J. Phys. I France

**3**(1993) 43-59

## RNA secondary structure: a comparison of real and random sequences

**Paul G. Higgs**

Service de Physique Théorique de Saclay, F-91191 Gif-sur-Yvette Cedex, France

(Received 23 July 1992, accepted in final form 23 September 1992)

** Abstract **

A sample of transfer RNA molecules is compared to a sample of random sequences having the same length and same percentage
composition of the different bases. For each sequence all possible secondary structures are constructed and a distribution
of free energies for the states is obtained. It is found that the ground state free energies of tRNA molecules are significantly
lower than for random sequences, and that tRNA molecules have significantly fewer alternative secondary structures at energies
close to the ground state than do random sequences. A distance
*D* is defined which measures the average difference between molecular configurations and the ground state configuration. At
realistic temperatures of order 300 K this distance is much larger for random sequences than for tRNA sequences. Thus the
secondary structure of tRNA molecules at finite temperature is more stable than for random sequences. Sequences are considered
which differ by a small number of mutations from real tRNA sequences. On average mutations destabilize the secondary structure.
This suggests that a stable secondary structure is one of the factors selected for by natural selection. The thermodynamic
behaviour of RNA sequences is compared to models for random heteropolymers which have a low temperature frozen phase.

**PACS**

87.15 - 36.20

**©**

*Les Editions de Physique 1993*