Michael Stich

The dawn of the RNA World: Toward functional complexity through ligation of random RNA oligomers

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.

Topological structure of the space of phenotypes: the case of RNA neutral networks.

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.

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

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.

Collective properties of evolving molecular quasispecies

BackgroundRNA molecules, through their dual appearance as sequence and structure, represent a suitable model to study evolutionary properties of quasispecies. The essential ingredient in this model is the differentiation between genotype (molecular sequences which are affected by mutation) and phenotype (molecular structure, affected by selection). This framework allows a quantitative analysis of organizational properties of quasispecies as they adapt to different environments, such as their robustness, the effect of the degeneration of the sequence space, or the adaptation under different mutation rates and the error threshold associated.ResultsWe describe and analyze the structural properties of molecular quasispecies adapting to different environments both during the transient time before adaptation takes place and in the asymptotic state, once optimization has occurred. We observe a minimum in the adaptation time at values of the mutation rate relatively far from the phenotypic error threshold. Through the definition of a consensus structure, it is shown that the quasispecies retains relevant structural information in a distributed fashion even above the error threshold. This structural robustness depends on the precise shape of the secondary structure used as target of selection. Experimental results available for natural RNA populations are in qualitative agreement with our observations.ConclusionAdaptation time of molecular quasispecies to a given environment is optimized at values of the mutation rate well below the phenotypic error threshold. The optimal value results from a trade-off between diversity generation and fixation of advantageous mutants. The critical value of the mutation rate is a function not only of the sequence length, but also of the specific properties of the environment, in this case the selection pressure and the shape of the secondary structure used as target phenotype. Certain functional motifs of RNA secondary structure that withstand high mutation rates (as the ubiquitous hairpin motif) might appear early in evolution and be actually frozen evolutionary accidents.

Phenotypic effect of mutations in evolving populations of RNA molecules

BackgroundThe secondary structure of folded RNA sequences is a good model to map phenotype onto genotype, as represented by the RNA sequence. Computational studies of the evolution of ensembles of RNA molecules towards target secondary structures yield valuable clues to the mechanisms behind adaptation of complex populations. The relationship between the space of sequences and structures, the organization of RNA ensembles at mutation-selection equilibrium, the time of adaptation as a function of the population parameters, the presence of collective effects in quasispecies, or the optimal mutation rates to promote adaptation all are issues that can be explored within this framework.ResultsWe investigate the effect of microscopic mutations on the phenotype of RNA molecules during their in silico evolution and adaptation. We calculate the distribution of the effects of mutations on fitness, the relative fractions of beneficial and deleterious mutations and the corresponding selection coefficients for populations evolving under different mutation rates. Three different situations are explored: the mutation-selection equilibrium (optimized population) in three different fitness landscapes, the dynamics during adaptation towards a goal structure (adapting population), and the behavior under periodic population bottlenecks (perturbed population).ConclusionsThe ratio between the number of beneficial and deleterious mutations experienced by a population of RNA sequences increases with the value of the mutation rate μ at which evolution proceeds. In contrast, the selective value of mutations remains almost constant, independent of μ, indicating that adaptation occurs through an increase in the amount of beneficial mutations, with little variations in the average effect they have on fitness. Statistical analyses of the distribution of fitness effects reveal that small effects, either beneficial or deleterious, are well described by a Pareto distribution. These results are robust under changes in the fitness landscape, remarkably when, in addition to selecting a target secondary structure, specific subsequences or low-energy folds are required. A population perturbed by bottlenecks behaves similarly to an adapting population, struggling to return to the optimized state. Whether it can survive in the long run or whether it goes extinct depends critically on the length of the time interval between bottlenecks.

Efficient HIV-1 inhibition by a 16 nt-long RNA aptamer designed by combining in vitro selection and in silico optimisation strategies

The human immunodeficiency virus type-1 (HIV-1) genome contains multiple, highly conserved structural RNA domains that play key roles in essential viral processes. Interference with the function of these RNA domains either by disrupting their structures or by blocking their interaction with viral or cellular factors may seriously compromise HIV-1 viability. RNA aptamers are amongst the most promising synthetic molecules able to interact with structural domains of viral genomes. However, aptamer shortening up to their minimal active domain is usually necessary for scaling up production, what requires very time-consuming, trial-and-error approaches. Here we report on the in vitro selection of 64 nt-long specific aptamers against the complete 5′-untranslated region of HIV-1 genome, which inhibit more than 75% of HIV-1 production in a human cell line. The analysis of the selected sequences and structures allowed for the identification of a highly conserved 16 nt-long stem-loop motif containing a common 8 nt-long apical loop. Based on this result, an in silico designed 16 nt-long RNA aptamer, termed RNApt16, was synthesized, with sequence 5′-CCCCGGCAAGGAGGGG-3′. The HIV-1 inhibition efficiency of such an aptamer was close to 85%, thus constituting the shortest RNA molecule so far described that efficiently interferes with HIV-1 replication.

Temporary mirror symmetry breaking and chiral excursions in open and closed systems

The reversible Frank model is capable of amplifying the initial small statistical deviations from the idealized racemic composition. This temporary amplification can be interpreted as a chiral excursion in a dynamic phase space. It is well known that if the system is open to matter and energy exchange, a permanently chiral state can be reached asymptotically, while the final state is necessarily racemic if the system is closed. In this work, we combine phase space analysis, stability analysis and numerical simulations to study the initial chiral excursions and determine how they depend on whether the system is open, semi-open or closed.

Variable Mutation Rates as an Adaptive Strategy in Replicator Populations

For evolving populations of replicators, there is much evidence that the effect of mutations on fitness depends on the degree of adaptation to the selective pressures at play. In optimized populations, most mutations have deleterious effects, such that low mutation rates are favoured. In contrast to this, in populations thriving in changing environments a larger fraction of mutations have beneficial effects, providing the diversity necessary to adapt to new conditions. What is more, non-adapted populations occasionally benefit from an increase in the mutation rate. Therefore, there is no optimal universal value of the mutation rate and species attempt to adjust it to their momentary adaptive needs. In this work we have used stationary populations of RNA molecules evolving in silico to investigate the relationship between the degree of adaptation of an optimized population and the value of the mutation rate promoting maximal adaptation in a short time to a new selective pressure. Our results show that this value can significantly differ from the optimal value at mutation-selection equilibrium, being strongly influenced by the structure of the population when the adaptive process begins. In the short-term, highly optimized populations containing little variability respond better to environmental changes upon an increase of the mutation rate, whereas populations with a lower degree of optimization but higher variability benefit from reducing the mutation rate to adapt rapidly. These findings show a good agreement with the behaviour exhibited by actual organisms that replicate their genomes under broadly different mutation rates.

Complex Pacemakers and Wave Sinks in Heterogeneous Oscillatory Chemical Systems

We investigate pattern formation in oscillatory reaction-diffusion systems where wave sources and sinks are created by a local shift of the oscillation frequency. General properties of resulting wave patterns in media with positive and negative dispersion are discussed. It is shown that phase slips in the wave patterns develop for strong frequency shifts, indicating the onset of desynchronization in the medium.

Chiral and chemical oscillations in a simple dimerization model.

We consider the APED model (activation-polymerization-epimerization-depolymerization) for describing the emergence of chiral solutions within a non-catalytic framework for chiral polymerization. The minimal APED model for dimerization can lead to the spontaneous appearance of chiral oscillations and we describe in detail the nature of these oscillations in the enantiomeric excess, which are the consequence of oscillations of the concentrations of the associated chemical species.