Evolution of complexity in RNA-like replicator systems

Abstract

Background: The evolution of complexity is among the most important questions in biology. The evolution of complexity is often observed as the increase of genetic information or that of the organizational complexity of a system. It is well recognized that the formation of biological organization--be it of molecules or ecosystems--is ultimately instructed by the genetic information, whereas it is also true that the genetic information is functional only in the context of the organization. Therefore, to obtain a more complete picture of the evolution of complexity, we must study the evolution of both information and organization.

Results: Here we investigate the evolution of complexity in a simulated RNA-like replicator system. The simplicity of the system allows us to explicitly model the genotype-phenotype-interaction mapping of individual replicators, whereby we avoid preconceiving the functionality of genotypes (information) or the ecological organization of replicators in the model. In particular, the model assumes that interactions among replicators--to replicate or to be replicated--depend on their secondary structures and base-pair matching. The results showed that a population of replicators, originally consisting of one genotype, evolves to form a complex ecosystem of up to four species. During this diversification, the species evolve through acquiring unique genotypes with distinct ecological functionality. The analysis of this diversification reveals that parasitic replicators, which have been thought to destabilize the replicator's diversity, actually promote the evolution of diversity through generating a novel "niche" for catalytic replicators. This also makes the current replicator system extremely stable upon the evolution of parasites. The results also show that the stability of the system crucially depends on the spatial pattern formation of replicators. Finally, the evolutionary dynamics is shown to significantly depend on the mutation rate.

Conclusion: The interdependence of information and organization can play an important role for the evolution of complexity. Namely, the emergent ecosystem supplies a context in which a novel phenotype gains functionality. Realizing such a phenotype, novel genotypes can evolve, which, in turn, results in the evolution of more complex ecological organization. Hence, the evolutionary feedback between information and organization, and thereby the evolution of complexity.

Figure 1

A schematic representation of the structure of our model. The arrows represent the direction of causal influence (see main text). The RNA secondary structures depicted under "Phenotype" are constructed from a genotype of the C-catalyst (the left one is from the catalytic strand; the right one is from the template strand) (see main text and Fig. 2 for the C-catalyst). The following can be skipped until Discussion: It is interesting to note that while the direction of causal influence is from information to organization, the direction of functional influence is from organization to information.

Figure 2

Phylogeny for various mutation rates. Phylogenies are constructed from 2000 genotypes selected from a simulation for various values of the mutation rate (μ). They were constructed through maximum likelihood method by using PHYML [43]. Due to great divergence among sequences and the procedure in genotype selection, the phylogeny depicts only the patterns in the population of sequences, but not necessarily the evolutionary relationship among them (see Methods for details). The leaves of the phylogenies were colored according to the sequence composition of a genotype's dangling-end. For catalytic genotypes, the 5'-dangling-end of the catalytic strand (which is to recognize templates) is chosen. If the dangling-end has more C's, the color becomes more cyan, whereas, if it contains more A's, then the color becomes more magenta. For non-catalytic genotypes, the 3'-dangling-end (which is to be recognized by catalysts) with the most extreme sequence composition among a pair of complementary sequences is chosen. If the dangling-end has more G's, the color becomes more red, whereas, if more U's, then more green. In this coloring scheme, the C-catalyst tends to appear cyan; the A-catalyst, magenta; the G-parasite, red; the U-parasite, green. However, it should be noted that the red leaves appearing in the clades of the C-catalyst are not the G-parasite (e.g., see (a)). Instead, these represent the mutants of the C-catalyst that have lost the catalytic structure, and they are members of the C-catalyst quasi-species (see also "Evolution of the ecological organization" in main text). This is also the case for the green leaves in the clades of the A-catalyst. Finally, for more precise color coding, insets indicate the colors as a function of nucleotide frequencies, where it reads 0.1 on scales (the frequency more than 0.5 are joined). The left (resp. right) inset is for catalytic (resp. non-catalytic) genotypes.

Figure 3

Sequence logos and typical secondary structures for each sequence classes. Genotypes were categorized into sequence classes through the phylogenies shown in Fig. 2 (see Methods for mode details). Sequence logos were produced by using WebLogo [45]. The typical secondary structures were produced as follows. For a set of aligned structures represented by dot-bracket notation, the frequencies of bound and unbound bases (i.e., '(', ')' and '.') are counted for each structure position. For each position, if the frequency of '(' or of ')' exceeds 20%, then the corresponding bracket is drawn; otherwise, '.' is drawn. The color of the brackets represents its frequency: the more frequent, the more red. Physical complexity C [40] was calculated from the sequence logos (see Discussion for details). For μ = 0.004, C_C = 41.3 for the C-catalyst; C_G = 22.5 for the G-parasite; C_A = 26.5 for the A-catalyst; C_U = 13.0 for the U-parasite; and C_∀ = 13.4 if all sequence classes are grouped together. For μ = 0.008, C_C = 41.5; C_G = 19.9; C_A = 20.9; and C_∀ = 15.7. For μ = 0.013, C_C = 37.9; C_G = 21.0; and C_∀ = 27.5. For μ = 0.015, C_C = 38.2 (C_C = C_∀ by definition).

Figure 4

A snapshot of a simulation. μ = 0.004. The snapshot depicts mutually invading wave patterns. Molecules are colored in the same way as in Fig. 2. In this color scheme, the wave fronts composed of the C-catalyst appears cyan; the wave backs composed of the G-parasite appear red; the wave fronts composed of the A-catalyst appear magenta; the wave backs composed of the U-parasite appear green. Empty space is white. The arrows represent the direction of the propagation of wave fronts. The black arrows are for the C-catalyst fronts, whereas the white arrows are for the A-catalyst fronts. A movie of this simulation is available as Additional file 1.

Figure 5

Dynamics of speciation. (a) Evolutionary dynamics of the G-parasite. The abscissa is time in simulation steps. There are three kinds of ordinate: (1) The ordinate labeled as distance (black) is the Hamming distance between the C-catalyst and non-catalytic molecules that have a stronger affinity to the C-catalyst than to the A-catalyst (for each of the chosen non-catalytic genotypes, the catalytic genotype that gives the strongest affinity to it is used to calculate the distance). The affinity is measured in the G score. The distinction between the C- and A-catalyst was done from the sequence composition of their 5-'dangling-end. Gray scale represents the frequency (occurrence) of phenotypes (the more frequent, the darker). The frequency was averaged over ca. 2000 time steps (100 bins). The plots are based on the top 1000 most abundant phenotypes chosen each from catalytic and non-catalytic replicators at every 500 time steps (this is also the case in (b); for the definition of phenotypes, see "Construction of phylogenies"). (2) The ordinate labeled as max(-G) (red) is the average of the theoretical maximal affinity of G-parasites (the sequences in the upper branch of the Hamming distance distribution are the G-parasites). (3) The ordinate labeled as best(-G) (blue) is the average of the maximal affinity G-parasites can gain from the C-catalyst. (b) Evolutionary dynamics of the A-catalyst. The abscissa is time. The ordinate is the frequency of C's minus that of A's in the 5'-dangling-end of catalytic molecules. Gray scale represents the number of occurrence of phenotypes. The frequency was averaged in the same way as in the Hamming distance in (a).

Figure 6

The number of evolved sequence classes (species) as a function of the mutation rate for five simulation series. For each series, simulations were initialized with a homogeneous population of different pre-evolved replicators. At some high mutation rate, the number of species drops to zero. This indicates that the system collapses because the mutation rate is above the error-threshold. Plots are not drawn for low mutation rates, because the number of species and their sequence patterns fluctuate in this region of the mutation rate. The red-colored plot is for the simulation series that are described in main text. For μ = 0.004, the system eventually evolved to the three species system (the C- and the A-catalyst, and the G-parasite) as explained in main text. The star depicted at μ = 0.004 designates the number of species at the metastable state (note that the phylogeny for μ = 0.004 in Fig. 2 is generated in this metastable state). The plot designated by (e) is for the simulation series that exhibited functional polymorphism without speciation (the details are explained in Additional file 2). In this plot, the dotted line denotes that the number of species can fluctuate between 2 and 3 (see also Additional file 2).