It is well known that the stability of a DNA fragment is a sequence dependent property and depends primarily on the sum of the interactions between the constituent dinucleotides. The overall stability for an oligonucleotide can thus be predicted from its sequence, if one knows the relative contribution of each nearest neighbour interaction in the DNA 18. The average stability profiles for three sets of bacterial promoter sequences calculated (using 15 nt moving window) based on this principle is shown in Figure 1. It is interesting that the promoters from diverse bacteria, which have quite different genome composition (A+T composition: E. coli 0.49, B. subtilis 0.56 and C. glutamicum 0.46), show strikingly similar features. Promoters from all the three bacteria show low stability peak around the -10 region. The second prominent feature in the free energy profiles of all the three bacteria is the difference in stabilities of the upstream and downstream regions. In all the three groups of promoter sequences, the average stability of upstream region is lower than the average stability of downstream region. But the three sets of promoter sequences differ in their basal energy level, which seems to be dependent on the nucleotide composition of the bacteria.

In order to get a better insight into the stability feature, we carried out a detailed analysis of E. coli promoter sequences. Our statistical analysis using "Wilcoxon signed test for equality of medians" (see METHODS) shows that the free energy distribution corresponding to a fragment extending from position -148 to 51 in the E. coli sequences is appreciably different from the energy distribution calculated in randomly selected windows, at a significance level as high as 0.0001. A comparison of free energy distribution at position -20 (corresponding to the promoter region) with distributions at positions -200 (corresponding to the region upstream of promoter region) and +200 (corresponding to the coding region) is shown in Figure 2. It is clearly seen that the region immediately upstream of TSS is much less stable than the other two regions. The average free energy at -20 position is -17.48 kcal/mol while average free energies at the -200 and +200 positions are -19.42 kcal and -20.19 kcal/mol respectively. The Kolmogorov-Smirnov test also confirms that the free energy distribution at position -20 significantly differs from that at -200 and +200 positions at a very high significance level (alpha = 10^-10).

This difference in free energy and the stability of promoter regions as compared to that of coding and other non-coding regions can be used to search for the promoters. Based on this consideration, a new scoring function D(n) is defined, which will look for differences in free energy of the neighbouring regions of position n:

D(n) = E1(n) - E2(n)

where,

Thus, E1(n) and E2(n) represent the free energy (see METHODS) average in the 50 nt region starting from nucleotide n and neighbouring 100 nt region starting from nucleotide n+99, respectively. The E1 value represents the basal energy level, which is characteristic of the given bacterial genome (e.g. in this case E. coli) and the D value represents the free energy difference in the two neighbouring regions. A stretch of DNA is assigned as promoter only if the average free energy of that 50 nt region (E1) and difference in free energy as compared to its neighbouring region (D) is greater than the chosen cut-offs. The protocol followed to calculate the true and false positives and hence sensitivity and precision is presented in the form of a flowchart in Figure 3. Identical sensitivity values can be achieved using different combinations of D and E1 cut-off values, which is obvious from the contour plot shown in Figure 4A. Similarly, different combinations of D and E1 cut-offs can lead to similar precisions (Figure 4B). But we observe that the use of different D and E1 cut-offs, corresponding to a given sensitivity level, results in a wide range of precisions (Figure 5). Hence, in order to attain a desired level of sensitivity the D and E1 cut-off values are chosen such that the number of false positives is minimum and the precision is maximum.

Initially, we divided the E. coli sequence data into two sets. The E1 and D cut-off values corresponding to different sensitivity levels were obtained for 100 randomly selected sequences (1^st set). These cut-off values were then applied to a second set consisting of remaining 127 sequences. The sensitivity and precision values calculated for the first and second set match very well. We also found that very similar results can be obtained when we use the whole dataset (Figure 6). Hence, we present the results for the whole dataset rather than separately for two sets. The D and E1 cut-offs and the number of false positives corresponding to different levels of sensitivity are given in Table 1. To confirm the validity of our choice, we used another set of 1000 nt long sequences extracted from the centre of the ORFs, which were more than 2000 nt long. The results corresponding to this set of control fragments are also given in Table 1 and show very few false positives.

In principle, D can also be calculated using equal sized windows, i.e. 50 nt, for both E1 and E2 instead of a 50 nt window for E1 and a 100 nt window for E2. However, our calculations show that use of equal sized windows, for E1 as well as E2 calculations, results in a slightly lesser precision than when 100 nt window is used for E2 calculations (Figure 7). Hence, in our promoter predictions, we chose a 100 nt window for E2 calculations.

A large number of promoter prediction programs have been developed for eukaryotic sequences and are easily accessible, while NNPP 1920 is the only available prokaryotic promoter prediction program. It is a neural network based method where prediction for each sequence element constituting promoter sequence is combined in time-delay neural networks for a complete promoter site prediction. Some other prokaryotic promoter prediction methods are based on weight matrix pattern searches 21222324. One of the representative weight matrix method, proposed by Staden 21, uses three weight matrices corresponding to the -35 sequence, the -10 sequence and the transcription start site. It also takes into account the spacing between the -35 and -10 motifs, as well as the distance between the -10 motif and the transcription start site. A brief comparison of the results obtained by our method and the other two methods (Staden method and NNPP program) is given in Table 2. It can be clearly seen from Table 2 that for similar sensitivity, our program gives much better accuracy than the other two programs. It is pertinent to mention here that our method differs from the other two methods in one major respect, namely our method tries to find a promoter region while the other two programs try to pinpoint the transcription start site. It may be argued that the lesser number of false positives in our prediction method, as compared to the other two algorithms, may be due to this difference. But even after taking this difference into consideration, the number of false positives predicted by our protocol turns out to be smaller than those predicted by the other two methods. For example, Figure 8 represents the case of argI and argF genes, where the NNPP program predicts a few extra TSS as compared to our method which correctly picks up a region in the vicinity of TSS. A combination of both the methods can therefore help in reducing the false predictions in the upstream and downstream regions. In principle, by restricting the pattern recognition using NNPP and Staden's methods only to the promoter region located initially with the help of our method, one can reduce the number of false positives. This composite approach will also help in pinpointing the TSS, which is not possible by use of our method alone. But at the same time it should be noted that both types of predictions fail to identify some of the promoters (Figure 8), e.g. for csiE gene, our program could correctly predict the promoter region but the NNPP program could not locate it. On the other hand, our program failed to find the promoter region for gyrA gene while NNPP could correctly position it. And in case of ilvA gene both the programs did not succeed in identifying the promoter region.

Very recently a study on improvement of NNPP prediction (TLS-NNPP), by combining this method with additional information such as distance between TSS and translation start site (TLS), has been published 25. With the use of additional information regarding TLS, Burden et al. could significantly increase the precision of NNPP. The TLS-NNPP method was tested on 510 E. coli sequences of length 500 bp. For comparable sensitivity levels, the precision achieved by TLS-NNPP was 0.188 (sensitivity = 0.452) as compared to 0.109 precision (sensitivity = 0.443) achieved by NNPP. It can be seen that, for similar sensitivity levels, the precision achieved by our method (~0.7) is higher as compared to both TLS-NNPP and NNPP (Figure-9).

Presence of high densities of promoter like signals in the upstream region of TSS may be one of the reasons why pattern matching programs result in low level of precision. This has been shown recently by a systematic analysis of sigma70 promoters from E. coli 24. In this study a number of weight matrices were generated by analysis of 599 experimentally verified promoters and these were tested on the 250 bp region upstream of gene start site. It was found that each 250 bp region on an average has 38 promoter-like signals. The study also presented a more rigorous patter searching method for locating promoters. With the use of this function the authors reach a sensitivity values of 0.86 but the corresponding precision achieved is only ~0.2. In case of our method, for a sensitivity of 0.9 we obtained a precision of 0.35 (as shown in Figure -9).

Recently Bockhorst et al. 26 proposed a very accurate method for predicting operons, promoters and terminators in E. coli. This method is based on sequence as well as expression data, but requires prior knowledge of coordinates of every ORF in the genome. We would like to emphasize here that our method is different from other methods in that it is independent of any such prior knowledge about the test gene or the organism and hence holds promise as being useful for promoter prediction in a newly sequenced genome.

The eukaryotic promoter prediction method proposed by Ohler et al. 27 is also worth mentioning here. Ohler et al. showed that a 30 % reduction of false positives can be achieved by use of physical properties, such as DNA bendability, in addition to other sequence properties of promoters. Interestingly, our method which also uses a physical property gives much smaller number of false positives as compared to Ohler et al.'s method. (For similar sensitivity, number of false predictions in case of Ohler et al.'s method are 1/4740 nt while in case of our method these are 1/8407 nt).

Another vertebrate promoter prediction program, 'Promfind' 28 identifies differences in hexanucleotide frequencies of promoter and coding region and is algorithmically quite similar to our method. But Promfind differs from our method in two important aspects. First, the Promfind program is developed mainly for vertebrate promoters and second, it assumes that in a given sequence, a promoter is always present and merely predicts its location. This need not necessarily be the case, as some of the sequences may not have any promoter at all. Our program differs from Promfind in that a promoter is predicted only when the sequence satisfies certain criteria and hence is much more appropriate for carrying out genome scale analysis.

In addition to protein coding genes there are genes present for the non-coding RNAs (ncRNAs), which play structural, regulatory and catalytic roles. It is a difficult task to find out ncRNA genes in a genome because unlike protein coding regions they lack open reading frames and also they are generally smaller in size. In addition, it is also difficult to do a homology sequence search as only the structure of ncRNA is conserved and not the sequence. There are around 156 E. coli RNA genes reported on the NCBI site 29 and in addition many more small RNA genes are known to exist. Argaman et al. 30 recently identified 14 novel sRNA genes by applying a heuristic approach to search for transcriptional signals. We have checked the performance of our algorithm with respect to the 42 RNA transcription units (TUs) reported in Ecocyc database. Our method could pick up around 57 % RNA TUs, at a cut-off corresponding to 60 % sensitivity. The program works much better in case of rRNA operons than tRNA transcription units. We could correctly pick up promoter regions in 6 out of 7 rRNA transcription units, 17 out of 33 tRNA TUs and 1 out of the 2 remaining RNA types.

Finally, it is very important to see whether the method works equally well for other organisms which have genome compositions substantially different from that of Escherichia coli. Hence, we also tested our method using the promoter sequences from 1) the A+T-rich bacteria, Bacillus subtilis and 2) a G+C rich bacteria such as Corynebacterium glutamicum. Figure 9 gives a summary of the predictions in case of bacillus and corynebacterium promoters, along with those of Escherichia coli. It can be clearly seen that, at present our method performs optimally for the Escherichia coli promoters and also performs quite well in case of Bacillus subtilis. The prediction accuracy in case of Corynebacterium glutamicum promoters is not as good as that for the other two classes of promoters. However, it should be noted that the number of experimentally determined Corynebacterium promoters is much smaller as compared to other two bacteria and a larger dataset is required to arrive at any firm conclusion.

All the promoter sequences used in this study are 1000 nt long, starting 500 nt upstream (position -500) and extending up to 500 nt downstream (position +500) of the TSS. In order to avoid having multiple TSS in a given 1000 nt sequence, we have excluded all the transcription start sites which are less than 500 nt apart. Our promoter set has 227 E. coli promoters, 89 B. subtilis promoters and 28 C. glutamicum promoters.

The stability of DNA molecule can be expressed in terms of free energy. The standard free energy change (ΔG^o₃₇) corresponding to the melting transition of an 'n' nucleotides (or 'n-1' dinucleotides) long DNA molecule, from double strand to single strand is calculated as follows:

where,

ΔG^o_ini is the initiation free energy for dinucleotide of type ij.

ΔG^o_sym equals +0.43 kcal/mol and is applicable if the duplex is self-complementary.

ΔG^o_i,j is the standard free energy change for the dinucleotide of type ij.

Since our analysis involves long continuous stretches of DNA molecules, in our calculation we did not consider the two terms, ΔG^o_ini and ΔG^o_sym, which are more relevant for oligonucleotides. In the present calculation, each promoter sequence is divided into overlapping windows of 15 base pairs (or 14 dinucleotide steps). For each window, the free energy is calculated as given in the above equation and the energy value is assigned to the first base pair in the window. The energy values corresponding to the 10 unique dinucleotide sequences are taken from the unified parameters proposed recently 3435.

The promoter predictions were also carried out using two other methods viz. NNPP and Staden's method. NNPP program is available at 20. All the NNPP predictions were carried out at a score cut-off 0.80.

The implementation of Staden's method was carried out as described in 2137. The weight matrix search was carried out with the help of PATSER program 38.

In case of NNPP as well as Staden's method, the true and false positives were scored as in case of our method (Figure 3), with a prediction in -150 to 50 region being considered as a true prediction.

The sensitivity and precision for the predictions are calculated using the following formulae: