No abstract

The evolution and adaptation of molecular populations is constrained by the diversity accessible through mutational processes. RNA is a paradigmatic example of biopolymer where genotype (sequence) and phenotype (approximated by the secondary structure fold) are identified in a single molecule. The extreme redundancy of the genotype-phenotype map leads to large ensembles of RNA sequences that fold into the same secondary structure and can be connected through single-point mutations. These ensembles define neutral networks of phenotypes in sequence space. Here we analyze the topological properties of neutral networks formed by 12-nucleotides RNA sequences, obtained through the exhaustive folding of sequence space. A total of 412 sequences fragments into 645 subnetworks that correspond to 57 different secondary structures. The topological analysis reveals that each subnetwork is far from being random: it has a degree distribution with a well-defined average and a small dispersion, a high clustering coefficient, and an average shortest path between nodes close to its minimum possible value, i.e. the Hamming distance between sequences. RNA neutral networks are assortative due to the correlation in the composition of neighboring sequences, a feature that together with the symmetries inherent to the folding process explains the existence of communities. Several topological relationships can be analytically derived attending to structural restrictions and generic properties of the folding process. The average degree of these phenotypic networks grows logarithmically with their size, such that abundant phenotypes have the additional advantage of being more robust to mutations. This property prevents fragmentation of neutral networks and thus enhances the navigability of sequence space. In summary, RNA neutral networks show unique topological properties, unknown to other networks previously described.

A main unsolved problem in the RNA World scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers obtained by random polymerization on mineral surfaces. A number of computational studies have shown that the structural repertoire yielded by that process is dominated by topologically simple structures, notably hairpin-like ones. A fraction of these could display RNA ligase activity and catalyze the assembly of larger, eventually functional RNA molecules retaining their previous modular structure: molecular complexity increases but template replication is absent. This allows us to build up a stepwise model of ligation-based, modular evolution that could pave the way to the emergence of a ribozyme with RNA replicase activity, step at which information-driven Darwinian evolution would be triggered.

Well-exposed Jurassic Navajo Sandstone iron oxide concretions preserve important diagenetic records of groundwater flow and water-rock interactions. Field relationships, precipitation patterns, and geometries of the Navajo concretions provide the basis for input parameters in numerical computer simulations and laboratory chemical bench tests. Although field geometries are very difficult to replicate, numerical simulations and laboratory experiments examine end results such as nucleation and growth of iron oxide concretions, produced from known input parameters. Three numerical simulations show the development of periodic self-organized nucleation centers through Liesegang-type double-diffusion of iron and oxygen. This numerical model simulates a scenario where oxygen is provided by shallow fresh water and iron is sourced from deeper reduced formation water. Concretions form in the region where the two waters interact with each other. Model sensitivities show that advection of water is an important mechanism for supplying the iron, and that acidic conditions in the iron-charged water can cause iron to stay in solution longer to produce nucleation centers that are farther from the input source. Laboratory bench tests with reactions of FeSO 4 or Fe(NO 3 ) 3 with KOH show how the precipitation of hydrated iron sulfates or iron-hydroxides may form rinds around an initial, spherical source of iron (i.e. nucleation center). These rinds may show inward growth depending on the concentration of the iron source in relation to the surrounding fluid. A number of complex factors such as concentration and flux, time, and multiple events can create banded patterns during rind growth. Comparisons of the terrestrial examples with numerical and laboratory models have strong implications for understanding similar hematite concretions on Mars.

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.