To evaluate the performance of PASS, we employed the two most common standards: sensitivity (Sn) and specificity (Sp). The definitions are:

S n = T P T P + F N S p = T P T P + F P = 1 − F P T P + F P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaafaqabeqacaaabaGaem4uamLaemOBa4Maeyypa0ZaaSaaaeaacqWGubavcqWGqbauaeaacqWGubavcqWGqbaucqGHRaWkcqWGgbGrcqWGobGtaaaabaGaem4uamLaemiCaaNaeyypa0ZaaSaaaeaacqWGubavcqWGqbauaeaacqWGubavcqWGqbaucqGHRaWkcqWGgbGrcqWGqbauaaGaeyypa0JaeGymaeJaeyOeI0YaaSaaaeaacqWGgbGrcqWGqbauaeaacqWGubavcqWGqbaucqGHRaWkcqWGgbGrcqWGqbauaaaaaaaa@4E60@

In these equations, TP (true positive) is the number of actual sites that are identified or predicted correctly. FN (false negative) is the number of actual sites that cannot be identified or predicted correctly. FP (false positive) is the number of false sites that are predicted by PASS. The value of Sn represents the fraction of the actual poly(A) sites that can be predicted, while Sp represents the fraction of actual poly(A) sites in all the predicted sites. The higher the Sp value is, the lower the fraction of false positive sites among predicted sites is.

To evaluate the algorithm, we tested 568 known poly(A) sites (randomly chosen from the 8K dataset described in 6 and the Methods) to calculate Sn. Because not all poly(A) sites have been identified in each sequence of the database, we cannot calculate the real Sp value. Therefore, we used several negative control datasets for Sp calculations. These include Arabidopsis 5' UTRs, introns, coding sequences, and a randomly generated sequence dataset that preserve the trinucleotide distributions found in the 8K dataset. Since all the sites predicted by PASS in these control sequences are false sites, FP was set to be the number of sites that were predicted in these sequences. (TP+FP) was set to be the total number of sites. The results are shown in Figure 1A. The horizontal value represents the threshold, which is an user selectable standard in determining whether or not a nucleotide is a poly(A) site. If the value of a nucleotide is higher than the threshold, this position is thought to be a poly(A) site. Sn_0, Sn_3, and Sn_10 represent the distance between the predicted site and the known site, which are 0, 3 and 10 nucleotides, respectively. Sn_0 means that the predicted site is exactly the same as the known poly(A) site (0 distance). Based on Figure 1A, when the threshold is increased, Sn decreases while Sp increases. There is no drastic different when the Sn are calculated with the three positions relative to the poly(A) sites. However, Sp can be quite different when different control sequences are used. For the coding sequences and the randomly generated sequences, both Sn and Sp reach 97% at a threshold 4. For 5' UTR, Sn and Sp are about 82% at a threshold of 5.2. In the intron sequences, Sn and Sp are lower than others at 72% at a threshold of 6. The lower Sp may reflect the feature of the sequences of 5'UTR and the introns, because these sequences tend to have higher A and T content, a characteristic shared by 3' UTR on which PASS design was based.

To evaluate the program, we tested the sequences in the above-mentioned datasets. Using the probability score, an output of PASS, we examined the distributions of the scores as shown in Figure 1B. The average scores of the 8K dataset peak at location 301, the authenticated poly(A) site position in these sequences. This is a demonstration of the efficacy of the program because it was designed to predict these positions as poly(A) sites. The average scores of the control sequences are much lower than that of 8K with the exception of the intron dataset. Again, this could be due the shared features between 3' UTR and the introns. Importantly, there is 1 point score difference between the average peak score of the poly(A) sites and that of the introns, which is significant enough to differentiate the poly(A) site from introns. This is demonstrated in the genomic sequence scan that is discussed later.

To further examine the prediction scores that are distinctive for poly(A) sites, the distributions of the scores at position 301 and the average scores of all other non-poly(A) sites in all the sequences of 8K dataset were compared (Figure 1C). The majority of the poly(A) sites have a score between 6 and 7, whereas the average scores of all other non-poly(A) sites peak at 4–5. Difference of 1 to 2 score points again could be significant enough to resolve the poly(A) site from the background at the sequence level.

To demonstrate the efficacy of the algorithm and the software, we tested many sequences including those with multiple poly(A) sites. Three of the typical results are shown graphically in Figure 2. In general, most of the experimentally authenticated poly(A) sites are found in the high probability area with scores larger than or around 6. However, not all predicted sites with high scores are confirmed by EST data. There are a few possible reasons for this. First, the EST data may not be exhaustive, meaning that not all sites have been found in the available EST dataset. Second, not all possible sites are efficiently used in the cells. Instead, some sites may only be used under certain environmental or developmental conditions. Third, some may be inaccurately predicted. This could be corrected by further optimization of the algorithm. It is very interesting to note that in several cases, there are authenticated poly(A) sites located in the low score area (e.g. the first site in Figure 2A, with a score around 2). The reason for this is not clear. One possible explanation could be that the use of this site could be facilitated by yet unknown trans-acting factors.

To see if PASS can differentiate multiple poly(A) sites, we further tested some genes that have been reported by others or collected from GenBank collections (e.g. NCBI's Unigenes). Tobacco RNA binding protein-30 gene (Accession# X65118), which is known as a gene with many alternative poly(A) sites 13, was scanned for poly(A) site scores by PASS. As shown in Figure 3, most of the poly(A) sites are in the highly scored (around 5) area of the 3'-UTR with a couple of exceptions (<4). However, the PASS predicted peaks at around location 280 were not validated. It is very likely that there are other factors contributing to the site selection, e.g. protein factors, RNA secondary structures, etc.

One way to further assess the software would be to see if it can predict the change of the utility of poly(A) sites after the polyadenylation signals are mutated. Examples of this can be found in the well-studied 3'-UTRs. The polyadenylation signals for two genes, pea rubisco small subunit gene (rbcS) E-9 and cauliflower mosaic virus (CaMV) 35S transcript, have been extensively studied by classical mutagenesis and genetic means 26714, and are being used widely in transgene constructions 1516. As shown on Figure 4A, the main poly(A) sites of the CaMV 3'UTR are located on the peak of the scores predicted by PASS. There are four validated poly(A) sites in rbcS, but sites 2 and 3 are the major poly(A) sites 17 (Figure 4B). Interestingly, our program predicted such site usage bias by 6–7 score points (compare to site 1). Again, similar to Fig. 3, there are a few peaks (meaning good poly(A) sites) after site 3 that are not used, presumably due to unknown factors that are not considered in this algorithm. It may also be possible that these sites are behind the major sites, and thus being skipped. Nonetheless, our predicted sites are typically in the near vicinity of the authenticated sites.

Detailed conventional mutagenesis experiments were performed on the poly(A) signal for rbcS site 1, which was chosen to avoid the overlapping signals of sites 2 and 3 7. Linker scanning, base substitution, and enhancing the signal by using AAUAAA all altered the site usage at different levels 7. Interestingly, these changes can also be predicted by our software as indicated in Figure 4C. This becomes evident when the PASS scores are compared with the site efficiency (the fraction of a poly(A) site being chosen and used in the pool of the rbcS mRNA) after mutation (Figure 4D). There is a tendency of linear relationship between PASS scores and site efficiencies following mutation. This suggests that our model can identify the poly(A) sites both qualitatively and may be also quantitatively.

One of the utilities of PASS is to predict poly(A) sites of unannotated genomic sequences, which could be helpful in genome annotation. This is because a poly(A) site marks the end of a 3'-UTR, which generally is the end of a gene. To test the effectiveness of PASS in this regard, we used it to scan several 50,000 nt genomic sequences downloaded from TAIR (18;Arabidopsis Genome Initiative release 5). Figure 5 shows one of these examples, in which many poly(A) sites were predicted. When the gene annotation data (gene units, from TAIR) were overlaid with the PASS prediction scores, several interesting phenomena became obvious. The ends of the 6 genes annotated in this region (from left to right orientation only, since PASS scans one direction from 5' to 3' of the sequence) all have the relative high score at the 3' termini of their transcripts, particularly when comparing the scores in the coding region and 3'-UTR (e.g. AT4G02510 and AT4G02540, Figure 5). Some of them show a few sites with good scores in the 3'UTR (AT4g02500) or even in the coding sequences (AT4G02750), which may reflect alternative poly(A) sites. More interestingly, however, the two regions with the highest scores (marked with "?") were not located in any annotated genes. This could be due to the traditional annotation process failing to recognize the genes. Alternatively, there may be some special sequences that possess the features of a poly(A) site. It is also possible that PASS produces false positive sites. These possibilities could be distinguished using wet lab experiments (RT-PCR approach with oligo-dT and a sequence specific primer to detect transcript with a poly(A) tail, for example).

The experimental dataset (also called the 8K dataset) used here has been described previously 6, and contains 8160 sequences from the genome of Arabidopsis thaliana. Briefly, all available expressed sequence tags (ESTs) were downloaded from GenBank, and those containing terminal poly(A) sequences [8 to 15 nucleotide (nt) with at least 80% adenine content] were recognized and trimmed. The terminal nt of each trimmed polyadenylated transcript was classified as the last nt before a poly(A) site. A total of 8160 such poly(A) sites were identified and confirmed through the comparison of genomic and EST sequences (The oligo(A) should not be found in the genomic sequence because these were added post-transcriptionally during the polyadenylation process). Using the poly(A) sites as a reference, the corresponding 400 nt genomic sequences were extracted in such a way that each sequence contained 301 nt upstream and 99 nt downstream of the poly(A) site. Thus, the poly(A) site in each sequence was between the 301^st nt and the 302^nd nt (from left to right; the poly(A) site was also the cleavage site. The cleavage reaction occurs between two nucleotides linked by a phosphodiester bond). The cleavage site is defined as the "0" position (note there is no nucleotide assigned to this position). Hence, the nucleotide sequences on the left (upstream) have a negative designation, and on the right have a positive (often omitted) designation. In general, for the purpose of easier description, the nucleotide on the left of the cleavage site (position 301 in the dataset) is normally referred to as the a poly(A) site.

This dataset was used to extract the features of the poly(A) signals and poly(A) sites. Other test sequences shown in the results were either downloaded from GenBank or from published papers as cited. For the Sp calculation, control datasets of the Arabidopsis coding (which do not include 5' and 3' UTRs and introns), 5'-UTR, and intron sequences were downloaded from The Arabidopsis Information Resources website (TAIR; 18; Arabidopsis Genome Initiative Release 5, 2004). These sequences were trimmed into 400 nt in length each for better comparison with the 8K dataset. The coding sequence datasets were extracted from downloaded sequences in the range of 300–700 to avoid the inclusion of UTRs. The random sequences for the Sp calculation were generated based on the second order trinucleotide distribution 5 in the 8K dataset. For the genomic sequence scan, the Arabidopsis chromosome 4 genomic sequence was used (ATH1_chr4.1con.01222004; from TAIR). It is worth mentioning that the sequences used in this work are in DNA form, so nucleotides in these sequences are ATCG instead of AUCG as in RNA. This does not impact the analysis.

The topological structure is one of the most important factors in designing a GHMM model. The regular expression of topological structures in GHMM models is based on all connection structures, in which every state can go to any other state. This kind of topological structure does not take advantage of the positions of the signal elements in the 3' UTR (Figure 6A). Therefore, we employed a GHMM model that recognized the signals from left to right, and only allowed the recognition of signals from the current state to the next state in one direction, as indicated in Figure 6B. Based on the analysis of the current model of plant poly(A) signals 6, we classified the sequences into five regions (Figure 6A). The poly(A) signals are distributed in these regions with some spacing between the two signal elements. Based on this, we added a background state between the two signal states. To simplify the model, we assumed that the length of every signal was fixed but the length of background was variable. It was also possible that two signals were next to each other and thus the length of the background may be 0. The final model was designed in such a way that all calculations began on the first state and ended at the last state (Figure 6B). The order of the algorithm is shown in Figure 6C.

In this model, some basic parameters were set as follows: the number of states was 11 (Figure 6B, from Bg1 through Bg6); the array of signals in every state is set to be {A, T, C, G}. States in odd numbers were the background state with variable length, and states in even numbers were signal states with fixed length. Because the model begins with the first state and ends at the last state, the initial state distribution is set in π = {1,0,...,0}. Because every state (i) can be only transferred to the i+1 state, only the value of a_i,i+1 is 1 in the state transition probability matrix, and other elements of the distribution matrix are 0. Other parameters such as distribution of nucleotides and length of state will be described below.

For modeling purposes, we needed to assign each state a few parameters including the signal nucleotide composition, signal pattern length, etc. To simplify the model, we assumed that the size or nucleotide length of each signal (FUE, NUE, CE, respectively) was fixed. As a first step, we had to designate reasonable signal lengths for each of them. To this end, we designed the following method to extract this data from the SignalSleuth experiments as described in Loke et al 6. The observed total count of 3 nt patterns was used as a basis to calculate the "expected count" of pattern sizes of 4 nt, and the observed total count of 4 nt patterns was used to calculate the "expected count" of 5 nt, and so on. For example, the expected count of 4 nt patterns should decrease by 25% of the actual total count of 3 nt patterns because of an increase in length by one of the four nucleotides. The difference between the predicted count of patterns (random chance) and the actual observed count is useful in measuring pattern length uniqueness. The measure of the deviation from the randomness of the patterns offers a clue as to the potential length of the signals, because the real signals should have greater deviation from randomness than that of non-signals. As indicated on the histogram (see Additional file 3), the greatest difference observed for FUE is at 8 nt, NUE at 6 nt, CE-L at 6 nt, and CE-R at 7 nt, respectively. Importantly, using this bioinformatics approach, the signal lengths of the NUE and FUE match the lengths of NUE and FUE defined by classical genetic analysis, in which it was found that the NUE signal length is 6 nt, and the FUE is about 8 nt 227. Note that the signal length is different from the range of signal region where the signal can be found. The latter is for modeling purposes, and is larger because it describes a collective area where the signals are found in different genes.

After determining the length of the signals, we needed to study the output probability B of the nucleotides (A, T, C, and G) in every signal state. To this end, we analyzed the distribution of nucleotides in each region (FUE, NUE and CEs) with the formula below, using the frequency data that was generated by SignalSleuth as described by Loke et al 6 using the 8K dataset.

D ε = ∑ i = 1 N ( ε i × W i ) ∑ ε ∈ { A , T , C , G } ( ∑ i = 1 N ( ε i × W i ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGebardaWgaaWcbaacciGae8xTdugabeaakiabg2da9maalaaabaWaaabCaeaadaqadaqaaiab=v7aLnaaBaaaleaacqWGPbqAaeqaaOGaey41aqRaem4vaC1aaSbaaSqaaiabdMgaPbqabaaakiaawIcacaGLPaaaaSqaaiabdMgaPjabg2da9iabigdaXaqaaiabd6eaobqdcqGHris5aaGcbaWaaabuaeaacqGGOaakdaaeWbqaamaabmaabaGae8xTdu2aaSbaaSqaaiabdMgaPbqabaGccqGHxdaTcqWGxbWvdaWgaaWcbaGaemyAaKgabeaaaOGaayjkaiaawMcaaiabcMcaPaWcbaGaemyAaKMaeyypa0JaeGymaedabaGaemOta4eaniabggHiLdaaleaacqWF1oqzcqGHiiIZcqGG7bWEcqWGbbqqcqGGSaalcqWGubavcqGGSaalcqWGdbWqcqGGSaalcqWGhbWrcqGG9bqFaeqaniabggHiLdaaaaaa@6264@

where Wi=Ci∑s=1NCs MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGxbWvdaWgaaWcbaGaemyAaKgabeaakiabg2da9maalaaabaGaem4qam0aaSbaaSqaaiabbMgaPbqabaaakeaadaaeWbqaaiabdoeadnaaBaaaleaacqqGZbWCaeqaaaqaaiabdohaZjabg2da9iabbgdaXaqaaiabb6eaobqdcqGHris5aaaaaaa@3C88@ is the statistical weight of sequence i, and the more repeats this sequence has, the higher the weight is; C_i is the frequency at which the i^th sequence occurs in this signal area; D_ε represents the probability of the nucleotide ε in the signal element, i.e. the distribution of nucleotides, which is ε ∈ {A, T, C, G}; ε_i is the frequency of ε in the i^th sequence, where 1 ≤ i ≤ N, and N is the number of signal patterns considered.

Taking signals in the FUE as an example, the representative nucleotide output probability B was calculated based on the top 50 patterns [see Additional file 4]. First, we calculated the weight of every pattern by count, and then calculated the repeat times ε_i of every nucleotide in these patterns. The nucleotide output probability B for FUE hence are 0.0485, 0.7740, 0.0479 and 0.1290 for A, T, C, and G, respectively.

Using the same method, the nucleotide output probability B for CE-L and CE-R are: CE-L: 0.09987, 0.74970, 0.06186, 0.08860; CE-R: 0.08520, 0.78700, 0.07050, 0.05680 for A, T, C, and G, respectively.

The NUE signals are slightly better conserved than other signals, and the transition from one nt to the next may be constrained. To present these interactions of hexamer signals, we used a subset of first order inhomogeneous Markov model to describe the feature information. A frequency transport matrix was used to analyze the 50 most predominant NUE signals 6. The equation is shown below:

P N = [ P N ( A / A ) P N ( T / A ) P N ( C / A ) P N ( G / A ) P N ( A / T ) P N ( T / T ) P N ( C / T ) P N ( G / T ) P N ( A / C ) P N ( T / C ) P N ( C / C ) P N ( G / C ) P N ( A / G ) P N ( T / G ) P N ( C / G ) P N ( G / G ) ] = [ S ( A A ) ∑ A S ( A T ) ∑ A S ( A C ) ∑ A S ( A G ) ∑ A S ( T A ) ∑ T S ( T T ) ∑ T S ( T C ) ∑ T S ( T G ) ∑ T S ( C A ) ∑ C S ( C T ) ∑ C S ( C C ) ∑ C S ( C G ) ∑ C S ( G A ) ∑ G S ( G T ) ∑ G S ( G C ) ∑ G S ( G G ) ∑ G ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@2912@

where PN(T/A) is the probability of a transition from state "A" to "T"; S(AT) is the sum of times of this transport; Σ_A = S(AA) + S(AT) + S(AC) + S(AG). The same rule was used for the others. Thus, we obtained parameters of the NUE sub-model as: probability distribution of the first nucleotide, PN₀ = [0.6276, 0.3563, 0.0001, 0.0161]. The distributions of the second to sixth nucleotides are listed below, respectively,

P N 1 = [ 0.6215 , 0.3785 , 0.0001 , 0.0001 0.6788 , 0.3212 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 ] , P N 2 = [ 0.5229 , 0.4464 , 0 , 0.0307 0.6003 , 0.2637 , 0.0441 , 0.0920 1 , 0.0001 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 ] , P N 3 = [ 0.5470 , 0.4258 , 0 , 0.0272 0.6700 , 0.2377 , 0.0418 , 0.0505 1 , 0.0001 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 ] P N 4 = [ 0.6181 , 0.3584 , 0.0001 , 0.0235 0.7537 , 0.2463 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 ] , P N 5 = [ 0.5550 , 0.4212 , 0.0001 , 0.0238 0.5277 , 0.4723 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 1 , 0.0001 , 0.0001 , 0.0001 ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@1DE0@

Therefore, for a certain hexamer sequence S = s₁s₂s₃s₄s₅s₆ we can calculate the probability of the NUE signal at the S position:

P[S | NUE] = PN₀(s₁)*PN₁(s₂|s₁)*PN₂(s₃|s₂)*PN₃(s₄|s₃)*PN₄(s₅|s₄)*PN₅(s₆|s₅).

The same kind of first order inhomogeneous Markov model was established for the poly(A) site signal (YA in the model, Fig. 6A). For this, we randomly selected 1000 sequences from the 8K dataset and obtained the poly(A) site parameters listed blow. Initiated state CSPN₀ = [0.0730,0.4630, 0.3250, 0.1390],

2^nd state CSPN1=[0.4247,0.3973,0.1096,0.06850.7171,0.1620,0.0648,0.05620.7785,0.1569,0.0431,0.02150.84890.09350.01440.0432] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@A448@

Based on the same method, we calculated a dimer sequence S = s₁ s₂ and obtained the probability at S position: P[S|CS] = CSPN₀(s₁)* CSPN₁(s₂|s₁).

Apart from the signal regions, there is not much information on the background states. Therefore, the parameters for background states were relatively random. Based on this condition, we first analyzed several basic factors in the background and modified them accordingly. The nucleotide output probabilities of background states were calculated by counting the nucleotide distribution of the whole sequence. We tested the distribution of nucleotides in the region of -160 to +100 nt.

The most important factor in the background state is the length between two signal states. Taking the background states near the poly(A) site as an example, Bg4 and Bg5 are located upstream and downstream of the poly(A) site, and both the CE-L and CE-R signal states could be about 10 nt distance from the poly(A) site. Therefore, the length of the background state can be set to a range with 0 nt to 10 nt. The maximum length D was set to 10. However, because the length of the background could change slightly, we set all the lengths to a uniform distribution, which can be calculated by P_i(d) = 1/(1+D_i), where P_i(d) is the probability of the length of the background i^th to be d, and D_i is the possible maximum length of the i^th background. All background lengths were set by this method. The initial possible maximum length of Bg1, Bg2, Bg3, Bg4, Bg5 and Bg6 were set to 100, 100, 20, 10, 10 and 15, respectively.

To identify the background region, we needed to consider the near signal region of both sides. For example, Bg3 lies between NUE and CE-L signal states, the range of NUE state is 10~30 nt and CE-L signal region is from 1 to 10 nt. Therefore, the range of Bg3 could be set in the center of these two regions which is 6~20 nt. The distributions of the background region and nucleotide output probability B are listed in [Additional file 5].

We applied a sliding 180 nt-wide window to calculate the output of scores for the sequences. For every nucleotide, our program computed a score in all windows that contained this nucleotide. The window slid along the entire sequence, combining values of forward-backward variables using the following equation for the output of the score at nucleotide t:

S c o r e ( t ) = max ⁡ w { S ( t ) } S ( t ) = { log ⁡ 10 P S w , t + 120 } / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakqaabeqaaiabdofatjabdogaJjabd+gaVjabdkhaYjabdwgaLjabcIcaOiabdsha0jabcMcaPiabg2da9maaxababaGagiyBa0MaeiyyaeMaeiiEaGhaleaacqWG3bWDaeqaaOWaaiWabeaacqWGtbWucqGGOaakcqWG0baDcqGGPaqkaiaawUhacaGL9baaaeaacqWGtbWucqGGOaakcqWG0baDcqGGPaqkcqGH9aqpdaGadeqaaiGbcYgaSjabc+gaVjabcEgaNnaaBaaaleaacqaIXaqmcqaIWaamaeqaaOGaemiuaaLaem4uam1aaSbaaSqaaiabdEha3jabcYcaSiabdsha0bqabaGccqGHRaWkcqaIXaqmcqaIYaGmcqaIWaamaiaawUhacaGL9baacqGGVaWlcqaIYaGmaaaa@5D81@

where w is all of the windows that include nucleotide t; PS_w,t is the forward-backward algorithm's probability that nucleotide t is a poly(A) site in window w; the two constants, 120 and 2, are used to adjust the scores to be in a manageable range.

The formulas for Sp and Sn calculations are given in the Results. The methods for the compiling false positive and false negative numbers are shown here. We employed a user defined value called threshold in these calculations. At a given threshold value (t), the score at an nt must be at least t in order for that nt to be a predicted poly(A) site. The False Positive sites (FP) were calculated as following: for a sequence of interest, let n represent the total number of nucleotides; let p represent the number of true poly(A) sites with a score equal or larger than a given t; let m represent the number of all sites with a score equal or larger than t. Then, FP = m-p. As one can see, using the 8K dataset sequences to calculate FP requires that all poly(A) sites have to be identified. Due to the fact that the identification of true poly(A) sites in a given 3'UTR is incomplete in plants (many alternative poly(A) sites may not be represented in the EST collection, or the dataset is not sufficiently large enough), sequences that are known to not possess poly(A) sites were used to tally FP. These sequences include protein-coding sequences, 5'-UTRs, and introns as indicated in "The Datasets" under Methods. Random sequences generated by preserving the trinucleotide distribution were also used. In these control datasets, FP = m. For True Positive sites (TP), at a given t, in the sequences with known poly(A) sites, TP = p. In the control sequences, TP = n-m. False negative (FN) is the number of actual sites that cannot be identified or predicted correctly. To calculate FN, let f represent the number of true poly(A) sites with a score smaller than a given t. Hence, at a given t, in the sequences with known poly(A) sites, FN = f.