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A substantial fraction of the bacterial cytosol is occupied by catalysts and their substrates. While a higher volume density of catalysts and substrates might boost biochemical fluxes, the resulting molecular crowding can slow down diffusion, perturb the reactions’ Gibbs free energies, and reduce the catalytic efficiency of proteins. Due to these tradeoffs, dry mass density likely possesses an optimum that facilitates maximal cellular growth and that is interdependent on the cytosolic molecule size distribution. Here, we analyze the balanced growth of a model cell, accounting systematically for crowding effects on reaction kinetics. Its optimal cytosolic volume occupancy depends on the nutrient-dependent resource allocation into large ribosomal vs. small metabolic macromolecules, reflecting a tradeoff between the saturation of metabolic enzymes, favoring larger occupancies with higher encounter rates, and the inhibition of the ribosomes, favoring lower occupancies with unhindered diffusion of tRNAs. Our predictions across growth rates are quantitatively consistent with the experimentally observed reduction in volume occupancy on rich media compared to minimal media in E . coli . Strong deviations from optimal cytosolic occupancy only lead to minute reductions in growth rate, which are nevertheless evolutionarily relevant due to large bacterial population sizes. In sum, cytosolic density variation in bacterial cells appears to be consistent with an optimality principle of cellular efficiency.

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.

An approximation to the ∼4-Mbp basic genome shared by 32 strains of Escherichia coli representing six evolutionary groups has been derived and analyzed computationally. A multiple alignment of the 32 complete genome sequences was filtered to remove mobile elements and identify the most reliable ∼90% of the aligned length of each of the resulting 496 basic-genome pairs. Patterns of single base-pair mutations (SNPs) in aligned pairs distinguish clonally inherited regions from regions where either genome has acquired DNA fragments from diverged genomes by homologous recombination since their last common ancestor. Such recombinant transfer is pervasive across the basic genome, mostly between genomes in the same evolutionary group, and generates many unique mosaic patterns. The six least-diverged genome pairs have one or two recombinant transfers of length ∼40–115 kbp (and few if any other transfers), each containing one or more gene clusters known to confer strong selective advantage in some environments. Moderately diverged genome pairs (0.4–1% SNPs) show mosaic patterns of interspersed clonal and recombinant regions of varying lengths throughout the basic genome, whereas more highly diverged pairs within an evolutionary group or pairs between evolutionary groups having >1.3% SNPs have few clonal matches longer than a few kilobase pairs. Many recombinant transfers appear to incorporate fragments of the entering DNA produced by restriction systems of the recipient cell. A simple computational model can closely fit the data. Most recombinant transfers seem likely to be due to generalized transduction by coevolving populations of phages, which could efficiently distribute variability throughout bacterial genomes. A significant fraction of the length of Escherichia coli genomes comprises mobile elements integrated at various sites in a ∼4-Mbp basic genome shared by the species. We find that the entire basic genome is continually exchanged by homologous recombination with genome fragments acquired from other genomes in the population. Evolutionary groups appear to exchange DNA preferentially within the same group but also with other groups to different extents. Entering DNA is often fragmented by restriction systems of the recipient cell, with surviving pieces replacing homologous parts of the recipient chromosome. Coevolving populations of phages that package genome fragments and deliver them to cells that have appropriate receptors are likely mediators of most DNA transfers, distributing variability throughout the species.

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. Synopsis Growth‐rate dependent sensitivity of E. coli to the antibiotic trimethoprim leads to a negative feedback loop that explains the extreme shallowness of the dose‐response curve. This feedback loop is mediated by the regulation of the drug target dihydrofolate reductase (DHFR). Reducing the growth rate generally renders E. coli less sensitive to the antibiotic trimethoprim. This effect leads to a negative feedback loop, which causes the extreme shallowness of the trimethoprim dose‐response curve. Growth‐rate dependent regulation of the drug target dihydrofolate reductase (DHFR) mediates this feedback loop. A mathematical model of cellular resource allocation accurately captures these phenomena. Graphical Abstract Growth‐rate dependent sensitivity of E. coli to the antibiotic trimethoprim leads to a negative feedback loop that explains the extreme shallowness of the dose‐response curve. This feedback loop is mediated by the regulation of the drug target dihydrofolate reductase (DHFR).

Bacterial genomes and large-scale computer software projects both consist of a large number of components (genes or software packages) connected via a network of mutual dependencies. Components can be easily added or removed from individual systems, and their use frequencies vary over many orders of magnitude. We study this frequency distribution in genomes of ∼500 bacterial species and in over 2 million Linux computers and find that in both cases it is described by the same scale-free power-law distribution with an additional peak near the tail of the distribution corresponding to nearly universal components. We argue that the existence of a power law distribution of frequencies of components is a general property of any modular system with a multilayered dependency network. We demonstrate that the frequency of a component is positively correlated with its dependency degree given by the total number of upstream components whose operation directly or indirectly depends on the selected component. The observed frequency/dependency degree distributions are reproduced in a simple mathematically tractable model introduced and analyzed in this study.

It has been reported that the number of transcription factors encoded in prokaryotic genomes scales approximately quadratically with their total number of genes. We propose a conceptual explanation of this finding and illustrate it using a simple model in which metabolic and regulatory networks of prokaryotes are shaped by horizontal gene transfer of coregulated metabolic pathways. Adapting to a new environmental condition monitored by a new transcription factor (e.g., learning to use another nutrient) involves both acquiring new enzymes and reusing some of the enzymes already encoded in the genome. As the repertoire of enzymes of an organism (its toolbox) grows larger, it can reuse its enzyme tools more often and thus needs to get fewer new ones to master each new task. From this observation, it logically follows that the number of functional tasks and their regulators increases faster than linearly with the total number of genes encoding enzymes. Genomes can also shrink, e.g., because of a loss of a nutrient from the environment, followed by deletion of its regulator and all enzymes that become redundant. We propose several simple models of network evolution elaborating on this toolbox argument and reproducing the empirically observed quadratic scaling. The distribution of lengths of pathway branches in our model agrees with that of the real-life metabolic network of Escherichia coli. Thus, our model provides a qualitative explanation for broad distributions of regulon sizes in prokaryotes.

In prokaryotic genomes the number of transcriptional regulators is known to be proportional to the square of the total number of protein-coding genes. A toolbox model of evolution was recently proposed to explain this empirical 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 the toolbox model. Here we answer this question by first analyzing the scaling properties of the toolbox model on arbitrary tree-like universal networks. We prove that critical branching topology, in which the average number of upstream neighbors of a node is equal to one, is both necessary and sufficient for quadratic scaling. We further generalize the rules of the model to incorporate reactions with multiple substrates/products as well as branched and cyclic metabolic pathways. To achieve its metabolic tasks, the new model employs evolutionary optimized pathways with minimal number of reactions. Numerical simulations of this realistic model on the universal network of all reactions in the KEGG database produced approximately quadratic scaling between the number of regulated pathways and the size of the metabolic network. To quantify the geometrical structure of individual pathways, we investigated the relationship between their number of reactions, byproducts, intermediate, and feedback metabolites. Our results validate and explain the ubiquitous appearance of the quadratic scaling for a broad spectrum of topologies of underlying universal metabolic networks. They also demonstrate why, in spite of \"small-world\" topology, real-life metabolic networks are characterized by a broad distribution of pathway lengths and sizes of metabolic regulons in regulatory networks.

Even closely related prokaryotes often show an astounding diversity in their ability to grow in different nutritional environments. It has been hypothesized that complex metabolic adaptations—those requiring the independent acquisition of multiple new genes—can evolve via selectively neutral intermediates. However, it is unclear whether this neutral exploration of phenotype space occurs in nature, or what fraction of metabolic adaptations is indeed complex. Here, we reconstruct metabolic models for the ancestors of a phylogeny of 53 Escherichia coli strains, linking genotypes to phenotypes on a genome-wide, macroevolutionary scale. Based on the ancestral and extant metabolic models, we identify 3,323 phenotypic innovations in the history of the E. coli clade that arose through changes in accessory genome content. Of these innovations, 1,998 allow growth in previously inaccessible environments, while 1,325 increase biomass yield. Strikingly, every observed innovation arose through the horizontal acquisition of a single DNA segment less than 30 kb long. Although we found no evidence for the contribution of selectively neutral processes, 10.6% of metabolic innovations were facilitated by horizontal gene transfers on earlier phylogenetic branches, consistent with a stepwise adaptation to successive environments. Ninety-eight percent of metabolic phenotypes accessible to the combined E. coli pangenome can be bestowed on any individual strain by transferring a single DNA segment from one of the extant strains. These results demonstrate an amazing ability of the E. coli lineage to adapt to novel environments through single horizontal gene transfers (followed by regulatory adaptations), an ability likely mirrored in other clades of generalist bacteria.

While bacteria divide clonally, horizontal gene transfer followed by homologous recombination is now recognized as an important contributor to their evolution. However, the details of how the competition between clonality and recombination shapes genome diversity remains poorly understood. Using a computational model, we find two principal regimes in bacterial evolution and identify two composite parameters that dictate the evolutionary fate of bacterial species. In the divergent regime, characterized by either a low recombination frequency or strict barriers to recombination, cohesion due to recombination is not sufficient to overcome the mutational drift. As a consequence, the divergence between pairs of genomes in the population steadily increases in the course of their evolution. The species lacks genetic coherence with sexually isolated clonal subpopulations continuously formed and dissolved. In contrast, in the metastable regime, characterized by a high recombination frequency combined with low barriers to recombination, genomes continuously recombine with the rest of the population. The population remains genetically cohesive and temporally stable. Notably, the transition between these two regimes can be affected by relatively small changes in evolutionary parameters. Using the Multi Locus Sequence Typing (MLST) data, we classify a number of bacterial species to be either the divergent or the metastable type. Generalizations of our framework to include selection, ecologically structured populations, and horizontal gene transfer of nonhomologous regions are discussed as well.

Adaptation of bacteria occurs predominantly via horizontal gene transfer (HGT). While it is widely recognized that horizontal acquisitions frequently encompass multiple genes, it is unclear what the size distribution of successfully transferred DNA segments looks like and what evolutionary forces shape this distribution. Here, we identified 1790 gene family pairs that were consistently co-gained on the same branches across a phylogeny of 53 E. coli strains. We estimated a lower limit of their genomic distances at the time they were transferred to their host genomes; this distribution shows a sharp upper bound at 30 kb. The same gene-pairs can have larger distances (up to 70 kb) in other genomes. These more distant pairs likely represent recent acquisitions via transduction that involve the co-transfer of excised prophage genes, as they are almost always associated with intervening phage-associated genes. The observed distribution of genomic distances of co-transferred genes is much broader than expected from a model based on the co-transfer of genes within operons; instead, this distribution is highly consistent with the size distribution of supra-operonic clusters (SOCs), groups of co-occurring and co-functioning genes that extend beyond operons. Thus, we propose that SOCs form a basic unit of horizontal gene transfer.