In this study, relative synonymous codon usage (RSCU) vectors are used as the measure of protein-coding potential for a given window of sequence. The RSCU value for a codon 'i' is defined as:

where Obs_i is the observed number of occurrences of codon 'i', and Exp_i is the expected number of occurrences of the same codon (based on the number of times the relevant amino acid is present in the gene and the number of synonymous alternatives to 'i', assuming a uniform choice of synonymous codons). In order to make the data more compatible with the mathematical methods used, the log of each RSCU_i value is found so that the resulting value is positive if the codon is used more than expected in that gene, and negative if the codon is used less than expected. Values were capped at ± 10, and set to 0 in the case of the non-occurrence of an amino acid in the sample. Taking the RSCU values for each of the codons with synonymous alternatives (and ignoring the 3 stop codons and the Trp and Met codons), each sample can be represented by a vector of 59 values.

The Self-Organizing Map (SOM) is based around the concept of a lattice of interconnected nodes, each of which contains a model. The models begin as random values, but during the iterative training process they are modified to represent different subsets of the training set. In this work for example, the training set and the lattice node models are 59-dimensional RSCU vectors, and the models change during training to become similar to common or repeated patterns in the training set. The algorithm is fully described elsewhere 27, but we briefly summarize for our context:

(1) A vector (X_i), corresponding to a gene's RSCU values, is loaded from the training dataset.

(2) The lattice node is found whose model vector most closely resembles the input pattern. This node is denoted the 'winning node'.

(3) The winning node's model, W (as well as a certain number of 'neighbourhood bubble' node models) is changed to be more similar to the input vector by the equation:

W_new = W_old + η (X_i - W_old)     (2)

(4) If all the vectors in the training dataset are processed, we say that an epoch has been completed. In this study, all SOMs are trained for 3000 epochs.

The 'neighbourhood bubble' mentioned in step 3 is a group of nodes centered at the winning node. The radius of this bubble is initialised to be large and is linearly decreased during training until only the winning node's model is changed. Changing the models on the winning node's neighbours allows the clustering of similar patterns. The learning rate (η) in step 3 is initialised close to 1 and is also linearly decreased during training until it is held constant at a predefined fraction. The linear decrease in learning rate means that each node's model will not get changed as much or as often as training progresses. Two recognised phases of training result; an ordering phase where the lattice takes its general shape, and a convergence phase where the nodes get more specialised to respond to specific patterns.

In this work, similarity between two vectors is measured by finding the cosine of the angle between them. A cosine of 1 represents exactly similar vectors while a cosine of 0 represents exactly dissimilar vectors.

The SOM is used mainly in data visualisation, as it can be effectively used to reduce high-dimensional data to a two dimensional map. One of the main strengths of the method is the ability to automatically cluster similar patterns in its training set. In the context of codon usage data, the SOM has been previously used to cluster genes on the basis of similar codon usage 282930. However, the previous studies have concentrated on identifying genes with atypical codon usage and hypothesising their origin as horizontally transferred genes. It has since been shown that atypical codon usage is not sufficient evidence to show that a gene has origins in horizontal transfer events 2231. In contrast, this study uses the fact that once a SOM has been trained using codon usage information, the nodes of the SOM encapsulate models that are representative of the major codon usage patterns within the training set.

If a new sequence is inputted to a trained SOM, we can easily be told which node's model is most similar to this new sequence, and most importantly, how similar. The similarity (cosine) score is then converted to the probability that the sequence is protein-coding. This is achieved by finding the mean cosine score received by a set of random length, random sequence genes that are generated using the same nucleotide bias as the mutational bias found in the genome. Using the mean score, each similarity score can be converted to a z-score, which is in effect the probability that the sequence is not a random sequence.

Separate SOMs are trained for each of the 15 genomes under test. The SOMs are each 15×15 nodes in size and trained for 3000 cycles. Finding genes via homology search is usually the first step to be carried out in a genome annotation process, so our training sets consist of all genes in the relevant organism that were previously confirmed by homology searches and are also at least 750 bp long. Note that unlike other gene-finding methods, no statistical knowledge of non-coding DNA is necessary as part of the SOM's training.

In analysing an entire genome sequence, a sliding window is used to split each of the six reading frames into small samples. The default window size is 110 triplets, which has been chosen as a balance between having a window size long enough to evaluate a meaningful RSCU vector, and short enough to predict short genes. Each window is offset from the next by 10 triplets. An arbitrary probability score of 0.1 is used as the threshold for deciding if a sequence was protein-coding, and all samples that scored higher than 0.1 are recorded as predictions. If a stop codon lies in the sample, the gene prediction is annotated as having ended at that point. Note, however, that no effort is made to find stop codons if they are not within the prediction, and no effort whatsoever is made to find any start codons in the prediction.

Once all the samples are processed, some simple post-processing is carried out. Naturally, all same-frame concurrent predictions are merged. Predictions that are totally overlapped by another prediction are deleted if they are less than 75% the length of the other. Similarly, any prediction in which more than half its length is overlapped is deleted if it is less than half the length of the other prediction. Alternatively, any prediction that is less than 90% as long as the overlapping prediction and receiving a lower score is deleted. Finally, any prediction that is overlapped on both ends to a total overlap of at least 70% is also deleted. A prediction size of 75 codons was found by trial and error to be the smallest gene-coding region that could accurately be found using RescueNet.

While the above rules aim to delete smaller erroneous predictions, it is recognised that the loose nature of the rules leave room for many other overlapping predictions. However, it was found that in many overlapping cases it was difficult to decide which prediction to delete. Therefore, the best solution is to leave both predictions rather than misleading an annotator by giving only one, possibly erroneous, prediction.

In assessing the accuracy of our method, we had to take into account that our method will not predict most start sites, and some stop sites, exactly. We assume that our method will be of most use to annotation teams who rigorously inspect the results of our method in conjunction with the results of other gene prediction programs. Such annotation teams base their final genome annotation on widespread evidence, so the fact that our method may produce inexact start and stop sites will not be a major disadvantage. Therefore, a correct prediction is defined here as one that predicts more than 50% of an annotated gene in the correct frame. This criterion means that only predictions that are useful to annotators are considered to be correct.

Previous studies discuss the possibility that the GenBank annotation of various genomes may be incomplete or incorrect in some cases 532. Since many GenBank annotations are not experimentally corroborated, this possibility remains strong. Large-scale benchmarking of gene-prediction algorithms is therefore difficult, because few 'gold standard' annotations exist for prokaryotic genomes. Also, in most cases hypothetical gene annotations in the public databases have their roots in the predictions of an ab initio method, thus biasing any comparison of accuracy in favour of the particular method used in the annotation of that genome. However, for the purpose of defining accuracy in this study we must assume that all GenBank annotations are correct and complete. Sensitivity (Sn) is defined here as the percentage of GenBank gene records that are predicted correctly by our method. Specificity (Sp) is defined as the percentage of total RescueNet gene predictions that are correct.

Table 1 shows the results of RescueNet's predictions in 15 genomes. All results were generated using the default settings described above. Sensitivity and specificity values for each genome are shown, along with sensitivity values for those genes that are above the prediction length threshold of 75 codons (225 bp) and sensitivity values for those genes that have database matches.

Sequence data used in this study include the following 15 genomes and associated published genes available from the GenBank database: A. aeolicus 33, B. subtilis 34, Buchnera sp. 35, B. burgdorferi 36, C. jejuni 37, D. radiodurans (chromosome 1) 38, E. coli 39, H. influenzae 40, H. pylori 41, M. genitalium 42, M. jannaschii 43, R. solanacearum 44, S. coelicolor 45, Synechocystis sp. 46, and Y. pestis 47. These genomes were chosen to be representative of a wide range of GC content.

Three of the genomes tested have very high G+C content (D. radiodurans, R. solanacearum and S. coelicolor). High G+C content genomes present a problem to many gene-finding methods because of the relative infrequency of randomly occurring stop codons. The scarcity of stop codons has the effect of a large number of long, overlapping ORFs occurring in the sequence, relatively few of which are actually protein-coding. Many of the current gene-finders fail to discriminate accurately between coding and non-coding ORFs in this type of situation.

In our method, the relatively high specificity in each high G+C content genome suggests that RescueNet may have advantages in their annotation (see Table 1). To illustrate a case where RescueNet may be of practical use, we can consider the ORF annotated as DR1142 (see Figure 1) from D. radiodurans. This ORF is annotated to be protein-coding on the basis of the Glimmer2 prediction only. The RescueNet prediction in this area overlaps DR1142, but on the opposite strand. This type of situation, where a RescueNet prediction directly contradicts a GenBank/Glimmer2 annotation, occurs at least 23 times in the D. radiodurans genome. It is entirely possible that the Glimmer2 predictions are wrong in some of these cases, and the RescueNet predictions correct, but this cannot be proven without biochemical characterisation of the relevant gene. However, in the specific case of the DR1142 annotation, the RescueNet prediction has a much stronger database match than the GenBank annotation, and so has a high possibility of being correct.

Another interesting pointer to the advantages of RescueNet in high G+C content genomes is the substantially higher percentage of genes with database matches that are correctly predicted by RescueNet (see Table 1). In D. radiodurans, for example, 92.54% of genes with database matches are correctly predicted by RescueNet compared with only 84.28% of the total GenBank gene annotations. These figures suggest that hypothetical genes that are predicted only by Markov-based methods are poorly recognised by RescueNet, possibly because many hypothetical genes in high G+C content genomes may in fact be false gene predictions.

The general location of frameshifts within a gene sequence can be found by our method. Two features of our approach facilitate this. Firstly, even though the overall codon usage of a frameshifted gene could seem unusual, the two coding sections of the gene should each retain the organism's native codon usage. Secondly, our approach does not require that a prediction be bounded by a start and a stop codon. The sliding window used in our algorithm can therefore predict the correct coding frames each side of the frameshift.

In an interesting example in Figure 1, two RescueNet predictions overlap the D. radiodurans gene DR1143 in such a way that it seems that there may be a frameshift that extends the protein-coding region of the gene past the annotated stop codon. In fact, combining the two RescueNet predictions offers a better database match to the same genes that the original annotation matches. This increases the possibility that the actual gene contains an authentic frameshift or at least that the extra RescueNet prediction is an evolutionary artefact.

Figure 2 shows another example of frameshifts which are detected by RescueNet. In this case, the H. influenzae genes HI0218 and HI0220 both contain frameshifts, but both are handled by RescueNet's predictions. Note that the GeneMark algorithms are known to show the location of frameshifted regions in much the same manner as we have described, but our approach has required no modification to our basic algorithm in order to facilitate the prediction of frameshifted genes.

There may be a perception that any method using codon usage as the coding measure will only give predictions that are a subset of the predictions given by a Markov-based method that uses a 4^th or 5^th order model. To counter this argument, we compared the predictions of our method in two genomes (H. influenzae and H. pylori) to those of the web-based version of GeneMark.hmm 2.1 for prokaryotes http://opal.biology.gatech.edu/GeneMark/gmhmm2_prok.cgi, which generated results using two models; the 'typical' and 'atypical' models.

The published sensitivity of GeneMark.hmm in the H. influenzae genome (96.2%, see 4) is higher than that of our method, and the published specificity (89.8%) is lower, so GeneMark.hmm should give more predictions overall for this genome. However, 11 H. influenzae genes are predicted correctly by our method which are not predicted by GeneMark.hmm using 5^th order models, and 14 genes are predicted correctly by our method which are not predicted by GeneMark.hmm using 4^th order models. In the H. pylori genome, GeneMark.hmm has again a higher sensitivity and a lower specificity (94.0% & 91.3% respectively), but even more genes are exclusively predicted by our method; 25 genes as compared to the 5^th order GeneMark.hmm models and 30 genes as compared to the 4^th order models. Although these genes represent a small proportion of the total number of genes in the respective organisms, the fact that they are only predicted by RescueNet gives some indication of the advantage of using RescueNet in conjunction with other gene prediction methods.

RSCU is only one of many possible criterion with which to measure coding potential (see 48 for a review of others). In-phase hexamers are accepted as the most accurate k-mer frequency based measure of coding potential, and so their use as the coding measure in a Self-Organizing Map may offer improvement in accuracy over RescueNet. However, the larger space dimension of the hexamer coding measure may force a larger sliding window to be used and therefore the use of hexamers could actually decrease the precision of gene prediction.

The future use of alternative coding measures with our approach may also help to overcome difficulties in recognising genes that are reputed to be horizontally transferred in origin. Horizontally transferred genes would be more likely to have dissimilar codon usage patterns to other genes in the genome. Since our approach currently relies on the codon usage patterns it finds in the training set, it is unlikely to mark areas of unseen codon usage as protein-coding regions. Note, however, we are not suggesting all genes that were not recognised by our approach are of horizontally transferred origin. There are many explanations for a gene displaying atypical codon usage, and codon usage cannot be used as an accurate indicator of horizontal transfer.

There may be other ways to improve the accuracy of our method. The current implementation has a rather simple post-processing step that does not rely on modifying the prediction in order to include start or stop codons. While the practise of not constraining a prediction to be bound by a start and stop codon stands in stark contrast to other methods, we did not wish to lengthen or shorten any predictions artificially, since doing so can mislead annotation teams (especially in start site annotation). Relatively simple post-processing steps may, in fact, be advantageous. Our predictions represent a raw account of regions of the genome that display typical or native codon usage patterns, and this in itself may be of interest to annotation teams who use codon usage plots as the basis for some genomic feature annotations.