In many applications, including ours, it is critical to reduce the number of false positives because of their experimental costs, while false negatives are not as detrimental. In our neural network, a 'cutoff' parameter determines the balance between specificity and sensitivity (i.e., the balance of false positives and false negatives) 25. Thus, we searched for putative domain linkers in 101602 SWISSPROT sequences using high cutoff values, ranging from 0.90 to 0.98, to minimize false predictions even at the cost of missing existing linkers. The number of putative domain linkers identified by our neural network ranged from 1469 to 20876 for cutoffs of 0.98 and 0.90, respectively. As expected, the use of a higher cutoff parameter increased the number of correct predictions, but decreased the total number of predicted domain linkers (Table 1). Overall, the same conclusions are reached independently from the cutoff value, when it is between 0.90 and 0.98. The following discussion is based on a search with a cutoff value of 0.95, which yielded 8133 putative domain linkers, representing 1.4% of the data set on a residue number basis (Table 1). These figures correspond to approximately one putative linker predicted for every 12 sequences, which is a tractable number for a high-throughput experiment.

For the purposes of this discussion, we define 'putative structural domains' as sequence segments with high similarity to PDB or CDD sequences (sequence identity >30% and sequence overlap > 85%; See details in the Material and methods section). Putative structural domains are thus able to fold into a native structure or at least to form a domain, and we used them to assess the correctness of the predicted domain boundaries. As anticipated, a substantial fraction of the SWISSPROT sequences is covered by known putative structural domains. Specifically, from a total of 101602 SWISSPROT sequences, 38470 sequences (corresponding to, respectively, 38% and 27% on a sequence and residue basis) had similarity to a PDB sequence, and 64349 sequences (43% on a residue basis) had similarity to a CDD sequence (Table 1).

Our method for evaluating the correctness of the predicted domain linkers was to assess their positions relative to those of putative structural domains. To this end, we classified the putative domain linkers into four classes (Figure 1A; see Materials and methods). Linkers that matched either one or both ends of a putative structural domain were classified into classes 1 and 2, respectively, and were considered as correctly predicted. Putative domain linkers overlapping with putative structural domains are likely to break them in two non-foldable sequences. They were thus counted as incorrect predictions, and classified in class 4. Finally, putative linkers that were located far away from any putative structural domains (farther than the error window discussed below) were categorized in class 3. These linkers could not be evaluated as either correct or incorrect.

The putative structural domains as defined above may contain multiple structural domains, and, hence, some linkers in class 4 may be correctly located. Our calculations thus slightly underestimate the actual performances of both the neural network and the LCRs predictions (see also next section). However, the underestimations are likely to be very small, and concern only a few percents of the putative linkers, as most proteins in the PDB (and many in the CDD) are single structural domain proteins 2829.

The above classification was performed by allowing an error window between the position of the predicted linker and the termini of the putative structural domain. As expected, when the error window was increased, the occurrence of correct matches increased while that of the overlaps decreased. With an error window of 20 residues, the percentages of correct matches (classes 1 and 2), overlaps (class 4) and unknown locations (class 3) were 27.5%, 9.2% and 63.4%, respectively (Figure 1B). Thus, 75% of the putative domain linkers with predictions that could be evaluated (classes 1, 2 and 3) were correctly located, suggesting that the boundaries of the putative structural domains can be predicted with reasonable confidence. On the other hand, almost two-thirds of the putative domain linkers were predicted in regions without a corresponding putative structural domain nearby, possibly delimiting novel structural domains not yet classified in the PDB or CDD (Figure 2).

Most large-scale sequence databases contain a substantial number of long, unstructured, disordered regions that may interfere with systematic searches for structural domains. Thus, the detection of unstructured portions of proteins as defined by low complexity regions (LCRs), which are unlikely to fold into a globular structure 42, or structurally disordered regions 43 may help predict domain boundaries, although this was not the original intent. Here, we examined whether LCRs as detected by SEG 42, overlapped with domain boundaries. Two parameters in the SEG program, called trigger and extension complexity, control the balance between the detection number (Table 1) and the ratio of correct matches relative to incorrect ones (data not shown). In order to analyze approximately the same number of sequences as that of the putative linkers detected with the cutoff of 0.95, we set the trigger complexity to 2.9 and the extension complexity to 3.2, which yielded 8539 low-complexity regions (Table 1). Using an error window of 20 residues, the percentages of correct matches (classes 1 and 2), overlaps (class 4) and unknown locations (class 3) were 26.3%, 10.3% and 63.4%, respectively (Figure 1C). Thus, the position of the LCRs correlate with the temini of the putative structural domains at a level similar to that observed for the domain linkers (Figure 1B).

Although both the domain linker and LCR predictions correlate well with the putative structural domain termini, it is important to note that the LCRs and linkers are located in different sequence regions. Indeed, only 2561 out of 8539 LCRs overlapped with the putative domain linkers predicted by our neural network, and, in turn, 2643 out of 8133 putative linkers were detected by the SEG program (Table 2). Furthermore, the sequence entropy of the putative linkers was higher than that of the LCRs, with the maximum of the sequence entropy distribution at around 3.5 for the linkers, while it was only 3.0 for the LCRs (sequence complexity values lower than 2.9 are unlikely to fold into a globular structure). Thus, our neural network appears to detect preferentially non-globular regions with higher sequence complexity than those detected by SEG. These results indicate that LCRs and linker sequences have different characteristics, and that the two methods are complementary for identifying domain boundaries (Figure 3).

As a result of their complementarity, the sensitivity of the domain detection was clearly improved by combining the LCR and linker predictions (Table 1; Figure 3). A combined search yielded 13946 domain boundaries, i.e., only 2726 sequences less than the total of the LCR and linker sequences. Furthermore, the domain boundary sequences identified by a combined LCR-linker search were categorized into the 4 classes in percentages similar to those identified by the separate LCR and linker searches. Thus, the total number of correctly predicted domain termini increased 1.6 fold, while the fraction of incorrect predictions (false positives) remained unchanged.

As a further assessment of both our neural network and the SEG program to detect putative structural domain termini, we estimated the success rate of a blind prediction. The blind prediction was defined as the probability that a randomly assigned residue in the query sequence matches with a putative structural domain terminal residue within the allowed error (Materials and methods). We compared the random guesses with our neural network and SEG prediction using a quality index calculated as the ratio of correct predictions relative to the sum of correct and incorrect predictions 444546, which is computed as the number of sequences in classes 1 and 2 divided by those in classes 1, 2 and 4. Figure 4 clearly shows that the quality index of the blind prediction is far below those of the two other methods. This result strongly supports our initial assumption that the occurrences of both the putative domain linkers and the low-complexity regions near the putative structural domain terminal regions are not fortuitous.

From a practical viewpoint, it is important to evaluate the error window within which the boundaries are predicted. The exact position of a domain boundary is obviously ambiguous. The first reason is that PDB sequences may include several unstructured terminal residues (without coordinates), causing some uncertainties about the exact positions of the putative structural domain termini. The uncertainty arising from the CDD sequence is even larger. Second, the smoothing windows used to reduce the spurious predictions introduce ambiguity in the positions of the predicted domain linkers, as they smear their C and N termini. These issues can be examined using an error window parameter that accommodates the positional ambiguity generated by both the putative structural domain termini and the predicted domain linkers (or LRCs). As shown in Figure 5, the positions of the first and last residues of the predicted domain linker are distributed randomly around the positions of the last and respectively first residue of the structural termini. This shows that the error distribution is random with a maximum at 0 residue, confirming that the linker positions are accurately assigned. The error is clearly limited to about 20 residues, and to 10 residues in most cases. Furthermore, the prediction quality index dependence on the error window also indicates that the ambiguity is limited to about 20 residues, as it reaches 70% for a 15 residue error window and then rapidly levels off for larger windows (Figure 4).

A total of 101602 SWISSPROT protein sequences 39 were used in the present investigation. Since the putative structural domains needed to be structurally independent units, we located all of the sequences with high similarity to PDB 47 and CDD 19 sequences, using the BLAST and RPS-BLAST programs4849. To ensure the structural identity, as much as possible, we required a sequence identity greater than 30% and a sequential overlap greater than 85% over the entire length of the corresponding PDB or CDD sequence. Thus, putative structural domains detected by similarity to a PDB sequence are likely to fold into a structure similar to the corresponding PDB structure. Analogously, putative structural domains detected by similarity to CDD sequences, which is a compilation of conserved protein domain sequences imported from Pfam 18 and SMART 16, are likely correspond to a natively folded domain, although their structures have not necessarily been determined.

We used a two hidden units neural network 50 trained to distinguish between domain linker and non-linker regions. The prediction procedure was identical to that reported in our previous paper 25, except for the following two points. (1) The prediction was carried out over the entire protein sequence, namely from the start to the end of each target sequence, because the SWISSPROT sequences may contain unstructured termini. Indeed, in our previous study, we assumed that a 60 residue length is the minimum for a polypeptide to fold independently, and we omitted the 60 terminal residues of the multi-domain protein sequences from the prediction, because the protein structures were known, and we knew that no unstructured termini were present. (2) Predicted domain linkers were not ranked, because under the stringent conditions (cutoff 0.90–0.98; see below) examined here, the prediction success rate was sufficiently high without such a procedure.

The smoothing window size and the threshold parameters were fixed to 19 and 0.5, respectively, as in our previous study. However, we set the cutoff parameter to values ranging from 0.90 to 0.98, because a high cutoff yields a better prediction specificity at the cost of the prediction sensitivity. The specificity and sensitivity for the first ranked domain linkers predicted with a cutoff of 0.90 are 81.8% and 10.3%, respectively, as calculated with a ten-fold jack-knife 25.

Sequence entropy (also called Shannon's entropy) has been used to quantify the complexity of amino acid sequences, and several studies have examined the relationship between the sequence entropy and the globularity of proteins 4243. According to these studies, the sequence entropy of globular proteins is generally high, with a lower limit of around 2.9.

SEG is a program that identifies low-complexity regions in protein sequences 51. This program was originally intended to distinguish between globular and non-globular regions. In this study, we used SEG to check whether a correlation between the low-complexity regions and the putative structural domain termini existed. Three parameters in SEG, the trigger window length, the trigger complexity and the extension complexity, are used to assign low complexity regions. We set the trigger window length to 45 residues, in line with previous studies 4351 To obtain a number of LCRs similar to that of the linkers predicted with a cutoff of 0.95, the trigger and extension complexities were set to 2.9 and 3.2, respectively (Table 1 and Figures 1 and 3).

We evaluated the validity of the prediction of the domain boundaries from their positions relative to the putative structural domains as defined above. The predicted domain boundaries were divided into four classes (Figure 1A), using an error window to accommodate the ambiguity in the termini position of both the predicted domain boundaries and the putative structural domains. A predicted domain boundary was considered to be correctly located when its end was separated from a putative structural domain by fewer residues than specified by the error window (Figure 1A). Class 1 includes predicted domain boundaries in which the closest ends are located within the error window of a putative structural domain. Predicted domain boundaries with both ends located within the error window of the N and C terminal ends of two putative structural domains are categorized in class 2. Class 3 consists of predicted domain boundaries that are separated from any putative structural domain by a number of residues larger than the error window.

We assumed the success rate of a blind prediction, i.e. a prediction without any a priori information, to be the probability that a randomly assigned position matches a terminal residue of a putative structural domain. Four classes were defined similarly to those used to evaluate the putative domain linkers and the low-complexity regions. For example, a randomly picked residue was considered to be correctly located and was classified in class 1, when the end of a putative structural domain was found within the error window. The success rates (quality index) for the blind prediction, the putative domain linkers and the low-complexity regions were calculated as the rate of correct matches (classes 1 and 2) relative to both the correct and incorrect matches (classes 1, 2 and 4).