Interplay of gene expression noise and ultrasensitive dynamics affects bacterial operon organization

Abstract

Bacterial chromosomes are organized into polycistronic cotranscribed operons, but the evolutionary pressures maintaining them are unclear. We hypothesized that operons alter gene expression noise characteristics, resulting in selection for or against maintaining operons depending on network architecture. Mathematical models for 6 functional classes of network modules showed that three classes exhibited decreased noise and 3 exhibited increased noise with same-operon cotranscription of interacting proteins. Noise reduction was often associated with a decreased chance of reaching an ultrasensitive threshold. Stochastic simulations of the lac operon demonstrated that the predicted effects of transcriptional coupling hold for a complex network module. We employed bioinformatic analysis to find overrepresentation of noise-minimizing operon organization compared with randomized controls. Among constitutively expressed physically interacting protein pairs, higher coupling frequencies appeared at lower expression levels, where noise effects are expected to be dominant. Our results thereby suggest an important role for gene expression noise, in many cases interacting with an ultrasensitive switch, in maintaining or selecting for operons in bacterial chromosomes.

Figure 1. Types of coupling in protein production affect correlations in their fluctuations.

A. Two proteins (A and B) can have coupled translation (1), coupled transcription with independent translation events (2), or uncoupled transcription (3). B, C. Scatter plots showing predicted single-cell distributions of copy numbers for proteins A and B with different coupling as indicated in models without (panel B) or with (panel C) transcriptional bursting. For simplicity, these models do not include extrinsic noise.

Figure 2. Noise levels in physiologically relevant variables depend on transcriptional coupling.

We computed coefficient of variation [CV] = σ/μ, where σ is the standard deviation and μ is the mean, for simplified modules representing modes of interaction between two proteins: A) catalysis of subsequent steps in a linear metabolic pathway, B) redundant catalysis of the same metabolic step, C) catalysis of metabolic steps following a branch point, D) redundant regulation of a downstream gene p encoding protein P, E) physical interactions resulting in heterodimer formation, and F) covalent modification of one protein by another. In metabolic modules, S, I and P represent substrate, intermediate, and product, respectively. Complete reaction diagrams and parameters are given in supplemental tables (S4, S5, S6). Error bars represent one standard deviation from bootstrap resampling. Results correspond to the single ribosome binding site model (translational coupling), but hold qualitatively for multiple ribosome binding sites as well.

Figure 3. An ultrasensitive response amplifies noise differences between cotranscribed and uncoupled linear metabolic pathway modules.

A. When copy numbers of enzymes A and B are matched, transient changes in production and consumption flux are matched, resulting in maintenance of a low concentration of metabolic intermediate. An increase in expression of A, unmatched by a change in expression of B, can cause the production flux of metabolic intermediate to exceed the saturation point of flux through enzyme B, resulting in accumulation of metabolic intermediate. B. Simulated timecourse of metabolic intermediate in cotranscribed and uncoupled configurations of the linear metabolic pathway model. C. Steady state response of metabolic intermediate to changes in the ratio of production flux to consumption flux (solid line), with stochastic simulation timecourses of intermediate in cotranscribed and uncoupled linear metabolic pathway module configurations plotted with respect to changing flux balance. Results represent the single ribosome binding site model (translational coupling), but are qualitatively the same for multiple ribosome binding sites as well.

Figure 4. Allolactose noise depends on transcriptional coupling in simulations of the E. coli lac operon.

A. Simplified reaction diagram of the model used. The complete reaction scheme and parameter values are given in Tables S7 and S8. Arrows depict flux arising from the mechanisms in the model. B. Predicted dynamics of allolactose (Alac) and permease (LacY) in excess inducer (extracellular lactose at 5,000 µM) are represented by 20 individual timecourses. C. Time correlation between permease and β-galactosidase (LacZ) for 100 timecourses. Error bars represent standard error of the mean. D. Coefficients of variation (CV = σ/μ, where σ is the standard deviation and μ is the mean) of metabolite allolactose at three extracellular lactose concentrations. E. CV of permease protein at three extracellular lactose concentrations. Bootstrapped mean and standard deviation of CVs (red bars in panels D and E) diverge from simulated CV when the distribution is highly skewed. Concentration 1.39 µM represents minimal induction of the lac operon; 83.0 µM represents mid-range induction; and 5,000 µM represents an excess of inducer with maximal lac operon induction. Error bars represent one standard deviation from bootstrap resampling.

Figure 5. Dependence on expression level for frequencies of gene pairs of physically interacting proteins sharing operons.

A dataset of single-cell protein and mRNA copy numbers in E. coli shows reduced frequency of coupling for abundant proteins (A) and mRNA (B). Error bars represent one standard deviation from bootstrapping the data 1,000 times. Significance levels were determined by a bootstrap test.