Quantitative dissection of the simple repression input-output function

Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.
Proceedings of the National Academy of Sciences (Impact Factor: 9.67). 07/2011; 108(29):12173-8. DOI: 10.1073/pnas.1015616108
Source: PubMed


We present a quantitative case study of transcriptional regulation in which we carry out a systematic dialogue between theory and measurement for an important and ubiquitous regulatory motif in bacteria, namely, that of simple repression. This architecture is realized by a single repressor binding site overlapping the promoter. From the theory point of view, this motif is described by a single gene regulation function based upon only a few parameters that are convenient theoretically and accessible experimentally. The usual approach is turned on its side by using the mathematical description of these regulatory motifs as a predictive tool to determine the number of repressors in a collection of strains with a large variation in repressor copy number. The predictions and corresponding measurements are carried out over a large dynamic range in both expression fold change (spanning nearly four orders of magnitude) and repressor copy number (spanning about two orders of magnitude). The predictions are tested by measuring the resulting level of gene expression and are then validated by using quantitative immunoblots. The key outcomes of this study include a systematic quantitative analysis of the limits and validity of the input-output relation for simple repression, a precise determination of the in vivo binding energies for DNA-repressor interactions for several distinct repressor binding sites, and a repressor census for Lac repressor in Escherichia coli.

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    • "Thermodynamic models have been widely used as a quantitative framework to describe transcriptional regulation in bacteria [56‐58], including in the analysis of gene regulation involving DNA looping [6, 43‐ 48, 59]. We have previously used a particular class of such models to explore, from both a theoretical and an experimental perspective, how each parameter of these models is a " knob " modulating gene regulation in the case of simple repression [57]. More recently, we used these thermodynamic models to validate how the knobs of operator binding energies and number of repressors per cell tune repression in the more complicated case of repression by loop formation [48]. "
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    • "Here, we added a layer of complexity that was previously neglected by explicitly including the global expression machinery regulation. Our results demonstrate that single input repressor circuit performance is not simply dictated by its own input–output relation (Garcia and Phillips, 2011), but also by the activity of the global expression machinery that sets the promoter capacity. Thus, understanding the quantitative role of network motifs in gene regulation (Alon, 2007) might require to characterize their relationship with global regulation by the expression machinery. "
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    • "The phenotypic outcome of this situation is dictated only by the time of presence of LacI, which is determined by the equilibrium constant of the LacI-LacO interaction. This mode of lac repression has been described through different approaches (Ozbudak et al., 2004; Garcia and Phillips, 2011) similarly assuming graded fractional occupation times, i.e. which can take any intermediate real value between 0 and 100%. These graded mechanisms do not forbid a certain degree of heterogeneity in case of slow LacO-LacI interactions leading to transcriptional bursts which could be the rate-limiting molecular events for reaching a switching threshold (Choi et al., 2008). "
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    ABSTRACT: The quasi-equilibrium approximation is acceptable when molecular interactions are fast enough compared to circuit dynamics, but is no longer allowed when cellular activities are governed by rare events. A typical example is the lactose operon (lac), one of the most famous paradigms of transcription regulation, for which several theories still coexist to describe its behaviors. The lac system is generally analyzed by using equilibrium constants, contradicting single-event hypotheses long suggested by Novick and Weiner (1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci. USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322, 442-446). In the present report, a lac repressor (LacI)-mediated DNA immunoprecipitation experiment reveals that the natural LacI-lac DNA complex built in vivo is extremely tight and long-lived compared to the time scale of lac expression dynamics, which could functionally disconnect the abortive expression bursts and forbid using the standard modes of lac bistability. As alternatives, purely kinetic mechanisms are examined for their capacity to restrict induction through: (i) widely scattered derepression related to the arrival time variance of a preferentially backward asymmetric random walk and (ii) an induction threshold arising in a single window of derepression without recourse to nonlinear multimeric binding and Hill functions. Considering the complete disengagement of the lac repressor from the lac promoter as the probabilistic consequence of a transient stepwise mechanism, is sufficient to explain the sigmoidal lac responses as functions of time and of inducer concentration. This sigmoidal shape can be misleadingly interpreted as a phenomenon of equilibrium cooperativity classically used to explain bistability, but which has been reported to be weak in this system.
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