Toolbox model of evolution of metabolic pathways on networks of arbitrary topology

In prokaryotic genomes the number of transcriptional regulators is known to quadratically scale with the total number of protein-coding genes. Toolbox model was recently proposed to explain this scaling for metabolic enzymes and their regulators. According to its rules the metabolic network of an organism evolves by horizontal transfer of pathways from other species. These pathways are part of a larger "universal" network formed by the union of all species-specific networks. It remained to be understood, however, how the topological properties of this universal network influence the scaling law of functional content of genomes. In this study we answer this question by first analyzing the scaling properties of the toolbox model on arbitrary tree-like universal networks. We mathematically prove that the critical branching topology, in which the average number of upstream neighbors of a node is equal to one, is both necessary and sufficient for the quadratic scaling. Conversely, the toolbox model on trees with exponentially expanding, supercritical topology is characterized by the linear scaling with logarithmic corrections. We further generalize our model to include reactions with multiple substrates/products as well as branched or cyclic metabolic pathways. Unlike the original model the new version employs evolutionary optimized pathways with the smallest number of reactions necessary to achieve their metabolic tasks. Numerical simulations of this most realistic model on the universal network from the KEGG database again produced approximately quadratic scaling. Our results demonstrate why, in spite of their "small-world" topology, real-life metabolic networks are characterized by a broad distribution of pathway lengths and sizes of metabolic regulons in regulatory networks.Comment: 34 pages, 9 figures, 2 table

A coarse-graining, ultrametric approach to resolve the phylogeny of prokaryotic strains with frequent homologous recombination

Abstract Background A frequent event in the evolution of prokaryotic genomes is homologous recombination, where a foreign DNA stretch replaces a genomic region similar in sequence. Recombination can affect the relative position of two genomes in a phylogenetic reconstruction in two different ways: (i) one genome can recombine with a DNA stretch that is similar to the other genome, thereby reducing their pairwise sequence divergence; (ii) one genome can recombine with a DNA stretch from an outgroup genome, increasing the pairwise divergence. While several recombination-aware phylogenetic algorithms exist, many of these cannot account for both types of recombination; some algorithms can, but do so inefficiently. Moreover, many of them reconstruct the ancestral recombination graph (ARG) to help infer the genome tree, and require that a substantial portion of each genome has not been affected by recombination, a sometimes unrealistic assumption. Methods Here, we propose a Coarse-Graining approach for Phylogenetic reconstruction (CGP), which is recombination-aware but forgoes ARG reconstruction. It accounts for the tendency of a higher effective recombination rate between genomes with a lower phylogenetic distance. It is applicable even if all genomic regions have experienced substantial amounts of recombination, and can be used on both nucleotide and amino acid sequences. CGP considers the local density of substitutions along pairwise genome alignments, fitting a model to the empirical distribution of substitution density to infer the pairwise coalescent time. Given all pairwise coalescent times, CGP reconstructs an ultrametric tree representing vertical inheritance. Results Based on simulations, we show that the proposed approach can reconstruct ultrametric trees with accurate topology, branch lengths, and root positioning. Applied to a set of E. coli strains, the reconstructed trees are most consistent with gene distributions when inferred from amino acid sequences, a data type that cannot be utilized by many alternative approaches. Conclusions The CGP algorithm is more accurate than alternative recombination-aware methods for ultrametric phylogenetic reconstructions

Study of the surface structures and patterns of the hydrophobic-polar model of protein

Proteins in nature exhibit special properties including high regularity in structure and high correlation between the motifs of the amino acid sequences and the corresponding substructures (secondary structures, active sites), which are absent in random sequences. Our study considers a model protein with twenty-seven residues that fold in a lattice space and attain different compact cubic conformations. Every residue of the protein sequence is decorated by two types of model amino acid that represent the twenty amino acids found in nature. A subset of protein sequences was defined for each cubic conformation such that every sequence in the set takes the conformation as its unique ground state. The substructures (the bonding between residues) and the patterns (decoration of amino acid on the residues) on the surfaces of the model protein were analyzed and the existence of preferential patterns on different substructures was observed, which is in agreement with our understanding of real proteins. Our finding of preferential patterns on the substructures demonstrates the strong correlation between protein structures and their sequences of amino acids, and provides a statistical justification for the use of various algorithms for protein structure and protein function prediction from its own sequence

Growth-mediated negative feedback shapes quantitative antibiotic response

Dose-response relationships are a general concept for quantitatively describing biological systems across multiple scales, from the molecular to the whole-cell level. A clinically relevant example is the bacterial growth response to antibiotics, which is routinely characterized by dose-response curves. The shape of the dose-response curve varies drastically between antibiotics and plays a key role in treatment, drug interactions, and resistance evolution. However, the mechanisms shaping the dose-response curve remain largely unclear. Here, we show in Escherichia coli that the distinctively shallow dose-response curve of the antibiotic trimethoprim is caused by a negative growth-mediated feedback loop: Trimethoprim slows growth, which in turn weakens the effect of this antibiotic. At the molecular level, this feedback is caused by the upregulation of the drug target dihydrofolate reductase (FolA/DHFR). We show that this upregulation is not a specific response to trimethoprim but follows a universal trend line that depends primarily on the growth rate, irrespective of its cause. Rewiring the feedback loop alters the dose-response curve in a predictable manner, which we corroborate using a mathematical model of cellular resource allocation and growth. Our results indicate that growth-mediated feedback loops may shape drug responses more generally and could be exploited to design evolutionary traps that enable selection against drug resistance