Abstract
Genes in coronaviruses are preceded by transcription regulatory sequences (TRSs), which play a critical role in gene expression mediated by the viral RNA-dependent RNA-polymerase via the process of discontinuous transcription. In addition to being crucial for our understanding of the regulation and expression of coronavirus genes, we demonstrate for the first time how TRSs can be leveraged to identify gene locations in the coronavirus genome. To that end, we formulate the TRS AND Gene Identification (TRS-Gene-ID) problem of simultaneously identifying TRS sites and gene locations in unannotated coronavirus genomes. We introduce CORSID (CORe Sequence IDentifier), a computational tool to solve this problem. We also present CORSID-A, which solves a constrained version of the TRS-Gene-ID problem, the TRS Identification (TRS-ID) problem, identifying TRS sites in a coronavirus genome with specified gene annotations. We show that CORSID-A outperforms existing motif-based methods in identifying TRS sites in coronaviruses and that CORSID outperforms state-of-the-art gene finding methods in finding genes in coronavirus genomes. We demonstrate that CORSID enables de novo identification of TRS sites and genes in previously unannotated coronaviruses. CORSID is the first method to perform accurate and simultaneous identification of TRS sites and genes in coronavirus genomes without the use of any prior information.
1 Introduction
Coronaviruses are comprised of a single-stranded RNA genome that is ready to be translated by the host ribosome (Fig. 1a). While the majority of messenger RNA (mRNA) in eukaryotes is monocistronic, i.e. each mRNA is translated into a single gene product, the coronavirus RNA genome is comprised of many genes, which are expressed and translated using two distinct mechanisms [15]. First, upon entry, the viral genome is translated to produce polypeptides corresponding to one or two overlapping open reading frames (ORFs). Second, the resulting polypeptides undergo auto-cleavage, producing many non-structural proteins, including RNA-dependent-RNA-polymerase (RdRP), which mediates the expression of the remaining viral genes via discontinuous transcription [22]. That is, RdRP is prone to perform template switching upon encountering transcription regulatory sequences (TRSs) located in the 5’ untranslated region (UTR) of the genome — called TRS-L where L stands for leader — and upstream of each viral gene — called TRS-B where B stands for body (Fig. 1b). This mechanism yields multiple subgenomic mRNAs that are translated into the structural and accessory viral proteins, necessary for the viral life cycle. Not only is the identification and characterization of TRS sites crucial to understanding the regulation and expression of the viral proteins, but here we hypothesize that the existence of these regulatory sequences can be leveraged to simultaneously identify TRS sites and associated viral genes in unannotated coronavirus genomes with high accuracy.
(a) A coronavirus genome v consists of a leader region vleader and a body region vbody. (b) Structural and accessory genes are expressed via discontinuous transcription with template switching occurring at transcription regulatory sequences (TRS, indicated in red), resulting in subgenomic messenger RNAs (sgmRNAs) for each gene. (c) In the TRS Identification (TRS-ID) problem, we wish to identify TRSs given a genome v with genes x0,…, xn. The TRS and Gene Identification (TRS-Gene-ID) asks to simultaneously identify genes and their associated TRSs given genome v. Throughout this manuscript we use ‘T’ (thymine) rather than ‘U’ (uracil).
While there exist methods for identifying either TRS sites or viral genes, no method exists that does so simultaneously (Table S1). More specifically, since TRSs contain 6 − 7 nt long conserved sequences, called core sequences [8,25], general-purpose motif finding methods [2,7,20,29] can be employed to identify TRS-L and TRS-Bs in coronaviruses. For instance, MEME [2] is a widely used method that employs expectation maximization to identify multiple appearances of multiple motifs simultaneously. The only method that is specifically developed for identifying TRS sites in coronaviruses is SuPER [28], which takes as input a coronavirus genome sequence with specified gene locations as well as additional taxonomic and secondary structure information. Importantly, SuPER as well as other general-purpose motif finding algorithms are unable to identify viral genes in unannotated coronavirus genome sequences. On the other hand, gene prediction is a well-studied problem with many methods including Glimmer3 [5, 21] and Prodigal [12, 13]. Glimmer3 uses a Markov model to assign scores to ORFs, and then processes overlapping genes to generate the final list of predicted genes. By contrast, Prodigal employs a more heuristic approach with fine-tuned parameters that are optimized to identify genes in prokaryotes. However, these general-purpose gene finding tools are not designed to leverage the genomic structure of coronaviruses, specifically the TRS sites located upstream of the genes in the genome, nor are they able to directly identify these regulatory sequences.
In this study, we introduce the TRS Identification (TRS-ID) and the TRS and Gene Identi-fication (TRS-Gene-ID) problems, to identify TRS sites in a coronavirus genome with specified gene annotations, and to simultaneously identifying TRS sites and genes in an unannotated coronavirus genome, respectively (Fig. 1c). Underpinning our approach is the concept of a TRS alignment, which is a multiple sequence alignment of TRS sites with additional constraints that result from template switching by RdRP. We introduce CORSID-A, a dynamic programming (DP) algorithm to solve the TRS-ID problem, adapting the recurrence that underlies the Smith-Waterman algorithm [24] for local sequence alignment. Additionally, we introduce CORSID to solve the TRS-Gene-ID problem via a maximum-weight independent set problem [11] on an interval graph defined by the candidate ORFs in the genome with weights obtained from the previous DP. We evaluate the performance of our methods on 468 coronavirus genomes downloaded from GenBank, demonstrating that CORSID-A outperforms MEME and SuPER in identifying TRS sites and, unlike these methods, possesses the ability to identify recombination events. Moreover, we find that CORSID vastly outperforms state-of-the-art gene finding methods. Finally, we illustrate how CORSID enables de novo identification of TRS sites and genes in previously unannotated coronaviruses. In summary, CORSID is the first method to perform accurate and simultaneous identification of TRS sites and genes in coronavirus genomes without the use of prior taxonomic or secondary structure information.
2 Problem Statement
We begin by introducing notation and key definitions (Section 2.1), followed by stating the TRS Identifi-cation problem (Section 2.2) and then the TRS and Gene Identification problem (Section 2.3).
2.1 Preliminaries
A genome v = v1 … v|v| is a sequence from the alphabet Σ = {A, T, C, G}. The first position of the genome is known as the 5’ end whereas the last position of the genome is known as the 3’ end. We denote the contiguous subsequence vp … vq of v by v[p, q]. We call a contiguous subsequence x of v also a region, denoted as x = [x−, x+] such that x = v[x−, x+]. Thus, coordinates x− and x+ of a subsequence x are in terms of the reference genome v, i.e. 
.Alternatively, we may refer to individual characters in a subsequence x using relative indices, i.e. x = x1 … x|x|. Our goals are twofold: given a coronavirus genome v, we aim to identify (i) TRS-L and TRS-Bs, and optionally, (ii) the associated genes (Fig. 1c). To begin, recall the following definition of an alignment.
Matrix A = [aij] with n + 1 rows is an alignment of sequences w0, …, wn ∈ Σ* provided (i) entries aij either correspond to a letter in the alphabet Σ or a gap denoted by ‘−’ such that (ii) no column of A is composed of only gaps, and (iii) the removal of gaps of row i of A yields sequence wi.
Here, we seek an alignment with two additional constraints, called a TRS alignment defined as follows.
An alignment A = [a0, …, an]T is a TRS alignment provided (i) a0 does not contain any gaps, and (ii) a1, …, an do not contain any internal gaps.
Intuitively, the first sequence a0 in the alignment A represents TRS-L, whereas a1, …, an represent TRS-Bs, each upstream of an accessory or structural gene. We do not allow gaps in the TRS-L sequence a0 as template switching by RdRP occurs due to complementary base pairing between TRS-L and the nascent strand of TRS-B [26]. For the same reason, we do not allow internal gaps in TRS-Bs ai. However, as each TRS-B may match a different region of the TRS-L, we do allow flanking gaps in these sequences (Fig. 1c). We score a TRS alignment A using a scoring function δ : Σ × (Σ ∪ {−}) → ℝ in the following way.
The score s(A) of a TRS alignment A = [a0, …, an]T is given by 
, whereas the minimum score smin(A) is defined as mini∈{1,…,n} s(a0, ai).
In other words, we score each TRS-B ai (where i ≥ 1) by comparing it to the TRS-L sequence a0 in a way that is consistent with the mechanism of template switching during discontinuous transcription. As such, our scoring function differs from the traditional sum-of-pairs scoring function [3] where every unordered pair (ai, aj) of sequences contributes to the score of the alignment. Furthermore, each TRS alignment uniquely determines the core sequence as follows.
Sequence c(A) is the core sequence of a TRS alignment A = [a0, …, an]T provided c(A) is the largest contiguous subsequence of a0 such that no character of c is aligned to a gap in any of a1, …, an.
Note that the core sequence is a subsequence of the TRS sequences. As such, the TRS alignment can include nucleotides immediately flanking the core sequence, which have been shown to play an important role in discontinuous transcription in previous experiments [26].
2.2 The TRS IDENTIFICATION problem
The first problem we consider is that of identifying TRS sites given a viral genome with known genes x0, …, xn. Specifically, we are given a candidate region w0 that contains the unknown TRS-L a0 upstream of gene x0 as well as candidate regions w1, …, wn that contain the unknown TRS-Bs a1, …, an of genes x1, …, xn. Section 3.1 details how to obtain these candidate regions when only given the gene locations. To further guide the optimization problem, we impose an additional constraint on the sought TRS alignment A in the form of a minimum length ω on the core sequence c(A) as well as a threshold τ on the minimum score smin(A) of the TRS alignment. We formalize this problem as follows.
Problem 1 (TRS Identification (TRS-ID)). Given non-overlapping sequences w0, …, wn, core-sequence length ω > 0 and score threshold τ > 0, find a TRS alignment A = [a0, …, an]T such that (i) ai corresponds to a subsequence in wi for all i ∈ {0, …, n}, (ii) the core sequence c(A) has length at least ω, (iii) the minimum score smin(A) is at least τ, and (iv) the alignment has maximum score s(A).
2.3 The TRS AND GENE IDENTIFICATION problem
In the second problem, we are no longer given an annotated genome with gene locations. Rather, we seek to simultaneously identify genes and TRS sites given a viral genome sequence v split into a leader region vleader and body region vbody. Section 3.2 describes a heuristic for identifying these two regions when only given v. The key idea here is that each TRS alignment will uniquely determine a set of genes it encodes. To make this relationship clear, we begin by defining an open reading frame as follows.
A contiguous subsequence x = [x−, x+] of v is an open reading frame provided x (i) has a length |x| that is a multiple of 3, (ii) starts with a start codon, i.e. x1 … x3 = ATG, and (iii) ends at a stop codon, i.e. x|x|−2 … x|x| ∈ {ATG, TAG, TGA}.
Each TRS-B ai is associated with at most one ORF that occurs immediately downstream of ai. Naively, to identify the ORF associated with ai, one could simply scan downstream of the TRS-B for the first occurrence of a start codon and continue scanning to identify the corresponding in-frame stop codon. However, this would not take ribosomal leaky scanning into account, where the ribosome does not initiate translation at the first encountered ‘ATG’. Section 3.2 provides a more robust definition of a downstream ORF that takes ribosomal leaky scanning into account. To summarize, we have that a TRS alignment A = [a0, …, an]T uniquely determines a set Γ(A) of candidate genes.
A set Γ(A) of ORFs are induced genes of a TRS alignment A = [a0, …, an]T provided Γ(A) is composed of the ORFs that occur downstream of each TRS-B a1, …, an in vbody.
Note that multiple TRS-Bs of a TRS alignment A = [a0, …, an]T can induce the same gene in vbody. Moreover, there may not be an ORF downstream of a TRS-B ai. As such, we have that |Γ(A)| ≤ n. By contrast, in coronaviruses, each viral gene typically has a unique TRS-B. Moreover, these viral genes are typically non-overlapping in the genome. Finally, coronavirus genomes tend to be compact with most positions coding for genes. To capture these biological constraints, we introduce the following definitions.
A TRS alignment A = [a0, …, an]T is concordant provided (i) each TRS-B ai corresponds to exactly one gene in Γ(A), and (ii) there are no two ORFs in Γ(A) whose positions in vbody overlap.
The genome coverage g(A) of a TRS alignment A is the number of positions in vbody that are covered by the set Γ(A) of induced genes.
This leads to the following problem.
Problem 2 (TRS and Gene Identification (TRS-Gene-ID)). Given leader region vleader, body region vbody, core-sequence length ω > 0 and score threshold τ > 0, find a TRS alignment A = [ai] such that (i) a0 corresponds to a subsequence in vleader, (ii) ai corresponds to a subsequence in vbody for all i ≥ 1, (iii) the core sequence c(A) has length at least ω, (iv) the minimum score smin(A) is at least τ, (v) A is concordant, and (vi) A induces a set Γ(A) of genes with maximum genome coverage g(A) and A subsequently has maximum score s(A).
3 Methods
Section 3.1 introduces CORSID-A, which solves the TRS-ID problem. Section 3.2 introduces CORSID, solving the TRS-Gene-ID problem. Both sections discuss practical considerations as well as several heuristics for obtaining the required input to each problem. We implemented both methods in Python. The source code is available at https://github.com/elkebir-group/CORSID.
3.1 Solving the TRS IDENTIFICATION problem
Recall that in the TRS-ID problem we seek a TRS alignment A given input candidate regions sequences w0, …, wn that each occur upstream of genes x0, …, xn. Intuitively, we define the candidate region for a gene xi as the region 
composed of positions w− ≤ p ≤ w+ such that any sgmRNA starting at p will lead to the translation of ORF xi by the ribosome. SuPER [28], the only other method for identifying TRSs in annotated coronavirus genomes, employs a heuristic by defining the candidate region wi of a gene 
, i.e. the candidate region wi is a subsequence of 170 nt immediately upstream of gene xi for 1 ≤ i ≤ n. Here, we take a more rigorous and flexible approach that takes ribosomal leaky scanning into account by skipping over previous ORFs with length smaller than 100 nt (details in Appendix A.1).
Recall that in a TRS alignment A = [a0, …, an]T only the TRS-Bs a1, …, an are allowed to have gaps (restricted to the flanks), and that the TRS-L a0 is gapless. To score a TRS alignment, we use a simple scoring function δ : Σ × (Σ ∪ {−}) → ℝ such that s(x, y) equals +1 for matches (i.e. x = y), 2 for mismatches (i.e. x ≠ y and y ≠ −), and 0 for gaps (i.e. y = −). In other words, while we reward matches and penalize mismatches, we do not penalize flanking gaps.
Recall that the sought TRS alignment A must induce a core sequence c(A) of length at least ω. Due to this constraint, the input sequences w0, …, wn depend on one another and cannot be considered in isolation. We break this dependency by considering a subsequence u within w0 of length ω, restricting the induced core sequence c(A) of output TRS alignments A to contain u. We solve this constrained version of the TRS-ID problem using dynamic programming in time O(|w0|L) where L is the total length of candidate regions w1, …, wn (details are in Appendix A.2 and Fig. 2a). We obtain the solution to the original TRS-ID problem by identifying the window u that induces a TRS alignment A with maximum score. As there are O(|w0|) windows in w0 of fixed length ω, this procedure takes O(|w0|2L) time.
(a) Given genes x0, …, xn, we obtain candidate regions w0, …, wn by identifying upstream ORFs, skipping over ORFs if they are of length less than 100 nt (indicated by ‘*’). CORSID-A solves the TRS-ID problem by sliding a window u through w0, solving n independent pair-wise dynamic programming problems, which together yield the optimal TRS alignment A for window u. (b) To solve the TRS-Gene-ID problem, CORSID additionally solves a maximum-weight independent set problem [11] on an interval graph defined by the candidate ORFs to simultaneously identify an optimal pair (A, Γ(A)) for window u.
3.2 Solving the TRS AND GENE IDENTIFICATION problem
In the TRS-Gene-ID problem, we require two sequences: vleader which contains TRS-L a0 and vbody which contains each TRS-B a1, …, an. We describe a heuristic to partition a genome v into vleader and vbody in Appendix A.3. This heuristic is performed in O(m2) time where m is the number of ORFs in v.
We will now define the relationship between a TRS alignment A = [a0, …, an]T and the set Γ(A) of induced genes. Upon removing (flanking) gaps, each aligned sequence ai corresponds to a contiguous subsequence vi of the viral genome v. Specifically, v0 occurs in vleader and vi occurs in vbody (where i ≥ 1). By Definition 4, each subsequence vi has positions that are aligned with the core sequence c(A).
These aligned positions induce the subsequence 
of length equal to c(A). Note that while c0 = c(A), it may be that ci ≠ c(A) where i ≥ 1 due to mismatches. Importantly, there are coronaviruses where the last three nucleotides of the core sequence within a TRS-B coincide with the start codon of the associated gene (Fig. S1). As such, we have the following definition.
Let A = [a0, …, an]T be a TRS alignment and let 
be the subsequence of ai that is aligned to the core sequence c(A). The ORF associated with TRS-B ai is the unique ORF x where position 
occurs within the candidate region of x.
As discussed, there may not exist an ORF associated with a TRS-B ai, which may happen when the TRS-B is located near the 3’ end of the genome. Given a TRS alignment A = [a0, …, an]T, the set Γ(A) of induced genes equals the set of ORFs that are associated with a1, …, an.
To solve the TRS-Gene-ID problem, we take a similar sliding window approach that we used to solve the TRS-ID problem. That is, we consider all subsequences u within vleader of length ω and solve a constrained version of the TRS-Gene-ID problem, additionally requiring that the sought TRS alignment A has a core sequence c(A) that fully contains u, using the following two steps. First, we construct a DP table similar to the previous table used in TRS-ID problem in O(|vleader||vbody|) time, and for each ORF, we select the alignment with the highest score in the corresponding candidate region. Second, given these ORFs and corresponding alignments, we build a vertex-weighted interval graph combining ORF lengths and alignment scores as weights. To identify the optimal TRS alignment A and associated genes Γ(A), we solve a maximum-weight independent set (MWIS) on this graph in O(m) time, where m is the number of candidate ORFs in vbody (Appendix A.4 and Fig. 2b). Each instance of the constrained TRS-Gene-ID problem takes O(|vleader||vbody|+ m) time. Since the number of windows of length ω in vleader is O(|vleader|), the total running time of CORSID to solve the TRS-Gene-ID problem is O(|vleader|2|vbody + vleader|m). In practice, the number m of candidate ORFs in vbody ranges from 21-92, the length vleader of leader region ranges from 171-716 and the length |vbody|of the body region ranges from 6280-11462 across all the coronaviruses studied in this paper. Finally, to obtain biologically meaningful solutions, we employ a progressive approach and consider overlapping genes (see Appendix A.5 for details).
4 Results
To evaluate the performance of CORSID-A and CORSID, we downloaded the same set of 505 assembled coronavirus genomes previously analyzed by SuPER [28] from GenBank along with their annotation GFF files, indicating gene locations. To benchmark methods for the TRS-ID problem, we assessed each method’s ability to correctly identify TRS-L as well as identify a TRS-B upstream of each gene. For the TRS-Gene-ID problem, we additionally assessed each method’s ability to identify ground-truth genes. Appendix B.1 describes how we established the set of genes and locations of TRS sites in the coronavirus genomes. We excluded 35 genomes due to incomplete leader sequences, thus lacking TRS-L. We excluded two more genomes due to empty GFF files, thus lacking gene annotations. The remaining 468 genomes comprised all four genera of the Coronaviridae family and spanned a total of 22 subgenera (Table S2).
4.1 CORSID-A finds TRS-L and TRS-Bs with higher accuracy than existing methods
We begin by comparing the performance of CORSID-A with MEME and SuPER for the TRS Identifi-cation problem. Recall that MEME is a general-purpose motif detection algorithm [2], whereas SuPER is specifically designed for identifying core sequences within coronavirus genomes annotated with genes [28]. To run CORSID-A, we extracted candidate regions w1, …, wn upstream of annotated genes x0, …, xn as described in Definition 11. The minimum length ω of core sequence is set to 7 following existing literature [8], and we use a minimum alignment score of τ = 2. We provided MEME with the same candidate regions w0, …, wn, and ran it in “zero or one occurrence per sequence” mode. As for SuPER, we analyzed the previously reported results on the same 468 sequences considered here. Detailed commands and parameters can be found in Appendix B.2.
As shown in Fig. 3b, CORSID-A correctly identified TRS-Ls in 466 out of 468 genomes, reaching a higher accuracy (99.6%) than MEME (442 genomes, 94.4%), but was outperformed by SuPER, which was correct in 467 genomes (99.8%). The two genomes where our method failed are outliers in their respective subgenera, indicative of possible sequencing errors (Appendix B.4). Fig. S2 discusses the one genome where SuPER failed to identify TRS-L correctly, showing that the TRS-L sequence identified by our method is supported by both secondary structure information as well as a split read in a corresponding RNA sequencing sample. Split reads map to non-contiguous regions of the viral genome and provide direct evidence of template switching at TRS sites.
(a) We used SuPER [28], MEME [2] and CORSID-A to identify TRS sites in 468 coronavirus genome with known gene locations. (b) The fraction of genomes for which the three methods identified the TRS-L correctly. (c) The fraction of genes of the genomes for which the three methods identified the corresponding TRS-B site correctly. (d) Number of coronavirus genomes of the four genera of the Coronaviridae family with different lengths of the TRS-L identified by the three methods. Fig. S4 provides the TRS alignment identified by CORSID-A for the genome indicated by ‘*’.
Of note, SuPER uses additional information to identify TRS-L and TRS-B sites compared to MEME and CORSID-A. That is, SuPER requires the user to specify the genus of origin for each input sequence, which is used to obtain a genus-specific motif of the core sequence from a look-up table. This motif is used to identify matches along the genome. In addition, SuPER takes as input the 5’ UTR secondary structure, restricting the region in which the TRS-L occurs until the fourth stem loop (SL4). Importantly, while CORSID-A does not rely on any prespecified motif, taxonomic or secondary structure information, our method identified more TRS-Bs than either SuPER or MEME (Fig. 3c). Specifically, we define the TRS-B recall as the fraction of genes for which TRS-Bs were identified. While the median TRS-B recall of all three methods is 1, CORSID-A found putative TRS-Bs of all genes in 387 genomes (82.7%), while SuPER and MEME did so in only 290 (62.0%) and 315 (67.3%) genomes, respectively.
To validate the identified TRS sites, we examined split reads in publicly available RNA-sequencing data of cells infected by coronaviruses. Here we considered two samples, SRR1942956 and SRR1942957, of SARS-CoV-1-infected cells (NC_004718) with a median depth of 2940× and 2765×, respectively. The TRS-B region predicted by CORSID-A is supported by 246 reads in sample SRR1942956 and 233 reads in sample SRR1942957, whereas the TRS-B region predicted by SuPER is supported by only 1 read in each sample (Fig. S3a). Our method was able to identify these positions due to use of flanking positions rather than focusing on identifying a short 6− 7 nt motif as done by SuPER.
Recombination plays a crucial role in the evolution of RNA viruses, and results from homologous or non-homologous template switching. In particular for coronaviruses, template switching occurs at TRS sites during discontinuous transcription [9], making these sites prone to recombination events. CORSID-A uses local alignment to identify TRSs, and unlike SuPER, is not restricted to identifying regulatory sequences of a fixed length. Therefore, as a by-product, our method will be able to find evidence for homologous recombination at these sites. Specifically, even though the length of the core sequence is fixed at 7, the length of the TRS-Ls identified by our method ranges from 9 to 45 (median: 22). This corroborates previous findings showing that recombination hotspots in coronaviruses are colocated with TRS sites [28]. In particular, the longest TRS-B with a length of 45 nucleotides occurs upstream of gene ns12.9 of NC 006213 with only 6 mismatches showing strong evidence of recombination (Fig. S4). In contrast, the core sequence identified by SuPER and MEME (Fig. 3d and Fig. S5) are at most 10 nt long. Furthermore, we note there is experimental evidence that not only the core sequence but also flanking nucleotides play an important role in discontinuous transcription [26]. This demonstrates the importance of identifying larger regulatory sequences, as done by our method, rather than identifying shorter recurring motifs as done by SuPER and MEME. In summary, CORSID-A outperforms existing methods, such as SuPER and MEME, in identifying TRS sites in coronavirus genomes with given gene locations.
4.2 CORSID identifies genes with higher accuracy than existing methods
We now focus on the TRS-Gene-ID problem, where we compared CORSID to two general-purpose gene finding methods: Glimmer3 [5, 21] and Prodigal [12, 13]. Each method was given as input the complete, unannotated genome sequence of each of the 468 coronaviruses. Following recommended instructions, we ran Glimmer3 by first building the required interpolated context model (ICM) on each genome sequence separately. We ran Prodigal in meta-genomics mode. For CORSID, we used window length ω = 7 and progressively reduced the score threshold τ from 7 to 2. We refer the reader to Appendix B.2 for the precise commands used to run previous tools, and to Appendix B.3 for details on how the predicted set of genes are compared to the ground truth.
Fig. 4a shows that CORSID outperformed Glimmer3 and Prodigal in terms of both precision and recall. The median precision and recall of CORSID is 0.818 and 1.00, respectively, whereas the median precision and recall is 0.556 and 0.556, respectively, for Glimmer3, and 0.636 and 0.667, respectively, for Prodigal. Additionally, the first quartile of both precision and recall for CORSID is greater than the third quartile of these metrics for either Glimmer3 and Prodigal, showing a significant performance advantage for CORSID. While Prodigal and Glimmer3 do not have the capability to identify TRS sites, CORSID identifies these regulatory sites in addition to the genes. Specifically, compared to CORSID-A, which identified TRS-L correctly for 466 (99.6%) genomes, CORSID does so for 443 (94.7%) genomes (Fig. S6). This is a modest reduction in performance, especially when taking into account that CORSID, unlike CORSID-A, is not given any additional information apart from the complete, unannotated genome sequence. Analyzing the previously discussed SARS-CoV-1 genome (NC 004718), we found that CORSID identified the same 10 genes as CORSID-A, while Prodigal missed four genes and Glimmer3 missed two genes (Fig. S3b).
(a) Precision and recall of Glimmer3 [5], Prodigal [12], and CORSID for gene prediction in 468 genomes. For clarity, we added a small jitter (drawn from N (0, 2.5 × 10−5)) to the 2D distribution plot. (b) Confusion matrices of the ground truth genes and the predicted genes by the three methods. In order to account for poorly annotated genomes, we used BLASTx [1] to verify the false positive genes predicted by the three methods. The adjusted confusion matrices are shown in the row below.
Given the large discrepancy between precision and recall for CORSID, we investigated whether genomes were poorly annotated, leading to incorrect false positives. To that end, we used BLASTx [1] to transfer gene annotation from well-annotated genomes to poorly-annotated genomes. To reduce computation time, we only assessed false positive (FP) genes occurring in vbody. We reclassified a FP gene as a true positive (TP) if the alignment reported by BLASTx spans at least 95% of both the query sequence (the FP gene) and the hit sequence in the database (detailed in Appendix B.2). The resulting confusion matrices of the predicted and the ground-truth genes are shown in Fig. 4b. Although BLASTx found 629 and 459 matches in the database for FPs of Glimmer3 and Prodigal, respectively, which is more than 387 for CORSID, CORSID maintains its lead in absolute numbers for TP and FP. As such, CORSID achieved the highest pooled precision and recall both before and after the BLASTx verification. In summary, CORSID accurately identifies TRSs and genes given just the unannotated genome, outperforming existing gene finding methods.
4.3 CORSID enables de novo identification of TRS sites and genes
To demonstrate how users can use CORSID to annotate genes and identify TRS-L and TRS-Bs given a newly assembled genome, we analyzed a previously-excluded genome that lacks gene annotation (genome DQ288927). This genome is 27534 nt long, which we provided as input to CORSID, Glimmer3 and Prodigal. CORSID identified nine genes spanning 91.66% of the genome, all of which match annotated genes in other Igacoviruses sequences in the BLASTx database (Fig. 5). By contrast, Glimmer3 identified a total of six genes spanning 80.52% of the genome, five of which match genes in the BLASTx database. On the other hand, Prodigal found six genes, all of which were present in the database, spanning 84.22% of the genome. In summary, CORSID identified more genes than existing methods, all of which occurred in homologous previously-annotated genomes in the BLASTx database, demonstrating that CORSID can be used to accurately annotate coronavirus genomes.
(a) The position of the genes identified by CORSID. The Venn diagram shows the genes found by CORSID, Glimmer3 and Prodigal. “*” indicates ≥ 95% query/hit coverage, and “**” indicates a hit coverage of 93.5% and a query coverage of 98.3%. (b) TRS alignment for genes identified by CORSID. (c) The fraction of positions in vbody covered by genes identified by the three methods.
5 Discussion
In this paper, we investigated the hypothesis that the presence of transcription regulatory sequences in coronavirus genomes can be leveraged to simultaneously infer these regulatory sequences and their associated genes in a synergistic manner. To that end, we formulated the TRS Identification (TRS-ID) problem of identifying TRS sites in a coronavirus genome with given gene locations, and the general problem, the TRS and Gene Identification (TRS-Gene-ID) problem of simultaneous identification of genes and TRS sites given only the coronavirus genome. Underpinning both problems is the notion of a TRS alignment, which extends the previous concept of core sequences to include flanking nucleotides that provide additional signal. Our proposed method for the first problem, CORSID-A, is based upon a dynamic programming formulation which extends the classical Smith-Waterman recurrence [24]. CORSID, which solves the general problem, additionally incorporates a maximum-weight independent set formulation on an interval graph to identify TRS sites and genes.
Using extensive experiments on 468 coronavirus genomes, we showed that CORSID-A outperformed two motif-based approaches, MEME [2] and SuPER [28]. Additionally, we showed that CORSID outperformed two general-purpose gene finding algorithms, Glimmer3 [5, 21] and Prodigal [12]. We performed direct validation of TRS sites predicted for the SARS-CoV-1 genome (NC 004718), showing that the TRS sites identified by our method are more strongly supported by split reads in RNA-seq samples than the TRS sites identified by SuPER. Lastly, we demonstrated that CORSID enables de novo identification of TRSs and genes in newly assembled coronavirus genomes by applying it on a previously unannotated coronavirus (DQ288927) belonging to the Igacovirus subgenus.
There are several avenues for future research. First, CORSID currently requires the complete genome as input to identify the TRS sites and the genes. We plan to extend our method to allow gene identification in the several coronaviruses available in GenBank with only partial reference genomes by leveraging knowledge from other coronaviruses with complete genomes with similar TRS sites. Second, while in this study we only focused on coronaviruses, discontinuous transcription occurs in all viruses in the taxonomic order of Nidovirales. However, CORSID, which assumes a single TRS-L region in the genome, cannot be directly applied to other families of viruses within Nidovirales such as the family Mesoniviridae that contain multiple TRS-L regions in the genome. Incorporating such features and extending CORSID to all Nidovirales viruses is a useful direction of future work. Finally, currently CORSID requires the reference genome of the virus as input. In the future, we plan to extend this method to simultaneously discover the reference genome and the core-sequences of the virus using de novo assembly. We envision that this will enable simultaneous genome assembly and gene annotation of coronaviruses.
A Supplementary Methods
A.1 Obtaining candidate regions for the TRS-ID problem
Intuitively, a candidate region for gene xi corresponds to the region 
composed of positions w− ≤ p ≤ w+ such that any sgmRNA starting at p will lead to the translation of ORF xi by the ribosome. Note that the first ORF x0 corresponds to ORF1ab. Accordingly, we restrict 
to match exactly the leader region, spanning the start of the genome at the 5’ end until the start codon of x0, i.e 
and 
. To define the remaining candidate regions w1, …, wn, we must take ribosomal leaky scanning into account, where the ribosome does not initiate translation at the first ‘ATG’ it encounters [14]. To model this, we make use of the fact that coronovirus genes have a length of at least 100 nucleotides. Specifically, when determining the candidate region of a gene, we skip over a previous ORF in case its length is less than 100. To that end, we introduce the following function.
Function prev(p) returns the first ORF x = [x−, x+] upstream of position p in the genome, i.e. for ORF x returned by prev(p) it holds that x− < p and there exists no ORF y = [y−, y+] such that x− < y− < p. If no such ORF x exists then prev(p) = [0, 0]. Moreover, prev(0) = [0, 0].
Using this function, we define a TRS-B candidate region w of an ORF x as follows.
Let x = [x−, x+] be an ORF, and let y = [y−, y+] = prev(x−) and z = [z−, z+] = prev(y−) be the previous two ORFs. The candidate region w = [w−, w+] of ORF x ends at the start of x, i.e. w+ = x− − 1, and begins at the first position of the genome if x has no previous ORF or the only preceding ORF y has a length smaller than 100; w begins at the first ORF y if the length of y is at least 100; otherwise w begins at the second ORF z if the first ORF y has a length smaller than 100 nucleotides. That is,
Finally, to remove overlap among candidate regions w0, …, wn, we set 
if 
for all i ∈ {1, …, n}.
A.2 Constrained TRS-ID problem
Here, we introduce the following constrained version of the TRS-ID problem.
Problem 3 (Constrained TRS Identification (TRS-ID-u)). Given non-overlapping sequences w0, …, wn, and a subsequence u of w0, find a TRS alignment A = [a0, … an]T such that (i) ai corresponds to a subsequence in wi for all i ∈ {0, …, n}, (ii) u is a subsequence of the core sequence c(A), and (iii) the alignment has maximum score s(A).
Let us focus on solving a single TRS-ID-u problem instance, where we are given non-overlapping sequences w0, …, wn and a subsequence u of w0. Each such instance decomposes into n TRS-ID-u instances each with exactly two sequences. That is, for any i ∈ 1, …, n, we seek a TRS alignment 
of sequences 
and 
such that the induced core sequence c(Ai) contains u = [u−, u+]. This is a variant of local alignment [24] with three key differences: (i) alignment Ai may not contain gaps, (ii) Ai must span u− and (iii) Ai must span u+. Letting be ℓ the relative position of u− in w0, we obtain
where s[p, q] indicates the optimal score of a constrained TRS alignment between w0,1 … w0,p and wi,1 … wi,q. The desired solution is then as follows.
Note that the recurrence (2) lacks the two cases of the Smith-Waterman [24] recurrence corresponding to a gap (i.e. s[p − 1, q] and s[p, q − 1]), thus satisfying constraint (i). Constraints (ii) and (iii) are satisfied because the first case, corresponding to initiating the alignment, is only enabled when p < thus covering u−, and by (3), we have that the alignment contains u+. Similarly to local alignment, we can identify (p*, q*) by filling out the table s[0, 0], …, s[|w0|, |wi|] using dynamic programming, and reconstruct the TRS alignment 
using a backtrace from (p*, q*). Letting 
be the total length of candidate regions w1, …, wn, solving the n pairwise TRS-ID-u problems and obtaining the pairwise TRS alignments A1, …, An that cover u takes O(|w0 L|) time.
Given these pairwise alignments A1, …, An that each span u, we construct the final TRS alignment A = [a0, …, an]T as follows. First, we exclude alignments Ai that have a score less than the threshold τ. Second, the TRS-L sequence a0 equals the subsequence of w0 that spans the positions covered by all pairwise alignments, i.e. a0 spans exactly the positions of w0 covered by 
. Third, we obtain the remaining gapped sequences a1, …, an of A by adding flanking gaps to each (ungapped) sequence 
so as to match the unaligned letters of a0 (Fig. 2a). As flanking gaps do not incur a penalty, this operation will not change the total score, i.e. 
. The running time of computing alignments A1, …, An and then subsequently merging them into A is dominated by the first step.
A.3 Partitioning the genome into vleader and vbody for the TRS-GENE-ID problem
To obtain these two sequences, vleader and vbody, for a given coronavirus genome, we developed a heuristic for identifying ORF1ab, the largest gene in coronavirus genomes. This heuristic begins by enumerating all ORFs x1, …, xm in the genome (Definition 5). As ORF1ab is the result of a frameshift upstream of the stop codon of ORF1a [18], we extend each enumerated ORF xi by performing either a − 1 or − 2 frameshift and subsequently scanning for an in-frame stop codon. We select the frameshift that results in the largest extended ORF, obtaining extended ORFs y1, …, ym. We designate the largest ORF among this set as ORF1ab. Finally, we set vleader as the region from the start of the genome until the 5’ coordinate of ORF1ab. As the TRS-B of the first gene downstream of ORF1ab may reside within ORF1ab, we set vbody as the region starting from 200 nucleotides upstream of the 3’ coordinate of ORF1ab until the 3’ end of the genome.
A.4 Constrained TRS-GENE-ID problem
Here, we introduce the constrained version of the TRS-Gene-ID problem.
Problem 4 (Constrained TRS and Gene Identification (TRS-Gene-ID-u)). Given leader region vleader, body region vbody and a subsequence u of vleader, find a TRS alignment A = [ai] such that (i) a0 corresponds to a subsequence in vleader, (ii) ai corresponds to a subsequence in vbody for all i ≥ 1, (iii) u is a subsequence of the core sequence c(A), (iv) A is concordant, and (v) A induces the set Γ(A) of genes with maximum genome coverage g(A) and subsequently has maximum score s(A).
We solve this problem in two steps. First, we use dynamic programming to compute s[p, q] for all values of 0 ≤ p ≤ |vleader| and 0 ≤ q ≤ |vbody|, i.e. the optimal score s[p, q] of a TRS alignment between vleader,1 … vleader,p and vbody,1 … vbody,q constrained to contain u. The quantity s[p, q] is defined using the same recurrence as for the TRS-ID-u problem – Eq. (2) – and the complete table can be filled out using dynamic programming in O(| vleader||vbody|) time.
Second, let x1, …, xm be the candidate ORFs in vbody, each with a length of at least 100 nucleotides (Fig. S7). For each ORF xi we find the position (p, q) that encodes the maximum scoring alignment 
where 
is associated with xi. We remove ORFs xi whose maximum scoring alignment Ai has a score s(Ai) less than the user-specified score threshold τ. Let s* indicate the maximum score among all TRS alignments A1, …, Am. Then, we construct a vertex-weighted interval graph G = (V, E) whose vertices V correspond to the intervals 
of the candidate ORFs. There is an edge (xi, xj) if and only if the two corresponding intervals overlap, i.e. 
. To capture the lexicographical ordering of the objective functions, i.e. first the genome coverage and then the score, each vertex/interval xi is assigned weight
In other words, among ORFs with the same length, we prefer those that have an associated TRS alignment with largest score. Finally, we solve a maximum-weight independent set (MWIS) problem, which can be done in O(|V |) time for interval graphs [11]. The maximum-weight independent set X = {xπ(1), …, xπ(|X|)} directly corresponds to the induced genes Γ(A) of the TRS alignment A that can be constructed by merging pairwise TRS alignments Aπ(1), …, Aπ(|X|) following the same procedure described in Section 3.1. For each window u of fixed length ω, the first step takes O(|vleader||vbody|) time and the second step takes O(|vleader||vbody| + m) time.
A.5 Practical considerations to solve the TRS-GENE-ID problem
In this section we discuss practical considerations for identifying genes in coronaviruses and the way they are addressed in CORSID.
Overlapping genes
In practice, coronavirus genes may overlap. That is, the start codon of a gene can be located within another gene. To support such cases, we shrink candidate ORFs x = [x−, x+] by 5% prior to solving the MWIS problem, i.e. the interval graph G = (V, E) has shortened intervals xi = [x− +α, x+ −α] where α = 0.05|x|.
Progressive approach
To obtain biologically meaningful solutions, we solve the TRS-Gene-ID problem in a progressive manner. More specifically, given user-specified parameters (τmin, τmax), we start with setting τ = τmax and solve the problem for a fixed window u. Then, for every subsequent iteration we decrement τ and require the solution to contain all ORFs that were identified in the previous iteration. The final iteration occurs when τ = τmin, yielding the final solution for window u. We consider all sliding windows u within vleader and return the solution with maximum genome coverage and subsequently maximum score. We show that the progressive approach performs better than solving the TRS-Gene-ID problem directly using τ = τmin or τ = τmax in Fig. S8.
B Supplementary Results
B.1 Establishing the ground truth of gene and TRS locations in coronavirus genomes
We established a ground-truth set of genes by processing the GFF annotation files and extracting a set of genes for each genome, removing duplicates and incomplete ORFs. In particular, we removed 10 ORFs (8 annotated as N and 2 annotated as ‘unknown’) that had duplicate names and were completely covered by another gene with the same name. This resulted in a median number of 8 genes per genome (min 3 and max 14, Fig. S9). We excluded two genomes that had no genes in their annotation (DQ288927 and EU526388). We used the following approach to establish the ground truth for TRS-B sites. As discussed in Section 3.1, we identified candidate regions (Definition 11) for each gene. If a method identified a TRS-B contained within any of the candidate regions, then we counted this as the method recalling the TRS-B for the corresponding gene.
We established ground-truth locations of TRS-Ls using the fact that these regulatory sequences occur between the second (SL2) and fourth stem loop (SL4) in the 5’ untranslated region (UTR) [17]. For Sarbecovirus genomes, a subgenus of the Betacoronavirus genus, we required TRS-Ls to occur in stem loop (SL3) [4]. Specifically, we analyzed leader regions upstream of ORF1ab, its location taken from the GFF annotation or determined by our own heuristic in case this gene was absent, and performed a multiple sequence alignment using ClustalW2 [16] of all sequences within each subgenus. We then superimposed secondary structure information from Rfam [10] onto each alignment to identify the relevant stem loops in each viral sequence, obtaining for each sequence a small range in which TRS-L may occur (Fig. S10).
B.2 Command-line arguments
MEME
We ran MEME v5.3.0 in mode “zero or one occurrence per sequence” (zoops) and maximum width of 10.
Glimmer3
We followed the steps written in the script g3-from-scratch.csh provided in the Glimmer3 package.
Prodigal
We ran Prodigal v2.6.3 in metagenomic mode.
ClustalW2
We used ClustalW2 v2.1 to align sequences.
BLASTx
We ran BLASTx on a FASTA file containing FP genes with the following parameters. We used a subset of protein sequences from the official “nr” database (downloaded on October 7, 2021), containing all species under the taxonomic unit Coronaviridae (taxid:11118). From the BLASTx output, we extracted the top hit for each FP gene, and calculated the coverage between the aligned subsequence, and the query and hit sequences. In particular, the hit coverage is fraction of position in the hit sequence that are aligned. On the other hand, the query coverage is the fraction the query sequence that are aligned. We set the threshold to 95% for both hit and query coverage, restricting solutions to almost exact matches.
B.2 Evaluating gene finding methods
To assess performance of gene finding methods, we say that a predicted gene x = [x−, x+] is correct provided there exists a ground-truth gene y = [y−, y+] in the same genome such that |x− y−|≤ 3 and |x+ y+| ≤ 3. In other words, the start and end positions may be off by the length of at most one codon, accounting for variation in annotation (e.g. sometimes the stop codon is omitted from ORFs). Moreover, as ORF1ab is not a real ORF, i.e. the corresponding polypeptide 1ab results from a−1 frameshift, we treat this gene differently. That is, we say that a method correctly identified y = [y−, y+] = ORF1ab if it found two genes 
and 
such that the start position of x1 is at most 3 nucleotides away from y− and the stop position of x2 is at most 3 nucleotides away from y+. Note that CORSID will identify a single gene x matching ORF1ab, in which case x = x1 = x2. Using this definition we classify each predicted and ground-truth gene as either a true positive (TP), i.e. the predicted gene matches a ground-truth gene; false positive (FP), i.e. the predicted gene does not match any ground-truth gene); or false negative (FN), i.e. the ground-truth gene has no matching predicted gene.
B.4 Two anomalous coronavirus genomes
CORSID-A was unsuccessful in identifying the correct TRS-L site in only two coronaviruses: MK211372 (from subgenus Pedacovirus of genus Alphacoronovirus) and MK472070 (unclassified subgenus of genus Alphacoronovirus).
To understand why CORSID-A failed on MK211372, we performed a multiple sequence alignment of the leader regions of all 45 genomes in the Pedacovirus subgenus. Inspecting the alignment, we see that MK211372 is an outlier, with multiple insertion/deletions in the TRS-L region compared to the other sequences (Fig. S11). This explains why CORSID-A was unable to accurately identify the TRS-L and TRS-B sites for this genome.
Since genome MK472070 has a known genus but unknown subgenus, we only aligned it to the covariance model of the alphacoronaviruses. From the alignment result we found a poor alignment in the TRS-L region. Based on the alignment, it resembles some nyctacoviruses, but it is still an outlier, as shown in Fig. S12. Specifically, the TRS-L consensus sequence, 5’-TCAACTAAAC-3’, differed significantly from the subsequence 5’-ACAATCTAAT-3’ of MK472070, with a Hamming distance of 5. Moreover, MEME also failed to identify TRS-L in this genome, and SuPER assigned a low confidence score to the identified TRS-Bs for important genes such as S and N.
In summary, we believe further investigation of genomes MK211372 and MK472070 is warranted in order to determine whether they harbor a TRS-L region or whether the deposited genome sequences are incomplete/incorrect.
C Supplementary Figures and Tables
We have the following supplementary figures and tables.
Fig. S1 shows an example of TRS regions overlapping with the start codon of the corresponding genes in coronaviruses.
Fig. S2 shows CORSID finds the correct TRS-L in a Sarbecovirus, verified using a RNA-seq dataset.
Fig. S3 shows RNA-seq data supports the TRS-B found by CORSID-A in SARS-CoV-1 (NC 004718), and CORSID identifies more genes than Glimmer3 and Prodigal in the same genome.
Fig. S4 shows the TRS alignment in genome NC 006213 where CORSID find the longest alignment between TRS-L and TRS-B.
Fig. S5 shows the number of coronaviruses with varying lengths of TRS-L regions broken down by the genus and the subgenus. Several coronaviruses of each genus have TRS-L regions much longer than the core sequences indicating recombination events.
Fig. S6 shows that CORSID shows modest reduction in TRS-L accuracy compared to CORSID-A.
Fig. S7 shows the distribution of length of annotated genes. Only 10 out of 3637 genes are shorther than 100 nt.
Fig. S8 shows that CORSID achieves better performance when using the progressive approach rather than directly solving τ = τmax = 7 or τ = τmin = 2.
Fig. S9 shows the histogram of length of annotated genes from 468 genomes, of which only 10 genes are shorter than 100 nt.
Fig. S10 shows the distribution of the length of the TRS-L regions, separated by four genera.
Fig. S11 shows the MSA of leader regions of pedacoviruses with genome MK211372 highlighted, indicating multiple INDELs.
In Table S1, we compare features of CORSID, CORSID-A, and other methods. We show that CORSID is the first method for simultaneous identification of TRS sites and genes in coronaviruses.
Table S2 shows the number of included and excluded genomes grouped by genera and subgenera.
The TRS alignment identified by CORSID when applied to a Sarbecovirus genome KP886808, showing th start codons of gene S, 7a, and 8 are partially contained in core sequences (highlighted in yellow. We note that MEME identified the same TRS-L as our method. As a side note, the TRS-B of gene N matches 25 nucleotides of the TRS-L, indicative of a possible a recombination event.
Although SuPER uses a hard-coded motif to identify core sequences, it incorrectly identified TRS-L (positions 19 −25) in genome MN996532 (Bat coronavirus RaTG13). By contrast, CORSID-A found the TRS-L at a different location (54 − 60). We verified CORSID-A’s position using the corresponding RNA-seq data (SRR11085797). We aligned the reads to the reference genome using a splice-aware aligner, STAR [6]. The resulting alignment had a single split read, spanning positions 54 and 28221, which matches CORSID-A’s TRS-L and the TRS-B for gene N. Moreover, TRS-L sites in sarbecoviruses occur in stem loop (SL3) [4], which co-incides with the TRS-L site identified by CORSID-A.
(a) For SARS-CoV-1 (NC 004718), CORSID-A identified a TRS-B corresponding to ORF7b supported by 246 and 233 split reads in RNA-sequencing samples SRR1942956 and SRR1942957, respectively. For the same genome, SuPER identified a TRS-B site that is supported by only one read in each RNA-sequencing sample. (b) A Venn diagram of the genes correctly identified by the three methods. (c) The TRS alignment of CORSID-A, and aligned core sequence with flanking regions of SuPER. “*”: SuPER identified a TRS-B for 9b but its start codon is located at the second to fourth nucleotide of the core sequence, and the Hamming distance is 2. CORSID-A did not find this TRS-B as it occurs outside the candidate region of 9b. Moreover, in previous studies ORF9b has been hypothesized to be translated via a ribosomal leaky scanning mechanism [19, 23, 27], explaining the absence of an associated TRS-B site.
This genome has the longest TRS-B with a length of 45 nucleotides (with only 6 mismatches) upstream of gene ns12.9, indicative of a recombination event.
(a) TRS-L accuracy of CORSID and CORSID-A. (b) Venn diagram of the TRS-L identified by CORSID and CORSID-A compared to the ground truth. Both methods failed on genomes MK211372 and MK472070 (discussed in Appendix B.4).
Histogram of annotated gene lengths from 468 genomes (ORF1ab not included). Only 10 out of the 3637 genes are shorter than 100 nt.
(a) The F1 score (harmonic mean between precision and recall) is shown in top left panel. We show the precision and recall in the top right and lower left panel, respectively, and the joint distribution in the lower right panel. (b) TRS-L accuracy of setting the minimum matching score threshold to τ = 2 and τ = 7, compared with the progressive approach. (c) Venn diagram of genome sets with correctly identified TRS-L by the three versions of CORSID.
(Median: 8, min: 3, max: 14).
We highlight the MK211372 genome and indicate the TRS-L region with a red bar on top. MK211372 differs from other sequences since it contains multiple indels in the TRS-L region. As such, the TRS-L region cannot be found in this genome.
We highlight MK472070 genome and indicate the TRS-L region with red bar on top. MK472070 differs from others since it contains multiple indels in the TRS-L region. As such, the TRS-L region cannot be found in this genome.
Acknowledgements
This material is based upon work supported by the National Science Foundation under award numbers CCF-1850502, CCF-2027669 and CCF-2046488. We thank Ayesha Kazi, Michael Xiang, and Yichi Zhang for developing the web-based visualization tool of CORSID solutions.
Footnotes
↵* Joint first authorship
References
