Determinants of bistability in induction of the Escherichia coli lac operon

Positive feedback exists and drives the glucose-mediated repression in Escherichia coli

The expression of the lac operon of E. coli is subject to positive feedback during growth in the presence of gratuitous inducers, but its existence in the presence of lactose remains controversial. The key question in this debate is: Do the lactose enzymes, Lac permease and β-galactosidase, promote accumulation of allolactose? If so, positive feedback exists since allolactose does stimulate synthesis of the lactose enzymes. Here, we addressed the above question by developing methods for determining the intracellular allolactose concentration as well as the kinetics of enzyme induction and dilution. We show that, during lac induction in the presence of lactose, the intracellular allolactose concentration increases with the lactose enzyme level, which implies that lactose enzymes promote allolactose accumulation, and positive feedback exists. We also show that, during lac repression in the presence of lactose + glucose, the intracellular allolactose concentration decreases with the lactose enzyme levels, which suggests that, under these conditions, the positive feedback loop turns in the reverse direction. The induction and dilution rates derived from the transient data show that the positive feedback loop is reversed due to a radical shift of the steady-state induction level. This is formally identical to the mechanism driving catabolite repression in the presence of TMG + glucose.

Physiological Modeling and Simulation-Validation, Credibility, and Application

In this review, we discuss the science of model validation as it applies to physiological modeling. There is widespread disagreement and ambiguity about what constitutes model validity. In areas in which models affect real-world decision-making, including within the clinic, in regulatory science, or in the design and engineering of novel therapeutics, this question is of critical importance. Without an answer, it impairs the usefulness of models and casts a shadow over model credibility in all domains. To address this question, we examine the use of nonmathematical models in physiological research, in medical practice, and in engineering to see how models in other domains are used and accepted. We reflect on historic physiological models and how they have been presented to the scientific community. Finally, we look at various validation frameworks that have been proposed as potential solutions during the past decade.

Optimization of the 503 antigen induction strategy of Leishmania infantum chagasi expressed in Escherichia coli M15

Leishmaniosis is a complex of diseases that can be fatal, if not given proper attention. Despite its relevance in the public health system, there is no vaccine capable of preventing the disease in humans so far and its treatment is expensive and aggressive to human health. The present study aims to optimize the induction parameters of the 503 Leishmania i. chagasi antigen expressed in recombinant Escherichia coli M15. The induction at different cell densities was evaluated in order to analyze the influence of the induction time on the yield of the protein of interest. In this segment, lactose and isopropyl-β-d-thiogalactopyranoside (IPTG) were used as inducer molecules, using various concentrations: 0.1 g/L, 1.0 g/L, and 10 g/L for lactose and 20 μM, 100 μM, 500 μM, and 1000 μM for IPTG. The results presented that the concentration of IPTG that obtained the higher antigen levels was that of 100 μM (0.087 g/L), a 10-fold lower concentration than was being previously used in this type of system and for lactose, it was 1 g/L (0.016 g/L). Thus, the induction with 100 μM allowed obtaining the antigen with a concentration 5.6 times higher than the lactose induction maximum concentration.

Prediction of Escherichia coli expression performance in microtiter plates by analyzing only the temporal development of scattered light during culture

Background

Escherichia coli is often used for recombinant protein production. The expression of recombinant proteins negatively affects the microbial growth, thus, a balance between protein expression and biomass formation is preferable to reach high product- and space-time-yield. Already in screening experiments, suboptimal conditions causing too weak or too strong induction must be avoided. High-throughput screening devices such as the BioLector are often applied for screening experiments. The BioLector allows optical online monitoring of each well in a continuously orbitally shaken microtiter plate via scattered light and fluorescence measurements. This technique enables a fast identification of promising clones. However, to determine the expression performance of non-fluorescent products elaborated offline analysis is often required.

Methods

A mathematical method is developed to distinguish between cultures, which are insufficiently, optimally or too strongly induced. Therefore, just the temporal development of the scattered light intensity signal is investigated. It is found that discrimination between the different intensities of induction is possible via principal component analysis. By fitting an extended sigmoidal function to the trajectory of the scattered light over time, two characteristic parameters are found. These are used in an empirical model to predict the expression performance.

Results

The method was established for a wide range of culture conditions based on 625 E. coli cultures. Three E. coli host strains (Tuner(DE3), BL21(DE3), and BL21-Gold(DE3)) expressing either flavin-mononucleotide-based fluorescent protein (FbFP) or Cellulase celA2 were investigated. Cultures were conducted in two different types of microtiter plates (48- and 96-wells), in two online measurement devices at four temperatures (28 °C, 30 °C, 34 °C, and 37 °C). More than 95% of the predicted values are in agreement with the offline measured expression performances with a satisfying accuracy of ±30%.

Conclusions

The properties of cultures studied can be represented by only two characteristic parameters (slope at and time of the inflection point) received from fitting an extended sigmoidal function to the respective scattered light trajectory. Based on these two characteristic parameters, predictions of the standardized expression performance are possible and for a first screen elaborated offline analysis can be avoided. To the best of our knowledge, this is the first work presenting a method for the general prediction of expression performance of E. coli based solely on the temporal development of scattered light signals.

Electronic supplementary material

The online version of this article (doi:10.1186/s13036-017-0064-5) contains supplementary material, which is available to authorized users.

Bistability and Nonmonotonic Induction of the lac Operon in the Natural Lactose Uptake System

The Escherichia coli lac operon is regulated by a positive feedback loop whose potential to generate an all-or-none response in single cells has been a paradigm for bistable gene expression. However, so far bistable lac induction has only been observed using gratuitous inducers, raising the question about the biological relevance of bistable lac induction in the natural setting with lactose as the inducer. In fact, the existing experimental evidence points to a graded rather than an all-or-none response in the natural lactose uptake system. In contrast, predictions based on computational models of the lactose uptake pathway remain controversial. Although some argue in favor of bistability, others argue against it. Here, we reinvestigate lac operon expression in single cells using a combined experimental/modeling approach. To this end, we parameterize a well-supported mathematical model using transient measurements of LacZ activity upon induction with different amounts of lactose. The resulting model predicts a monostable induction curve for the wild-type system, but indicates that overexpression of the LacI repressor would drive the system into the bistable regime. Both predictions were confirmed experimentally supporting the view that the wild-type lac induction circuit generates a graded response rather than bistability. More interestingly, we find that the lac induction curve exhibits a pronounced maximum at intermediate lactose concentrations. Supported by our data, a model-based analysis suggests that the nonmonotonic response results from saturation of the LacI repressor at low inducer concentrations and dilution of Lac enzymes due to an increased growth rate beyond the saturation point. We speculate that the observed maximum in the lac expression level helps to save cellular resources by limiting Lac enzyme expression at high inducer concentrations.

Evolutionary Phase Transitions in Random Environments

We present analytical results for long-term growth rates of structured populations in randomly fluctuating environments, which we apply to predict how cellular response networks evolve. We show that networks which respond rapidly to a stimulus will evolve phenotypic memory exclusively under random (i.e., nonperiodic) environments. We identify the evolutionary phase diagram for simple response networks, which we show can exhibit both continuous and discontinuous transitions. Our approach enables exact analysis of diverse evolutionary systems, from viral epidemics to emergence of drug resistance.

Light-induced gene expression with photocaged IPTG for induction profiling in a high-throughput screening system

BACKGROUND

Inducible expression systems are frequently used for the production of heterologous proteins. Achieving maximum product concentrations requires induction profiling, namely the optimization of induction time and inducer concentration. However, the respective experiments can be very laborious and time-consuming. In this work, a new approach for induction profiling is presented where induction in a microtiter plate based cultivation system (BioLector) is achieved by light using photocaged isopropyl β-D-1-thiogalactopyranoside (cIPTG).

RESULTS

A flavin mononucleotide-based fluorescent reporter protein (FbFP) was expressed using a T7-RNA-polymerase dependent E. coli expression system which required IPTG as inducer. High power UV-A irradiation was directed into a microtiter plate by light-emitting diodes placed above each well of a 48-well plate. Upon UV irradiation, IPTG is released (uncaged) and induces product formation. IPTG uncaging, formation of the fluorescent reporter protein and biomass growth were monitored simultaneously in up to four 48-well microtiter plates in parallel with an in-house constructed BioLector screening system. The amount of released IPTG can be gradually and individually controlled for each well by duration of UV-A exposure, irradiance and concentration of photocaged IPTG added at the start of the cultivation. A comparison of experiments with either optical or conventional IPTG induction shows that product formation and growth are equivalent. Detailed induction profiles revealed that for the strain and conditions used maximum product formation is reached for very early induction times and with just 6-8 s of UV-A irradiation or 60-80 µM IPTG.

CONCLUSIONS

Optical induction and online monitoring were successfully combined in a high-throughput screening system and the effect of optical induction with photocaged IPTG was shown to be equivalent to conventional induction with IPTG. In contrast to conventional induction, optical induction is less costly to parallelize, easy to automate, non-invasive and without risk of contamination. Therefore, light-induced gene expression with photocaged IPTG is a highly advantageous method for the efficient optimization of heterologous protein production and has the potential to replace conventional induction with IPTG.

Determining the bistability parameter ranges of artificially induced lac operon using the root locus method

This paper employs the root locus method to conduct a detailed investigation of the parameter regions that ensure bistability in a well-studied gene regulatory network namely, lac operon of Escherichia coli (E. coli). In contrast to previous works, the parametric bistability conditions observed in this study constitute a complete set of necessary and sufficient conditions. These conditions were derived by applying the root locus method to the polynomial equilibrium equation of the lac operon model to determine the parameter values yielding the multiple real roots necessary for bistability. The lac operon model used was defined as an ordinary differential equation system in a state equation form with a rational right hand side, and it was compatible with the Hill and Michaelis-Menten approaches of enzyme kinetics used to describe biochemical reactions that govern lactose metabolism. The developed root locus method can be used to study the steady-state behavior of any type of convergent biological system model based on mass action kinetics. This method provides a solution to the problem of analyzing gene regulatory networks under parameter uncertainties because the root locus method considers the model parameters as variable, rather than fixed. The obtained bistability ranges for the lac operon model parameters have the potential to elucidate the appearance of bistability for E. coli cells in in vivo experiments, and they could also be used to design robust hysteretic switches in synthetic biology.

Memory and fitness optimization of bacteria under fluctuating environments

Bacteria prudently regulate their metabolic phenotypes by sensing the availability of specific nutrients, expressing the required genes for their metabolism, and repressing them after specific metabolites are depleted. It is unclear, however, how genetic networks maintain and transmit phenotypic states between generations under rapidly fluctuating environments. By subjecting bacteria to fluctuating carbon sources (glucose and lactose) using microfluidics, we discover two types of non-genetic memory in Escherichia coli and analyze their benefits. First, phenotypic memory conferred by transmission of stable intracellular lac proteins dramatically reduces lag phases under cyclical fluctuations with intermediate timescales (1–10 generations). Second, response memory, a hysteretic behavior in which gene expression persists after removal of its external inducer, enhances adaptation when environments fluctuate over short timescales (<1 generation). Using a mathematical model we analyze the benefits of memory across environmental fluctuation timescales. We show that memory mechanisms provide an important class of survival strategies in biology that improve long-term fitness under fluctuating environments. These results can be used to understand how organisms adapt to fluctuating levels of nutrients, antibiotics, and other environmental stresses.

Bacterial adaptation to new environments typically involves reorganization of gene expression that temporarily decreases growth rates. By exposing cells to fluctuating conditions using an innovative microfluidic device, we discover that E. coli cells can remember past environments, which accelerates their physiological adaptation. Using a modeling approach combined with experiments, we demonstrate the adaptive advantage of memory for organisms that 1) transmit long-lived intracellular proteins between generations or 2) respond to fluctuations in a history-dependent manner. Our work describes one of the simplest examples of adaptive memory in a living organism and provides significant insights into the behavior of genetic networks under diverse fluctuations, including nutrients, antibiotics, and other environmental stresses.

Single-cell dynamics reveals sustained growth during diauxic shifts

Stochasticity in gene regulation has been characterized extensively, but how it affects cellular growth and fitness is less clear. We study the growth of E. coli cells as they shift from glucose to lactose metabolism, which is characterized by an obligatory growth arrest in bulk experiments that is termed the lag phase. Here, we follow the growth dynamics of individual cells at minute-resolution using a single-cell assay in a microfluidic device during this shift, while also monitoring lac expression. Mirroring the bulk results, the majority of cells displays a growth arrest upon glucose exhaustion, and resume when triggered by stochastic lac expression events. However, a significant fraction of cells maintains a high rate of elongation and displays no detectable growth lag during the shift. This ability to suppress the growth lag should provide important selective advantages when nutrients are scarce. Trajectories of individual cells display a highly non-linear relation between lac expression and growth, with only a fraction of fully induced levels being sufficient for achieving near maximal growth. A stochastic molecular model together with measured dependencies between nutrient concentration, lac expression level, and growth accurately reproduces the observed switching distributions. The results show that a growth arrest is not obligatory in the classic diauxic shift, and underscore that regulatory stochasticity ought to be considered in terms of its impact on growth and survival.

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

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.

In some species, most notably bacteria, chromosomal genes are arranged into clusters called operons. In operons, the process of transcription is physically coupled: a single pass of the RNA polymerase enzyme reading that region of the chromosome simultaneously produces messenger RNA encoding multiple proteins. So far, we do not have a satisfying explanation for what evolutionary forces have maintained operons on bacterial chromosomes. We hypothesized that different types of interactions between operon-coded proteins affect how strongly operons are selected for between two genes. The proposed mechanism for this effect is that operons correlate gene expression noise, changing how it manifests in the post-translational network depending on the type of protein interaction. Mathematical models demonstrate that operons reduce noise for some types of interactions but not others. We found that operon-dependent noise reduction has an underlying dependence on surprisingly high sensitivity of the network to the ratio of proteins from each gene. Databases of genetic information show that E. coli has operons more frequently than random if operons reduce noise for the type of interaction various gene pairs have, but not otherwise. Our study thus provides an example of how the architecture of post-translational networks affects bacterial evolution.

lac operon induction in Escherichia coli: Systematic comparison of IPTG and TMG induction and influence of the transacetylase LacA

Most commonly used expression systems in bacteria are based on the Escherichia coli lac promoter. Furthermore, lac operon elements are used today in systems and synthetic biology. In the majority of the cases the gratuitous inducers IPTG or TMG are used. Here we report a systematic comparison of lac promoter induction by TMG and IPTG which focuses on the aspects inducer uptake, population heterogeneity and a potential influence of the transacetylase, LacA. We provide induction curves in E. coli LJ110 and in isogenic lacY and lacA mutant strains and we show that both inducers are substrates of the lactose permease at low inducer concentrations but can also enter cells independently of lactose permease if present at higher concentrations. Using a gfp reporter strain we compared TMG and IPTG induction at single cell level and showed that bimodal induction with IPTG occurred at approximately ten-fold lower concentrations than with TMG. Furthermore, we observed that lac operon induction is influenced by the transacetylase, LacA. By comparing two Plac-gfp reporter strains with and without a lacA deletion we could show that in the lacA(+) strain the fluorescence level decreased after few hours while the fluorescence further increased in the lacA(-) strain. The results indicate that through the activity of LacA the IPTG concentration can be reduced below an inducing threshold concentration-an influence that should be considered if low inducer amounts are used.

Deterministic and stochastic population-level simulations of an artificial lac operon genetic network

BACKGROUND

The lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Previously, we have investigated the effect of stochasticity in an artificial lac operon network at the single cell level by comparing corresponding deterministic and stochastic kinetic models.

RESULTS

This work focuses on the dynamics of cell populations by incorporating the above kinetic scheme into two Monte Carlo (MC) simulation frameworks. The first MC framework assumes stochastic reaction occurrence, accounts for stochastic DNA duplication, division and partitioning and tracks all daughter cells to obtain the statistics of the entire cell population. In order to better understand how stochastic effects shape cell population distributions, we develop a second framework that assumes deterministic reaction dynamics. By comparing the predictions of the two frameworks, we conclude that stochasticity can create or destroy bimodality, and may enhance phenotypic heterogeneity.

CONCLUSIONS

Our results show how various sources of stochasticity act in synergy with the positive feedback architecture, thereby shaping the behavior at the cell population level. Further, the insights obtained from the present study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations.

Design of the lac gene circuit revisited

The lactose (lac) operon of Escherichia coli serves as the paradigm for gene regulation, not only for bacteria, but also for all biological systems from simple phage to humans. The details of the systems may differ, but the key conceptual framework remains, and the original system continues to reveal deeper insights with continued experimental and theoretical study. Nearly as long lasting in impact as the pivotal work of Jacob and Monod is the classic experiment of Novick and Weiner in which they demonstrated all-or-none gene expression in response to an artificial inducer. These results are often cited in claims that normal gene expression is in fact a discontinuous bistable phenomenon. In this paper, I review several levels of analysis of the lac system and introduce another perspective based on the construction of the system design space. These represent variations on a theme, based on a simply stated design principle, that captures the key qualitative features of the system in a largely mechanism-independent fashion. Moreover, this principle can be readily interpreted in terms of specific mechanisms to make predictions regarding monostable vs. bistable behavior. The regions of design space representing bifurcations are compared with the corresponding regions identified through bifurcation analysis. I present evidence based on biological considerations as well as modeling and analysis to suggest that induction of the lac system in its natural setting is a monostable continuously graded phenomenon. Nevertheless, it must be acknowledged that the lac stability question remains unsettled, and it undoubtedly will remain so until there are definitive experimental results.

Transcription by the numbers redux: experiments and calculations that surprise

The study of transcription has witnessed an explosion of quantitative effort both experimentally and theoretically. In this article we highlight some of the exciting recent experimental efforts in the study of transcription with an eye to the demands that such experiments put on theoretical models of transcription. From a modeling perspective, we focus on two broad classes of models: the so-called thermodynamic models that use statistical mechanics to reckon the level of gene expression as probabilities of promoter occupancy, and rate-equation treatments that focus on the temporal evolution of the activity of a given promoter and that make it possible to compute the distributions of messenger RNA and proteins. We consider several appealing case studies to illustrate how quantitative models have been used to dissect transcriptional regulation.

Emergent bistability by a growth-modulating positive feedback circuit

Synthetic gene circuits are often engineered by considering the host cell as an invariable 'chassis'. Circuit activation, however, may modulate host physiology, which in turn can substantially impact circuit behavior. We illustrate this point by a simple circuit consisting of mutant T7 RNA polymerase (T7 RNAP*) that activates its own expression in the bacterium Escherichia coli. Although activation by the T7 RNAP* is noncooperative, the circuit caused bistable gene expression. This counterintuitive observation can be explained by growth retardation caused by circuit activation, which resulted in nonlinear dilution of T7 RNAP* in individual bacteria. Predictions made by models accounting for such effects were verified by further experimental measurements. Our results reveal a new mechanism of generating bistability and underscore the need to account for host physiology modulation when engineering gene circuits.