Understanding the relationship between robustness and evolvability is key to understand how living things can withstand mutations, while producing ample variation that leads to evolutionary innovations. Mutational robustness and evolvability, a system's ability to produce heritable variation, harbour a paradoxical tension. On one hand, high robustness implies low production of heritable phenotypic variation. On the other hand, both experimental and computational analyses of neutral networks indicate that robustness enhances evolvability. I here resolve this tension using RNA genotypes and their secondary structure phenotypes as a study system. To resolve the tension, one must distinguish between robustness of a genotype and a phenotype. I confirm that genotype (sequence) robustness and evolvability share an antagonistic relationship. In stark contrast, phenotype (structure) robustness promotes structure evolvability. A consequence is that finite populations of sequences with a robust phenotype can access large amounts of phenotypic variation while spreading through a neutral network. Population-level processes and phenotypes rather than individual sequences are key to understand the relationship between robustness and evolvability. My observations may apply to other genetic systems where many connected genotypes produce the same phenotypes.

The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics e¡orts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and ¢nd that this network is a small-world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The smallworld architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.

Abstract. Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g., mutations) or nonheritable perturbations (e.g., the weather). Here we primarily focus on the first kind of robustness-genetic robustness-and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory; (2) understanding the evolution of genetic robustness; and (3) exploring the implications of genetic robustness for future evolution.

BackgroundPlate readers can measure the growth curves of many microbial strains in a high-throughput fashion. The hundreds of absorbance readings collected simultaneously for hundreds of samples create technical hurdles for data analysis.ResultsGrowthcurver summarizes the growth characteristics of microbial growth curve experiments conducted in a plate reader. The data are fitted to a standard form of the logistic equation, and the parameters have clear interpretations on population-level characteristics, like doubling time, carrying capacity, and growth rate.ConclusionsGrowthcurver is an easy-to-use R package available for installation from the Comprehensive R Archive Network (CRAN). The source code is available under the GNU General Public License and can be obtained from Github (Sprouffske K, Growthcurver sourcecode, 2016).

The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems.

I here estimate the energy cost of changes in gene expression for several thousand genes in the yeast Saccharomyces cerevisiae. A doubling of gene expression, as it occurs in a gene duplication event, is significantly selected against for all genes for which expression data is available. It carries a median selective disadvantage of s > 10(-5), several times greater than the selection coefficient s = 1.47 x 10(-7) below which genetic drift dominates a mutant's fate. When considered separately, increases in messenger RNA expression or protein expression by more than a factor 2 also have significant energy costs for most genes. This means that the evolution of transcription and translation rates is not an evolutionarily neutral process. They are under active selection opposing them. My estimates are based on genome-scale information of gene expression in the yeast S. cerevisiae as well as information on the energy cost of biosynthesizing amino acids and nucleotides.

In this paper, the structure and evolution of the protein interaction network of the yeast Saccharomyces cerevisiae is analyzed. The network is viewed as a graph whose nodes correspond to proteins. Two proteins are connected by an edge if they interact. The network resembles a random graph in that it consists of many small subnets (groups of proteins that interact with each other but do not interact with any other protein) and one large connected subnet comprising more than half of all interacting proteins. The number of interactions per protein appears to follow a power law distribution. Within approximately 200 Myr after a duplication, the products of duplicate genes become almost equally likely to (1) have common protein interaction partners and (2) be part of the same subnetwork as two proteins chosen at random from within the network. This indicates that the persistence of redundant interaction partners is the exception rather than the rule. After gene duplication, the likelihood that an interaction gets lost exceeds 2.2 x 10(-3)/Myr. New interactions are estimated to evolve at a rate that is approximately three orders of magnitude smaller. Every 300 Myr, as many as half of all interactions may be replaced by new interactions.

The history of life involves countless evolutionary innovations, a steady stream of ingenuity that has been flowing for more than 3 billion years. Very little is known about the principles of biological organization that allow such innovation. Here, we examine these principles for evolutionary innovation in gene expression patterns. To this end, we study a model for the transcriptional regulation networks that are at the heart of embryonic development. A genotype corresponds to a regulatory network of a given topology, and a phenotype corresponds to a steady-state gene expression pattern. Networks with the same phenotype form a connected graph in genotype space, where two networks are immediate neighbors if they differ by one regulatory interaction. We show that an evolutionary search on this graph can reach genotypes that are as different from each other as if they were chosen at random in genotype space, allowing evolutionary access to different kinds of innovation while staying close to a viable phenotype. Thus, although robustness to mutations may hinder innovation in the short term, we conclude that long-term innovation in gene expression patterns can only emerge in the presence of the robustness caused by connected genotype graphs.evolutionary novelty ͉ evolvability ͉ genotype-phenotype maps L ife's enormous creativity is evident from earth's millions of species with unique life styles, from dazzlingly different modes of development to macromolecules, like proteins and RNA, in which many different molecular functions (catalysis, support, and communication) have evolved. There are many wonderful case studies of individual evolutionary innovations, from the beaks of Darwin's finches (1) to the biochemical innovations represented by the highly refractory eye lens proteins derived from various enzymes (2, 3). These and all other evolutionary innovations are produced by a combination of mutation and natural selection, without apparent foresight and planning. However, mutation and selection do not automatically produce evolutionary innovation. For instance, man-made systems, such as computer hardware and software, seem to be outright incapable of innovation through mutation and selection. Those complex systems exhibit brittleness: Modifying one component often leads to disastrous failure. Diligent research in areas such as ''evolvable hardware'' (4-6) is needed to understand how complex functionalities can be rendered insensitive to individual component changes, thereby facilitating innovation. It is important to discover what renders living beings so capable of innovation, partly because the lessons learned could be applied to the design of complex systems with specific functions.Biologists increasingly realize that genetic systems need to be robust to both genetic and nongenetic change (7-14). Robustness means that a system keeps performing its function in the face of perturbations. For example, many proteins can continue to catalyze chemical reactions, regulate transcription, communicate signals, and serve ot...