Mapping hidden potential identity elements by computing the average discriminating power of individual tRNA positions

Abstract

The recently published discrete mathematical method, extended consensus partition (ECP), identifies nucleotide types at each position that are strictly absent from a given sequence set, while occur in other sets. These are defined as discriminating elements (DEs). In this study using the ECP approach, we mapped potential hidden identity elements that discriminate the 20 different tRNA identities. We filtered the tDNA data set for the obligatory presence of well-established tRNA features, and then separately for each identity set, the presence of already experimentally identified strictly present identity elements. The analysis was performed on the three kingdoms of life. We determined the number of DE, e.g. the number of sets discriminated by the given position, for each tRNA position of each tRNA identity set. Then, from the positional DE numbers obtained from the 380 pairwise comparisons of the 20 identity sets, we calculated the average excluding value (AEV) for each tRNA position. The AEV provides a measure on the overall discriminating power of each position. Using a statistical analysis, we show that positional AEVs correlate with the number of already identified identity elements. Positions having high AEV but lacking published identity elements predict hitherto undiscovered tRNA identity elements.

Figure 1.

Illustration of calculating the AEV using short artificial sequences. (A) Identifying DEs using an artificial set of short sequences belonging to three amino acid identity sets. Identities are labelled as 1aa, 2aa and 3aa and are highlighted as cyan, yellow and magenta, respectively. Each identity set contains four short, tetramer sequences. The calculated DE is either one base or a combination of bases and it is labelled by IUPAC codes of bases or base sets. Each step of the DE-generating algorithm is explained in Section 2. (B) The calculated DE for each identity pairs. Note that the DE-generating relationship is non-symmetrical, i.e. the 1aa vs. 2aa pair has a DE different from that of the 2aa vs. 1aa pair. (C) Positional summation of DE. Positional sum of the DE values (shown in the lowest row) provides the number of pairwise discriminations provided by the given position. The sums of the DE values are input data for calculating the AEVs). AEV is generated by dividing the positional sum of DE with the number of the identities (which in a real case is 20 while in this didactic case 3). Formalism and more detailed description are provided in Section 2. This figure can be viewed in colour online.

Figure 2.

Results of the Bacterial (A and B); Eukaryote (C and D) and Archaea (E and F) data set. ECP-diagrams (A, C, E). In each ECP diagram, each column belongs to a position. The upper column set refers to positional AEVs. The colour codes for statistical analysis. For each kingdom, the weighted average of AEV calculated for all positions from 0 to 73 as a single set and the corresponding standard deviation is as follows: Bacteria 6.45 ± 3.54; Eukaryote 6.31 ± 3.49 and Archaea 6.72 ± 3.69. Segments of columns are colour coded based on their deviation from the weighted average as follows: below −1.5 SD blue; between −1.5 and −0.5 SD cyan; between −0.5 SD and +0.5 SD green; between +0.5 and +1.5 yellow; above +1.5 SD red. White illustrates positions where the analysis is not applicable. These are the 3′ CCA end for each kingdom, and the unpopulated e1 position in the Achaea set. The lower column set illustrates the positional NPDs. The logic of the colour-coding scheme is the same as for the AEVs. For each kingdom, the weighted average of NPD calculated for all positions from 0 to 73 as a single set and the corresponding standard deviation is as follows: Bacteria 1.63 ± 3.63; Eukaryote 0.49 ± 1.7. Archaea have too few experimentally verified determinants (listed in Table 2) to perform this analysis. ECP-cloverleaf (B, D, F). The cloverleaf structure illustrates spatial relationships of many base-pairing residues. Each position is illustrated as a circle. The upper half of the circle corresponds to the AEV and its colour coding is the same as for the corresponding ECP diagram. The lower half of the circle corresponds to the number of published identity elements. The colour coding is similar to that in the corresponding ECP diagrams except for positions where the NPD is zero. These positions are indicated as gray. White illustrates positions where the analysis is not applicable. These are the 3′ CCA end for each kingdom, and the single unpopulated position e1 in the Achaea set. This figure can be viewed in colour online.

Figure 3.

Hitherto unidentified potential identity elements. Positions having high AEV but low NPDs could harbour hitherto unidentified identity elements. Grey or black highlights the most likely positions of such elements. For positions highlighted as black, we also propose the corresponding identity: bold corresponding to yeast, while italic to E. coli. Middle grey highlights ‘core region’ positions having high AEV and low NPD in all three kingdoms. Light grey highlights the highest AEV base pair in the Archaea kingdom.

Figure 4.

Comparison of tRNA^Asp/AspRS structures from E. coli and yeast. (A) Structure of the E. coli tRNA^Asp/AspRS complex; PDB: 1IL2. (B) Structure of the yeast tRNA^Asp/AspRS complex; PDB: 1ASY. Colour coding: AARS, ‘wheat’; tRNA, pale cyan; Lys58 (E. coli, panel A) and Lys88 (yeast, panel B) and the G30:C40 (E. coli, panel A) and G30:U40 (yeast, panel B) base pairs are green. Other bases illustrated as sticks are already published identity elements. See Section 3 for details. This figure can be viewed in colour online.