A Coarse-Grained Biophysical Model of E. coli and Its Application to Perturbation of the rRNA Operon Copy Number

We propose a biophysical model of Escherichia coli that predicts growth rate and an effective cellular composition from an effective, coarse-grained representation of its genome. We assume that E. coli is in a state of balanced exponential steadystate growth, growing in a temporally and spatially constant environment, rich in resources. We apply this model to a series of past measurements, where the growth rate and rRNA-to-protein ratio have been measured for seven E. coli strains with an rRNA operon copy number ranging from one to seven (the wild-type copy number). These experiments show that growth rate markedly decreases for strains with fewer than six copies. Using the model, we were able to reproduce these measurements. We show that the model that best fits these data suggests that the volume fraction of macromolecules inside E. coli is not fixed when the rRNA operon copy number is varied. Moreover, the model predicts that increasing the copy number beyond seven results in a cytoplasm densely packed with ribosomes and proteins. Assuming that under such overcrowded conditions prolonged diffusion times tend to weaken binding affinities, the model predicts that growth rate will not increase substantially beyond the wild-type growth rate, as indicated by other experiments. Our model therefore suggests that changing the rRNA operon copy number of wild-type E. coli cells growing in a constant rich environment does not substantially increase their growth rate. Other observations regarding strains with an altered rRNA operon copy number, such as nucleoid compaction and the rRNA operon feedback response, appear to be qualitatively consistent with this model. In addition, we discuss possible design principles suggested by the model and propose further experiments to test its validity

Technical Report on "Limitations and trade-offs in gene expression due to competition for shared cellular resources"

This is a technical report accompanying the paper entitled “Limitations and trade-offs in gene expression due to competition for shared cellular resources”.This work was supported by AFOSR grant FA9550-12-1-0129 and NIGMS grant P50 GM098792

Limitations and trade-offs in gene expression due to competition for shared cellular resources

Gene circuits share transcriptional and translational resources in the cell. The fact that these common resources are available only in limited amounts leads to unexpected couplings in protein expressions. As a result, our predictive ability of describing the behavior of gene circuits is limited. In this paper, we consider the simultaneous expression of proteins and describe the coupling among protein concentrations due to competition for RNA polymerase and ribosomes. In particular, we identify the limitations and trade-offs in gene expression by characterizing the attainable combinations of protein concentrations. We further present two application examples of our results: we show that even in the absence of regulatory linkages, genes can seemingly behave as repressors, and surprisingly, as activators to each other, purely due to the limited availability of shared cellular resources.United States. Air Force Office of Scientific Research (Grant FA9550-12-1-0129)National Institute of General Medical Sciences (U.S.) (Grant P50 GM098792

Systematic NMR Analysis of Stable Isotope Labeled Metabolite Mixtures in Plant and Animal Systems: Coarse Grained Views of Metabolic Pathways

BACKGROUND: Metabolic phenotyping has become an important 'bird's-eye-view' technology which can be applied to higher organisms, such as model plant and animal systems in the post-genomics and proteomics era. Although genotyping technology has expanded greatly over the past decade, metabolic phenotyping has languished due to the difficulty of 'top-down' chemical analyses. Here, we describe a systematic NMR methodology for stable isotope-labeling and analysis of metabolite mixtures in plant and animal systems. METHODOLOGY/PRINCIPAL FINDINGS: The analysis method includes a stable isotope labeling technique for use in living organisms; a systematic method for simultaneously identifying a large number of metabolites by using a newly developed HSQC-based metabolite chemical shift database combined with heteronuclear multidimensional NMR spectroscopy; Principal Components Analysis; and a visualization method using a coarse-grained overview of the metabolic system. The database contains more than 1000 (1)H and (13)C chemical shifts corresponding to 142 metabolites measured under identical physicochemical conditions. Using the stable isotope labeling technique in Arabidopsis T87 cultured cells and Bombyx mori, we systematically detected >450 HSQC peaks in each (13)C-HSQC spectrum derived from model plant, Arabidopsis T87 cultured cells and the invertebrate animal model Bombyx mori. Furthermore, for the first time, efficient (13)C labeling has allowed reliable signal assignment using analytical separation techniques such as 3D HCCH-COSY spectra in higher organism extracts. CONCLUSIONS/SIGNIFICANCE: Overall physiological changes could be detected and categorized in relation to a critical developmental phase change in B. mori by coarse-grained representations in which the organization of metabolic pathways related to a specific developmental phase was visualized on the basis of constituent changes of 56 identified metabolites. Based on the observed intensities of (13)C atoms of given metabolites on development-dependent changes in the 56 identified (13)C-HSQC signals, we have determined the changes in metabolic networks that are associated with energy and nitrogen metabolism

Genome-Scale Reconstruction of Escherichia coli's Transcriptional and Translational Machinery: A Knowledge Base, Its Mathematical Formulation, and Its Functional Characterization

Metabolic network reconstructions represent valuable scaffolds for ‘-omics’ data integration and are used to computationally interrogate network properties. However, they do not explicitly account for the synthesis of macromolecules (i.e., proteins and RNA). Here, we present the first genome-scale, fine-grained reconstruction of Escherichia coli's transcriptional and translational machinery, which produces 423 functional gene products in a sequence-specific manner and accounts for all necessary chemical transformations. Legacy data from over 500 publications and three databases were reviewed, and many pathways were considered, including stable RNA maturation and modification, protein complex formation, and iron–sulfur cluster biogenesis. This reconstruction represents the most comprehensive knowledge base for these important cellular functions in E. coli and is unique in its scope. Furthermore, it was converted into a mathematical model and used to: (1) quantitatively integrate gene expression data as reaction constraints and (2) compute functional network states, which were compared to reported experimental data. For example, the model predicted accurately the ribosome production, without any parameterization. Also, in silico rRNA operon deletion suggested that a high RNA polymerase density on the remaining rRNA operons is needed to reproduce the reported experimental ribosome numbers. Moreover, functional protein modules were determined, and many were found to contain gene products from multiple subsystems, highlighting the functional interaction of these proteins. This genome-scale reconstruction of E. coli's transcriptional and translational machinery presents a milestone in systems biology because it will enable quantitative integration of ‘-omics’ datasets and thus the study of the mechanistic principles underlying the genotype–phenotype relationship

The Systemic Imprint of Growth and Its Uses in Ecological (Meta)Genomics

Microbial minimal generation times range from a few minutes to several weeks. They are evolutionarily determined by variables such as environment stability, nutrient availability, and community diversity. Selection for fast growth adaptively imprints genomes, resulting in gene amplification, adapted chromosomal organization, and biased codon usage. We found that these growth-related traits in 214 species of bacteria and archaea are highly correlated, suggesting they all result from growth optimization. While modeling their association with maximal growth rates in view of synthetic biology applications, we observed that codon usage biases are better correlates of growth rates than any other trait, including rRNA copy number. Systematic deviations to our model reveal two distinct evolutionary processes. First, genome organization shows more evolutionary inertia than growth rates. This results in over-representation of growth-related traits in fast degrading genomes. Second, selection for these traits depends on optimal growth temperature: for similar generation times purifying selection is stronger in psychrophiles, intermediate in mesophiles, and lower in thermophiles. Using this information, we created a predictor of maximal growth rate adapted to small genome fragments. We applied it to three metagenomic environmental samples to show that a transiently rich environment, as the human gut, selects for fast-growers, that a toxic environment, as the acid mine biofilm, selects for low growth rates, whereas a diverse environment, like the soil, shows all ranges of growth rates. We also demonstrate that microbial colonizers of babies gut grow faster than stabilized human adults gut communities. In conclusion, we show that one can predict maximal growth rates from sequence data alone, and we propose that such information can be used to facilitate the manipulation of generation times. Our predictor allows inferring growth rates in the vast majority of uncultivable prokaryotes and paves the way to the understanding of community dynamics from metagenomic data

Fundamental Principles in Bacterial Physiology - History, Recent progress, and the Future with Focus on Cell Size Control: A Review

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and major contributors to the field have often brought together tools and ways of thinking from multiple disciplines. This article presents a comprehensive overview of major ideas and approaches developed since the early 20th century for anyone who is interested in the fundamental problems in bacterial physiology. This article is divided into two parts. In the first part (Sections 1 to 3), we review the first `golden era' of bacterial physiology from the 1940s to early 1970s and provide a complete list of major references from that period. In the second part (Sections 4 to 7), we explain how the pioneering work from the first golden era has influenced various rediscoveries of general quantitative principles and significant further development in modern bacterial physiology. Specifically, Section 4 presents the history and current progress of the `adder' principle of cell size homeostasis. Section 5 discusses the implications of coarse-graining the cellular protein composition, and how the coarse-grained proteome `sectors' re-balance under different growth conditions. Section 6 focuses on physiological invariants, and explains how they are the key to understanding the coordination between growth and the cell cycle underlying cell size control in steady-state growth. Section 7 overviews how the temporal organization of all the internal processes enables balanced growth. In the final Section 8, we conclude by discussing the remaining challenges for the future in the field.Comment: Published in Reports on Progress in Physics. (https://doi.org/10.1088/1361-6633/aaa628) 96 pages, 48 figures, 7 boxes, 715 reference