slight loss of accuracy [7]. In this paper, we propose a novel prescreening ethod based on atched filtering of ste patterns. nlike the previous ethods, the proposed ethod can scan the database solely based on structural siilarity, which can be especially useful for RN failies with low sequence siilarity. s the 1 M can be viewed as a SF (stochastic context-free graar) with a special structure.

2 atched filter is constructed fro the secondary structure of the reference RN instead of a specific statistical odel, the proposed ethod can be used in cobination with any kind of odel, including profile-cshmms and Ms. Furtherore, as the atched filter can be constructed for any kind of RN secondary structure, the proposed ethod can be used for searching any RN faily, including those with pseudoknots 2 Finally, the proposed ethod has a low coputational cost, yet very effective in detecting the structural siilarity, as will be deonstrated in our experients. This paper is organized as follows. In Sec. II, we present a brief review of the existing prescreening ethods. The proposed prescreening ethod based on structural siilarity is elaborated in Sec. III. We present experiental results in Sec. IV that deonstrate the effectiveness of the proposed ethod, and the paper is concluded in Sec. V. II. FST RN SERH SIN PRESREENIN FILTERS typical RN siilarity search is carried out as follows. iven a set of related RNs that belong to the sae faily, we first find their ultiple sequence alignent based on their sequence and/or structural siilarity. There exist any heuristic ethods that can be used to find a reasonably good alignent of the given sequences [2]. Based on this ultiple sequence alignent, we predict the coon secondary structure of the RNs and construct a statistical odel such as a profilecshmm [8], [11] or a M (covariance odel) [1] that can closely represent the alignent. 3 Once the odel is constructed, it can be used for searching a genoe database to find siilar sequences which ight be new ebers of the sae RN faily. iven a target RN, we copute a siilarity score based on the constructed odel, to find out how uch it resebles the reference RN faily. The observation probability of the target RN is a coon choice for the siilarity score, although it is typical to use either the log-probability or a log-likelihood ratio after noralizing the log-probability with respect to a rando sequence odel. nfortunately, coputing the observation probability of a target RN based on profile-cshmms or Ms is coputationally expensive. This is due to the coplexity of these odels that is necessary for describing the coplicated base correlations in RN sequences. For exaple, the coputational coplexity of the optial alignent algorith 4 for Ms called the YK (ocke-younger Kasai) algorith is O(L 3 M), where L is the length of the target RN and M is the nuber of states in the odel. The nuber of states 2 RN secondary structures that have crossing base-pairs are called pseudoknots. 3 lthough we have described the procedure in three separate steps (i.e., finding the alignent, predicting the coon secondary structure, and constructing the odel) for siplicity, these steps are closely interrelated and it is typical to repeat these steps until the odel converges to the optial one. 4 In general, there can be any different state sequences (or paths ) that give rise to the sae sybol sequence. n optial alignent algorith tries to find the optial path aong all feasible paths that axiizes the observation probability of the sequence based on the given odel. s this is conceptually identical to finding the best alignent between the sybol sequence and the statistical odel, it is typically called an optial alignent algorith. Fig. 1. Target RN Prescreening Filter Is it siilar? yes Full Model (profile-cshmm,m) Is it siilar? yes Report as a Match (New Meber) no no Reject (False andidate) Prescreening Stage Main Stage sing a prescreening ethod can ake the search significantly faster. M is proportional to the length of the reference RN. Siilarly, the S (sequential coponent adjoining) algorith for profile-cshmms has a high coputational coplexity. The coplexity of the S algorith is variable, typically between O(L 2 M) and O(L 4 M), depending on the structure of the reference RN. opared to O(LM) of the Viterbi algorith 5 for profile-hmms, the coputational coplexity of the YK and S algoriths is relatively high. Because of the high coputational cost of these algoriths, RN search based on profile-cshmms and Ms are usually too slow for scanning a large database, especially if the size of the RN is large. In order to overcoe this proble, a general prescreening ethod has been proposed in [3] to ake M-based searches faster. The basic idea of the prescreening ethod is as follows. Instead of using a M to scan the entire database, the ethod first uses a siple prescreening filter to scan the database. 6 The prescreening filter quickly filters out regions that are dissiilar, and passes only the regions that are siilar enough to the reference RN faily to the second stage. In the second stage, a full M is used to investigate these regions ore closely. The basic idea of the prescreening approach is illustrated in Fig. 1. If the prescreening filter runs fast enough copared to the ore coplex odel (a M, in this case) yet effective enough to filter out ost of the dissiilar regions, the overall speed of the search can be iproved significantly. In [3], profile-hmms were used as prescreening filters, whose paraeters were chosen based on the M paraeters such that it guarantees that there is no loss in the prediction accuracy. It was shown that the search speed could be iproved by 25 ties on average, and by ore than The coplexity of the Viterbi algorith for general HMMs is O(LM 2 ). 6 This should not be confused with the filters in signal processing. The prescreening filters are in fact siple statistical odels that are used to filter out the dissiilar regions, hence called filters.

3 Fig. 2. RN 1: < < < > > > - RN 2: < < < > > > RN 3: < < < - - > > > RN 4: < < < - - > > > - Exaples of RNs with siilar secondary structures. ties for any ncrn failes [4]. Siilarly, a prescreening ethod for profile-cshmms was proposed in [10], which also used profile-hmms for prescreening. nlike Ms that cannot be used for finding RNs with pseudoknots, profilecshmms have the advantage that they can represent any kind of RNs, including pseudoknots. The original prescreening ethod proposed in [3] was iproved further. For exaple, in [4], the profile-hmm based filters were augented with soe secondary structure inforation (though liited), and in [7], profile-hmm based heuristic filters were proposed that allow us to trade prediction accuracy for speed. One disadvantage of the previous ethods is that they ainly rely on sequence siilarity. lthough the ethod proposed in [4] augents the profile-hmm with sub-ms (parts of the full M) to detect siple ste-loops (hairpins), this hybrid prescreening filter can represent the structure of the reference RN only partially. Furtherore, although the hybrid filter will still be faster than the full M, it is considerably slower than the one solely based on the profile- HMM. In the following section, we propose a novel prescreening ethod that effectively overcoes the shortcoings of the previous ethods. The proposed ethod is based on atched filtering of ste patterns, which can scan the database to find regions that are structurally siilar to the reference RN. The structural atched filter can be constructed for any kind of RN secondary structure, aking the proposed approach generally applicable. Furtherore, it has a very low coputational cost, hence suitable for scanning large databases. III. MTHED FILTERIN FOR STRTRL SIMILRITY ssue that we have a reference RN with a known secondary structure. iven a target RN sequence with no structural annotation, how can we quickly find out if a siilar structure can be also found in the target RN? For exaple, let us consider the RNs shown in Fig. 2. s we can see in Fig. 2, all four RNs have siilar secondary structures, where every RN has a single ste-loop at a different location and/or a different loop size. Their structural siilarity can be easily recognized if we draw the dot-plots for their structures. iven an RN sequence x = x 1 x 2... x L with a structural annotation, we define the corresponding L L dot-plot atrix P as follows. The (, n)-th eleent p n of the dot-plot Fig. 4. RN 1 3 RN 3 RN RN Fig. 3. The dot-plots corresponding to the RNs in Fig. 2. (a) Reference RN 3 (c) Base-pairing atrix 5 3 (b) Ste pattern 5 3 (d) Maxiu overlap 5 3 Detecting structural siilarity by coparing the dot-plot patterns. atrix (base-pairing atrix) is defined as { 1, if xi and x p n = j for a base-pair 0, otherwise. The dot-plot atrix P is always syetric by definition. Fig. 3 shows the dot-plots that correspond to the structure of the RNs in Fig. 2. Fro Fig. 3, we can readily recognize the structural siilarity aong the four RNs. This shows that using dot-plots can be very useful in detecting the structural siilarity between RNs. To deonstrate this idea, let us consider the following exaple. ssue that RN-1 in Fig. 2 is used as the reference, and we assue that we know its structure. Based on its secondary structure, let us construct the base-pairing atrix P r as shown in Fig. 4(a). s the atrix P r is syetric, we keep only the uppertriangular portion of P r to obtain P r. This (strictly) uppertriangular atrix P r is shown in Fig. 4(b), where the reoved (1) Reference Target

4 portion is shown in gray. Note that this atrix contains the structural pattern (or the ste pattern) of the reference RN. Now assue that RN-4 is the target RN whose structure we do not know. In order to find out whether the target (RN-4) has a siilar structure as the reference (RN-1), we copute the base-pairing atrix P t of RN-4. Since we do not know its structure, we cannot construct P t = {p n } based on the actual base-pairing inforation. Instead, we set p n = 1 for all (, n) where x can for a base-pair with x n. For exaple, if x =, then we let p n = 1 for every n that satisfies x n =. s P t is also syetric, we keep only the upper-triangular portion of P t, and denote it as P t. The atrix P t is shown in Fig. 4(c). Now that we have P r and P t, we can copare these atrices to find out whether the target RN has a siilar structure as the reference RN. One way to do this is to find the axiu overlap between the atrices as illustrated in Fig. 4(d). s expected, the ste pattern in P r copletely overlaps with the base-pairing region in P t, showing that the target (RN-4) has a (nearly) identical structure as the reference (RN-1). Based on this idea, we propose an efficient ethod for coparing the structural siilarity between a structured reference RN and an unstructured target RN. The proposed ethod is as follows. Firstly, we construct a L r L r base-pairing atrix P r = {p n } based on the secondary structure of the reference RN, where L r is the length of the RN. We keep the uppertriangular portion of P r to construct an upper-triangular atrix P r = { p n } as follows { pn, if < n p n = (2) 0, otherwise. Fro P r, we construct the atched filter atrix S = {s n } such that s n = p (Lr )(L r n). This is identical to keeping the lower-tringular portion of P r to obtain S. Secondly, for a target RN of length L t, we construct a L t L t basepairing atrix P t for all possible base-pairs. s before, we take the upper-triangular portion of P t to get Pt. Thirdly, in order to copare the structures of the RNs, we find the axiu overlap between the atrix P r, which contains the ste pattern of the reference RN, and the atrix P t, which shows the base-pairing region of the target RN. The axiu overlap can be easily found by coputing Y = P t S, (3) and finding the largest eleent of Y, where B denotes the two-diensional convolution of and B. For Y = {y n }, we define λ to be the value of the largest eleent λ = ax,n (y n ). (4) This λ gives us the axiu nuber of base-pairs that the two RNs have in coon. The larger the value of λ, the closer will be the structure of the reference RN and that of the target RN. The process described so far can be viewed as atched filtering of a noisy signal (structural pattern of the target RN) based on the shape of the original signal (a) Base-pairing atrix P r of the reference RN (d) Matched filtering P t Fig. 5. * (b) Matched filter S S = (c) Base-pairing atrix P t of the target RN Matched filtering based on ste patterns. (structural pattern of the reference RN). The entire atched filtering process is illustrated in Fig. 5. t first sight, the coputational coplexity of the proposed ethod sees to be O(L 2 rl 2 t ) as it involves the convolution of an L r L r atrix and an L t L t atrix. However, the actual coplexity is uch saller, because the atrix S is very sparse. In fact, the nuber of non-zero eleents in S is identical to the nuber of base-pairs in the reference RN. The actual coputational coplexity will be O(NL 2 t ), where N ( 1 2 L r) is the nuber of base-pairs. lthough the coplexity is still quadratic in L t (length of the target RN), this is not a serious proble in practice, as it siply corresponds to the addition of N atrices of size L t L t. IV. EXPERIMENTL RESLTS To deonstrate the effectiveness of the proposed ethod, we perfored nuerical experients using the RNs in the ORON PK3 and FLVI PK3 failies in the Rfa database [5]. Note that both RN failies contain pseudoknots, which cannot be represented by Ms though they can be represented by profile-cshmms. The coputational coplexity of the S algorith would be O(L 4 M) for these RN failies [11]. Due to the high coputational cost, an RN search based on profile-cshmm alone would be too slow for scanning a large database, and it necessitates the incorporation of an efficient search strategy such as the prescreening approach. In our experients, we used the RNs in the seed alignents [5] of the RN failies. For each faily, we carried out the following cross-validation experient. We first chose one of the ebers as the reference RN, and constructed the atched filter atrix S based on its secondary structure. sing this atrix S, we carried out the atched filtering process elaborated in Sec. III for the reaining ebers and coputed λ as in (4). This value has been noralized to obtain the noralized structural siilarity score σ = λ/n, (5) Y

5 uulative Probability uulative Probability oronapk3 0.2 oronapk3 0.1 Rando Noralized Score Flavipk3 0.2 Flavipk3 0.1 Rando Noralized Score Fig. 6. uulative distribution of the structural siilarity score. (Top) Score distribution of the ORON PK3 RN faily. (Botto) Score distribution of the FLVI PK3 RN faily. where N is the nuber of base-pairs in the reference RN. Note that we always have 0 λ N, hence the noralized score σ is in the region 0 σ 1. This experient has been repeated by using every eber in the given faily as the reference RN, so that we can obtain a better estiate of σ. For coparison, we also coputed the average structural siilarity score for randoly generated RN sequences. If the score distribution of real RNs (with siilar secondary structures) is well-separated fro that of rando RNs, we can use this score σ for filtering out the sequences that are structurally dissiilar fro the reference RN. In order to ake this ore reliable, we considered only stes with ore than three base-pairs. Furtherore, we liited the region for finding the largest eleent of Y as follows λ = ax e D, n n e D (y n ). (6) In (6), ( e, n e ) is the expected location of the largest eleent for the case when the target RN has an identical structure as the reference RN. The paraeter D restricts the region for finding the largest eleent around ( e, n e ). The experiental results are shown in Fig. 6, which shows the cuulative distribution function (DF) F σ (s) = P (σ s) (7) of the structural siilarity score σ. Fig. 6 (Top) shows the score distribution of real RNs and that of rando RNs, where the reference RN faily was the ORON PK3. s we can see in Fig. 6 (Top), the score distributions of real and rando RNs are well-separated. 7 For exaple, if we 7 We used D = 3 in our experients. choose a threshold value of σ = 0.45, prescreening based on the proposed ethod can filter out 97% of the unrelated RNs at a false negative prediction rate of 3% (i.e., 97% sensitivity). onsidering that the proposed ethod perfors uch faster than the S algorith for finding the optial alignent, a rejection rate of 97% leads to a 33 (= 1/0.03) ties increase in the average search speed. For FLVI PK3 faily, the proposed ethod perfored even better. Fro Fig. 6 (Botto) we can see that if we choose the threshold as σ = 0.33, ore than 98% of the unrelated RNs can be rejected at no loss of sensitivity. In this case, the search speed can be ade around 50 ties faster without any loss in the prediction perforance. V. ONLDIN REMRKS In this paper, we proposed an efficient ethod for coparing the structural siilarity of RNs, based on atched filtering of ste patterns. The proposed ethod has a very low coputational cost, yet it is applicable to RNs with arbitrary secondary structures. s deonstrated in this paper, the proposed ethod can ake RN searches faster by prescreening the database based on structural siilarity. Experiental results show that the search speed can be iproved up to 50 ties by the proposed ethod alone. We expect that the search speed can be iproved even further when cobined with other sequence-based prescreening ethods. KNOWLEDMENT This work was supported in part by the NSF grant F REFERENES [1] R. Durbin, S. Eddy,. Krogh, and. Mitchison, Biological sequence analysis, abridge niv. Press, abridge, K, [2] R.. Edgar and S. Batzoglou, Multiple sequence alignent, urrent Opinion in Structural Biology, vol. 16, pp , [3] Z. Weinberg and W. L. Ruzzo, Faster genoe annotation of non-coding RN failies without loss of accuracy, Proc. 8th nn. Int. onf. on oputational Molecular Biology (REOMB), pp , [4] Z. Weinberg and W. L. Ruzzo, Exploiting conserved structure for faster annotation of non-coding RNs without loss of accuracy, Bioinforatics, vol. 20, pp. i334-i340, [5] S. riffiths-jones, S. Moxon, M. Marshall,. Khanna, S. R. Eddy and. Batean, Rfa: annotating non-coding RNs in coplete genoes, Nucleic cids Research, vol. 33, pp. D121-D124, [6]. Storz, n expanding universe of noncoding RNs, Science, vol. 296, pp , [7] Z. Weinberg and W. L. Ruzzo, Sequence-based heuristics for faster annotation of noncodingrn failies, Bioinforatics, vol. 22, pp , [8] B.-J. Yoon and P. P. Vaidyanathan, Profile context-sensitive HMMs for probabilistic odeling of sequences with coplex correlations, Proc. 31st ISSP, Toulouse, May [9] B.-J. Yoon and P. P. Vaidyanathan, oputational identification and analysis of noncoding RNs - nearthing the buried treasures in the genoe, IEEE Signal Processing Magazine, vol. 24, no. 1, pp , Jan [10] B.-J. Yoon and P. P. Vaidyanathan, Fast search of sequences with coplex sybol correlations using profile context-sensitive HMMs and pre-screening filters, Proc. 32nd ISSP, Honolulu, Hawaii, pr [11] B.-J. Yoon and P. P. Vaidyanathan, Structural alignent of RNs using profile-cshmms and its application to RN hoology Search: Overview and new results, IEEE Trans. utoatic ontrol & IEEE Trans. ircuits and Systes: Part-I (Joint Special Issue on Systes Biology), to appear in Jan