The Purine Bias of Coding Sequences is Determined by Physicochemical Constraints on Proteins

Abstract

For this report, we analyzed protein secondary structures in relation to the statistics of three nucleotide codon positions. The purpose of this investigation was to find which properties of the ribosome, tRNA or protein level, could explain the purine bias (Rrr) as it is observed in coding DNA. We found that the Rrr pattern is the consequence of a regularity (the codon structure) resulting from physicochemical constraints on proteins and thermodynamic constraints on ribosomal machinery. The physicochemical constraints on proteins mainly come from the hydropathy and molecular weight (MW) of secondary structures as well as the energy cost of amino acid synthesis. These constraints appear through a network of statistical correlations, such as (i) the cost of amino acid synthesis, which is in favor of a higher level of guanine in the first codon position, (ii) the constructive contribution of hydropathy alternation in proteins, (iii) the spatial organization of secondary structure in proteins according to solvent accessibility, (iv) the spatial organization of secondary structure according to amino acid hydropathy, (v) the statistical correlation of MW with protein secondary structures and their overall hydropathy, (vi) the statistical correlation of thymine in the second codon position with hydropathy and the energy cost of amino acid synthesis, and (vii) the statistical correlation of adenine in the second codon position with amino acid complexity and the MW of secondary protein structures. Amino acid physicochemical properties and functional constraints on proteins constitute a code that is translated into a purine bias within the coding DNA via tRNAs. In that sense, the Rrr pattern within coding DNA is the effect of information transfer on nucleotide composition from protein to DNA by selection according to the codon positions. Thus, coding DNA structure and ribosomal machinery co-evolved to minimize the energy cost of protein coding given the functional constraints on proteins.

Keywords: RNY; ancestral codon; energy cost; genomics; helix; purine bias; ribosome; secondary structure; sheet; translation; turn coil.

Figure 1

Relative frequency of secondary structures according to the protein size. The sample size for each structure is n = 10,731. Notes: A, aperiodic (median = 49%, average = 50%, σ = 14.2%, skewness = 1.0) (A). B, α-helix (median = 32%, average = 33%, σ = 18.4%, skewness = 0.5) (H). C, β-sheets (median = 19%, average = 24%, σ = 14.7%, skewness = 0.7) (E).

Figure 2

Relationships between the H and E proportions in protein sequences from PDB. The regression line is y = −1.33x + 60.07 with a correlation coefficient r = −0.75.

Figure 3

Average features of amino acids encoded by the G1, A1, C1, and T1 codons weighted by relative frequencies per structure. In A, codons in G1, A1, C1, and T1 account for 37, 27, 21, and 15%, respectively. In H, codons in G1, A1, C1, and T1 account for 36, 26, 22, and 16%, respectively. In E, codons in G1, A1, C1, and T1 account for 33, 29, 18, and 20%, respectively (see Tables S7–S9). Notes: A, MW. B, number of chemical bonds. C, energy cost for synthesis. D, hydropathy.

Figure 4

Average frequencies of amino acids with A1, G1, C1, and T1 codons (see Tables S6–S9) according to MW. Notes: A, dataset of non-redundant proteins from PDB (r = −0.584, P < 0.05). B, A structures in PDB (r = −0.626, P < 0.01). C, H structures in PDB (r = −0.236, P = 0.321). D, E structures in PDB (r = −0.272, P = 0.251).

Figure 5

Relationships between purines in the three codon positions according to periodic and aperiodic structures from PDB. The sample size for each structure is n = 10,731. Notes: Panel A, r_A = 0.476**, A: y = 0.98x + 7.66, r_H = 0.308**, H: y = 0.95x + 9.17, r_E = 0.111**, and E: y = 0.42x + 11.98. Panel B, r_A = 0.549**, A: y = 2.16x − 39.05, r_H = 0.426**, H: y = 2.38x − 41.33, r_E = 0.400**, and E: y = 1.84x − 35.92. Panel C, r_A = 0.318**, A: y = 0.53x − 1.18, r_H = −0.017, H: y is not defined because P > 0.05, r_E = −0.001, and E: y = −0.07x + 16.56. Panel D, r_A = 0.255**, A: y = 3.01x − 86.68, r_H = 0.193**, H: y = 3.85x − 107.85, and r_E = 0.187**, E: y = 2.97x − 72.90 (**statistical significance at P < 0.001).

Figure 6

Relationships between A, G, and T in the second codon position according to periodic and aperiodic structures. The sample size for each structure is n = 10,731. Notes: Panel A, r_A = −0.141**, A: y = −6.61x + 167.03, r_H = −0.320**, H: y = −2.28x + 105.66, r_E = 0.506**, and E: y = −0.80x + 59.65. Panel B, r_A = −0.530**, A: y = −1.60x + 68.33, r_H = −0.422**, H: y = −2.31x + 65.95, and r_E = −0.189**, E: y = −2.91x + 65.62 (**statistical significance at P < 0.001).

Figure 7

Relationships between purines in the three codon positions according to periodic and aperiodic structures. The sample size for each structure is n = 10,731. Notes: Panel A, r_A = 0.289**, A: y = 0.71x + 18.48, r_H = −0.016, H: y is not defined because P > 0.05, and r_E = −0.257**, E: y = −0.81x + 89.15. Panel B, r_A = 0.164**, A: y = 1.85x − 73.87, r_H = 0.135**, H: y = 1.79x − 59.92, and r_E = 0.108**, E: y = 1.14x − 27.24 (**statistical significance at P < 0.001).

Figure 8

Relationships between GC2 and GC3 according to periodic and aperiodic structures. The sample size for each structure is n = 10,731. Notes: r_E = 0.223**, E: y = 9.79x − 250.91, r_H = 0.376**, H: y = 5.49x − 131.49, and r_A = 0.459**, A: y = 5.21x − 181.28 (**statistical significance at P < 0.001).

Figure 9

Scatter plot of G3 versus C3. The sample size for each structure is n = 10,731. Notes: Red is for H (r = 0.397**, y = 0.67x + 12.01), green is for E (r = 0.325**, y = 0.43x + 12.42), and black is for A (r = 0.550**, y = 0.49x + 9.88) (**statistical significance at P < 0.001).

Figure 10

Relationships between hydropathy, ASA, average MW, and the energy cost of amino acid synthesis in protein secondary structures. The sample size for each structure is n = 10,731. Notes: Panel A, ASA, r_A = −0.755**, A: y = −0.031x + 0.463, r_H = −0.821**, H: y = −0.03x + 0.446, and r_E = 0.840**, E: y = −0.029x + 0.435. Panel B, MW, r_A = −0.454**, A: y = −29.24x + 103.00, r_H = −0.575**, H: y = −18.89x + 129.52, and r_E = −0.523**, E: y = −16.78x + 144.62. Panel C, energy cost of amino acid synthesis, r = 0.605, y = 4x + 21 (**statistical significance at P < 0.001).

Figure 11

Relationships between the number of heteroatoms (NOS), hydropathy, and ASA. The sample size for each structure is n = 10,731. Notes: Panel A, r_A = −0.821**, A: y = −0.28x + 0.80, r_H = −0.862**, H: y = −0.28x + 0.88, and r_E = 0.893**, E: y = −0.29x + 0.90. Panel B, r_A = 0.406**, A: y = 20.4x − 8.94, r_H = 0.598**, H: y = 14.70x − 5.68, and r_E = 0.665**, E: y = 12.50x − 4.16 (dashed line of panel B: y = 3.0x − 1.25) (**statistical significance at P < 0.001).

Figure 12

Relationships between MW, the energy cost of amino acid synthesis, A2, and G1. The sample size for each structure is n = 10,731. Notes: Panel A, amino acid synthesis, r_A = 0.486**, A: y = 4.59x + 44.14, r_H = 0.527**, H: y = 3.35x + 63.28, and r_E = 0.602**, E: y = 2.52x + 71.80. Panel B, A2, r_A = 0.619**, A: y = 0.47x + 109.98, r_H = 0.560**, H: y = 0.43x + 117.53, and r_E = 0.564**, E: y = 0.50x + 119.62. Panel C, G1, r_A = −0.590**, A: y = −0.48x + 143.97, r_H = −0.526**, H: y = −0.41x + 147.21, r_E = −0.586**, E: y = −0.44x + 146.39 (**statistical significance at <0.001).

Figure 13

Relationships between T2, ASA, hydropathy, and the energy cost of amino acid synthesis. The sample size for each structure is n = 10,731. Notes: Panel A, r = −0.903**, A: y = −345.45x + 190.0. Panel B, r_A = 0.597**, r_H = 0.670**, and r_E = 0.863**, E: y = 17.27x + 30.97. Panel C, r = 0.605, y = 4.23x − 55 (**statistical significance at P < 0.001).