Statistical mechanics for metabolic networks during steady-state growth

Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes within the allowed stoichiometry so as to maximize their growth. Here, we generalize this framework to single cell level using maximum entropy models from statistical physics. We define and compute, for the core metabolism of Escherichia coli, a joint distribution over all fluxes that yields the experimentally observed growth rate. This solution, containing FBA as a limiting case, provides a better match to the measured fluxes in the wild type and several mutants. We find that E. coli metabolism is close to, but not at, the optimality assumed by FBA. Moreover, our model makes a wide range of predictions: (i) on flux variability, its regulation, and flux correlations across individual cells; (ii) on the relative importance of stoichiometric constraints vs. growth rate optimization; (iii) on quantitative scaling relations for singe-cell growth rate distributions. We validate these scaling predictions using data from individual bacterial cells grown in a microfluidic device at different sub-inhibitory antibiotic concentrations. Under mild dynamical assumptions, fluctuation-response relations further predict the autocorrelation timescale in growth data and growth rate adaptation times following an environmental perturbation.Comment: 12 pages, 4 figure

Uncovering cis Regulatory Codes Using Synthetic Promoter Shuffling

Revealing the spectrum of combinatorial regulation of transcription at individual promoters is essential for understanding the complex structure of biological networks. However, the computations represented by the integration of various molecular signals at complex promoters are difficult to decipher in the absence of simple cis regulatory codes. Here we synthetically shuffle the regulatory architecture — operator sequences binding activators and repressors — of a canonical bacterial promoter. The resulting library of complex promoters allows for rapid exploration of promoter encoded logic regulation. Among all possible logic functions, NOR and ANDN promoter encoded logics predominate. A simple transcriptional cis regulatory code determines both logics, establishing a straightforward map between promoter structure and logic phenotype. The regulatory code is determined solely by the type of transcriptional regulation combinations: two repressors generate a NOR: NOT (a OR b) whereas a repressor and an activator generate an ANDN: a AND NOT b. Three-input versions of both logics, having an additional repressor as an input, are also present in the library. The resulting complex promoters cover a wide dynamic range of transcriptional strengths. Synthetic promoter shuffling represents a fast and efficient method for exploring the spectrum of complex regulatory functions that can be encoded by complex promoters. From an engineering point of view, synthetic promoter shuffling enables the experimental testing of the functional properties of complex promoters that cannot necessarily be inferred ab initio from the known properties of the individual genetic components. Synthetic promoter shuffling may provide a useful experimental tool for studying naturally occurring promoter shuffling