Dinucleotide weight matrices for predicting transcription factor binding sites: generalizing the position weight matrix

Abstract

Background: Identifying transcription factor binding sites (TFBS) in silico is key in understanding gene regulation. TFBS are string patterns that exhibit some variability, commonly modelled as "position weight matrices" (PWMs). Though convenient, the PWM has significant limitations, in particular the assumed independence of positions within the binding motif; and predictions based on PWMs are usually not very specific to known functional sites. Analysis here on binding sites in yeast suggests that correlation of dinucleotides is not limited to near-neighbours, but can extend over considerable gaps.

Methodology/principal findings: I describe a straightforward generalization of the PWM model, that considers frequencies of dinucleotides instead of individual nucleotides. Unlike previous efforts, this method considers all dinucleotides within an extended binding region, and does not make an attempt to determine a priori the significance of particular dinucleotide correlations. I describe how to use a "dinucleotide weight matrix" (DWM) to predict binding sites, dealing in particular with the complication that its entries are not independent probabilities. Benchmarks show, for many factors, a dramatic improvement over PWMs in precision of predicting known targets. In most cases, significant further improvement arises by extending the commonly defined "core motifs" by about 10 bp on either side. Though this flanking sequence shows no strong motif at the nucleotide level, the predictive power of the dinucleotide model suggests that the "signature" in DNA sequence of protein-binding affinity extends beyond the core protein-DNA contact region.

Conclusion/significance: While computationally more demanding and slower than PWM-based approaches, this dinucleotide method is straightforward, both conceptually and in implementation, and can serve as a basis for future improvements.

Figure 1. The distribution of gaps in correlated dinucleotide pairs () in yeast TFs, as described in the text.

The graph on top shows the full distribution, and the graph below shows only those pairs that are sufficiently abundant (either the predicted or actual number being at least 30% of the total). The green “normalised” bars include a correction for there being fewer possible pairs with larger “gaps”. With this correction, the graphs are more uniform.

Figure 2. The relative performance of PWMs and DWMs in predicting binding targets in yeast.

The figure shows Pearson correlation coefficients of binding site predictions with ChIP binding -values reported by Harbison et al. , using the “raw” position weight matrices from MacIsaac et al. , dinucleotide weight matrices with the same “width” as the “raw” matrices, and dinucleotide weight matrices with a 10bp “flanking sequence” on either side of the input matrices. Details are in Materials and Methods.

Figure 3. The precision, as a function of sensitivity, of PWMs and DWMs in predicting targets from MacIsaac et al. .

The precision is the fraction of predictions above a certain logodds cutoff that correspond to documented target genes. The sensitivity is fraction of known targets that are predicted above that cutoff. These are for the same benchmark data as in Figure 2.

Figure 4. The performance of different methods on individual site predictions in yeast.

For the same benchmark as in Figure 2, these are the fraction of site predictions that agree with annotated sites in SCPD, as a function of the total number of SCPD sites predicted.

Figure 5. The precision of site predictions in fruitfly.

For predictions in synthetic sequence embedding binding site footprints from the REDfly database as well as “fake” sites that are samples of PWMs corresponding to the same factors, this plot shows the precision in predicting REDfly sites, that is, the fraction of predictions that overlap with REDfly footprints, as a function of sensitivity, that is, the fraction of real (REDfly) sites that are predicted. Details of the construction of the synthetic sequence are in Materials and Methods.

Figure 6. The discriminative precision of predictions in fruitfly.

For the same predictions as in Figure 5, this plot shows the “discriminative precision” for REDfly sites, that is, difference in the fraction of predictions that overlap with REDfly footprints and the fraction of predictions that overlap with “fake” sites, as a function of sensitivity.