New experimental results on bacterial growth inspire a novel top-down approach to study cell metabolism, combining mass balance and proteomic constraints to extend and complement Flux Balance Analysis. We introduce here Constrained Allocation Flux Balance Analysis, CAFBA, in which the biosynthetic costs associated to growth are accounted for in an effective way through a single additional genome-wide constraint. Its roots lie in the experimentally observed pattern of proteome allocation for metabolic functions, allowing to bridge regulation and metabolism in a transparent way under the principle of growth-rate maximization. We provide a simple method to solve CAFBA efficiently and propose an “ensemble averaging” procedure to account for unknown protein costs. Applying this approach to modeling E. coli metabolism, we find that, as the growth rate increases, CAFBA solutions cross over from respiratory, growth-yield maximizing states (preferred at slow growth) to fermentative states with carbon overflow (preferred at fast growth). In addition, CAFBA allows for quantitatively accurate predictions on the rate of acetate excretion and growth yield based on only 3 parameters determined by empirical growth laws. The intracellular protein levels of exponentially growing bacteria are known to vary strongly with growth conditions, as described by quantitative “growth laws”. This work introduces a computational genome-scale framework (Constrained Allocation Flux Balance Analysis, CAFBA) which incorporates growth laws into canonical Flux Balance Analysis. Upon introducing 3 parameters based on established growth laws for E. coli, CAFBA accurately reproduces empirical results on the growth-rate dependent rate of carbon overflow and growth yield, and generates testable predictions about cellular energetic strategies and protein expression levels. CAFBA therefore provides a simple, quantitative approach to balancing the trade-off between growth and its associated biosynthetic costs at genome-scale, without the burden of tuning many inaccessible parameters.

A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of 'entropy', and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data.

We derive the global phase diagram of a self-gravitating $N$-body system enclosed in a finite three-dimensional spherical volume $V$ as a function of total energy and angular momentum, employing a microcanonical mean-field approach. At low angular momenta (i.e., for slowly rotating systems) the known collapse from a gas cloud to a single dense cluster is recovered. At high angular momenta, instead, rotational symmetry can be spontaneously broken and rotationally asymmetric structures (double clusters) appear.

Living cells react to changes in growth conditions by re-shaping their proteome. This accounts for different stress-response strategies, both specific (i.e., aimed at increasing the availability of stress-mitigating proteins) and systemic (such as large-scale changes in the use of metabolic pathways aimed at a more efficient exploitation of resources). Proteome re-allocation can, however, imply significant biosynthetic costs. Whether and how such costs impact the growth performance are largely open problems. Focusing on carbon-limited E. coli growth, we integrate genome-scale modeling and proteomic data to address these questions at quantitative level. After deriving a simple formula linking growth rate, carbon intake, and biosynthetic costs, we show that optimal growth results from the tradeoff between yield maximization and protein burden minimization. Empirical data confirm that E. coli growth is indeed close to Pareto-optimal over a broad range of growth rates. Moreover, we establish that, while most of the intaken carbon is diverted into biomass precursors, the efficiency of ATP synthesis is the key driver of the yield-cost tradeoff. These findings provide a quantitative perspective on carbon overflow, the origin of growth laws and the multidimensional optimality of E. coli metabolism.