A Sequence-to-Function Map for Ribozyme-catalyzed Metabolisms

Annual Review of Ecology, Evolution, and Systematics, 2007

Recent advances in molecular biology and computation have enabled evolutionary biologists to develop models that explicitly capture molecular structure. By including complex and realistic maps from genotypes to phenotypes, such models are yielding important new insights into evolutionary processes. In particular, computer simulations of evolving RNA structure have inspired a new conceptual framework for thinking about patterns of mutational connectivity and general theories about the nature of evolutionary transitions, the evolutionary ascent of nonoptimal phenotypes, and the origins of mutational robustness and modular structures. Here, we describe this class of RNA models and review the major conceptual contributions they have made to evolutionary biology.

Plos One, 2011

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 4 12 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.

Physical Review E, 1993

Journal of Theoretical Biology, 1999

We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space -sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than one). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with biological data. 1 The number of amino acid matches obtained by pairing two random sequences of the same length is given by the binomial distribution with p = 1/20 if one assumes that the 20 amino acids have the same probability to occur. For sequences of length N there will be on average pN identical amino acids, with a variance N p(1 − p). For random sequences, 95% of pairwise comparisons yield a sequence identity between 1% and 9%.

Medical Hypotheses, 1998

We are proposing an analytical matrix that models a logical process simulating the emergence of the bases of vital nucleotides. The construction and properties of the matricial model are outlined. The Graph 1 matrix specifies a unique distribution pattern of eight terms coded in binary triplet configurations and obeys specific dynamic laws. The whole set of binary triplet configurations is in dynamic equilibrium. For that reason, it is possible to carry out an analysis by entering by any one of the eight terms on the condition that the operating mode obeys all the internal laws of orientation and symmetries inherent in the matrix. The four chemical elements at the origin of life are distributed following their atomic structures in the order hydrogen (H), carbon (C), nitrogen (N) and oxygen (O) and organized according to the model. The dynamic properties of the model necessitate the running of three successive circular periodic studies per analysis in order to show the emergence of the four bases--adenine, guanine, cytosine and thymine--precisely in that order. The fifth base of the nucleotides--uracil--shows up twice but always in an intermediate position, thus in transition, as it is the case for messenger ribonucleic acid (mRNA). We show also that the model provides for a logical explanation of the law of complementarity of the bases and their chemical classification. It is proposed that subsequent developments of the dynamic laws of this matrix may lead to the study of the logical operations for the formation of protein sequences and of their analysis and to genetic bioprogramming in general. Thus, a strictly logical and dynamic approach to molecular genetics is possible.

Conventional population genetics is extended by support dynamics and genotypephenotype mapping in order to conceive a comprehensive dynamical model of evolution. Support dynamics describes migration of populations through genotype space. The relation between genotypes and phenotypes is a core issue of evolution. In the simplest conceivable case, in vitro evolution of RNA molecules, both phenomena can be incorporated into computer simulations. Application of replication-mutation kinetics to processes in the space of genotypes led to the notion of quasispecies which has been applied successfully to evolution of molecules and viruses. In molecular evolution mapping of genotypes into phenotypes is tantamount to sequence-structure relations of RNA molecules. Systematic studies were performed on secondary structures. They revealed a number of regularities which are reported. The number of sequences is much larger than the number of secondary structures and thus neutrality is a central issue of sequence-structure mappings. Evolution of populations of RNA molecules towards a predefined target structure were carried out and analyzed in molecular detail. The results derived for RNA molecules suggested to define a statistical relation of nearness between phenotypes which constitutes a kind of statistical topology. This probabilistic concept of neighborhood in sequence space can be generalized and appears to be of widespread validity in evolution.

Journal of Biomolecular Structure and Dynamics, 2008

The process of designing novel RNA sequences by inverse RNA folding, available in tools such as RNAinverse and InfoRNA, can be thought of as a reconstruction of RNAs from secondary structure. In this reconstruction problem, no physical measures are considered as additional constraints that are independent of structure, aside of the goal to reach the same secondary structure as the input using energy minimization methods. An extension of the reconstruction problem can be formulated since in many cases of natural RNAs, it is desired to analyze the sequence and structure of RNA molecules using various physical quantifiable measures. In prior works that used secondary structure predictions, it has been shown that natural RNAs differ significantly from random RNAs in some of these measures. Thus, we relax the problem of reconstructing RNAs from secondary structure into reconstructing RNAs from shapes, and in turn incorporate physical quantities as constraints. This allows for the design of novel RNA sequences by inverse folding while considering various physical quantities of interest such as thermodynamic stability, mutational robustness, and linguistic complexity. At the expense of altering the number of nucleotides in stems and loops, for example, physical measures can be taken into account. We use evolutionary computation for the new reconstruction problem and illustrate the procedure on various natural RNAs.

PLOS ONE, 2020

The origins of life on Earth have been the subject of inquiry since the early days of philosophical thought and are still intensively investigated by the researchers around the world. One of the theories explaining the life emergence, that gained the most attention recently is the RNA World hypothesis, which assumes that life on Earth was sparked by replicating RNA chains. Since wet lab analysis is time-consuming, many mathematical and computational approaches have been proposed that try to explain the origins of life. Recently proposed one, based on the work by Takeuchi and Hogeweg, addresses the problem of interplay between RNA replicases and RNA parasitic species, which is crucial for understanding the first steps of prebiotic evolution. In this paper, the aforementioned model has been extended and modified by introducing RNA sequence (structure) information and mutation rate close to real one. It allowed to observe the simple evolution mechanisms, which could have led to the more complicated systems and eventually, to the formation of the first cells. The main goal of this study was to determine the conditions that allowed the spontaneous emergence and evolution of the prebiotic replicases equipped with simple functional domains within a large population. Here we show that polymerase ribozymes could have appeared randomly and then quickly started to copy themselves in order for the system to reach equilibrium. It has been shown that evolutionary selection works even in the simplest systems.

Bulletin of Mathematical Biology, 1997

Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of any two di erent structures almost touch each other, and sequences folding into almost all \common" structures can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared with data obtained by folding large samples of RNA sequences. Di erences are explained in terms of RNA molecular structures.

Plos One, 2014

The error threshold of replication limits the selectively maintainable genome size against recurrent deleterious mutations for most fitness landscapes. In the context of RNA replication a distinction between the genotypic and the phenotypic error threshold has been made; where the latter concerns the maintenance of secondary structure rather than sequence. RNA secondary structure is treated as a proxy for function. The phenotypic error threshold allows higher per digit mutation rates than its genotypic counterpart, and is known to increase with the frequency of neutral mutations in sequence space. Here we show that the degree of neutrality, i.e. the frequency of nearest-neighbour (one-step) neutral mutants is a remarkably accurate proxy for the overall frequency of such mutants in an experimentally verifiable formula for the phenotypic error threshold; this we achieve by the full numerical solution for the concentration of all sequences in mutation-selection balance up to length 16. We reinforce our previous result that currently known ribozymes could be selectively maintained by the accuracy known from the best available polymerase ribozymes. Furthermore, we show that in silico stabilizing selection can increase the mutational robustness of ribozymes due to the fact that they were produced by artificial directional selection in the first place. Our finding offers a better understanding of the error threshold and provides further insight into the plausibility of an ancient RNA world.