On the structural repertoire of pools of short, random RNA sequences

Abstract

A detailed knowledge of the mapping between sequence and structure spaces in populations of RNA molecules is essential to better understand their present-day functional properties, to envisage a plausible early evolution of RNA in a prebiotic chemical environment and to improve the design of in vitro evolution experiments, among others. Analysis of natural RNAs, as well as in vitro and computational studies, show that certain RNA structural motifs are much more abundant than others, pointing out a complex relation between sequence and structure. Within this framework, we have investigated computationally the structural properties of a large pool (${10}^8$ molecules) of single-stranded, 35 nt-long, random RNA sequences. The secondary structures obtained are ranked and classified into structure families. The number of structures in main families is analytically calculated and compared with the numerical results. This permits a quantification of the fraction of structure space covered by a large pool of sequences. We further show that the number of structural motifs and their frequency is highly unbalanced with respect to the nucleotide composition: simple structures such as stem-loops and hairpins arise from sequences depleted in G, while more complex structures require an enrichment of G. In general, we observe a strong correlation between subfamilies—characterized by a fixed number of paired nucleotides—and nucleotide composition. Our results are compared to the structural repertoire obtained in a second pool where isolated base pairs are prohibited.

Introduction

The distribution of RNA structural motifs within pools of random sequences is extremely heterogeneous, as theoretical studies and observation of natural secondary structures demonstrate (Fontana et al., 1993, Schuster et al., 1994). Knowledge of the relationship between sequence and structure space has a theoretical and practical relevance, among other reasons because structural diversity conditions the spectrum of different functionalities present in—and thus selectable from—a random pool of sequences (Lorsch and Szostak, 1994). The role played by parameters such as the sequence length (Sabeti et al., 1997) or the nucleotide composition (Knight et al., 2005, Kim et al., 2007) has been addressed as a way of modifying the functional diversity of random molecular ensembles. Two frequent goals of those studies are to maximize the structural diversity present in the pool and to enhance the presence of certain structures able to perform new functions (Wilson and Szostak, 1999, Gan et al., 2003).

Every RNA sequence can be mapped onto a secondary structure that corresponds to its minimum free energy folded state. The first mathematical studies on this correspondence readily revealed the huge degeneracy existing between the set of all sequences—genotype space, of magnitude $4^n$ if n denotes the length of the sequences—and the set of their possible secondary structures—a first approximation to the phenotype space (Stein and Waterman, 1978, Waterman, 1978). Calculations based on the compatibility between sequences and structures yield estimates of the average number of sequences that fold into a secondary structure. If isolated pairs are allowed in the secondary structure, there are, on average, about $1.402n^{3/2}1.{748}^n$ sequences of length n folding into each possible secondary structure (Stein and Waterman, 1978). However, this huge number is of little practical relevance in the light of empirical observations and computational results with random pools: the so-called common structures are typically many orders of magnitude more frequent than rare structures (Schuster et al., 1994, Grüner et al., 1996a, Joyce, 2004). While common structures are easily obtained, even in small populations, and do not depend strongly on the nucleotide composition, sequences folding into rare structures often need to be designed, for instance by means of inverse folding algorithms (Schuster et al., 1994, Hofacker et al., 1994).

A main concern of experimentalists seeking new ribozyme or aptamer activities is how to deviate the structural composition of the initial pools in the in vitro experiments from average expectations, thus enhancing for instance the presence of rare structures, or forcing the ensemble to be structurally biased towards specific common structures. One approach has been to maximize the length of the sequences in the starting pool in an attempt to increment the number of different motifs available (Bartel and Szostak, 1993). However, quantitative analyses have shown that long sequences offer little advantage to isolate simple motifs, and their effect might be even inhibitory (Sabeti et al., 1997). More recently, attention has focused on how the probability to obtain a fixed structural motif depends on the nucleotide composition (Knight et al., 2005, Kim et al., 2007). Interestingly, though increases in the size of the initial pool should imply an increase in the amount of different structures present, the dependence of structural diversity on population size has been rarely addressed. Furthermore, computational results indicate that the number of different major topological motifs present in the pool depends very weakly on its size (Gevertz et al., 2005). Modular evolution has been suggested as a plausible way to generate complex structures in a constructive way. This approach can be implemented either through the isolation of simple modules from random populations of short sequences, their directed modification and eventual combination (Sabeti et al., 1997), or as the selective evolution of populations towards specific modules, together with their ligation in suitable environments (Manrubia and Briones, 2007). The latter approach is of particular relevance at prebiotic stages, when the biochemical function had to emerge in an unsupervised way.

Though our knowledge of the genotype–phenotype map has expanded largely in the last three decades, our understanding still has to be improved in order to comprehend the multiple implications it has on evolution, on setting the conditions for further selection, and on the dynamic behavior of highly heterogeneous molecular populations. This is the main motivation to undertake the study here presented, where we fold ${10}^8$ random sequences of length $n=35\mathrm{nt}$ and classify the obtained structures into main structure families. We find correlations between the frequency of certain structure families and the nucleotide composition, and conclude that rare structures are to be found far from the average composition. Hence, they could be enhanced by tuning the fraction of each nucleotide in the sequences. One of our main results concerns the high fraction of sequences folding into topologically simple structure families: most abundant motifs resulting from random polymerization could constitute simple building blocks able to combine into more complex structures.