Abstract
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.
Highlights
The cell synthesizes various types of ribonucleic acids (RNAs) that play distinctive and essential roles in living systems, including coding, decoding, catalytic, regulatory, and structural functions
To investigate on the relationship of minimum free energy (MFE) and length-normalized MFE with sequence size, we computed MFE by two of the most common software programs used to predict RNA secondary structure through the free energy minimization approach: Quikfold application, which is incorporated in the MFEs computed by Quickfold (Mfold) webserver for multiple molecule processing [13,14], and RNAfold, which is included in the ViennaRNA software package [15,16]
We found that the average length of each RNA family is not significantly correlated with its average MFE density (MFEden) (Pearson correlation coefficient (Rp) = 20.1531, N = 13, p = 0.6176), indicating that sequence length does not appear to be significantly constrained by folding free energy demands
Summary
The cell synthesizes various types of RNAs that play distinctive and essential roles in living systems, including coding (mRNA), decoding (tRNA), catalytic (ribozymes), regulatory (e.g., microRNA), and structural (e.g., rRNA) functions. It has been found that mRNAs and microRNA precursors, unlike other non-coding RNAs, have greater negative MFE than expected given their nucleotide numbers and compositions [2,3] This led to the observation that free energy can be employed as a criterion for the identification of functional RNAs. when the folding energies of different classes of RNA are compared, the dependence of MFE to sequence length can represent a disturbing element. AMFE is calculated by dividing MFE by the sequence length and multiplying the result by 100 to relate the index to a segment of 100 nucleotides Based on their supposed weak relationship with sequence length, normalized MFEs have been used in a number of published works to compare the free energy among different classes of RNAs. it has been reported that, after this adjustment, the MFEs of all nucleotide sequences are comparable [9]. Using the new normalized index, termed MFE density (MFEden), we report the analysis of a set of human coding and functional RNA families
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