The algorithm allows the input orthologous sequences to be related by any user-specified phylogenetic tree. It is based on the Expectation-Maximization technique, and scales well with the number of species and the length of input sequences. We evaluate the algorithm on synthetic data, and also present results for data sets from yeast, fly, and human.We propose an algorithm that integrates two important aspects of a motif's significance – The results demonstrate that the new approach improves motif discovery by exploiting multiple species information. This paper presents a probabilistic algorithm, called "PhyME" (Phylogenetic Motif Elicitation), for ab-initio detection of binding site motifs in such heterogeneous sequences.The discovery of novel transcription factor binding sites in regulatory sequences of genes has been an important scientific challenge for some years now. Computational approaches to this problem have come in two flavors. One class of methods looks for overrepresented motifs in sequences that are believed to contain several binding sites for the same factor (such as promoters of co-regulated genes) -6. The soverrepresentation, which depends on the number of occurrences of the motif in each species. The other axis is the level of conservation of each motif instance across the species. A real motif that is not sufficiently significant along any one axis may turn out to be significant when both axes are considered simultaneously, leading to increased sensitivity and specificity of the integrated approach. Given the regulatory regions of potentially co-regulated genes along with their orthologs from other species, PhyME uses an Expectation-Maximization (E-M) algorithm to search for the motif that best explains the data. When evaluating a motif, its orthologous occurrences are assumed related to each other by a probabilistic model of evolution that takes into account the varying phylogenetic distances among the species. (The species may be related by any user-specified phylogenetic tree.) Each E-M iteration scales linearly with the total length of the input sequences and also with the number of species. The algorithm can also handle cases where the heterogeneous data is incomplete, i.e., where the orthologous regulatory regions are missing from some species. This capability makes it particularly suitable for applications that include data from incomplete genomes, or where orthology information is incomplete.PhyME integrates two different axes of information in evaluating a candidate motif's significance. One axis is that of An important feature of PhyME is that it allows motifs to occur in (evolutionarily) conserved as well as unconserved regions in orthologous promoters, treating the two kinds of occurrences differently when scoring a motif. It does not require each binding site occurrence in one promoter to have an orthologous occurrence in any or all other species. As a result, PhyME affords some flexibility in terms of the evolutionary distances spanned by the input sequences. For instance, using a distantly related ortholog will help pinpoint motifs located in conserved regions but will not hamper the discovery of motifs absent from that ortholog.conservation of motifs will be assumed to mean conservation across species.)Traditionally, motif finding algorithms have treated input sequences as being independently generated, and searched for statistically overrepresented motifs in them. These algorithms -6 do notAnother class of motif-finding methods take as input sets of orthologous sequences, either aligned  or unaliSome algorithms ,10 take et al. [et al. [et al. and Kellis et al. have a broader range of applications, since these are genome-wide searches for motifs.There are algorithms that attempt to handle the two axes of information by a two-step approach. For instance, Cliften et al.  and Kell [et al.  find a s [et al.  takes a  [et al. . In eithet al. [D. melanogaster and D. pseudoobscura) the promoters are known to have a mix of conserved and unconserved binding sites [A recent algorithm called orthoMEME  tacklesng sites . PhyME tet al. [Our approach is most similar to the algorithm PhyloGibbs , the maet al. [D. melanogaster and D. pseudoobscura. Therefore, PhyME can handle a broader range of species divergence in its input. Another important difference between EMnEM and PhyME is the probabilistic model that each uses to model evolution. While EMnEM is implemented to use the Jukes-Cantor model [β depends on the fitness of a binding site with β at that position. The evolutionary model used in PhyME reflects this dependence, and the incorporation of the model into an Expectation-Maximization framework is one of the main technical contributions of our work. The Results section includes a preliminary comparison of PhyME's performance with that of EMnEM, orthoMEME and PhyloGibbs, on real data.The algorithm EMnEM  uses E-or model , PhyME uet al. [The algorithm PhyloCon (Wang and Stormo ) extendset al. ) to incoIn this section, we first present the new algorithm, and then describe its evaluation on synthetic data, as well as biological data sets from various organisms.n different promoters (e.g., from co-regulated genes), and for each promoter there are sequences for K species. (K may be different for different promoters.) PhyME requires that there be one designated "reference species" σr in the input, for which there is sequence data corresponding to each of the n promoters. We shall describe PhyME's algorithm for the special case n = 1, though allowing multiple motif instances in this one sequence. The extension to n > 1 is trivial, and omitted here for simplicity. Thus, the input consists of a set of sequences S = {S1, S2 ,..., SK}, where Si is the orthologous sequence from species i, and one of the Si's comes from species σr. The input also includes the motif length l, and the phylogenetic tree Ψ over the K species, with neutral point mutation rates (probabilities) along each branch. The output is a position weight matrix (PWM) representing the discovered motif, and its score.Suppose that the input includes  that are highly conserved in . It then inputs all the sequences, along with the locations of the conserved blocks, to the core motif-finding algorithm.PhyME first partially aligns the input sequences and identifies contiguous regions ("blocks") in each  and each of the other Si. The assumption is that such regions are of common evolutionary origin, and any sequence outside them is independently evolved. PhyME runs the LAGAN alignment program of Brudno et al. [, Si|i ≠ σr), and extracts all ungapped aligned blocks of a certain minimum size (of the order of the motif's length) and percent identity, to serve as the blocks of common origin. This is illustrated in Figure σ1 (the reference species), σ2 and σ3. An example of a block is region BC in σ1, aligned with region UV in σ3. Note how blocks can overlap in the reference species (BC overlaps with KL).In this pre-processing step, PhyME computes the regions of high local similarity between o et al.  on each The input is now reorganized into two kinds of sequences:σ2 and blocks UV, WX of σ3 aligned with corresponding blocks in σ1.) Thus, any position in this sequence either has a single base from the reference species, or has an alignment of bases from multiple species, one of which is the reference species. This entire construct is called the "reference sequence".1. The sequence from the reference species, with aligned blocks of the other species "hanging off" it. . For the moment, let us assume that the sequence S being generated is entirely from one species, with no aligned positions. The HMM parameters include a "motif weight matrix" Wm of length l, and a "background weight matrix" Wb of length 1. (The (k, j)th entry of a weight matrix is the probability of emitting the base j at position k of the sequence being sampled from the matrix.) At each step, the generative process of the HMM chooses either Wm or Wb according to their transition probabilities pm = p and pb = 1 - p respectively, where p is a model parameter. A sequence is then sampled from the chosen weight matrix, and appended at the end of the sequence S created so far. The process then proceeds to the next step. It stops when the length of S reaches its known length L. The series of motifs chosen in the successive steps of the process is called a "parse" of the sequence. The model parameters θ, which include Wm, Wb, and p, associate a well-defined probability Pr(S, T|θ) with each parse T of the sequence S. The probability that S was generated by an HMM with parameters θ is then given by Pr(S|θ) = ΣTPr(S, T|θ). Let Pr(S|θb) be the probability of generating S by using only Wb. For a given θ, we defineThe probabilistic process that is assumed to generate sequences is described by a very simple Wm and p are trained so as to maximize F(S, θ).  The value of the objective function for a set of independent sequences is the sum of its values for the sequences taken separately. This additive property allows easy extension of the parameter training procedure to the general case of multiple sequences (n > 1). The objective function maximized then is , the set S now including, for each of the n input promoters, the "reference sequence" as well as all "bracketed sequences" (defined earlier) as separate elements.This log-likelihood ratio is the function optimized by PhyME – the parameters F(S, θ) is the subsequence probability Pr(s|W). This is the probability of generating a subsequence s of length l, (length of W), when sampling from weight matrix W; so , where s = s1s2 ... sl, and Wkj is the probability of sampling base j at the kth position of W. This formula applies when subsequence s has a single base at each position. However, we need to adapt this formula to the case where one or more positions in subsequence s may be an alignment of orthologous bases from multiple species. In this general case, we can write s as ψ1ψ2 ... ψl, where each ψk is either a single base, or an alignment of orthologous bases at a single position of the reference sequence. The subsequence probability Pr(s|W) can then be computed as , where Pre(ψ|W, k) denotes the probability of observing ψ at position k when sampling from W. Let the vector ψ = (s1, s2, ... sK), where sσ is the nucleotide from species σ in the single-base alignment ψ. If the sσ were independent, we could write . However, the sσ's occur in an alignment (ψ), meaning that this assumption of independence is obviously untenable. Thus we need an expression for Pre(ψ|W, k) that explicitly takes the phylogenetic relationships among the species (given by the phylogenetic tree Ψ) into account. We present such an expression in the next section, and we shall thereafter return to the topic of maximizing the function F(S, θ).An important aspect of computing Pre(ψ|W, k) mentioned above. It was first proposed in Sinha et al. [α → β at position k is proportional to the weight matrix entry of β at that position. If we further assume, for simplicity of exposition, that the phylogenetic tree Ψ has a star topology, then the model assumptions give us  or mutated in species σ with probability μσ and a new base selected with a frequency defined again by W.where In the general case, when Ψ does not have a star topology, Formula (1) can be written in a recursive manner. (See Methods.)F(S, θ) that is maximized by PhyME measures how much more likely it is that S was generated using the motif weight matrix, than without it. Naturally, a PWM that maximizes this score is the motif that best explains the data. PhyME tries to find such a motif by training the parameters (Wm, p) of the HMM, using the Baum-Welch algorithm [θ using Expectation Maximization (E-M).The function lgorithm , which i, for i ∈ {m, b} be the expected number of times the HMM plants motif Wi in generating the sequence(s), the expectation being over all parses. Similarly, let  be the expected number of times that the nucleotide alignment ψ is sampled at the kth position of the motif Wm.  and  are expected values of hidden variables of the HMM. These averages are computed during the "E-step" in each iteration, using dynamic programming .,  computed in the E-step. The parameter p is updated according to . The motif weight matrix Wm is updated by solving, for each column k of the matrix, the following set of five simultaneous equations, in variables uβ (β ∈ Σ) and λ.In the "M-step", two kinds of updates are made, using the values of uβ is used to update the (k, β)th entry of Wm, according to Wmkβ = euβ. Newton's method involves computation of the first and second partial derivatives of log Pre(ψ|Wm, k), as described in Methods. In practice, we found that Newton's method always converges from a single initial condition, and the convergence almost always happens within 3–5 iterations.The derivation of the update formulas is somewhat involved, and is described in the Methods section. The equations are solved using Newton's method, and the solution value of LKl), where L is the length of the sequences, K is the number of species, and l is the length of the motif desired. (See Methods for details.)The time complexity of (each E-M iteration in) PhyME is O and a common "background mutation rate" μb along each branch. (No insertions or deletions were included in this simulated evolution, for simplicity.) The motif instances are subjected to a common "motif mutation rate" μm , which is the probability of mutation of any position in a motif. The ancestral set of sequences is then removed and the remaining K orthologous sets are input to the motif discovery algorithm, with one arbitrarily designated the reference species. The algorithm is made to report 3 different motifs, thereby making some allowance for false positives, especially when R is low. For each reported motif, its 20 best occurrences in the reference species are compared with the planted occurrences, to give a score ranging between 0 and 1.  The score for the best of the 3 reported motifs is the "performance score" of the algorithm. The three algorithms being compared are PhyME, MEME [μb. MEME and GIBBS were run on the entire data set pooled together, ignoring the orthology of sequences.We first present the results of running PhyME on synthetic data. The experimental framework is largely borrowed from Wang and Stormo . In eachME, MEME . PhyME wK on performance scores of the algorithms. Note that the performance of PhyME, while similar to MEME and GIBBS for K = 1, improves relative to them as K increases. The absolute performance score of GIBBS (and of MEME, to some extent) deteriorates with increasing K. With more orthologous sequences, conserved stretches of background sequence may distract the algorithm from the motif occurrences. PhyME, with the additional knowledge of orthology, is able to pick out the motif better.Figure μb was varied from 0.2 to 0.5 and the motif mutation rate μm was varied between 0.1 and μb - 0.1). As per expectation, the performance of each algorithm improved with decreasing μm (for a fixed μb). Interestingly, as μb decreases, the performance of PhyME for μm = 0.1 first improves and then falls down. The initial improvement is because the alignment step is able to find more conserved blocks with diminishing background mutation rate. However, when the latter approaches the motif mutation rate, the distinction (in cross-species conservation) between motif and background becomes weaker, hence performance goes down. In another set of experiments, we examined the effect of the alignment step on the performance. Sequences were created with K = 2, μb = 0.3, μm = 0.1 and R = 12. After the alignment step of PhyME , we artificially "unpaired" some number n of the planted orthologous motif occurrences, i.e., the alignment was modified so that these n pairs fell outside conserved blocks. This was followed by the usual motif-finding step, and the entire procedure was repeated for various values of n. We find a gradual degradation in performance as PhyME moves from maximum utilization of motif orthology (n = 0, no unpaired motifs) to minimum (n = 20, no motif pairs considered orthologous).  to 0.5 (overestimate). We observed that underestimates of μb resulted in significantly greater performance degradation than overestimates of equal magnitude. (Data not shown.) For instance, using μb = 0.4 instead of the true value of 0.3 made no difference to the performance, whereas using μb = 0.2 resulted in 15 – 50% decline.We also evaluated the effect of mis-estimates of the neutral mutation rates on performance. PhyME was run on random sequences created with experiment parameters In the following sections, we present results of running PhyME on real data sets from yeast, fly and human. The results are compared to MEME (run by pooling orthologous sequences together), orthoMEME , PhyloGiS. cerevisiae, S. mikatae, S. kudriavzevii and S. bayanus was used. We performed motif-finding (with PhyME, MEME, orthoMEME, PhyloGibbs and EMnEM) on some regulons from the SCPD [η motif occurrences in S. cerevisiae reported by the algorithm (η being the number of known sites in S. cerevisiae) were examined for "matches" to the known weight matrix for that regulon's motif. (See Methods for details.) The number of matches was the performance score of the algorithm. We counted matches to the weight matrix, rather than to known sites, so that a reported motif occurrence that is very similar to the known motif (but not annotated as a site by SCPD) will not be counted as a false positive. Each algorithm reported 3 motifs (with η occurrences for each motif), and the results are for the best scoring motif, thereby making some allowance for false positives, such as simple repeats. Even though PhyME is implemented to handle arbitrary phylogenies, for efficiency it was run with a phylogenetic tree with a star topology, having S. cerevisiae at the center and the mutation rate along the branches of S. mikatae, S. kudriavzevii, and S. bayanus being (0.25, 0.3, 0.35) respectively. These values are based on average substitution rate per base in the corresponding pairs of species. , since its current implementation can only handle two species data. The other four programs were run for K = 1, 2, 3, 4, in separate executions.We first present some examples in yeast, where sequence data from four species, the SCPD  databases et al. .) For muSee Methods for details on how orthoMEME, PhyloGibbs and EMnEM were run.K for RAP1 and MIG1. For CAR1, both PhyME and MEME improve from K = 1 to K = 2, and then deteriorate for higher K, but PhyME at K = 3 is still better than at K = 1. For PHO4, PhyME's performance first goes up (for K = 2) and then dips below the K = 1 level, whereas MEME shows best performance at K = 4. For MCM1, PhyME scores well (over 90% matches) for K ∈ {1,3,4}, whereas MEME's performance degrades for K > 1. Thus, these examples illustrate that PhyME's approach can lead to improved motif discovery in multiple species data, and also that there may be situations when more orthologous sequences distract either algorithm from the true motif. For regulons CSRE, GCN4, MATα2, URS1H, REB1, and PDR3, the performance score was high  and largely invariant of the number of species.Figure K = 3, 4 in MCM1.) PhyME has better scores on MIG1 and RAP1, though PhyloGibbs' scores on RAP1 with a different choice of parameters ("-G 0.7", see Methods) were similar to PhyME. (Data not shown.) We also report the scores of EMnEM in Figure K = 2 (comparable to the best scores in the data sets RAP1, PHO4 and MCM1). For K = 3, 4 also, EMnEM scores are comparable to PhyloGibbs. PhyME typically performs better than EMnEM (with K = 3, 4) for RAP1, MIG1, MCM1, and comparably for PHO4.Figure K = 2). However, we observed that in all five regulons reported, orthoMEME reported fewer than η occurrences in S. cerevisiae per motif. This is because orthoMEME was run in the "zoops" mode (zero or one motif occurrence per sequence), since the "tcm" mode (any number of occurrences per promoter) does not perform well. Thus, with the total number of predictions being fewer than η, orthoMEME's scores are expected to be lower than other programs even for the same level of specificity.We find the scores of orthoMEME, as reported in Figure et al. (unpublished). A similar assessment of the motif-finding programs in the context of the heterogeneous data problem is an important topic for future work.We suggest caution in comparing PhyME's scores directly with those of the other programs, since we lacked expertise in choosing optimal parameter settings for them. This is particularly true for EMnEM, which has several parameters for modeling the evolution of motifs, and we lacked experience in setting these parameters optimally. We clearly have more expertise at using PhyME than the other programs, and this makes the comparisons biased. Our goal in these experiments was to provide some examples of how multiple species data can be exploited to improve performance, rather than assessing the different motif finding programs available. A proper comparative assessment of these programs has to address several challenges not addressed here. Such a task was undertaken for several motif finding programs, in the work of Tompa D. melanogaster and D. pseudoobscura, is available. Nine different enhancers were chosen – enhancers eve1, eve2, eve5, ftz3', gtposterior, hairy2, hairy34, and run1 have binding sites for the Kr transcription factor, and btdhead has Bcd sites.Next, we present results from fruitfly, where data from two species, Kr and Bcd [η motif occurrences (in D. melanogaster) reported by the algorithm (η being the number of "strong" occurrences of the known weight matrix in D. melanogaster – see Methods) were examined, and the number of matches was the performance score of the algorithm. Six different motif-finding strategies were tested separately – (i) MEME_1 (MEME on single species) (ii) MEME_2 (MEME on both species pooled together), (iii) PhyloGibbs, (iv) orthoMEME, (v) EMnEM and (vi) PHYME (PhyME on both species, with μ = 0.5). Each strategy was required to report occurrences only in D. melanogaster. (See Methods for details of how orthoMEME, PhyloGibbs and EMnEM were run.)Well-defined weight matrices are available for both  and Bcd . For eacftz3'), thereby making the case for using two species data. Moreover, on btdhead, gtposterior and hairy2, PhyME performs significantly better than MEME_2, demonstrating the advantage of using orthology information. Similarly, we find PhyME to perform better than PhyloGibbs on gtposterior, hairy2 and hairy34. EMnEM performs well in these data sets, scoring comparably to PhyME or PhyloGibbs, except on btdhead, eve2, and gtposterior, where both PhyME and PhyloGibbs perform better, and hairy2, where PhyME alone performs better. OrthoMEME was run in the "tcm" mode, since the "zoops" mode is not appropriate here, with several putative sites to be found in each promoter. However, orthoMEME tends not to perform well in the "tcm" mode in general, and in our tests also, its scores were poor on most of the enhancers. We thus find that PhyME is preferable to orthoMEME for cases where we expect several motif occurrences per sequence.Figure As in the yeast data sets, the comparison of scores between PhyME and the other programs should be interpreted with caution, since we lacked expertise in choosing optimal parameter settings for the other programs.et al., unpublished) failed to report the correct motif in them. The first set corresponds to the transcription factor SP1, a zinc-finger protein. The heterogeneous sequence data included 35 human promoters (of length 2 Kbp each), of which four have orthologous promoters from mouse and rat, 20 from mouse only, 4 from rat only, and 7 have no orthologs. Each of the human promoters is known to have at least one functional Sp1 binding site, with a total of 76 known sites overall. Figure Finally, we present results of running PhyME on two data sets from human, where orthology with mouse and rat was utilized. These data sets were chosen because all of 15 different motif-finding programs tested in an assessment project (Tompa The second data set used in our tests corresponds to the leucine zipper transcription factor c-Jun. The heterogeneous data set included 500 bp promoters for 11 human genes targeted by c-Jun, as well as orthologs from mouse and rat for 3 genes, from mouse only for 5 genes, and from rat only for the remaining three genes. PhyME was run exactly as in the previous data set. The known binding sites of c-Jun (in human) were aligned to produce a weight matrix that is shown in Figure  and each of the other Si may then be extracted.  Furthermore, the implementation may be modified in the future to drop the requirement of a reference species, since this requirement is not crucial to the motif finding step of PhyME. For instance, the alignment step may utilize the "Threaded Block Alignment" (TBA) program of Blanchette et al. [In the alignment step, PhyME extracts blocks of high sequence similarity between the reference species and each of the other species. Motif occurrences in such locally conserved regions are deemed orthologous, an assumption well-justified by traditional interpretations of sequence alignment. Conversely, all orthologous motif occurrences are assumed to be aligned in such blocks. This assumption is not always true since there may be orthologous motif occurrences not aligned by the alignment program, but it heavily constrains the space of orthologous motif occurrences, implying greater efficiency of the search algorithm. Moreover, the assumption does not mean that "true" orthologous occurrences in unaligned regions are ignored – they are merely treated as independent occurrences. Our experiments on synthetic data (see Results) demonstrate that the performance is not very sensitive to the correct alignment of all orthologous motif pairs. The blocks computed in the alignment step have to be with respect to the reference species, but the alignment itself need not be done in a pairwise manner. A multiple alignment of all sequences may be computed  made during the process, meaning that the HMM is of zeroth order, nor on the position in the sequence, meaning that any information about spatial distribution of motifs is ignored. The model, unlike that of MEME, does not fragment the sequence into all μσ is small (as for very closely related species), then finding different bases in orthologous positions has low probability Pre(ψ|W, k), even if their frequency in W is the same. This mirrors the intuition that mutations in locally conserved regions of closely related species are evidence against a binding site residing there. For largely diverged species (i.e., if μσ~1, ∀ σ), Pre(ψ|W, k) reduces to the product of the individual bases' probabilities. It is worth emphasizing here that the weight matrix W being searched by the algorithm is assumed to be unchanged over the entire phylogenetic tree (including the ancestor).The evolutionary model described by Formula 1 applies only to phylogenies having a star topology. The general case of arbitrary tree topology is described in Methods. In Formula 1, if et al. [The neutral mutation rates (probabilities) along each branch of Ψ are input by the user and not trained during E-M. Training them on input data may cause overfitting, producing values that are largely inconsistent with the known evolutionary distances. The work of Moses et al.  studies Pre(ψ|Wm, k). Other models of evolution, e.g., F81 [Pre(ψ|Wm, k) can be computed efficiently.Note that the evolutionary model used by PhyME comes into play only in Equations 2 as the term .g., F81 , can be We have developed a new algorithm, PhyME, that detects motifs in heterogeneous sequence data by integrating two important aspects of a motif's significance – overrepresentation and cross-species comparison – into one probabilistic score. We have evaluated different aspects of the algorithm on synthetic data, and demonstrated on some biological data sets that the new approach improves motif detection.α → β at position k is proportional to the weight matrix entry of β at that position. Suppose we are given a phylogenetic tree Ψ, with the species {σ1, σ2, .... σK} at the leaves. Let the vector ψ = (s1, s2, ... sK), where sσ is the nucleotide from species σ in the (single position) alignment ψ. The term Pre(ψ|W, k) denotes the probability of observing ψ at position k when sampling from weight matrix W. For each node j of the tree, except the root, let μj be the probability of a base in the parent species of j having mutated  in species j. Also, let ψj be the vector formed by elements of ψ that correspond to leaf nodes descended from node j. Let C(j) denote the set of children of node j and let r be the root of the tree. Then, we can write (using the model assumptions):The evolutionary model makes the following assumptions: (i) Nucleotides in an aligned position are evolved from a common ancestor. (ii) The weight matrix applies to the common ancestor and to all descendants, a reasonable assumption given the propensity of DNA binding domains of proteins to evolve slower than cis-regulatory modules. (iii) All positions evolve independently, at equal rates, and the probability of fixation of a mutation f(ψj, α) denotes the probability of observing ψj given that the base at the parent of j is α. For a leaf node σ, this can be written as , from the model assumptions. (δij = 1 if i = j, and 0 otherwise.) For an internal node j (except root r), the expression is :where For the special case where Ψ has a star topology, Equation 4 reduces to Equation 1.S and a set of position weight matrices {Wi}, the objective function to be maximized is F(S, θ) = log(Pr(S|θ)/Pr(S|θb)), where Pr(S|θ) is the probability of generating the sequence S using the parameters θ, and θb represents the parameter values that only allow the background motif Wb to be used by the HMM. The sequence S can be written as ψ1ψ2 ... ψL, where each ψi is either a single base or an alignment of orthologous bases at a single position. θ includes the weight matrices Wi and their transition probabilities pi. Since Pr(S|θb) depends only on Wb, which is assumed constant, we shall outline how to maximize log Pr(S|θ), following the description in [S in terms of the Wi (i.e., the series of motifs chosen in the successive steps of the generative probabilistic process) is denoted by T.Given a sequence ption in . A parseWe thus havetth iteration computing a model θt + 1 that improves the objective function from the current model θt. In classical E-M fashion, let us define a function Q(θ|θt) asThe maximization is iterative, with the Pr(S|θ) - log Pr(S|θt) ≥ Q(θ|θt) - Q(θt|θt). Thus, if we maximize Q(θ|θt) over all θ, we shall always improve upon log Pr(S|θt), or remain there if the local maximum has been reached. Let Ai(T, S) be the number of times Wi occurs in the parse T of S. Also, let Eikψ(T, S) denote the number of times that the alignment ψ is emitted (sampled) at the kth position of the matrix Wi, in parse T of S. Let li denote the length of Wi. Then we haveIt is easily shown that log which gives uspi, and only the second term depends on Wi. Hence, we maximize each of these terms independently, with respect to the appropriate free parameters. We first maximize the termNote that the only the first term in this expression depends on  is the average number of occurrences of Wi in S over all parses T.Note that , and this is maximized whenThus the term to maximize is Next, we maximize the second term: is the average number of times that the alignment ψ is sampled at the kth position of the matrix Wi while generating S, the average being over all parses T. Thus, the term to maximize is . We first note that in our case, there is a single weight matrix Wm to be trained. Hence, we need to maximize Q with respect to Wm. We can do this maximization with respect to each column k independently. Let Wkβ denote the (k, β)th entry of Wm. Thus, for each k = 1 ... l, we need to maximize Q with respect to Wkβ (β ∈ Σ), with the constraint Σβ Wkβ = 1. Using Lagrangian multiplier λ, the objective function becomes Q + λ (Σβ Wkβ - 1).Again, note that uβ = log Wkβ to ensure that the Wkβ remain positive during optimization, we then have the following necessary conditions for optimality (in addition to the constraint ) :Transforming to log variables uβ (∀β ∈ Σ and λ. Denoting the vector of these five variables by u, we solve this system of equations using Newton's iterative method. Let us write the above system of equations as F(u) = 0, where F(u) = [[fβ], fλ], with fβ being the left side of Equation 9, and . Newton's method uses the update relation:We therefore have a system of five equations (including the constraint) in the variables u = -(J(u))-1F(u)Δu is the change in u in the current iteration and J is the Jacobian matrix of F. The important terms in the computation of F and J are the first and second partial derivatives of log Pre(ψ|Wm, k) with respect to the uβ variables. For this purpose, we need to compute Pre(ψ|Wm, k) and its first and second partial derivatives. Computation of Pre(ψ|Wm, k) uses the formulas 4 and 5. The partial derivatives can be computed recursively (over the tree Ψ) by using the chain rule of differentiation. These recursive computations are implemented in a bottom-up manner, so as to avoid redundant computations. Newton's method uses F and J to iteratively compute new values of u, until convergence. The Jacobian matrix J in our case is not positive definite, hence Newton's method is not guaranteed to converge. However, in practice, we found the method to always converge from a single initial seed. Upon convergence, the log variables uβ are transformed back to Wkβ = euβ. The procedure is repeated for each k = 1 ... l, and Wm is then updated with the new values. This update, along with that given by Equation 8, is used iteratively to improve F(S|θ) until the local maximum is reached, as indicated by a very small change in its value.where Δ,  and , for k = 1 … l, ∀ ψ. The Forward-Backward algorithm is run once, in O(LKl) time, where L is the total length of the input sequences, K is the number of species, and l is the length of the motif Wm. (This time complexity assumes that nodes in the phylogenetic tree have a fixed maximum degree.) Thereafter, ,  are computed in O(L) time, and all the  are computed in one scan of the input, expending O(Ll) time.The E-step computes Wm. Each run of Newton's method goes through a small number (3–5) of iterations. Each iteration computes the first and second partial derivatives of log Pre(ψ|Wm, k) Each of these derivatives can be computed in O(K) time, where K is the number of species (since |ψ| ≤ K) Hence, F and J can be computed in O(LK) time, where L is the total length of the sequence. Hence, Newton's method takes O(LK) time, and is run l times, for an overall time complexity of O(LKl) for the M-step.The M-step runs Newton's method to solve a system of equations, once for each column of Thus, the running time of (each E-M iteration in) PhyME scales linearly with the length of the sequences, the length of the motif desired, and the number of species.. The current implementation runs in a few minutes (on a workstation) for typical applications with total sequence length ~10000 bp, 2–4 species, and motif length of ~10.PhyME is implemented in C++ for Linux, and the source code will be made freely available at et al. [PhyME uses the LAGAN alignment tool of Brudno et al.  for the Wm, and truncating the E-M procedure after a small number of iterations. The seed with greatest score F(S, θ) among these runs is then used to run the E-M to convergence and the trained motif is reported, along with all its instances with posterior probability above a certain threshold. To find more motifs, PhyME masks out the central base of each of these instances. Optionally, the user may specify nsites, the expected number of occurrences of each of the desired motifs. In such a case, PhyME turns off training of the parameter p, and uses a fixed value computed from nsites. Similarly, an option maxsites specifies the maximum number of occurrences expected.The E-M algorithm is guaranteed to converge only to a local optimum. To address this problem, the motif-finding step is executed a fixed number of times, each time using a randomly chosen substring of the input sequence as the "seed" to initialize Wr, and an associated transition probability pr, in the HMM parameters. The weight matrix is constrained to be the reverse complement of Wm. The model has a fixed bias of planting the motif in one orientation versus the other, and this bias is trained from the data. PhyME also has the option of capturing local correlations in background nucleotide composition. To implement a κth order Markov background, PhyME uses a special background weight matrix that is of length 1 but uses the knowledge of the previous κ bases generated to determine the emission probabilities of the next base.PhyME considers occurrences on both strands by introducing a new weight matrix S = {S1, S2, ... Sn} be the set of n input sequences. For any motif m, let Imi be the set of positions in sequence Si that are occupied by an occurrence of m. We know the occurrences of the planted motif mk, and are evaluating the motif mr reported by an algorithm. The performance score Φ is defined as follows:We use the following score for measuring the performance of a motif-finding algorithm on synthetic data. Let or the reported motif occurs. Note that if the reported occurrences exactly concur with the known occurrences, the score is 1, and when the reported and known occurrences have no position in common, it is 0.In other words, it is the number of positions, over all sequences, where occurrences of the known and reported motifs overlap, divided by the total number of positions at which the known S. cerevisiae) from the RSA-Tools web site [et al. [η be the number of known binding sites in S. cerevisiae. The input to the motif finding algorithm consisted of the sequences from S. cerevisiae and their orthologs from one or more of the other species, depending on K. (In addition to S. cerevisiae, we used S. mikatae for K = 2, S. mikatae and S. kudriavzevii for K = 3, and S. mikatae, S. kudriavzevii and S. bayanus for K = 4.) The length of the motif was also input to each program. Each algorithm was made to report 3 motifs, and for each motif, the top η reported occurrences in S. cerevisiae were examined. For each such occurrence, the logarithm of the probability of sampling it from the known weight matrix was computed, and a z-score of this logarithm was obtained. If the z-score was above 3, the occurrence was called a "match". To allow for slight offsets in the reported motif, each reported occurrence was padded with 3 bp of its context, on either side.The genes regulated by each transcription factor are listed in SCPD. For each such "regulon", the known sites and the known weight matrix were extracted from SCPD. Also, 800 bp long upstream sequences of the genes in each regulon were extracted  and 1.2*η ("maxsites"). PhyloGibbs was run with mutation probability 0.7 ("-G 0.3") for all species, and was asked to report three motifs (three "colors") each with 1.5 × η occurrences ("-I") initially. A 3rd order Markov background ("-N 3") trained on the full complement of yeast promoters was used, as with PhyME and MEME. The "loose align" option ("-D 1") and the "stop after anneal" option ("-X") were used. These options were suggested by an author of PhyloGibbs . We experimented with a different value for the mutation probability ("-G 0.7"), with no improvement, except in the RAP1 regulon. EMnEM was run with default parameters, the motif length being input through the "-w" parameter. Phylogenetic trees were derived from each input promoter, using the fastDNAML software of Olsen et al. [et al. [η/n and η/n + 1 in separate runs, where n is the number of input promoters. For each data set, and for each value of K, we took the best scoring choice of parameters. This was done to give some advantage to EMnEM, since we lacked expertise in choosing optimal parameter values.PhyME was run with the n et al. . The ali [et al. . In sepaD. melanogaster were obtained from [D. melanogaster) with the known weight matrix, and counted matches, by the same measure as above. This count was the value of η used in the experiment. An extra complication in the fly data is caused by the fact that each enhancer typically contains sites for multiple transcription factors. We restricted our tests to the factors Kr and Bcd, because their weight matrices are of better quality than others. Moreover, for each enhancer, we chose to test with the transcription factor with most putative sites (matches to its weight matrix).The locations of cis-regulatory modules involved in body-patterning of the early embryo in ned from , and thened from . The evand order Markov background ("-N 2"), trained on non-coding regions in fly. We also experimented with a higher value of the mutation probability, and tried specifying the initial number of occurrences per motif ("-I") differently, with no clear improvement. EMnEM was run with the Jukes-Cantor evolutionary model ("-m 0") and with the relative rate of motif to background ("-p") set to 0.5 and 0.25 in separate runs. The expected number of motifs was set to η and 1.5 × η in separate runs. The best performing choice of parameters was used for each data set.OrthoMEME was run as in the yeast data sets (see above), except that the "tcm" mode was used now. PhyloGibbs was also run as in the yeast data sets, except that we used a mutation probability of 0.5 ("-G 0.5"), and a 2The genes comprising each regulon were obtained from TRANSFAC . Mouse aAll authors participated in initial discussions leading to the key idea of using Expectation-Maximization and a phylogenetic model to search in a weight-matrix space. SS designed the algorithm details, derived the E-M calculations, implemented and tested the program, and drafted the manuscript. All authors contributed to, read and approved the final manuscript.


During lymphocyte development, V(D)J recombination assembles antigen receptor genes from component V, D, and J gene segments. These gene segments are flanked by a recombination signal sequence (RSS), which serves as the binding site for the recombination machinery. The murine Jβ2.6 gene segment is a recombinationally inactive pseudogene, but examination of its RSS reveals no obvious reason for its failure to recombine. Mutagenesis of the Jβ2.6 RSS demonstrates that the sequences of the heptamer, nonamer, and spacer are all important. Strikingly, changes solely in the spacer sequence can result in dramatic differences in the level of recombination. The subsequent analysis of a library of more than 4,000 spacer variants revealed that spacer residues of particular functional importance are correlated with their degree of conservation. Biochemical assays indicate distinct cooperation between the spacer and heptamer/nonamer along each step of the reaction pathway. The results suggest that the spacer serves not only to ensure the appropriate distance between the heptamer and nonamer but also regulates RSS activity by providing additional RAG:RSS interaction surfaces. We conclude that while RSSs are defined by a “digital” requirement for absolutely conserved nucleotides, the quality of RSS function is determined in an “analog” manner by numerous complex interactions between the RAG proteins and the less-well conserved nucleotides in the heptamer, the nonamer, and, importantly, the spacer. Those modulatory effects are accurately predicted by a new computational algorithm for “RSS information content.” The interplay between such binary and multiplicative modes of interactions provides a general model for analyzing protein–DNA interactions in various biological systems. Spacers not only ensure that the distance between the nonamer and heptamer is correct but they also regulate recombination activity by providing protein-binding sites along the DNA sequences that affect recombination During B- and T-lymphocyte development, the immunoglobulin (Ig) and T-cell receptor (TCR) genes are assembled from discrete V, D, and J gene elements via a process of genomic rearrangements known as V(D)J recombination . V(D)J rRSSs are an essential part of V(D)J recombination, as their presence is both necessary and sufficient to direct RAG-mediated recombination on artificial substrates. Sequence alignments of RSSs suggested that each signal can be dissected into three components: a conserved heptamer (consensus: 5′-CACAGTG) and a conserved nonamer (consensus: 5′-ACAAAAACC), separated by a poorly conserved spacer of either 12 ± 1 or 23 ± 1 bp . The hepDespite the enormous specificity that RSSs confer on the recombination process, the recombination signals themselves demonstrate a remarkable degree of sequence heterogeneity. Only the first three nucleotides of the heptamer and the fifth and sixth positions of the nonamer show almost perfect conservation  and are Our current knowledge about the functional role of the spacer is that its length is crucial in directing V(D)J recombination . ComprehOne limitation inherent in many prior RSS studies is that they have often been performed in the context of RSSs with a preponderance of consensus nucleotides. While such analyses have been useful in characterizing the most conserved or critical determinants of RSS function, the contributions of other nucleotides are potentially masked in RSSs with high consensus nucleotide representation. That most endogenous RSSs do not contain consensus heptamer and/or nonamer motifs further suggests the need for a careful study of individual RSS nucleotides in the context of physiologically relevant RSSs.We have performed an extensive analysis of the functional properties of RSS elements in the context of endogenous recombination signals. To explore the nature of the complex relationships that might exist among different elements and positions in the RSS, we started with the nonfunctional RSS associated with the murine Jβ2.6 pseudogene element of the TCRβ locus (Jβ2.6 RSS). While most such pseudogene elements are flanked by RSSs with crippling mutations , Jβ2.6 iApaLI restriction endonuclease, which cuts precise RSS–RSS junctions (data not shown). The amount of recombination substrate recovered from each transfection was measured by PCR and used to normalize the recombination activity. Although we assayed primarily for SJ formation, analyses of CJ formation yielded parallel results (data not shown). As a reference, we used a substrate containing the 12-RSS from the TCR Jβ2.2 gene element . This standard 23-RSS was used instead of the natural Jβ2.6 RSS partner (the 23-RSS flanking Dβ2), since the substrates containing the Dβ2 23-RSS showed much lower levels of recombination in our hands (data not shown). The 12-RSS coding flank was the same for all constructs, namely that of Jβ2.6. For our study, a polymerase chain reaction (PCR)-based assay , top wasment see , which rment see .Recombination of Jβ2.6 RSS is below the level of detection of our assay . SubstitIn combination with a consensus heptamer and/or a consensus nonamer, the presence of either the VκL8 or the consensus spacer markedly enhances recombination activities above those observed with the Jβ2.6 RSS spacer (The heptamer and nonamer of Jβ2.6 RSS differ from the consensus in only five positions see : the lasSubstitution of a consensus nucleotide at either the second or fourth position of the nonamer (N[2] or N[4], respectively), alone or in combination with a consensus heptamer and/or spacer, partially reproduces the effects of the full consensus nonamer A. IntereIn the presence of a consensus heptamer and/or nonamer, a consensus spacer markedly enhances recombination levels over the Jβ2.6 RSS spacer. We therefore wondered whether the presence of an artificial anticonsensus spacer (Sac) see , containTwo important questions arise from the results of these in vivo assays. First, do the differences in the RSS nucleotide sequences affect the cleavage or the joining phase of the reaction? Second, are the RAG proteins by themselves the only proteins that mediate the discrimination between various RSSs? To address these questions, we performed standard 12–23 coupled cleavage reactions using purified, truncated (core) RAG proteins A. The liInterestingly, a favorable spacer sequence (Sk or Sc), when paired with H or N, boosts cleavage over the Jβ2.6 RSS spacer B and 4D.It is likely that differences in the nucleotide sequences of the RSS lead to variations in the stability of RAG–RSS complexes . This idIn the context of a consensus nonamer, the consensus spacer reproducibly enhances binding more than a consensus heptamer (Sc–N > H–N). In contrast, the anticonsensus spacer (H–Sac–N) reduces binding about 3-fold compared to H–Sc–N A and 5B.Taken together, the results of our binding studies underline clearly that the reduced ability of the Jβ2.6 RSS to participate in the initial interaction with the RAG complex, and hence the subsequent steps of V(D)J recombination, is caused not solely by the Jβ2.6 RSS nonamer but also by the “inefficient” spacer sequence. This indicates that the spacer helps the nonamer to efficiently lock the RAG proteins onto the RSS. The heptamer can contribute to this only when interactions with the other two elements are favorable.Although the RSS spacer is poorly conserved and no naturally occurring RSS has yet been identified that bears the published consensus spacer sequence, our results show that the presence of the most- or least-conserved nucleotides at all positions of the spacer dramatically alters recombination activities of RSSs that contain a consensus heptamer and/or nonamer. This suggests that a functional preference exists for certain spacer sequences over others. We therefore established a genetic screen for functional spacer sequences in which each position of the spacer was randomized to contain either a consensus or an anticonsensus nucleotide (Sc/Sac). Because the greatest effect of the consensus spacer in our experiments is seen in combination with a consensus heptamer (H–Sc), the randomized spacer was analyzed in the context of 12-RSSs containing a consensus heptamer and the Jβ2.6 RSS nonamer (H–Sc/Sac). The H–Sc/Sac library contained roughly 80,000 clones, sufficient to represent each of the 4,096 possible spacer sequences multiple times (data not shown).RAG1 and RAG2, and we cloned and sequenced PCR-amplified SJs. As a control, we analyzed PCR products corresponding to unrearranged substrates from library pools transfected in the absence of RAG1 and RAG2 J recombination has recently been developed , 2003. TSr = 0.90) than with binding (Sr = 0.86) and most correlated with SJ formation (Sr = 0.96). The correlations between our experimental data and RIC scores suggest that the failure of Jβ2.6 RSS to recombine and the ability of consensus heptamer, spacer, and nonamer elements to rescue Jβ2.6 RSS activity are functions of how well RSS structure corresponds to that of a preferred sequence. In this case, the selective advantage of the consensus RSS is not limited to a few critical nucleotides in the heptamer or nonamer but, rather, extends throughout the length of the RSS, even in regions (e.g., the spacer) that were previously thought to be unimportant.We calculated RIC scores for the hybrid Jβ2.6/consensus RSSs used in this study, and we compared them to the experimental binding, cleavage, and recombination values . This indicates that the RIC score is able to predict the quality of RSSs and that this ability is not limited to the well-conserved heptamer and nonamer but also applies to the far more diverse spacer.Further support for the potential of the RIC score as a theoretical measure for RSS activity arises from our genetic screen. For both the in vivo and the in vitro screens, the mean RIC score of the 12-RSSs in the enriched population is higher than that of the starting pool (data not shown), and those differences are statistically significant (Student's RSSs are the DNA elements that direct and control the V(D)J recombination reaction. In the TCR loci, differences in the abilities of individual RSSs to recombine with each other are a significant determinant of variations in the frequencies with which gene elements appear in the mature TCR population  into a completely nonfunctional, pseudogene-type RSS. Our experiments demonstrate that all RSS nucleotides, including the spacer element and the noncritical positions of the heptamer and nonamer, have some sequence-directive roles. In general, we observe that the magnitude of the effects of unfavorable nucleotides in noncritical RSS positions is dependent on the presence of other unfavorable nucleotides. This explains why, in previous studies using largely consensus RSSs, the effects of nonconsensus nucleotides at the noncritical positions were concluded to be less significant .Hin recombinase . The Jβ2.6 RSS nonamer differs from the consensus in the second and fourth positions see , and theombinase  suggest ombinase . Hence, ombinase . Having ombinase ; while pPrevious binding studies have shown that the nonamer is the key element for initial RAG–RSS interactions and that mutations within the nonamer can strongly reduce or even completely abolish formation of the 12-SC  . In contThe effect of a consensus spacer on 12-SC formation exhibits striking plasticity see . AdditioOur in vitro cleavage assay integrates the effects of RSS binding, pairing, and actual DNA cleavage. Hence, the differences between the results of binding and cleavage assays suggest that the steps following initial binding (paired complex [PC] formation and DNA cleavage) are also regulated by spacer sequences. PC formation requires the recognition of the partner RSS with respect to its spacer length, and thus it is plausible that the sequence of spacers influences the protein–DNA contacts required for this compatibility test. Since it is within the PC that coordinated, synchronous DNA cleavage takes place , it is cFinally, the differences between the in vitro cleavage and in vivo recombination assays indicate an additional role of the spacer sequence in the joining phase of the reaction. This seems plausible, since joining is thought to start with the controlled disassembly of the postcleavage complex in which the four DNA ends, including the RSSs, are held in intimate contact with each other, presumably by the RAG proteins . Spacer Based on comprehensive sequence alignments showing a small but significant degree of spacer sequence conservation , a few sPpoI and I-CreI homing endonucleases, which cleave at recognition sites approximately 20 bp in length  interactions of a strictly sequence-specific nature, and “analog” (or multiplicative) contacts that fine-tune the strength of the digital contacts . Digitalmax, where A = effect on binding efficiency due to analog interactions) to no activity (0 × Amin). Hence, the noncritical residues are crucial for determining how well a protein complex can exert its biological function.This duality in the nature of protein–DNA contacts present within the RAG–RSS recombinase may be applicable to other biological systems, including other transposases, transcription factors, and DNA-binding proteins. In most protein–DNA interaction systems, the target sequence to which a protein binds contains some nucleotides that are absolutely critical, and others that are noncritical. Digital interactions are established with the absolutely conserved nucleotides in the form of sequence-specific binding, conferring a binary specificity; the digital contacts therefore determine whether a protein will bind (+1) or not (0). Analog contacts are then established with the lesser-conserved nucleotides; the analog interactions act as functional multipliers that determine the efficiency of complex stability, yielding a spectrum of binding efficiencies ranging from full activity (1 × ABy including so many nucleotides as requirements for RSS function, the V(D)J recombination system may have evolved to avoid random cleavage of DNA and translocation errors. If only the critical heptamer and nonamer nucleotides were required for activity, the frequency of cleavage at inappropriate or “cryptic” sites in the genome would be expected to be quite high. By contrast, the required participation of noncritical nucleotides in complex stability safeguards the reaction against uncontrolled cleavage. Hence, from the standpoint of controlled diversification of reaction specificity, it is beneficial for the recombinase to have evolved a spacer with a high degree of sequence heterogeneity, while maintaining intimate contact with the spacer nucleotides via analog interactions. The complex multiplier effect of analog contacts throughout the length of the RSS, superimposed onto specific digital contacts in the heptamer and nonamer, therefore confers upon the recombinase the critical ability to distinguish between inappropriate sites that happen to contain the requisite absolutely conserved nucleotides (e.g., the Jβ2.6 RSS) versus true binding sites whose sequences diverge markedly from the consensus (e.g., most endogenous RSSs).RIC scores provide a powerful tool for the prediction of RSS quality based on nucleotide sequence. This method generates statistical predictions of RSS function based on the physiologic 12- and 23-RSSs in the mouse antigen receptor gene loci. In our study, RIC scores accurately predicted the relative efficiencies with which RSSs were bound, cleaved, and rearranged  make distinct contributions to the different steps of the V(D)J recombination reaction. This concept is consistent with previous findings showing that the nonamer is a major determinant of binding while the influence of the heptamer becomes most apparent at the level of cleavage. Hence, the efficiency with which an RSS recombines represents an integration of its protein–DNA interactions throughout all steps of the reaction, and RIC scores provide a remarkably accurate prediction of this.RIC models should be useful not only in guiding RSS mutation studies, but also in identifying potential cryptic RSSs in the genome, whose usage could lead to genomic alterations as an initial event leading to chromosomal translocations and cancer , 2003. FINNE1, CIT4A, TL1, TL2, TL3, TL4, TL5, and TL6) have been described previously , and the double-stranded fragment was digested with HindIII and SalI and ligated into the linearized p299-Jβ2.6 vector. Ligation reactions were transformed into DH5α, colonies were harvested into 120 ml of Luria broth (containing 100 μg/ml ampicillin), and plasmid DNA was prepared after an additional incubation at 37°C at 250 rpm for 15 min.To generate the library for the genetic screen, the oligonucleotide pEBB, pEBB-RAG1, and pEBB-RAG2 expression constructs have been described elsewhere .2, 0.1 mM each dNTP, 0.5 μM each oligo, and 0.2 U Taq (Invitrogen). To quantify DNA recovery, the oligonucleotide pair TL5/TL6 was used for the PCR (94°C for 15 s, 60°C for 15 s, 72°C for 30 s, for 18 cycles). To detect SJs, DNA samples were treated with DpnI, MluI, and XhoI to remove unreplicated and unrecombined plasmids. Oligonucleotides INNE1 and CIT4A were used to amplify SJs (94°C for 15 s, 60°C for 15 s, 72°C for 30 s, for 28 cycles). To detect CJs, RAP samples were treated with DpnI and CJs were amplified using primers TL2 and TL3. All PCR products were electrophoresed on native 4.5% polyacrylamide gels, stained with SYBR green, visualized using a Fluoroimager 595 , and quantified using ImageQuant software (Molecular Dynamics).Human embryonic kidney 293T cells were transfected with 6 μg of recombination substrate and 3 μg each of pEBB-RAG1 and pEBB-RAG2 using calcium phosphate as described previously ; for conDpnI/MluI/XhoI (for cloning of SJs) or DpnI only (for cloning of unrearranged bands in no-RAG controls). PCR was performed using INNE1 and CIT4A primers, and samples were electrophoresed and stained as indicated above. The products corresponding to the appropriate SJ or unrearranged bands were excised, purified, and cloned into pCR2.1 using a TOPO-T/A cloning kit (Invitrogen). DNA was prepared from individual transformed colonies and sequenced.293T cells were transfected with the plasmid library and RAG or pEBB constructs as described in the Results. Extrachromosomal DNA was extracted and samples were digested with either The in vitro screen was performed using the plasmid library as the substrate in a standard coupled cleavage reaction. After proteinase K digestion, the products were precipitated and dissolved in 100 μl of 1× ligase buffer. T4 DNA ligase (1 μl) (New England Biolabs) was added and the mixture incubated at 16 °C for 4 h to create artificial SJs. The resulting plasmids were treated identically to the plasmids recovered after transfection in the in vivo screen.Recombinant GST-RAG2, MBP-RAG1, and HMG2 were expressed and purified as described previously .TL1, TL4, and the respective recombination substrate as a template. The 12-RSS oligonucleotide substrates used in EMSA were generated by annealing the 5′-end-labeled top strand with an equimolar amount of the unlabeled respective bottom strand .Click here for additional data file.Table S1(31 KB DOC).Click here for additional data file.Table S2(23 KB DOC).Click here for additional data file.


Since LPS is highly antigenic, the variation at lps loci is attributed to be of advantage in evading the host immune system. Although LPS has been suggested as a potentiator of plant defense responses, interstrain variation at lps biosynthetic gene clusters has not been reported for any plant pathogenic bacterium.In animal pathogenic bacteria, horizontal gene transfer events (HGT) have been frequently observed in genomic regions that encode functions involved in biosynthesis of the outer membrane located lipopolysaccharide (LPS). As a result, different strains of the same pathogen can have substantially different Xanthomonas oryzae pv. oryzae (Xoo) encoding six genes whose products are homologous to functions involved in LPS biosynthesis and transport. All six open reading frames (ORFs) have atypical G+C content and altered codon usage, which are the hallmarks of genomic islands that are acquired by horizontal gene transfer. The lps locus is flanked by highly conserved genes, metB and etfA, respectively encoding cystathionine gamma lyase and electron transport flavoprotein. Interestingly, two different sets of lps genes are present at this locus in the plant pathogens, Xanthomonas campestris pv. campestris (Xcc) and Xanthomonas axonopodis pv. citri (Xac). The genomic island is present in a number of Xoo strains from India and other Asian countries but is not present in two strains, one from India (BXO8) and another from Nepal  as well as the closely related rice pathogen, Xanthomonas oryzae pv. oryzicola (Xoor). TAIL-PCR analysis indicates that sequences related to Xac are present at the lps locus in both BXO8 and Nepal624. The Xoor strain has a hybrid lps gene cluster, with sequences at the metB and etfA ends, being most closely related to sequences from Xac and the tomato pathogen, Pseudomonas syringae pv. tomato respectively.We report here the complete sequence of a 12.2 kb virulence locus of lps locus between different strains of a plant pathogenic bacterium. Our results indicate that multiple HGT events have occurred at this locus in the xanthomonad group of plant pathogens.This is the first report of hypervariation at an  Pseudomonas aeruginosa, an opportunistic human pathogen [Vibrio cholerae is considered as a major cause for the cholera epidemic that originated in India in 1992 [lps gene repertoire is to be expected within different strains of plant pathogenic bacteria.LPS is an important constituent of the outer membrane of gram-negative bacteria. Variation in LPS composition can have profound consequences for these cells by potentially providing resistance against bacteriophages and antimicrobial compounds as well as facilitating evasion of the host immune system in animal pathogens. Extreme variation at LPS gene clusters has been reported in animal pathogenic bacteria. Recently, eleven highly divergent gene clusters were reported to occupy an LPSspecific locus in pathogen . The acq in 1992 -8. LPS h in 1992  and in s in 1992 ,12 as we in 1992 . Since LXanthomonas oryzae pv. oryzae (Xoo) and Xanthomonas oryzae pv. oryzicola (Xoor) cause diseases of rice [The genus Xathomonas includes a number of plant pathogenic bacteria. Two related members of this genus,  of rice . They ex of rice -19. In IwxoD, wzt and wzm, that are postulated to be involved in LPS biosynthesis and transport. These newly described genes also have atypical G+C content and all the six genes at this locus exhibit altered codon usage pattern, as compared to other Xoo genes. We present evidence that this locus is present in many, but not all, Xoo strains and that it is absent in Xoor. Our results indicate that there is substantial variation at this locus among various xanthomonads. The possible significance of these results is discussed.In previous research, we have reported a 5.5 kb region in the genome of Xoo strain BXO1 and demonstrated that it encodes three genes that are involved in biosynthesis of LPS and extracellular polysaccharide (EPS) as well as in virulence . All theEcoRI fragments (0.6, 2.2, 3.5, 4.0, 6.0, 9.0 and 10 kb). We subcloned all the fragments into pBlueScript. Based on the end sequences of the inserts in the subclones and pSD5, the lps locus was mapped to four of these EcoRI fragments (0.6, 4, 3.5 and 9 kb). The previously obtained sequence was found to include all of the 3.5 kb and part of the 4 kb fragment and the remaining sequence of this region was obtained by sequencing the 0.6 kb and the 9 kb fragment (Please refer Methods). A total sequence of 13.18 kb was constituted by joining 6.14 kb of previously obtained sequence [lps locus and some flanking regions. The additional sequence of the lps locus encodes three putative genes which encode a predicted O-antigen acetylase, a predicted ABC transporter permease and a predicted ATP-binding protein and three insertion sequence (IS) elements.In an earlier study, a novel Xoo locus was reported to be required for LPS and extracellular polysaccharide (EPS) production as well as virulence. A 35 kb cosmid, pSD5, that complements mutations in this region was isolated . PartialwxoA (encodes a predicted epimerase), wxoB and wxoC (both encode predicted glycosyl transferases) have been described earlier. The fourth gene is wxoD and encodes a predicted 327 amino acids long protein. A BLAST [Mesorhizobium loti . Interestingly, no homologs of this gene have been reported in any other xanthomonad. The fifth gene, wzt, encodes a predicted 436 amino acid long protein. A BLAST search reveals homology to functions involved in LPS transport. The best match is with the ATPase component of an ABC-type polysaccharide transport system from Burkholderia fungorum . The sixth gene, wzm, encodes a predicted 437 amino acid long protein which is homologous to integral membrane protein components of ABC transporter systems that are involved in LPS transport. The best match is with a permease component of the ABC-type polysaccharide export system from Pseudomonas fluorescens PfO-1 . The start codon of wzt overlaps with the stop codon of wzm. Homologs of wzt and wzm are typically present in many lps gene clusters. Interestingly, two complete Insertion Sequence (IS) elements (ISXo8 and IS1113) and one truncated IS element (IS1114) interrupt this cluster between the genes, wxoD and wzt. ISXo8 is a novel 1320 bp long insertion sequence and a BLAST search shows homology to transposase of ISRSO17 encoded by Ralstonia solanacearum . A complete copy of the IS1113 element (AF482989) and a truncated copy of the IS1114 element (AF232058) are also present as indicated in Fig. lps loci [wxoA, wxoB, wxoC and wxoD might constitute one operon and that ORFs wzm and wzt might be transcribed together. The overlap between the start codon of wzt and the stop codon of wzm also suggests that these two genes are co-transcribed.All of the putative genes have been named as per Bacterial Polysaccharide Genes Nomenclature (BPGN) . The fir A BLAST  search rlps loci . Transcrlps locus is flanked by metB, which encodes a predicted cystathionine gamma lyase, and etfA which encodes a predicted electron transport flavoprotein. The genome sequences of Xanthomonas campestris pv. campestris  and Xanthomonas axonopodis pv. citri  have been obtained [metB gene  exhibits within the sequenced region, 91% and 88% nucleotide identity to metB genes of Xac (AE012010.1) and Xcc (AE012157.1), respectively. The Xoo etfA gene  exhibits within the sequenced region, 93% and 91% nucleotide sequence identity, respectively, with etfA genes in Xac (AE012009.1) and Xcc (AE012159.1). Interestingly, the lps biosynthetic gene cluster of Xcc, which comprises fifteen genes, is also located between the metB and etfA genes [The obtained . The XoofA genes . In Xac,lps locus is 50.46% (excluding the IS elements) [Fig. wxoD) to 56.3% (wxoC). Atypical G+C content is a characteristic feature of "genomic islands" that are believed to be acquired by horizontal gene transfer. The transposase genes encoded by ISXo8 and IS1113 have a G+C content that is >61%, a value which is typical for the genomes of Xoo and other xanthomonads. The G+C content of metB and etfA genes that flank the genomic island have G+C content of 64.3% and 61% respectively  which is typical of the Xoo genome.The average G+C content of Xoo and other Xanthomonads is estimated to be around 65% , while tts) Fig. . The varCodon Usage Pattern or CUP (Please refer Methods). Eight aminoacids, i.e., Glycine, Valine, Threonine, Leucine, Arginine, Serine, Proline and Alanine, were selected to study CUP because they have atleast four synonymous codons. The percentage of synonymous codons that end with G or C was calculated for each aminoacid and gene. This analysis was conducted for six genes of the lps island and six genes from elsewhere in the Xoo genome (please refer Methods). We show that CUP of the genes present in the genomic island is dramatically different from the typical Xoo genes  of Xoo strains that we have examined from India , and different sized bands in BXO8 (lane 3), Nepal624 (lane 4) and BXOR1 (lane 2) indicating that the metB gene is present but located in different EcoRI fragments  PCR is an efficient technique for isolation of target DNA segments adjacent to known sequences [metB and etfA genes suggests that sequences which are significantly similar to the Xac lps gene cluster are present at this genomic location in both of these strains. Next to metB, a wzm homolog is present in BXO8  and Xac with 69.2% identity at nucleotide level within the sequenced region. Next to etfA, a putative integral membrane protein encoding gene is present in both BXO8  and Xac with 91.3% identity at nucleotide level within the sequenced region. The BXO8 and Nepal624 strains exhibit 100% nucleotide sequence identity within the sequenced region. TAIL- PCR analysis of the Xoor strain indicates that it has a hybrid lps gene cluster. Next to metB, a unique wzm gene is located  which exhibits 62.8% nucleotide identity to wzm gene of Pseudomonas syringae pv. tomato strain DC3000 (AE016859.1). Next to etfA, a putative inner membrane protein encoding gene is located  which exhibits 97% and 92% nucleotide sequence identity, respectively, with similarly located genes in BXO8 and Xac. Because the BXO8 and Nepal624 strains have different sequences at the lps locus, as compared to other Xoo strains, we inoculated these strains along with appropriate controls onto leaves of the susceptible rice cultivar Taichung Native-1. We find that BXO8 and Nepal624 strains are able to cause typical bacterial leaf blight disease symptoms that are indistinguishable from those elicited by other Xoo strains (data are not shown).What are the sequences present at this genomic location in the Xoo strains that lack the equences . TAIL-PCmetB and etfA genes in BXO1 and BXO8. The homology breakpoints appear to localise to the 3' regions of metB and etfA genes, exactly 18 bp upstream of their respective stop codons. Upto the break points, within the sequenced region at either end of the lps locus, the nucleotide sequence is identical in BXO1, BXO8 and Nepal624. The DNA sequence immediately preceding the break points was examined manually for presence of direct or inverse repeats. Interestingly, we could find three inverted repeats (I, II and III) within the 3' regions of metB and etfA near the homology breakpoints between BXO1 and BXO8  flanking the lipopolysaccharide gene cluster has been reported in Mycobacterium avium subsp. paratuberculosis [Escherichia coli strain K5, Vibrio cholera, etc. This sequence was implicated to be involved in gene regulation and has also been suggested to have a role in recombination [The presence of invert repeats in the regions that flank the rculosis . Anotherbination ,36.lps loci of animal pathogenic bacteria are under intense host selection and extreme variation is reported in lps specific gene clusters [lps gene clusters suggests that the plant pathogenic bacteria are also under selection to vary their LPS. Alterations in LPS composition might result in resistance against predators like bacteriophages [As LPS is highly immunogenic, clusters . The obsiophages ,10 or reiophages  in the hlps biosynthetic gene clusters within different strains of a plant pathogenic bacterium. The results also indicate that multiple HGT events have occurred at this locus in various xanthomonads and provide a new parallel in the mechanisms that plant and animal pathogenic bacteria can employ to generate variability in cell surface molecules.These results provide, for the first time, evidence for substantial variation in lps locus was cloned as part of a 35 kb cosmid clone, pSD5. The insert includes 0.6, 2.2, 3.5, 4.0, 6.0, 9.0 and 10 kb fragments upon EcoRI (New England Biolabs [NEB], Beverly, MA) digestion and all the fragments were subcloned in to pBlueScript (Stratagene, La Jolla, CA). Most of the sequence obtained in this study was generated by sequencing the 9 kb subclone, pBP4, using a modified shotgun sequencing procedure. Here, pBP4 was digested with EcoRI and the 9 kb fragment was gel eluted. Then the fragment was partially digested (1.5–2.5 kb) using a blunt-end cutter, HaeIII (NEB) and cloned into pMOS (Amersham Pharmacia Biotech, Buckinghamshire, England). The inserts were amplified from random clones by colony PCR using vector primers and were sequenced using an ABI Prism 3700 automated DNA sequencer (Applied Biosystems, Foster City, CA). After editing, the assembly of the sequence data was done using GeneTools (BioTools, Alberta, Canada) and Blast2 [lps locus that was obtained using long range PCR (Triple Master™, Eppendorf, Hamburg, Germany) with BXO1 genomic DNA as template. The sizes of the fragments corresponded to the sizes that are predicted by in silico analysis of the sequence (data are not shown). The ORF's were assigned using ORF finder [EcoRI fragment which is also a part of the lps locus. The Pbp1 primer binds just after the wxoC ORF (which forms part of the 3.5 kb EcoRI fragment) and Pbp2 binds within the wxoD ORF (which forms part of the 9.0 kb EcoRI fragment). A 0.67 kb PCR amplified fragment is obtained from BXO1 genomic DNA using Pbp1 and Pbp2. The band was gel eluted and was sequenced using Pbp1 and Pbp2. The sequence was found to include the 0.6 kb EcoRI fragment. In addition, the sequences of all six ORFs were confirmed by sequencing of PCR amplified fragments from genomic DNA using specific sets of gene specific primers (see the list of primers in Table The d Blast2 . MultiplF finder . Two prilps locus. These genes encode: a putative siderophore receptor (AF325732), Xanthomonas adhesin like protein (AF288222), a putative phytase (AY151260), rpfF (AF411962), shikimate dehydrogenase (AF258797) and secreted xylanase (AF331922). The second group comprised the six genes (excluding transposases) encoded in the Xoo lps gene cluster (AF337647).For each gene the frequency of codon usage for different aminoacids was calculated using a web based program . FurtherEcoRI (NEB) according to supplier's instructions. Digested genomic DNA was separated on a 0.8% agarose gel and vacuum transferred to a Hybond N+ filter (Amersham) using 0.4% NaOH as described by Sambrook et al. [32P dATP using random primer labelling kit (Board of Radiation Technology, Mumbai, India). Prehybridization, hybridisation and washings were done at 68°C as described by Yashitola et al [Specific oligonucleotide primer pairs were designed and used to amplify gene specific fragments for each of the ORFs encoded in the BXO1 genomic island  was lysed in 100λ of 0.01 N NaOH by boiling for 10 minutes. After spinning at 13 K for 1 min., 2λ of supernatant was used as template for PCR using the gene specific primers described above. The products were separated by electrophoresis on 1.5% agarose gels and visualized by ethidium bromide staining.To screen for the presence of the genomic island in different strains, a procedure for colony PCR was standardized. A portion of a single colony ; Sequences of TAIL-PCR products from metB end of BXO8 (AY319936), Nepal624 (AY319938) and BXORI (AY319940); Sequences of TAIL-PCR products from etfA end of BXO8 (AY319937), Nepal624 (AY319939) and BXORI (AY319941).The nucleotide sequences obtained in this study have been deposited in GenBank with the following Accession numbers: Sequence of PBP carried out all the aspects of the work and drafted the manuscript. RVS conceived the study, and participated in its design and coordination. All authors read and approved the final manuscript.


Most of the existing RNA structure prediction programs fold a completely synthesized RNA molecule. However, within the cell, RNA molecules emerge sequentially during the directed process of transcription. Dedicated experiments with individual RNA molecules have shown that RNA folds while it is being transcribed and that its correct folding can also depend on the proper speed of transcription.The main aim of this work is to study if and how co-transcriptional folding is encoded within the primary and secondary structure of RNA genes. In order to achieve this, we study the known primary and secondary structures of a comprehensive data set of 361 RNA genes as well as a set of 48 RNA sequences that are known to differ from the originally transcribed sequence units. We detect co-transcriptional folding by defining two measures of directedness which quantify the extend of asymmetry between alternative helices that lie 5' and those that lie 3' of the known helices with which they compete.We show with statistical significance that co-transcriptional folding strongly influences RNA sequences in two ways: (1) alternative helices that would compete with the formation of the functional structure during co-transcriptional folding are suppressed and (2) the formation of transient structures which may serve as guidelines for the co-transcriptional folding pathway is encouraged.These findings have a number of implications for RNA secondary structure prediction methods and the detection of RNA genes. However, theoretical studies of RNA molecules [functional structure which confers the desired functionality within the organism to the RNA molecule.Most of the existing computational methods for RNA secondary structure prediction fold an already completely synthesized RNA molecule. This is done either by minimizing its free energy  which target the emerging RNA or whether the primary structure of the RNA molecule itself conveys the desired properties to guide its own correct co-transcriptional folding.In this paper, we propose several statistics in order to detect, if and how co-transcriptional folding influences RNA sequences. Using these statistics, we show that the effects of co-transcriptional folding are widespread in RNA genes.We want to show that an RNA sequence is organized in such a way to help the formation of the functional secondary structure during transcription. We aim to support this hypothesis by detecting two different features:Possible competitors of helices in the functional structure are suppressed. When the 3' end of a helix that is part of the final secondary structure emerges during transcription, the number of possible competitors for the 5' part of the helix should be as low as possible in order to promote the formation of the correct helix.• The folding pathway is engineered. During transcription, several temporary helices are formed which may guide the folding process.• H0 case, when we suppose no co-transcriptional folding. However, verifying that these statistics have an expectation value of zero in the H0 case cannot simply be achieved by analyzing random sequences. Indeed, even generating random sequences is not trivial. First, it is hard to reliably predict the minimum free energy structure for the randomized sequences as most secondary structure prediction algorithms discard pseudo-knots and, even without pseudo-knots, predict only on average about 70 % of the base-pairs correctly. In addition, there is no guarantee that the secondary structure with the lowest free energy would correspond to the functional one. Second, even if the random sequences are generated by a shuffling algorithm which keeps the given secondary structure fixed, it cannot be guaranteed that the fixed structure remains the correct one for the new primary sequence. Generating random sequences therefore provides no straightforward solution for obtaining a H0 statistics with expectation value zero.We investigate these features using several statistics which are based on the known primary and secondary structures of our RNA sequences. A crucial point in investigating these features is to define a set of statistics that have expectation of zero in the H0 case and where one statistics has a bias away from the H0 expectation value in case of co-transcriptional folding, while the other statistics is not affected by co-transcriptional folding. By studying the difference of these two statistics, we thus gain a new statistics with expectation value zero in the case of no co-transcriptional folding and an expectation value larger or smaller than zero in the case of co-transcriptional folding.We circumvent this problem by studying pairs of statistics, where both statistics have the same, unknown expectation value in the minstem = 9 consecutive base-pairs of type {G - C, C - G, A - U, U - A, G - U, U - G} and are calculated by a dynamic programming procedure in which the known primary and secondary structure of the RNA is fixed, see Figure minstem values (data not shown). While calculating all helices of at least minstem length, we test which of these helices constitute competing alternatives to helices of the known secondary structure and record each such competing case in one of our statistics. These alternative helices may be part of a pseudo-knotted structure and we do not discard them. As each of the two bases i and  of a base-pair in a known helix can have a competing alternative base-pairing partner within an alternative helix and as this alternative partner can either be found 5' (before), 3' (behind) or between the two strands of the known helix, all cases can be classified into six different classes. Of these six, we discard the two classes where the alternative helix falls between the two strands of the known helix as this un-paired loop region is typically too short to accommodate an alternative helix of at least minstem length. The remaining four classes, see Figure cis- and two trans- alternative classes, depending on whether the known base-pairing partners lie between the alternative base-pairing partners (trans) or not (cis). The four statistics 3'cis, 3'trans, 5'cis and 5'trans that we use correspond to these four classes.The statistics (which we will define in detail below) measure the presence of alternative helices which compete for at least one base-pair with the helices of the known secondary structure. These competing alternative helices are required to consists of at least cis- and trans-alternative helices are not necessarily the same as the stacking energies are not symmetric with respect to the 5' → 3' direction of the RNA sequence [cis-pairing partners are closer to the known pairing partners than trans-pairing partners and may thus lead more easily to incorrect helices. We may therefore compare only cis-competitors with other cis-competitors and trans-competitors with other trans-competitors. This yields two possible comparisons: 3'trans versus 5'trans and 5'cis versus 3'cis, see Figure It is important to note that even without co-transcriptional folding, the destabilizing effects of competing cis, 3'trans, 5'cis and 5'trans, where an alternative helix competes with a known helix. Each such event is given two different weights, see Table d·log(l)), where d is the distance between the two competing helices and l is the length of the sub-sequence 5' or 3' of the known helix on which the competing helix falls, or (2) a weight of |G| / (d·log(l)), where the former weight is multiplied by the absolute value of the free energy G of the competing, alternative helix. The factor 1/d gives alternative helices that are far away from the known helix a smaller weight than closer ones. The factor 1/log (l) accounts for the fact that log (l) is proportional to the expected sum of 1/d statistics for a sub-sequence of length l . The free energy factor G in the second type of weights gives stable alternative helices which have a larger impact on the folding pathway a greater weight than helices which are easily unfolded. Statistics derived from weights of type 1/(d log(l)) are denoted by an index p (for plain) and those of type |G| / (d·log(l)) by an index g (for free energy). By summing the weighted counts for each of the four classes of events, we thus arrive at eight different scalar values which characterize each RNA sequence: 3'Transx, 3'Cisx, 5'Transx and 5'Cisx for x ∈ {p,g}.We proceed as follows to detect if co-transcriptional folding takes place: For every RNA sequence of the data set, we detect events of type 3'We can now define the two statistics which are capable of measuring the two main types of asymmetry within each RNA sequence:Cis := 5'Cis - 3'CisTrans := 3'Trans - 5'Trans configurations, see Figure  configurations). Both types of effects are indicated by an expectation value larger than zero for the respective statistics.which can calculate for both types of weights. Without co-transcriptional folding, the expectation value of these two statistics is zero. Co-transcriptional folding induces two types of asymmetries by suppressing the number of alternative helices which compete with the final helices (indicated by an increased number of (pos) thus follows a binomial distribution with parameter p = 0.5 and the statisticWithout co-transcriptional folding, the introduced statistics have an expectation of zero, moreover, the distributions should be symmetric. The number of positive cases n is the number of all cases, approximately follows a standard normal distribution. If this value is sufficiently positive, we have to reject the hypothesis that co-transcriptional folding is not encoded within RNA genes.where All 16S rRNA, 23S rRNA as well as Group I and Group II type intron sequences with completely known secondary structures were downloaded from the Comparative RNA Web (CRW) Site ,36, resuOrganellar 23S rRNA sequences frequently contain Group I introns and recent research revealed that the 23S rRNA of several hyperthermophilic bacteria also have Group I intron . Other sVibrio harvey, the order is 23S-16S-5S [Vibrio cholerae [Vibrio parahaemolyticus [rRNA genes in bacteria are encoded in the so-called rrn-operon (see for example ). The caS-16S-5S , but notcholerae  and Vibrolyticus , whose 1We divided the gathered sequences into two sets: data set A which consists of all RNA sequences that are thought to correspond to the originally transcribed sequence units and data set B which contains all those RNA sequences that are known to differ from the originally transcribed sequence units. Data set B thus contains the Group I and II intron sequences, organellar and hyperthermophilic bacteria 23S RNA sequences. As we neither know the sequence nor the secondary structure of the original transcript units from which the sequences of data set B were derived, we are limited to detecting the effects of co-transcriptional folding within these shorter sequences. We expect this to be much more difficult than in sequences that correspond to the originally transcribed sequence units as co-transcriptional folding introduces long range effects which are harder to detect the shorter the investigated sub-sequence gets. See Table 3'Cisx, 3'Transx, 5'Cisx and 5'Transx values for both types of weights, i.e. x ∈ {p,g}, for each sequence in the two data sets. From these values we then derived each sequence's Cisx and Transx values, again for both x types of weights. Their distributions are shown in Figure We calculated the The first thing to note in Figure Cis and Trans in Table The mean values of Cis value larger zero means that configurations of type  outnumber those of type , see Figure c and i that can later yield to the final secondary structure element containing the base-pair between i and  thus seems to be encouraged. However, these transient structure elements may not be too stable if they are to guide rather than impede the proper folding. The presence of transient helices could thus be further substantiated by showing that these transient helices are less stable than the final helix. In contrast to the  configuration, the competing ic helices in the  case are suppressed as they lie 3' of the final  helix and thus emerge later in time during co-transcriptional folding. A Cis value larger than zero can therefore be explained by the presence of temporary helices which may guide the formation of the final, functional secondary structure during co-transcriptional folding.A Trans value larger than zero means that  configurations are less frequent than  configurations, see Figure  configuration, both c and  are competing pairing partners for i as they both emerge before i during transcription. This may lead to the formation of wrong ci helices, whereas the order of pairing partners in the  configuration has a lower risk of mis-folding due the c emerging only after the  and thus only after the  helix could have already formed.A 3'Trans > 3'Cis in Table  or  helix temporarily break up. In the case of the 3'Trans configuration, the pairing partners come in the order  along the RNA sequence, whereas they come in the order  in the 3'Cis configuration. In the  order, the c part is in vicinity to the i part, so the possibility of ending up with a wrong refolding due to a ic helix is larger than in the  case.In addition, (3'Trans > 3'Cis), that the formation of temporary helices may guide the structure formation and that these helices may thus be used to actively engineer a folding pathway (Cis >0) and that secondary structure elements which may interfere with the formation of the final, functional secondary structure during co-transcriptional folding are suppressed (Trans >0).Overall, we can thus conclude from the average values in Table In order to quantify the influence of co-transcriptional folding further, we calculated two statistics, a t-test for the hypothesis that the given statistics have an expectation value of zero as well as the p-value of the number of positive cases for our two co-transcriptional folding indicators, see Table Recent experimental studies ,24,19 haAlthough our statistics are able to reveal two general effects of co-transcriptional folding within data set A, we cannot conclude that they would be powerful enough to serve as a reliable indicator of co-transcriptional folding for single RNA sequences, as some of the sequences in data set A may not correspond to the originally transcribed sequence units. In addition, all of our statistics consider only a first order effect of co-transcriptional folding by studying alternative helices for the known helices, but do not take higher order effects into account as e.g. alternative helices of alternative helices etc.Based on computer simulations, H. Isambert et. al.  conjectuTo summarize, our findings show that co-transcriptional folding is a guiding principle in the formation of functional RNA structure and that it can influence both the primary and potential secondary structures of an RNA molecule. This has several implications. Current algorithms for RNA secondary structure prediction can probably be improved by adopting co-transcriptional folding as a guiding principle rather than only free energy minimization. This may hopefully provide the extra information needed to be able to reliably detect RNA genes . Severalhow RNA sequences fold. This should in turn enable us to also understand why some RNA sequences mis-fold and fail to function properly in the organism. Even though protein folding is known to differ in many respects from RNA folding, they also have some features in common [co-translational folding.Most importantly, co-transcriptional folding should lead to a better understanding of n common . One of In this study, we neither attempted to study the effects that co-transcriptional folding may have on sequences that are transcribed together (e.g. genes in an operon) nor to study the influence that the binding by proteins or RNA sequences or RNA editing may have on the co-transcriptional folding pathway and the final, functional RNA structure. This will almost certainly require more refined investigation methods, but we hope that this study provides enough insight and motivation to start to tackle these exciting questions.I.M.M. proposed this work and contributed the main idea for the statistics. I.M. selected the data and evaluated the statistical significance of the results. Both authors shared the programming tasks and the writing of the manuscript.