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Open Access Research article

Neutral network sizes of biological RNA molecules can be computed and are not atypically small

Thomas Jörg12, Olivier C Martin23 and Andreas Wagner4567*

  • * Corresponding author: Andreas Wagner

  • † Equal contributors

Author Affiliations

1 Inria Saclay – Ile-de-France, INRIA, Parc Orsay Université 4, rue Jacques Monod 91893 ORSAY Cedex, France

2 Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, 91405 Orsay Cedex, France

3 UMR0320/UMR8120 Génétique Végétale, Université Paris-Sud, F-91190 Gif-sur-Yvette, France

4 Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland

5 The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

6 Swiss Institute of Bioinformatics, Quartier Sorge, Batiment Genopode, 1015 Lausanne, Switzerland

7 University of New Mexico, Department of Biology, 167 Castetter Hall, Albuquerque, MSC03 2020, USA

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BMC Bioinformatics 2008, 9:464  doi:10.1186/1471-2105-9-464

Published: 30 October 2008



Neutral networks or sets consist of all genotypes with a given phenotype. The size and structure of these sets has a strong influence on a biological system's robustness to mutations, and on its evolvability, the ability to produce phenotypic variation; in the few studied cases of molecular phenotypes, the larger this set, the greater both robustness and evolvability of phenotypes. Unfortunately, any one neutral set contains generally only a tiny fraction of genotype space. Thus, current methods cannot measure neutral set sizes accurately, except in the smallest genotype spaces.


Here we introduce a generalized Monte Carlo approach that can measure neutral set sizes in larger spaces. We apply our method to the genotype-to-phenotype mapping of RNA molecules, and show that it can reliably measure neutral set sizes for molecules up to 100 bases. We also study neutral set sizes of RNA structures in a publicly available database of functional, noncoding RNAs up to a length of 50 bases. We find that these neutral sets are larger than the neutral sets in 99.99% of random phenotypes. Software to estimate neutral network sizes is available at webcite.


The biological RNA structures we examined are more abundant than random structures. This indicates that their robustness and their ability to produce new phenotypic variants may also be high.