The origins of life on Earth required the establishment of self-replicating chemical systems capable of maintaining and evolving biological information. In an RNA world, single self-replicating RNAs would have faced the extreme challenge of possessing a mutation rate low enough both to sustain their own information and to compete successfully against molecular parasites with limited evolvability. Thus theoretical analyses suggest that networks of interacting molecules were more likely to develop and sustain life-like behaviour. Here we show that mixtures of RNA fragments that self-assemble into self-replicating ribozymes spontaneously form cooperative catalytic cycles and networks. We find that a specific three-membered network has highly cooperative growth dynamics. When such cooperative networks are competed directly against selfish autocatalytic cycles, the former grow faster, indicating an intrinsic ability of RNA populations to evolve greater complexity through cooperation. We can observe the evolvability of networks through in vitro selection. Our experiments highlight the advantages of cooperative behaviour even at the molecular stages of nascent life.

Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces assortative mixing to a desired degree. This degree is governed by one parameter p. Changing this parameter one can construct networks ranging from fully random (p = 0) to totally assortative (p = 1). We apply the algorithm to a Barabási-Albert scale-free network and show that the degree of assortativity is an important parameter governing geometrical and transport properties of networks. Thus, the diameter of the network and the clustering coefficient increase dramatically with the degree of assortativity. Moreover, the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different.

The origin of life is believed to have progressed through an RNA world, in which RNA acted as both genetic material and functional molecules. The structure of the evolutionary fitness landscape of RNA would determine natural selection for the first functional sequences. Fitness landscapes are the subject of much speculation, but their structure is essentially unknown. Here we describe a comprehensive map of a fitness landscape, exploring nearly all of sequence space, for short RNAs surviving selection in vitro. With the exception of a small evolutionary network, we find that fitness peaks are largely isolated from one another, highlighting the importance of historical contingency and indicating that natural selection would be constrained to local exploration in the RNA world.T he nucleotide sequence of an organism's genome determines its fitness in a given selective environment. All possible sequences of length L constitute a discrete sequence space containing 4 L points. Including fitness as another variable creates a "landscape" in sequence space, in which highly fit sequences occupy peaks (1, 2). Evolution can be thought of as a random walk on this landscape with a bias toward climbing peaks (3). Knowledge of the fitness landscape is a fundamental prerequisite for a quantitative understanding of evolution. Although several models of theoretical landscapes have been proposed (reviewed in refs. 4 and 5), there is a lack of empirical data. Landscapes based on RNA secondary structure have been explored computationally, but the relationship to function is unknown (6-10). Experimental efforts at determining a comprehensive fitness landscape are generally stymied by the astronomical size of sequence space, but synthesis of nearly every variant is feasible for relatively short sequences (i.e., RNAs with length L <30 nucleotides). Therefore, complete landscapes for short RNAs could be mapped in principle. Such landscapes are of particular interest for understanding evolution in the RNA world of early life (11)(12)(13)(14).Limited fitness landscapes localized around known functional sequences have been explored for proteins (15-17), viruses (18, 19), and functional nucleic acids, including ribozymes and ribosomal RNA (20-24). The local fitness landscape around a known RNA ligase ribozyme (L = 54) was mapped using highthroughput sequencing (25). However, random sampling of RNA and DNA sequence space can be done by in vitro selection, or SELEX, for de novo discovery of functional molecules (26)(27)(28)(29). Such studies generally take very sparse samples of sequence space, owing to their focus on obtaining functional, and therefore longer, sequences. Thorough sampling techniques have been used to explore all possible DNA targets for a known DNAbinding protein (30). Such studies illuminate the biology of extant organisms but do not address the initial evolution of macromolecular activity. The entirety of a macromolecular fitness landscape has not yet been explored. Therefore, fundamental questions about the shape of fitn...