For most organisms, DNA is the primary information storing molecule in the cell. Since the discovery of its molecular structure [1–3], it had been generally accepted that information in DNA is exclusively contained within its nucleobase sequence. At about the same time, Claude Shannon formalized the most important generalized mathematical definition of information [4] expanding on Norbert Weiner’s work in probability and thus founding the modern statistical subdiscipline of information theory. The application of information theoretics to DNA sequence did not occur until much later, after the advent of automated forms of DNA sequencing, when Schneider and Stevens [5] utilized Shannon information in the form of the ‘sequence logo’ plot to describe empirically-determined binding sequence preferences of transcription factors.

Historically, studies of transcription factor binding sites (TFBS) have focused primarily upon DNA nucleobase sequence at points of major groove contact, where base sequence is directly readable at the molecular level. Thus, these studies have been largely confined to a single-dimensional bioinformatic perspective. However, recent studies have illuminated the importance of a more biophysical and less sequence-specific second mechanism involved in TF binding, whereby TF’s are drawn near to their cognate sites through a process commonly referred to as “indirect readout” [6–12], or “shape readout” [13]. This form of recognition of local DNA sequence occurs without direct base contacts at the major groove, and is dependent upon local DNA shape, deformability (e.g. an ability to kink) and charge. The ability of any given sequence to bind through indirect readout is also related to the base sequence by its correlation with the local spacing of phosphate groups determining the width of the minor groove [14] as well as the dynamic behavior of phosphate linkages that define the structural dynamics of dinucleotides in aqueous solution [15, 16]. Thus, indirect readout can involve many complex correlated aspects of both DNA’s structure and structural dynamics [17]. DNA shape involves subtle local sequence-dependent variations in minor groove width and subsequent electrostatic charge [14]. The structural dynamics of DNA can be observed in its intrinsic flexibility measured freely in solution as BI-BII conformation shifts in phosphate linkages on the backbone [15] and DNA flexibility has been recently become the subject of both evolutionary and global mapping studies in yeast and other micro-organisms [16, 18–20]. It is also readily observed in measurements of its deformation energy to the nucleosome core [21, 22], other proteins [23], base stacking energy [24], solvent accessibility [25], and pattern of cleavage by nucleases [26] as well. Many of these biophysical aspects involved in indirect readout are generally correlated to organism-specific genomic features influencing gene function [16, 17] and evolution [20, 27–29] including local GC content [20, 30] and purine-pyrimidine states of nucleobases flanking the phosphate linkages (e.g. YR dimers; [23]). Recent studies have even shown that alignments tuned to the DNA shape can even significantly enhance TFBS identification, again furthering the now well-known understanding of the role of indirect readout in TF binding [31, 32].

While traditional sequence logo plots have wide utility and popularity for describing TFBS [5, 33], they cannot display information content most relevant to indirect readout mechanisms (e.g. structural features affecting major and minor grooves as well as backbone conformation, hydration, deformation and flexibility [9]). This information can depend partly upon the DNA backbone’s structural shape and dynamic conformational states of the phosphate linkages defined over very short sequences (i.e. dimer, trimer or tetramer). There is no reason why an information theoretic such as the Shannon information, cannot be calculated using an alphabet representing the structural dynamic state of any given phosphate linkage. The dynamic states of dinucleotide have recently been reported in a meta-analysis of experimental data by Heddi et al. [15]. They have devised a twist, roll and X displacement scale (or TRX scale) that is a simple, nonlinear metric that relates a given length of DNA sequence to its inherent structural dynamics (i.e. intrinsic flexibility), due to BI – BII chemical shifts in phosphate linkage conformation on the DNA backbone while freely in solution in the absence of other DNA binding proteins [15]. The TRX scale represents the percentage of time a phosphate linkage spends in the BII conformation and ranges from 0 to 43 and is positively correlated to GC content of a given dinucleotide. While the TRX metric ignores higher-order aspects of DNA flexibility, it has been well validated as an excellent predictor of DNA-protein interaction, including nucleosome positioning, as most interactions are generally facilitated by the local landscape of DNA flexibility and charge in the genome. Other less recent empirical metrics of DNA flexibility have also been successfully based on lower-order interactions (i.e. trimer [19]) and recent computer simulation studies of tetranucleotide suggest that the influence of DNA structure on dynamics could extend slightly beyond adjacent nucleobases (i.e. dinucleotides) [34, 35]. Dinucleotide-based TRX scores have been shown to correlate well with tetranucleotide-based minor groove widths [16]. Because the TRX scale is a simple dinucleotide-based numerical scale, and thus treats each phosphate linkage position independently, it can also be easily incorporated into the positional graphical framework of the traditional sequence logo plot. Here we offer TRX-LOGOS, an R graphics module that produces a traditional sequence logo plot that includes the addition of vertical bars representing the information content calculated at each phosphate linkage as well. Shannon information on the DNA backbone in calculated at each dinucleotide position using an alphabet of nine different probabilistic phosphate linkage dynamic states of the TRX scale. In addition to the R module, we also offer a Perl wrapper script that allows TRX-LOGOS to interface with output obtained directly from the Computational Regulatory Genomics database JASPAR [36]. The plotting module uses gray-scaled bars at intervening phosphate linkage positions to represent both the information content of the DNA backbone (height of bar) as well as its average intrinsic flexibility (shaded from black = no flexibility (TRX = 0) to white = high flexibility (TRX = 43)). TRX-LOGOS can easily identify where DNA structural dynamics are functionally important in DNA-protein interaction and where local structural dynamics involved in this interaction may contrast the surrounding genomic background that defines the chromatin context of a binding site [27].

To demonstrate the utility of TRX logo plots, we analyzed the information content of both DNA sequence and DNA backbone for 416 TFBS functionally confirmed for Saccharomyces cerevisiae in the YEASTRACT database [37] including 25 bp upstream and downstream flanking regions. We then produced TRX-logo plots for 16 broader TF classifications (e.g. leucine zipper, copper fist, homeobox etc.) defined for S. cerevisiae by the JASPAR database. We used TRX-LOGOS in combination with a JASPAR search to compare TP53 tumor suppressor binding sites with different sample sizes and different experimental methods for detection of binding. We also used JASPAR and MEGA 6.0 [38] to produce a visual example of TRX logos plots of Forkhead box (FOX) DNA binding sites combined with a neighbor-joining tree representing the evolution of FOX genes in humans. We also used TRX-LOGOS to investigate a sequence-independent signature of coding region backbone dynamics by center-aligning all S. cerevisiae genes at the start codon.