The minimum free energy (MFE) of ribonucleic acids (RNAs) increases at an apparent linear rate with sequence length. Simple indices, obtained by dividing the MFE by the number of nucleotides, have been used for a direct comparison of the folding stability of RNAs of various sizes. Although this normalization procedure has been used in several studies, the relationship between normalized MFE and length has not yet been investigated in detail. Here, we demonstrate that the variation of MFE with sequence length is not linear and is significantly biased by the mathematical formula used for the normalization procedure. For this reason, the normalized MFEs strongly decrease as hyperbolic functions of length and produce unreliable results when applied for the comparison of sequences with different sizes. We also propose a simple modification of the normalization formula that corrects the bias enabling the use of the normalized MFE for RNAs longer than 40 nt. Using the new corrected normalized index, we analyzed the folding free energies of different human RNA families showing that most of them present an average MFE density more negative than expected for a typical genomic sequence. Furthermore, we found that a well-defined and restricted range of MFE density characterizes each RNA family, suggesting the use of our corrected normalized index to improve RNA prediction algorithms. Finally, in coding and functional human RNAs the MFE density appears scarcely correlated with sequence length, consistent with a negligible role of thermodynamic stability demands in determining RNA size.

The solution structure of the complex between 4', 6-diamidino-2-phenylindole (DAPI) and DNA oligomer [d(GCGATTCGC)]2, containing a central T.T mismatch, has been characterized by combined use of proton one- and two-dimensional NMR spectroscopy, molecular mechanics and molecular dynamics computations including relaxation matrix refinement. The results show that the DAPI molecule binds in the minor groove of the central region 5'-ATT-3' of the DNA oligomer, which predominantly adopts a duplex structure with a global right-handed B-like conformation. In the final models of the complex, the DAPI molecule is located nearly isohelical with its NH indole proton oriented towards the DNA helix axis and forming a bifurcated hydrogen bond with the carbonyl O2 groups of a mismatched T5 and the T6 residue of the opposite strand. Mismatched thymines adopt a wobble base pair conformation and are found stacked between the flanking base pairs, inducing only minor local conformational changes in global duplex structure. In addition, no other binding mechanisms were observed, showing that minor groove binding of DAPI to the mismatch-containing site is favoured in comparison with any other previously reported interaction with G.C sequences.

Codons that code for the same amino acid are often used with unequal frequencies. This phenomenon is termed codon bias. Here, we report a computational analysis of codon bias in yeast using experimental and theoretical genome-wide data. We show that the most used codons in highly expressed genes can be predicted by mRNA structural data and that the codon choice at each synonymous site within an mRNA is not random with respect to the local secondary structure. Because we also found that the folding stability of intron sequences is strongly correlated with codon bias and mRNA level, our results suggest that codon bias is linked to mRNA folding structure through a mechanism that, at least partially, operates before pre-mRNA splicing. Consistent with this, we report evidence supporting the adaptation of the tRNA pool to the codon profile of the most expressed genes rather than vice versa. We show that the correlation of codon usage with the gene expression level also includes the stop codons that are normally not decoded by aminoacyl-tRNAs. The results reported here are consistent with a role for transcriptional forces in driving codon usage bias via a mechanism that improves gene expression by optimizing mRNA folding structures.