There were 38 different transcription factors in TRANSFAC Saccharomyces Module, of which 32 were made up of raw counts. Of these, 16 were also found in the ChIP-chip dataset. These were tested against the 1259 different probes in the chromatin immunoprecipitation experiment. This gives 20144 different TF-probe pairs where we can classify whether the TF binds to the probe, and then check the classification. These results are shown in .

We generated a ROC curve () for SBaSeTraM, by varying the posterior probability cut-off, and hence the trade-off between sensitivity and selectivity.

The point on the ROC curve generated using the parameters from

[10] with GMATIM appears slightly below the ROC curve for BaSeTraM (GMATIM has 71.61% true positive rate for a 53.27% false positive rate). We found a posterior cutoff that generates a FPR close to this (with a posterior probability cut-off of 0.407, BaSeTraM achieved a 72.07% TPR at a FPR of 53.25%). At this point, we tested for a significant difference in the proportion of predictions which were correct; that is,

. We performed a comparison of these two binomial proportions, using the prop.test function in R

[14], and obtained a one-sided p-value of 0.4603 (

*i.e.* not significant to a 95% confidence level).

SBaSeTraM outperforms MAST when used through WrapMAST. It is worth noting that MAST is not typically used with TRANSFAC PWMs, and usually, multiple PWMs are used for each TF, and so the results cannot be used to make inferences about how well MAST performs together with MEME. The results do, however, illustrate the benefit of methods which take into account uncertainty in the foreground model.

We also carried out an analysis to see whether any particular TFs were making a large contribution to the overall prediction accuracy at this point. shows the differences between the two methods in the ROC space for each TF PWM. For each transcription factor, we have plotted an arrow from the point in the ROC space corresponding to the results for SBaSeTraM, to the point corresponding to the results from GMATIM. Some of the predictions are quite different; for example, for ADR1, SBaSeTraM found no occurrences, while GMATIM made numerous predictions, resulting in a true positive rate of 91.3% and a false positive rate of 96.0% (putting the accuracy for that particular TF below the line of no-discrimination). There was only one TF, GAL4, for which SBaSeTraM fell below the line of no-discrimination (which GMATIM predicted with a 17.4% true positive rate and a 0.8% false positive rate), and three TFs for which GMATIM fell below the line of no-discrimination (all of which were above or on the line of no-discrimination for SBaSeTraM). Unlike for SBaSeTraM, GMATIM predictions for HSF1, ROX1, and STE12 had true and false positive rates approaching 100%.

We also analysed the spread of true and false positive rates for each method. shows box-and-whisker plots for the true and false positive rates for SBaSeTraM and GMATIM. Notably, there is a much greater distance between the upper and lower quartiles in both the true and false positive rates for GMATIM than there is for SBaSeTraM. This demonstrates that the BaSeTraM algorithm is more consistently controlling the trade-off between sensitivity and selectivity for each individual TF.

In addition, we used the bisection method to find a separate posterior probability cutoff for each of the 16 TFs that gave the SBaSeTraM method a FPR (for that TF) close to the FPR obtained with GMATIM. We allowed the method to terminate when a cutoff was found that brought the

distance of the two FPRs within

, when an increase in cutoff resulted in an increased FPR (or a decrease in the cutoff resulted in a decrease in the FPR), or when no improvement in FPR was achieved after 4 iterations of the algorithm. The latter two conditions are necessary because there are a finite number of probes (1259), and there is no guarantee that there will be a cutoff which brings the SBaSeTraM FPR within

of the GMATIM FPR. In practice, for 8 of the 16 TFs, the difference between the final FPRs for the two methods was less than

, for 11 it was within

, and for 13 was within

. For HAC1, the final SBaSeTraM FPR was

higher than the GMATIM one, for XBP1 the GMATIM FPR was

higher, and for HAP1, the final SBaSeTraM FPR was

higher.

Using the same methodology used on the entire dataset (as discussed above), we tested for a statistically significant difference in proportion of predictions which were correct for each transcription factor, between GMATIM and SBaSeTraM (with the posterior probability cutoffs discussed in the previous paragraph). We obtained only one result where the p-value was less than

, for GCN4 (p

=

0.00886). For this TF, the FPR for both methods was

, the TPR for SBaSeTraM was

, while it was

for GMATIM. When we applied the Holm-Bonferroni procedure for multiple comparisons

[15], none of the TF-by-TF results were significant to a 5% familywise error rate (FWER).

Conclusions

We have developed a Bayesian classifier for identifying TFBSs, which performs comparably to an existing algorithm, but which has a more principled statistical explanation, so that the trade-off between sensitivity and selectivity can be trivially adjusted, and the method can be altered to use different background models.

It is clear that the two methods are very similar in overall performance, and there is insufficient data in TSM to tell the two apart. The 95% confidence interval for the difference of the proportion correctly classified above runs from SBaSeTraM being 1.03% better, to GMATIM being 0.93% better. We therefore conclude that until there is more evidence that one method is better, from a performance standpoint, the two methods can be used interchangeably.

However, the fact that the statistical interpretation of BaSeTraM has been explained in rigorous terms, combined with the ease with which the posterior probability cut-off can be adjusted (as opposed to needing to adjust two separate parameters and re-run the analysis) makes the use of BaSeTraM preferable for many applications.

We note that despite the similarity in accuracy, the predictions made are not all the same; only 62.8% of all predictions of transcription factor binding made by SBaSeTraM with this posterior probability cut-off were also made by GMATIM.

The BaSeTraM statistical model includes a background model to be used. While a relatively uninformative background model is useful with the synthetic probes used in ChIP-chip analyses, using a different background model is likely to be important on genomic scale data, where there are localised variations in base frequencies.

When dealing with genomic scale data, it is also important that computation is reasonably efficient. It is also preferable that this computation can occur on modest hardware, so it is usable by groups without access to high-performance computing infrastructure.

In order to achieve these goals, we also developed a C++ implementation of BaSeTraM, called CBaSeTraM, which we optimised for the AMD64 architecture. We used Callgrind

[16] to identify places where cache misses were occurring. We then used a customised allocator to ensure that all data which is needed in the inner loop (which is executed for each matrix for each alignment for each position) does not result in any cache misses, due to it being present in one cache page. As reading the level 1 and 2 caches are approximately 10 and 300 times faster than RAM, respectively, this leads to significant speed-ups. In this tool, we also implemented a sliding window determination of background model parameters

and

. Our implementation supports two distinct sliding windows; the intention is that one window is much larger than the other. The final estimate of each

and

is the geometric mean of the two estimates. By default, the small window is 501 BP wide, and the large window is 2001 BP wide. Both windows are centred on the same base, which is used as the first position when testing for TFBSs. In addition, CBaSeTraM can use MPI

[17] to search multiple sequences in parallel.

GMATIM, SBaSeTraM, and CBaSeTraM, as well as the programs used to test the methods, are Free/Open Source software. Instructions for building these programs are included as an online supplement.