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Three-nucleotide periodicity of nucleotide diversity in a population enables the identification of open reading frames

Abstract Accurate prediction of open reading frames (ORFs) is important for studying and using genome sequences. Ribosomes move along mRNA strands with a step of three nucleotides and datasets carrying this information can be used to predict ORFs. The ribosome-protected footprints (RPFs) feature a significant 3-nt periodicity on mRNAs and are powerful in predicting translating ORFs, including small ORFs (sORFs), but the application of RPFs is limited because they are too short to be accurately mapped in complex genomes. In this study, we found a significant 3-nt periodicity in the datasets of populational genomic variants in coding sequences, in which the nucleotide diversity increases every three nucleotides. We suggest that this feature can be used to predict ORFs and develop the Python package ‘OrfPP’, which recovers ~83% of the annotated ORFs in the tested genomes on average, independent of the population sizes and the complexity of the genomes. The novel ORFs, including sORFs, identified from single-nucleotide polymorphisms are supported by protein mass spectrometry evidence comparable to that of the annotated ORFs. The application of OrfPP to tetraploid cotton and hexaploid wheat genomes successfully identified 76.17% and 87.43% of the annotated ORFs in the genomes, respectively, as well as 4704 sORFs, including 1182 upstream and 2110 downstream ORFs in cotton and 5025 sORFs, including 232 upstream and 234 downstream ORFs in wheat. Overall, we propose an alternative and supplementary approach for ORF prediction that can extend the studies of sORFs to more complex genomes.


Introduction
Annotation of open reading frames (ORFs) in genomes is one of the most important processes required for downstream analyses and the use of reference genomes. Various algorithms have been developed to predict ORFs [1][2][3][4][5] in genomes, but these sequence-based methods are powerless in predicting small/short ORFs (sORFs) because many nonsense sORFs can arise by chance as random combinations of nucleotides. Recent studies have shown the crucial roles of sORFs, which encode peptides shorter than 100 amino acids, in various biological processes, including responses to abiotic and biotic stresses in plants [6] and oncogenesis in humans [7] and some of them are pertinent to cancer therapy [8]. The prediction of sORFs has long been problematic due to their short lengths and the use of alternative start codons, such as near-cognate codons (CUG, GUG, UUG) [4,9]. Early attempts at sORF prediction were based on the sequence similarity across near or distant species, assuming that the functional sORFs would be conserved in sequence. For example, 26 conserved upstream ORFs (uORFs) were identified by comparing the full-length complementary DNA (cDNA) sequences between rice and Arabidopsis [10]. The recent application of the Ribo-Seq technique, which profiles ribosomeprotected messenger RNA (mRNA) footprints (RPFs), has enabled accurate prediction of translated ORFs, including sORFs, in several genomes [4,6,8,[11][12][13][14][15][16]. Protected by a single ribosome sliding along the mRNA strand with a consistent step size of 3-nt, the RPFs should be uniform in size and show a 3-nt periodicity along the mRNAs if they are properly prepared [2], allowing the identification of the translating frame on mRNAs.
Although the Ribo-seq technique has been used in studies of many species, including yeast, humans, animals and plants [16], most of these species are model organisms with a simple genome. This is because a typical eukaryotic ribosome footprint is 28 nt in length [2,17,18], which is too short for accurate mapping in genome sequences, and this problem would be even worse in polyploid genomes. Due to multiple duplication events during evolutionary history, many plant genomes are polyploid and complex, featuring high repetitiveness and high heterozygosity [19,20], limiting the application of Ribo-Seq in many plants, including several staple crops, such as bread wheat (Triticum aestivum) (6X) and cotton (Gossypium hirsutum) (4X). In addition, the challenges in preparing high-quality RPFs also limit the application of this technique to a broader range of non-model organisms. Incomplete digestion of unprotected mRNAs can reduce or eliminate the 3-nt periodicity of RPFs [21,22], becoming useless for ORF identification.
Although the 3-nt periodicity shown by high-quality RPFs is powerful in ORF prediction, the application of RPFs for this purpose is hampered by the complexity of genomes, particularly in plant studies. We noticed that the populational diversity of nucleotides in coding sequences (CDSs) also shows a significant 3-nt periodicity, as observed for high-quality RPFs, and thus propose to use this periodicity to predict ORFs. In this study, to achieve this, we developed a Python package, ORF predictor using population genomic dataset (OrfPP), which identifies ORFs using the nucleotide diversities in populational datasets of single-nucleotide polymorphisms (SNPs). We tested OrfPP and recovered an average of 83.20% of the annotated ORFs with an average accuracy of 94.77%. The performance of OrfPP is robust even when a small subset of the SNPs is used. Finally, we applied OrfPP to two polyploidy genomes, cotton and wheat and identified 4704 and 5025 novel ORFs, respectively, with reliability comparable to the annotated ORFs in the genomes. Our study suggests that predicting ORFs from SNPs can be an approach supplementary to the existing methods and can be used to identify sORFs in complex genomes, for which the existing methods are not yet workable. We believe that this approach will play a greater role in future studies of animals and plants, given the rapidly growing number of SNP datasets for different species and the application of advanced techniques of DNA sequencing and SNP calling.

Comparison of ORFs predicted from RPFs and SNPs
To simplify the comparisons, the RPF-based ORF prediction in all the tested datasets was performed using RiboCode (v1.2.11) [23], ORFquant [24] and Ribotricer [25] with default parameters, and the ORFs predicted by the one performing the best (measured by F-score) were chosen to represent the ORFs predicted from RPFs. The predicted ORFs identical to the annotated ORFs in the reference genome were counted as true positives and the others were considered false positives. The accuracy, recall and F-score were calculated following the formula: F-scores were used to comprehensively assess the performance of OrfPP. It should be noted that although the unannotated ORFs were counted as false positives, many of them are bona fide ORFs, such as sORFs that were not included in the annotation of reference genomes.

Metagene analysis and periodicity assessment
Metagene analyses have been used to illustrate the read distribution pattern of RPFs on mRNAs, which show a clear 3-nt periodicity in various organisms [9,[11][12][13]26].
To perform metagene analysis of CDSs, the diversity for each nucleotide in the first 50 nucleotides was determined for each ORF and used to calculate the average nucleotide diversity at each position in the first 50 nucleotides for all the ORFs in the genome. Similarly, the diversity for each nucleotide in the 50 nucleotides upstream of start codons was selected for the analysis of the 5 untranslated region (UTR), and those downstream of stop codons were selected for analysis of the 3 UTR.
To analyse intergenic regions, 10 000 50 bp windows were randomly selected and aligned to calculate the average diversity for the nucleotides at each position. The periodicity in the plot of metagene analyses was evaluated using an F test implemented in the 'multitaper' R package (version 1.0-14) [27], which detects the spectra and frequencies of the changes of nucleotide diversities within the window and calculates the P-values for all the frequencies. As a frequency of 0.33 Hz (1/3) indicates the periodic appearance/increase of the diversity of every three nucleotides, a significant P-value is expected for a pattern with 3-nt periodicity.

Quantification of translation levels of ORFs
The RPFs used for ORF prediction in this study were also used to calculate the translation levels of the predicted ORFs. Briefly, the RPFs were mapped to the genomes using HISAT2 [28] with default parameters and the number of mapped RPFs in each ORF was counted and used to calculate translation levels.

Datasets
Several datasets from model organisms, including fission yeast, Arabidopsis and rice, were selected to test the performance of OrfPP. These organisms usually have high-quality reference genomes, SNP datasets [35][36][37][38][39] and high-quality RPFs [11,26], allowing a comprehensive comparison between the ORFs predicted from RPFs and those predicted from SNPs by OrfPP. SNP datasets of cotton and wheat were also used to identify novel ORFs in the genome. The datasets used in this study are listed in detail in Table S1 (see Supplementary Data available online at http://bib.oxfordjournals.org/).

3-nt periodicity of nucleotide diversity in coding regions
We performed metagene analyses of sequences from intergenic regions, 5 and 3 UTRs, and coding regions in different genomes ranging from yeast to higher plants (Arabidopsis and rice), the population size of which varied from 148 (yeast) to as large as ∼3000 in rice. Our results show highly consistent patterns for all these tested populations; only the nucleotide diversities in CDSs showed a significant 3-nt periodicity, while the diversities in other regions appeared to vary randomly ( Figure 1). The wobble nucleotides in codons are more tolerant to mutation and have experienced less purification selection during evolution. Indeed, higher diversities were observed for the third nucleotides in codons ( Figure 1). In line with this observation, the nucleotide diversities in the non-coding regions were generally higher than those in CDSs, with those in intergenic regions being the highest, indicative of the smallest selective pressure on these regions. These results suggest that this 3-nt periodicity of nucleotide diversity in CDSs is common in natural populations. Such a periodic increase in nucleotide diversity in CDSs is reminiscent of the 3-nt periodicity of RPFs' depth on mRNAs ( Figure 2A); therefore, we propose that this periodicity of nucleotide diversity can also be used to predict ORFs.

Design of OrfPP
To utilize the periodicity of nucleotide diversity to predict ORFs in genomes, we developed a pipeline named 'OrfPP', which is available as a Python package (https://pypi. org/project/OrfPP/1.0/). Given that the 3-nt periodicity of nucleotide diversity only appears in CDSs, as shown in Figure 1, it can distinguish CDSs from non-CDSs, determine the reading frame of ORFs and predict ORFs in the genome. Codon usage is also considered in OrfPP. The use of different codons varies considerably across different genomes, which are strongly correlated to the abundance of their corresponding tRNAs in the genome [40][41][42] and, therefore, is an intrinsic feature unique to each genome. It is reasonable to assume that all the ORFs in a genome use codons with the same preferences because they all share the same pool of tRNAs. Briefly, OrfPP uses the 3-nt periodicity of nucleotide diversity in populational genomic datasets and codon usage preferences to predict ORFs in the genome. It takes three input files: the nucleotide diversity (derived from the SNP dataset), the reference genome sequence (in fasta format) and genome annotation (in gtf format) and includes three major steps, as shown in Figure 2B.

Codon usage training
To calculate genome-wide codon usages, OrfPP first predicts ORFs solely based on nucleotide diversity. The pipeline extracts the transcripts according to the genome annotation and allocates the values of nucleotide diversity onto each position on transcripts, from which candidate ORFs (start with 'AUG' and end with stop codons with a length multiple of three) are extracted for the prediction of ORFs. Two Student's t-tests are performed to test whether the nucleotide diversities in frame 2 (the third nucleotides of codons) are greater than those in frame 0 and frame 1 in OrfPP, and are combined to report a final P-value for the identification of ORFs. To obtain ORFs with higher reliability for codon usage training, several stringent criteria are applied in this process of preliminary prediction. For example, at this stage, OrfPP only predicts ORFs starting with the canonical initiation codon 'AUG' from the candidates longer than 300 bp. The codon usages are then calculated from these predicted ORFs and used to represent the genome-wide usages.

ORF prediction
Transcript sequences are extracted according to the genome annotation information, and candidate ORFs were retained ( Figure 2B) for further tests. In addition to the tests of nucleotide diversity between the frames (frame 0 versus frame 2, frame 1 versus frame 2), the pipeline also tests the codon usages between the frames for each candidate ORF by assigning to each nucleotide a value corresponding to the usage of the corresponding triplet as a codon in the genome. As for the diversity tests, OrfPP tests whether the values of codon usage at frame 0 are higher than those at frames 1 and 2 and combines the P-values from these four Student's t-tests to give a final P-value for the prediction of ORFs. To also report sORFs, OrfPP reports ORFs shorter than 100 bp and the initiation codons can be customized.

ORF classification
The predicted ORFs are classified into 11 categories following previous definitions [1,3,5]. They are (i) annotated ORF, (ii) truncated ORF, (iii) extended ORF, (iv) uORF, (v) overlapped uORF, (vi) downstream ORF (dORF), (vii) overlapped dORF, (viii) ORFs located in non-coding RNAs, (ix) internal ORF, (x) ORFs located in transposable elements and (xi) ORFs in pseudogenes [3]. Although the ORFs are classified according to the previous annotation of ORFs in the reference genome, OrfPP can also be used for de novo prediction of ORFs when the annotation of ORFs is not yet known. In this situation, the predicted ORFs will all be annotated as 'Novel ORFs'.

Comparison of annotated ORFs recovered from RPFs and SNPs
Several species (Table S1, see Supplementary Data available online at http://bib.oxfordjournals.org/), including yeast, Arabidopsis and rice, all with high-quality reference genomes and available datasets of both RPFs and SNPs, were selected to assess the performance of OrfPP. The accuracy, recall and F-score of prediction were used to describe the performance of OrfPP in these genomes. We used the annotated ORFs in the reference genomes as a benchmark to measure the performance of OrfPP, with the predicted ORFs identical to the ORFs annotated in the reference genome considered true positives and false positives otherwise. A note of caution should be made that many unannotated ORFs may be bona fide ORFs, such as sORFs, not included in the annotation of reference genomes but considered false positives in this computation.
As RPFs were the most direct evidence recording the reading frame on the mRNAs, the ORFs predicted by OrfPP were also compared with those predicted from RPFs. RPF-based ORF prediction was performed using three different tools, RiboCode [5], ORFquant [24] and Ribotricer [25], the results of which varied substantially, with ORFquant performing the best in yeast datasets, while RiboCode was the best for Arabidopsis and rice (Table S2, see Supplementary Data available online at http://bib.oxfordjournals.org/; Figure S1, see Supplementary Data available online at http://bib.oxfordjournals.org/). We then used the yeast ORFs predicted by ORFquant and Arabidopsis and rice ORFs predicted by RiboCode to compare with those predicted from SNPs. Our analysis showed that 89.57, 83.82 and 79% of the known ORFs in the reference genome of fission yeast, Arabidopsis and rice were successfully recovered by OrfPP with accuracies of 98.03, 95.6 and 90.19%, respectively, from the SNP datasets. Many of the annotated ORFs in these genomes were also recovered from RPFs, but there were fewer than those found using SNPs by OrfPP (Figure 3A-C; Table S2, see Supplementary Data available online at http://bib.oxfordjournals.org/; Figure S1, see Supplementary Data available online at http://bib.oxfordjournals.org/), probably because the RPFs included only actively translating ORFs. RPFs from silenced ORFs under the tested conditions would have been absent in the RPF dataset. However, the accuracies of prediction are similar between these two tools for all the tested genomes, suggesting a comparable accuracy between the ORFs predicted from SNPs and those from RPFs. The comparison between the ORFs predicted from RPFs and those from SNPs indicates that most of the former were included by the latter (Figure 3D-F).
To further investigate the impacts of translation levels on the prediction of ORFs, we roughly categorized the known ORFs into three major groups: (i) commonly predicted from both RPFs and SNPs, (ii) predicted only from SNPs and (iii) not predicted, and calculated their translation levels using the corresponding RPFs used for ORF predictions in this study. Our data revealed the highest translation levels for the ORFs commonly predicted from both SNPs and RPFs ( Figure 3G-I), suggesting that RPFs are efficient in predicting actively translated ORFs. However, the ORFs in the other two groups showed lower levels of translation ( Figure 3G-I). These results suggest that in addition to the active ORFs that RPFs can capture, OrfPP can also predict inactive ORFs by utilizing the SNPs accumulated during the evolutionary history of the species.

Comparison of sORFs identified from RPFs and SNPs
RPFs have been used to predict sORFs in many studies, but a shortcoming of this method has often been ignored. Due to the short size of RPFs, only a few of them can be uniquely mapped to genomes ( Figure S2,see Supplementary Data available online at http://bib.oxfordjournals. org/). For example, for the RPFs tested in this study, the unique mapping rates of RPFs varied from 9 to 54%, while the unique mapping rates of wholegenome sequencing (WGS) reads can be as high as 92% ( Figure S2, see Supplementary Data available online at http://bib.oxfordjournals.org/). The usual solutions to this multimapping problem are using only the uniquely mapped RPFs or randomly assigning the RPFs to one of the potential mapping sites [6,11,43,44]. These solutions could potentially result in the misidentification of ORFs or missing some of the ORFs in the genome. Given the higher unique mapping rate of WGS reads, the sORFs predicted from SNPs are likely to be more complete than those from RPFs. Therefore, we also tested the performance of OrfPP in the identification of sORFs and compared those predicted from SNPs with those predicted from RPFs. In this comparison, to better illustrate the performance of OrfPP, we used the sORFs predicted from RPFs as a benchmark to assess the accuracy and recall rate of the predictions by OrfPP. The OrfPP-predicted sORFs identical to those predicted from RPFs were considered true positives and the others were tentatively considered false positives.
In total, RPF-based tools predicted 72, 422 and 562 uORFs in the yeast, Arabidopsis and rice genomes, respectively ( Figure 4A-D). However, only three uORFs were predicted by OrfPP from yeast SNPs, and none were identical to the uORFs predicted from RPFs. We found that the difference between these two prediction algorithms could be attributed to the difference in sORF definition in the tools. The yeast ORFs from RPFs were predicted by ORFquant, which reports sORFs as short as 9 bp, while OrfPP only reports ORFs longer than 60 bp. The other two RPF-based tools also report longer sORFs, but none of them predicted sORFs from yeast RPFs in this work. Therefore, the yeast sORFs predicted by ORFquant are not comparable to those predicted by OrfPP. For this reason, we compared only Arabidopsis and rice sORFs predicted from RPFs or SNPs. In total, 377 and 974 uORFs were predicted from Arabidopsis and rice SNPs and of these, 98 and 231 were identical to the uORFs predicted from RPFs, accounting for 23.22 and 41.10% of the total predictions from RPFs, respectively. Two ORFs commonly identified from RPFs and SNPs are shown for Arabidopsis ( Figure 4A) and for rice ( Figure 4B). These results suggest that more than a quarter of the uORFs predicted from RPFs can be recovered by OrfPP from SNPs. However, fewer dORFs were commonly identified from both SNPs and RPFs (Figure 4). Among the 840 dORFs identified using Arabidopsis RPFs, 150 (17.86%) were also identified from SNPs by OrfPP; 289 of the 840 (34.4%) dORFs identified from rice RPFs were recovered by OrfPP from SNPs ( Figure 4C and D). As above, we categorized the sORFs into three groups: (i) ORFs identified from both SNPs and RPFs, (ii) ORFs identified from only RPFs and (iii) ORFs identified only from SNPs. Our data showed that the ORFs commonly identified from both the SNPs and RPFs were more actively translated. In contrast, the ORFs in the other two groups, particularly the ORFs in group (iii), identified from SNPs but not from RPFs, had lower translation levels ( Figure 4E and F). The difference between these two predictions suggests a rare translation of dORFs but implies a potential to encode micropeptides in the 3 UTR regions.

ORF prediction from SNPs of polyploidy genomes
We further applied OrfPP to two polyploid genomes, tetraploid cotton (G. hirsutum) and hexaploid wheat (T. aestivum), to test its performance in complex genomes. SNP datasets derived from either 1913 cotton accessions [45] or 507 wheat accessions [46,47] were used in this test. Both datasets showed a significant 3-nt periodicity in CDSs ( Figure S3, see Supplementary Data available online at http://bib.oxfordjournals.org/), which allows the identification of ORFs. As a result, 91 594 ORFs were identified from cotton SNPs, among which 86 890 (94.86%) and 4704 (5.14%) were annotated and novel ORFs, respectively, and 114 929 ORFs, including 109 904 (95.63%) annotated and 5025 (4.37%) novel ORFs, were identified from wheat SNPs. The annotated ORFs recovered from SNPs accounted for 87.43 and 76.17% of all the annotated ORFs in the genome of cotton and wheat, respectively ( Figure 5A-D), values comparable to the results using the model genomes ( Figure 3). In addition to these annotated ORFs, several novel ORFs, including a variety of sORFs, were also identified from these datasets ( Figure 5E and F), including 1182 and 2110 uORFs and dORFs, respectively, in the cotton genome and 232 and 234 uORFs and dORFs, respectively, in the wheat genome. These results suggest that ORF prediction from SNPs is also workable for complex genomes.

Validation of novel ORFs identified from SNPs
Novel ORFs, including a variety of sORFs, were identified from both the RPF and SNP datasets in our tests. To verify the reliability of these predictions, we obtained protein MS data for each organism and searched for evidence supporting the existence of the peptides encoded by the novel ORFs. We computed the percentage of ORFs supported by MS data in each ORF class and, given the higher representation in MS datasets for ORFs with higher expression levels, measured the degree of MS support by normalizing this percentage to the average expression levels of ORFs in each class. Although more annotated ORFs were found in MS data compared to the novel ORFs, the degree of MS support for the annotated and novel ORFs predicted was generally comparable in our tests ( Figure 6A). For the ORFs predicted from SNPs, the MS support for the novel ORFs is proportional to that of the annotated ORFs in the genome. Support values are near the diagonal of the plot (Figure 6A), suggesting equivalent reliability between these two categories of ORFs. Therefore, the novel ORFs predicted from SNPs could be as reliable as the annotated ORFs, validated by many different lines of evidence.
The overall support for ORFs derived from MS data appears to be variable across these genomes; therefore, we normalized the MS support degree of novel ORFs by calculating the ratio of MS support for novel ORFs to the support for annotated ORFs (MS support of novel ORF/MS support of annotated ORF) to enable intraspecies comparison. We found a higher normalized MS support for the novel ORFs identified from the yeast and Arabidopsis SNPs ( Figure 6A and Figure S4A, see Supplementary Data available online at http://bib.oxfordjournals.org/). We compared the MS support to the ORFs predicted from SNPs and RPFs ( Figure 6A and Figure S4A,see Supplementary Data available online at http://bib. oxfordjournals.org/). For the ORFs predicted from RPFs, the MS support for the novel ORFs was weaker than that for the annotated ORFs ( Figure 6A and Figure S4A, see Supplementary Data available online at http://bib. oxfordjournals.org/). This suggests the novel ORFs predicted from SNPs are more reliable than those from RPFs, given that the former was supported to a degree nearly equivalent to that of annotated ORFs ( Figure 6A). The normalized MS support also allowed a comparison of MS support between different categories of novel ORFs. Although substantial variation was observed across ORFs in different categories, the support for both uORFs and dORFs was generally comparable, both of which being somewhat higher than those for the annotated ORFs ( Figure 6B and C and Figure S4B and C, see Supplementary Data available online at http://bib.oxfordjournals. org/).
We also performed this analysis to verify the ORFs identified from the SNPs of cotton (4 X) and wheat (6 X). Our data indicated that the novel ORFs identified from both the cotton and wheat SNPs were supported by MS data to a degree comparable to that of the annotated ORFs in the genome ( Figure 6A). We could not compare the reliability of wheat novel ORFs identified from SNPs and RPFs because the latter is not yet available for wheat and cotton due to the short sequence lengths. However, our data show that the normalized MS support for cotton and wheat novel ORFs is stronger than that of yeast, Arabidopsis and rice novel ORFs identified from RPFs ( Figure 6A and Figure S4A, see Supplementary Data available online at http://bib.oxfordjournals.org/). Taken together, our data suggest that the novel ORFs identified from SNPs are as reliable as the annotated ORFs in either the simple or the complex genomes. Additionally, the reliability of novel ORFs identified from SNPs is higher than those identified from RPFs.

ORF prediction independent of population size
Given that most studied populations [48][49][50][51][52] are smaller than the ones tested in this work, we further explored whether SNP datasets from small populations can also be used to predict ORFs with acceptable accuracy. The datasets of Arabidopsis (1135 accessions) and rice (3024 accessions) were used in this test, from which 100 to 1000 accessions were randomly sampled and used for ORF prediction. Our results suggest that the performance (measured by F-score) of OrfPP was robust even when a small subset of Arabidopsis datasets was used ( Figure 7A). The number of predicted ORFs generally increased as a function of population size but became saturated when the population size reached ∼400 ( Figure 7B) for rice. Although the recall rate was somewhat affected in small rice populations, the accuracy was independent of population size. Generally, the recall rates and accuracy of the ORFs predicted from SNPs are acceptable even for the smallest tested population (100 accessions). These results suggest that although the performance of OrfPP is somewhat compromised in small populations, it can be applied in most studied populations.

Discussion
Synonymous codon mutations do not change the amino acid and are therefore subject to a more relaxed purification selection [53]. The third nucleotides in codons are wobble nucleotides that can change to other  synonymous counterparts without changing the protein sequence, structure and function. Therefore, the third position of codons should have a higher diversity in the population, which would lead to a periodic increase in the nucleotide diversity every 3 nt along the CDSs. This characteristic formed the basis for identifying ORFs in the genome using SNPs.

Application of OrfPP
In this work, we tested OrfPP in a total of 5 species representing fungi and plants, from haploid (S. pombe) to hexaploid (T. aestivum) species, with genome sizes ranging from ∼12 Mb (S. pombe) to ∼16000 Mb (T. aestivum). OrfPP successfully recovered most (∼83%) of the known ORFs annotated in the reference genomes with considerable accuracy in all these tests, suggesting that the information recorded in SNP datasets can be a powerful ORF predictor. However, the predicted sORFs from SNPs appeared different from RPFs ( Figure 4). In particular, dORFs were rarely predicted from RPFs, but many were predicted from SNPs, and only rare overlaps were found between the two methods. This difference could be explained by the fact that RPFs only capture the ORFs translated under the tested conditions, and the conf lict between these two predictions implies potential biological roles of dORFs, although they are not usually translated. In fact, it is difficult to translate dORFs because ribosomes are usually stalled at stop codons and then released, so the translation of dORFs can probably only be initiated when stop-codon read-through occurs under some special conditions or by the new recruitment of ribosomes [54,55]. Despite the divergence between the novel ORFs identified from SNPs and RPFs, evidence from MS data suggests comparable reliability for the annotated ORFs and the novel ORFs identified from either the RPFs or the SNPs ( Figure 6).
Given the important biological roles of sORFs, we applied OrfPP to identify the sORFs in the polyploid plants, cotton and wheat, for which the RPF approach is not workable thus far due to the short lengths of RPFs. As a result, ∼80% of the annotated ORFs in these genomes were successfully recovered and a total of 4704 and 5025 novel ORFs, including uORF and dORFs, were identified from cotton and wheat SNPs (Tables S3  and S4), respectively. As assessed by support from MS data, these novel ORFs are as reliable as the annotated ORFs in the genomes ( Figure 6). Since identifying sORFs from RPFs is not yet feasible for polyploidy genomes, our work provides a good example showing that sORFs can be identified from SNPs. Additionally, the cotton and wheat sORFs provided here (Tables S3  and S4, see Supplementary Data available online at http://bib.oxfordjournals.org/) can be used in future works interested in the roles of sORFs in these crops.

Comparison of RPF-and SNP-based approaches
Although RPFs have been proven powerful in predicting ORFs, several drawbacks have limited their application to a broader range of species. For example, RPFs can only be used to predict the translating ORFs, thus resulting in incomplete identification of ORFs. In addition, RPFs are too short to be correctly mapped to the loci where they originate, particularly in polyploid genomes. Lastly, the preparation of high-quality RPFs can be difficult, particularly in many non-model organisms. Although some quality-insensitive predictors have been developed to use low-quality RPFs [3,23], RPFs with poor or no periodicity introduce unpredictable errors into the results and even lead to ORF prediction failure. Indeed, when we attempted to test OrfPP in many other species, such as Solanum lycopersicum, S. pennelli and Medicago truncatula [56], we found that the RPFs published in this study were not periodic and thus could not be utilized to predict ORFs. In contrast, nucleotide diversity accumulates during long-term genome evolution since the origin of this species so that this information can be used for genome-wide prediction. Compared to the problems of RPFs caused by their short size, populational SNPs are usually called by using 100 or 150 paired-ended reads, which are much longer than RPFs. Even for reads longer than 100 bp, incorrect or multiple mapping is also an inevitable problem in polyploidy or repetitive genomes, so special attention should be given to the interpretation of the results [47,57]. It can be imagined that mapping RPFs with a size of 28 nt in these genomes would certainly be problematic. Furthermore, future application of longread techniques in population studies would be helpful in finally solving the problems in SNP calling. Therefore, we propose that predicting ORFs from SNPs can be an alternative or supplementary approach to the existing methods and an efficient approach that can extend the study of sORFs to complex genomes, which cannot be currently achieved.

Caution for the use of OrfPP
As OrfPP directly utilizes the periodicity of nucleotide diversities calculated from SNP datasets, any factors that can potentially affect the accuracy of SNPs would introduce mistakes into the final outputs.
(1) Low-quality reference genome More than 700 plant genomes have been released in recent decades, but many are of poor quality [19,20]. The SNPs identified based on such low-quality reference genomes could contain many unpredictable mistakes.
(2) Mixture of SNPs from different species In many studies, accessions from several, instead of only one, close species were included, but the SNPs were called based on only one reference [51,58]. Mistakes could have been introduced when SNPs were called from the non-reference species. (3) Autoploidy and repetitive genomes Studies of polyploid genomes are usually challenged by incorrect and multiple mapping problems caused by the short length of whole-genome sequencing reads. To address this problem, in some works, the authors remove the reads with multiple hits and use only the reads mapping to gene regions for further analyses [57]. However, polyploidy, particularly autoploid genomes, also has multiple and incorrect mapping problems in gene regions, affecting the predictions. With the decreasing cost of long reads, we believe these problems can eventually be solved when long reads are widely applied in population studies of these complex genomes. (4) Young genomes ORF prediction from SNPs relies heavily on nucleotide diversity in the population. Although our tests show considerable independence from population size, the prediction could be incomplete for young genomes because only a few nucleotide substitutions have accumulated since the divergence of these genomes.

Usage OF OrfPP
OrfPP has been distributed to the Python Package Index (https://pypi.org/project/OrfPP/1.0/) and can be easily installed using pip tools. Three compulsory inputs are needed: genome sequence (-genome), genome annotation (-gtf) and populational nucleotide diversity (-pi). The diversity of nucleotides at each position can be calculated using vcftools [58] with the command 'vcftools -gzvcf SNPs.vcf.gz -site-pi -out output.pi'. The other five options can be customized. For example, OrfPP allows ORFs starting with noncanonical initiation codons to facilitate the prediction of ORFs initiated by alternative start codons. An option of '-nCores' is implemented to use multiple processors to speed up the processing of data, which might be required to deal with genomes of enormous size.

Key Points
• Population nucleotide diversity shows that a 3-nt periodicity can be used to predict open reading frames (ORFs). • A python package 'OrfPP' is developed to predict ORFs from single-nucleotide polymorphisms datasets. • Application 'OrfPP' in polyploidy genomes recovered ∼83% of the annotated ORFs. • OrfPP could help extend the studies of small ORFs to organisms with complex genomes.

Supplementary data
Supplementary data are available online at http://bib. oxfordjournals.org/.