The Freezing of Random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.Comment: 4 pages, 8 figures. v2: presentation improve

Multiple Crossover Phenomena and Scale Hopping in Two Dimensions

We study the renormalization group for nearly marginal perturbations of a minimal conformal field theory M_p with p >> 1. To leading order in perturbation theory, we find a unique one-parameter family of ``hopping trajectories'' that is characterized by a staircase-like renormalization group flow of the C-function and the anomalous dimensions and that is related to a recently solved factorizable scattering theory. We argue that this system is described by interactions of the form t phi_{(1,3)} - t' \phi_{(3,1)} . As a function of the relevant parameter t, it undergoes a phase transition with new critical exponents simultaneously governed by all fixed points M_p, M_{p-1}, ..., M_3. Integrable lattice models represent different phases of the same integrable system that are distinguished by the sign of the irrelevant parameter t'.Comment: 20 pages, 5 figure

Adaptive evolution of transcription factor binding sites

The regulation of a gene depends on the binding of transcription factors to specific sites located in the regulatory region of the gene. The generation of these binding sites and of cooperativity between them are essential building blocks in the evolution of complex regulatory networks. We study a theoretical model for the sequence evolution of binding sites by point mutations. The approach is based on biophysical models for the binding of transcription factors to DNA. Hence we derive empirically grounded fitness landscapes, which enter a population genetics model including mutations, genetic drift, and selection. We show that the selection for factor binding generically leads to specific correlations between nucleotide frequencies at different positions of a binding site. We demonstrate the possibility of rapid adaptive evolution generating a new binding site for a given transcription factor by point mutations. The evolutionary time required is estimated in terms of the neutral (background) mutation rate, the selection coefficient, and the effective population size. The efficiency of binding site formation is seen to depend on two joint conditions: the binding site motif must be short enough and the promoter region must be long enough. These constraints on promoter architecture are indeed seen in eukaryotic systems. Furthermore, we analyse the adaptive evolution of genetic switches and of signal integration through binding cooperativity between different sites. Experimental tests of this picture involving the statistics of polymorphisms and phylogenies of sites are discussed.Comment: published versio

Universality and predictability in molecular quantitative genetics

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology

Rate and cost of adaptation in the Drosophila Genome

Recent studies have consistently inferred high rates of adaptive molecular evolution between Drosophila species. At the same time, the Drosophila genome evolves under different rates of recombination, which results in partial genetic linkage between alleles at neighboring genomic loci. Here we analyze how linkage correlations affect adaptive evolution. We develop a new inference method for adaptation that takes into account the effect on an allele at a focal site caused by neighboring deleterious alleles (background selection) and by neighboring adaptive substitutions (hitchhiking). Using complete genome sequence data and fine-scale recombination maps, we infer a highly heterogeneous scenario of adaptation in Drosophila. In high-recombining regions, about 50% of all amino acid substitutions are adaptive, together with about 20% of all substitutions in proximal intergenic regions. In low-recombining regions, only a small fraction of the amino acid substitutions are adaptive, while hitchhiking accounts for the majority of these changes. Hitchhiking of deleterious alleles generates a substantial collateral cost of adaptation, leading to a fitness decline of about 30/2N per gene and per million years in the lowest-recombining regions. Our results show how recombination shapes rate and efficacy of the adaptive dynamics in eukaryotic genomes